Unfortunately the accuracy with which an impurity dependent physical or chemical property of sodium can be measured decreases with decreasing impurity concentration . 
To get over this difficulty Alcock has suggested that instead of measuring directly the concentration of oxygen in the flowing sodium its thermodynamic potential should be measured by a suitable galvanic cell incorporated in the circuit . 
The principal advantages of this should be continuous monitoring of the sodium and an accuracy of monitoring which , if the sodium-oxygen system obeys Henry 's law , should increase with decreasing concentration of the impurity. 2 . 
Theoretical ( a ) The Cell 
The use of solid electrolytes in galvanic cells has been described in detail by Kiukkola and Wagner . 
In a reversible cell consisting of two metal-metal oxide electrodes and a solid oxide electrolyte through which current is transported solely by 0= ions , the change in free energy { 15DG accompanying the passage of one mole of oxygen is given by : — 
2EF 
where E is the voltage developed across the cell and F is the Faraday . 
If the electrodes are sodium saturated with its own oxide and unsaturated sodium the change of free energy accompanying the transfer of one mole of 0= from the saturated to the unsaturated metal will be given by : — **f 
where **f , **f are the activities of oxygen in saturated sodium ( concentration c0 ) and in the unsaturated sodium ( concentration c < c0), T the absolute temperature and R the gas-constant. If the activity of oxygen dissolved in sodium is proportional to its concentration as is required by Henry 's law then the free energy change per mole 0= ion may be written **f 
Thus **f 
The solubility of oxygen as Na20 in sodium has been determined and is given by the relationship **f 
Substitution of equation ( 3 ) in equation ( 2 ) with appropriate values for the various constants gives **f 
Values of this function between 400° and 800°C at 100° intervals and for oxygen concentrations between 0.1 and 100 p.p.m. are presented in Fig. 1 . 
At the present time maximum sodium coolant temperatures are around 500°C and oxygen concentrations are usually intended to be maintained in the range 1-10 p.p.m . 
According to the above this cell under these conditions should give voltages ranging from 224-147 mv. ( b ) The effect of small changes of oxygen concentration and temperature on the cell E.M.F. 
The E.M.F. of such a cell placed in a sodium circuit will be affected by fluctuations in oxygen content and temperature . 
These may be estimated from equation ( 4 ) or the following derived equations : — **f **f 
Equation ( 5 ) indicates that any voltage fluctuation arising from a sudden small concentration change will be controlled principally by the original concentration . 
Thus changes from 0.1 to 1 p.p.m. 1-10 p.p.m. 10-100 p.p.m. would result in the same change in voltage ( 1776 mv . ) . 
For relevant reactor conditions ( 500°C , C = 1-10 p.p.m. ) the finite change of voltage { 15DE accompanying finite concentration changes { 15DC is plotted in Fig. 3 . 
The latter as might be expected vary considerably . 
A rise of oxygen concentration from 1-2 p.p.m. is accompanied by a voltage drop of 1723 mv. while , a rise from 9-10 p.p.m. would produce a change of only 173 mv . 
Changes in voltage accompanying fluctuations of coolant temperature according to equation ( 6 ) vary only slightly with concentration and are proportional to the temperature change . 
Values at various oxygen concentrations of **f together with apparent changes in oxygen level for temperature fluctuations of 14 10°C at 500°C are presented in Table 1 . 
The above figures show that a 14 10°C temperature fluctuation at oxygen levels in the range 1-10 p.p.m. would indicate an apparent change of 1712% in oxygen concentration . 
Providing a cell of the above type works satisfactorily the above arguments suggest that it will be sufficiently accurate as an oxygen monitor in a hot trapped sodium coolant circuit . 
( c ) Contamination of the sodium circuit by oxygen from the cell 
Experiments with solid oxide electrolyte galvanic cells have indicated that it is difficult to obtain reproducible voltages using normal potentiometric methods at temperatures below 750°C . 
The author has obtained reproducible results with such cells at 400°C and above by using vibrating reed voltmeters that draw current from the cell only as a result of leakage through insulation resistance of **f . 
Thus if voltmeters of this type were used with the NaNa20 cell it is possible to estimate the contamination of the circuit sodium from oxygen continuously diffusing through the electrolyte . 
If it is assumed that in practise the maximum voltage developed by the cell at 500°C will be around 300 mv. ( see Fig. 1 ) then in the case of the instrument with the lower resistance the current will be : — 3 x 10-14 coulombssec . 
The charge on 0= ion 183.2 x 10-19 coulombs . 
Thus the number of 0= ions travelling through the electrolyte per second 18105 . 
The mass of oxygen per year at this rate would be approximately 8 x 10-1 g.year which is a quite insignificant quantity . 
( d ) The use of the cell as a corrosion meter 
With the cell electrodes consisting of sodium with oxygen at different activities a voltage will be developed that is a function of the difference in the oxygen potential at the two electrodes . 
Unless it is known at what oxygen potential a given material in the sodium coolant circuit will start to oxidise the cell can only be used as has been suggested above , as an oxygen concentration monitor . 
However , if a material oxidizes in sodium at a given oxygen potential the reference electrode could be held at that potential and oxidizing or reducing conditions in the coolant circuit for that material would be indicated by a negative or positive potential at the reference electrode . 
Thus for the specific case of niobium in a sodium circuit a corrosion indicator could be a reference electrode of sodium saturated and equilibrated with niobium separated from the coolant by a solid anionic electrolyte . 
A negative voltage from the reference electrode would mean oxidizing conditions for niobium and positive voltage , non-oxidizing conditions . 
3 . 
Practical 
The practical application of the above idea will involve considerable experimentation before it can be realised . 
The first requirement is for an anionic electrolyte , which can be fabricated into suitable shapes impervious to gases and liquid sodium and which is neither corroded by sodium nor by sodium monoxide . 
Possible materials are zirconia stabilised with lime and thoria doped with rare earth oxides . 
If such a material can be made with these properties a possible way in which the cell may be incorporated in a sodium circuit is depicted in Fig. 4 . 
The electrolyte A is made in the form of a thin walled closed off round end tube or probe fitting vertically into the sodium coolant circuit B. The +ve electrode consisting of a small quantity of sodium saturated with sodium monoxide C is situated at the bottom of the tube . 
The potential acquired by this pool of sodium is transmitted to the voltmeter V by a nickel conductor D , nickel being resistant to corrosive attack by oxide saturated sodium at 500°C . 
The -ve electrode which is the coolant stream , is joined to the voltmeter by an earthed nickel conductor attached to the bottom of a well E in the coolant stream . 
Provided the temperatures at C and E are the same , thermoelectric contributions to the voltage should be zero . 
The probe extends out of the sodium stream through a close fitting thin walled T-Junction F and passes into the open via a water-cooled O ring seal G. The open end of the probe is sealed with a vacuum coupling H which also positions the +ve nickel conductor with respect to the sodium by circlips on either side of the seal I. Evaporation of sodium from the pool C is minimised by a close fitting cylindrical block of electrolyte J attached to the +ve nickel conductor by nickel circlips . 
Fixing and positioning of the probe relative to the coolant stream is effected by tie-bars of insulating material K joining the vacuum coupling H to the water cooled flange G. The probe can be evacuated and filled with inert gas via the tube L which must of course be electrically isolated after this has been carried out . 
4 . 
Discussion 
It is not suggested that the above proposal will be successful but rather that it is worth a trial in the event of the inadequacy of some simpler method of monitoring the oxygen in a sodium circuit . 
The principal difficulty encountered by the author , in determining partial molal free energies by solid electrolyte cells of very stable oxides such as UO2 , MnO etc. was vapour phase transfer of oxygen by carbonaceous impurities in the blanket gas . 
This resulted in the oxidation of the -ve electrode and reduction of the +ve electrode which of course led to a loss in E.M.F. from the cell . 
In the above design the two electrodes are completely separated from one another so that this major source of trouble should not be present . 
However , the stability of the system may be adversely affected by the thermal gradient up the probe and this can only be tested by experiment . 
Whether such an apparatus can be incorporated in a reactor circuit in a manner that will satisfy safety requirements will need further study . 
On the face of it however , there seems to be no reason why the cell should not be double-contained to prevent loss of sodium in the event of the ceramic tube being fractured . 
Such containment however , will be complicated by the necessity of providing suitable insulating seals through its walls . 
5 . 
Conclusions 
If other monitoring methods for oxygen in sodium in the concentration range 1-10 p.p.m. are found to be inadequate then this galvanic cell may be worth investigating . 
However , it will require development of a suitable electrolyte and even then it will only be useful if the activity of the dissolved oxygen varies sufficiently with changes in its concentration . 
A. OUTLINE OF METHOD 
To a measured portion of the sample , niobium and zirconium carriers are added together with hydrofluoric acid to ensure complete isotopic interchange . 
Rare earth elements are co-precipitated with lanthanum as fluorides . 
Niobium is precipitated with ammonia , partially separating it from zirconium . 
The niobium precipitate is dissolved in a mixture of oxalic and nitric acids , and niobic acid precipitated by boiling and adding potassium bromate . 
The niobic acid is dissolved in acid ammonium fluoride and the cycle from the ammonia precipitation repeated . 
The niobic acid is washed , ignited to niobium pentoxide , which is mounted on a tared counting tray and weighed . 
The { 15g-activity is measured through a leadaluminium sandwich using standard gamma scintillation equipment , which has been calibrated with known amounts of niobium-95 . 
B. REAGENTS REQUIRED 
All reagents are Analytical Reagent Quality where available . 
1 . 
Standard niobium carrier solution ( **f ) 
Fuse 20 g of pure niobium pentoxide with 72 g of potassium carbonate in a platinum dish . 
Cool and dissolve the solidified melt in about 400 ml of hot water . 
Transfer the solution and any undissolved solid to a glass beaker , stir thoroughly and add 16M nitric acid until the solution is strongly acid to litmus . 
Stand the beaker on a hot plate and keep the solution warm for 30 minutes to coagulate the precipitate . 
Transfer to four 200 ml polythene bottles , centrifuge , decant and discard each supernate . 
Wash each portion of the precipitate three times by stirring with 100 ml of 2% ammonium nitrate . 
Use a glass rod for stirring . 
Centrifuge and discard the supernates after each wash . 
Dissolve each portion of the precipitate in 25 ml of 30% ammonium fluoride and 15 ml of 16M nitric acid . 
Combine the solutions from each of the 200 ml polythene bottles , and dilute to 2 litres with distilled water in a polythene bottle . 
Standardize as follows : — 
Pipette 10 ml of the solution into a 400 ml polythene beaker and add 100 ml of a saturated solution of ammonium chloride . 
Heat the solution nearly to boiling , by placing the polythene beaker in a glass beaker of water , heated on a hot plate , and add to the solution 1 g of tannic acid dissolved in hot water . 
The removal of the library and catalogues to the Bodleian destroys the incentive to study and add to the collection because of the absence of readily accessible reference works . 
Divorced from the specimens the catalogues become neglected , and ultimately the specimens are thrown away because the catalogues are not to hand . 
So are lost all Dr. Plot 's figured specimens and the great collection of Edward Lhwyd , his assistant . 
It is very interesting to see the composition of a seventeenth-century palaeontologist 's reference library . 
Plot , in addition to Biblical quotations and Philosophical Transaction references , alludes to no less than fifty-two works . 
Amongst these the elder Pliny 's writings are prominent . 
His classification of fossils is essentially that of Gesner erected 111 years before . 
When I say that the four main groups in this classification are stones relating to heavenly bodies ; those relating to the inferior heavens ; those relating to the atmosphere ; and those relating to the Watery Kingdoms , you will gather that it does not rest on any sound scientific footing . 
Dr. Plot himself has no tremendous regard for this method ; but he says it is better than classifying the things alphabetically . 
I beg leave to doubt this . 
Then there comes out of Yorkshire the learned Dr. Martin Lister with an opinion on fossils , which , emanating as it does from the foremost conchologist of the day , can hardly be ignored . 
Lister has figured recent and fossil shells , side by side , not , as might be imagined , to show their essential similarity but as an illustration of the plagiarism of Nature . 
Lister 's theory might well be christened ( acknowledging our indebtedness to Siegfried Sassoon ) the pseudomorphic hieroglyphic hypothesis , since whilst denying the former vitality of fossils he suggests that different types of self-generated shell-like stones might characterize different rocks . 
It might therefore be said that his lapse in regarding fossils as sports of nature is here offset by his penetration as to their possible use . 
It would certainly be possible to use a tool of which the true nature was unknown , if , empirically , it had been found to serve a useful purpose . 
But to credit Lister with the first formulation of the basic principle of stratigraphy , as has been claimed , would be to bestow credit falsely . 
I think Lister had in mind merely the characterizing of different types of rocks by distinctive fossils . 
Today this would be called recognizing the facies of the rocks and Lister 's " ingenious proposal " , as it was entitled , to make a map showing the surface distribution of strata was a proposal for a mineral , not a true geological map . 
Such a map would , for instance , colour all limestone outcrops under the same shade . 
Although of value in mining and quarrying operations it is academically barren . 
It can make no contribution to working out earth-history . 
The primary division of strata in the hierarchy of their classification is according to age not lithology . 
To elevate the latter is to produce a barren classification . 
Edward Lhwyd , assistant and later successor to Dr. Plot as curator of the Ashmolean Museum , had a more intimate acquaintance with fossils than any man in England and possibly in the world . 
This study , together with his scholarly researches into the Welsh and other Gaelic languages , formed his life 's work . 
Whenever he could afford it , he travelled widely to collect fossils and examine Welsh , Irish , Cornish and Breton manuscripts . 
He wrote the first illustrated textbook on fossils . 
His familiarity with them showed him that their resemblance to living things was no mere coincidence , but the inference that fossiliferous beds were elevated sea-floors was too much for him . 
He adopted the " stray seed " hypothesis , but in a spirit of candour he wrote to John Ray , " I am not so fond of this Hypothesis , as not to be sensible myself , that it lies open to a great many objections " . 
Still it was the best compromise he could come to . 
A poor museum curator with a salary of £40 { 6per annum plus what he could get from selling fossils at a time when there was no great demand for them , was in no position to tilt at the thirty-nine articles . 
In rejecting the Flood hypothesis , he says , in effect , that he demurs first because it is not in accord with the Sacred Scriptures and , secondly , because it does not accord with the facts . 
We may note the order of the objections . 
The doubts entertained by Leonardo da Vinci about the Flood theory were explained away by John Woodward . 
In 1695 , he published a much-admired Essay on the natural history of the earth . 
This was intended to repair imagined omissions in the Mosaic narrative in general and the account of Noah 's Flood in particular . 
In the Essay , Woodward promises to " give myself up to be guided wholly by Matter of Fact ; intending to steer that Course which is thus agreed of all hands to be the best and surest : and not to offer anything but what hath due warrant from Observations ; and those both carefully made and faithfully related " . 
Never can a promise made so fervently have been so lamentably forgotten in the course of a few pages . 
Woodward imagined that the Flood had transformed the globe into a porridge-like mass and that the strata and the organic remains had subsided to stratify in layers according to their specific gravity . 
Fantastic as the theory is , it becomes more so when we learn that it was acceptable to Diluvialists in England and abroad for many years . 
With regard to the Deluge , let me say that it is its world-wide occurrence which makes physical difficulties . 
An extensive , though local , inundation can easily be explained , but where did the water issue from and to where did it retreat to if there was enough to cover the whole surface ? 
I like Woodward 's approach to this problem . 
" For my part , " he says , " my Subject does not necessarily oblige me to look after this Water ; or to point forth the place whereunto 't is now retreated . 
For when , from the Sea-shells and other Remains of the Deluge , I shall have given you undeniable Evidence that it did actually cover all parts of the Earth ; it must needs follow that there was then Water enough to do it , where it may be now hid , or whether it be still in being or not . " 
One is tempted to say , " When you come to an insurmountable obstacle look it squarely in the face and pass on " , were it not that the argument is sound , granted the premises . 
As might have been expected , the hint of the marvellous and the untrammelled speculation emanating from "fossil stones " could not fail to attract the attention of that delightful character , John Aubrey . 
We turn to his Natural History of Wiltshire confidently expecting some delicious things . 
Now there is a great deal of truth in the notion that the geological environment is the primary factor in determining the character of a country ; not only topographically but historically . 
If the course of history is channelled by economics , then surely natural resources lie at the foundation of a country 's development . 
And as men are the products of their times , the national character contains at least an element imposed upon it by the inanimate environment . 
Aubrey recognizes this on a very fine scale indeed . 
I quote : " according to the several sorts of earth in England ( and so all the world over ) the Indigenae are respectively witty or dull , good or bad . 
In North Wiltshire ... a dirty clayey country the Indigenae speake drawling ; they are phlegmatique , skins pale and livid , slow and dull , heavy of spirit ... melancholy , contemplative and malicious ; by consequence whereof come more law suites out of North Wilts , at least double to the southern parts " which , bye the bye , are composed of Chalk . 
As to Aubrey 's notions on fossils we simply record that he was much plagued with notions about earthquakes and their possible consequences on the earth 's rotation ; and if he recognized that fossils give " clear evidence that the earth hath been all covered over by water " and when he " often-times wishes for a mappe of England coloured according to the colours of the earths with marks of the fossiles and minerals " , we conclude that he read his Philosophical Transactions and was acquainted with Hooke and Lister . 
As an example of the type of ingenuity provoked by a chance stimulus , we have the Theory of the Earth due to Whiston . 
In the latter years of the seventeenth century comets were "in the air " , as it were . 
The comet which led Newton to predict their parabolic orbits was visible between December 1680 and March 1681 . 
Halley 's even more famous comet with a much less eccentric elliptical orbit , having a period of 75 to 76 years , was visible in 1682 . 
Whiston conjectures that Newton 's comet was the same as that recorded in 44 B.C. , A.D. 531 and A.D. 1106 which suggested a period of 575 years or so . 
He notes that , of two postulated dates for Noah 's flood , namely , 2349 B.C. and 2926 B.C. , the discrepancy of 577 years is near enough to the assumed period of Newton 's comet ; so that what ever date for the Flood be accepted , the interval between it and 1681 was an integral multiple ( 7 or 8 ) of the postulated period of revolution of Newton 's comet . 
Note , however , that this period was not calculated from the observed visible portion of the comet 's orbit , but inferred from certain coincidental dates . 
Nevertheless , having convinced himself that a comet stood above the earth at the time of the Deluge he invoked one to explain the other . 
The earth passed through the watery vapours of the comet 's tail , and the " floodgates of heaven " were opened whilst its gravitational attraction fractured the earth 's crust whence emerged the " waters of the deep " . 
The rest of Whiston 's theory is according to Woodward with wholesale extinction of life and its stratification according to specific gravity in a porridgey mass which ultimately hardened into the stratified crust . 
The whole theory is ludicrous ; but if the rules of the game are first to invoke only recorded catastrophes and , secondly , to pay due regard to contemporary scientific fashions , then , surely , Whiston 's attempt is a gem of its kind . 
Molyneux 's suggestion that the extinction of the Irish Elk was due to plague is perhaps a similar piece of opportunism . 
It is the type of explanation involved in explaining wet summers by atom-bomb explosions . 
Amidst this welter of conflicting opinion the truth was there waiting to be disseminated . 
Robert Hooke in England and Nicholas Steno in Italy had published opinions which , had they been combined , would have opened up the subject 150 years before it was destined to flower . 
But these were writing in advance of their times and were consequently ignored . 
Thus Hooke in 1688 in a Discourse on Earthquakes not only knew fossils for what they were but said that " it would not be impossible to raise a chronology out of them " . 
The occurrence of fossil Turtles in the London Clay of the Isle of Sheppey led him to conclude that England had formerly enjoyed a warmer climate than today . 
This was the first suggestion for an investigation into palaeoclimatology , a subject which is not completely established today , although inferences made from fossil faunas lie at the heart of its present development . 
Nineteen years before Hooke 's Discourse , the implications of stratification had been announced to an indifferent scientific world by Steno . 
As founder of the science of crystallography , Steno would hardly confuse crystals with true fossils . 
It is a pity that their chronological possibilities were not added to his insight into stratification . 
But both Hooke and Steno threw out their geological ideas incidentally to their main pursuits ; and their contemporaries to whom Geology was their main interest were unable to appreciate their foresight . 
For instance , their record of fossils at either a particular height above sea-level or depth below the surface in mines and quarries shows their ignorance of the subject of stratification . 
Except in the rare horizontally bedded rocks these data have no significance chronologically . 
Dr. Smithson , I think it was , mentioned the evidence to be obtained through the examination of stones . 
Their orientation will give a sense of the direction of movement and often a good deal can be learned from the kind of stone . 
I would make a plea here that I have heard Dr. Smithson make so often . 
A stone , if it is to be examined at all , deserves it only after it has been scrubbed clean in the laboratory , and indeed after the macro-examination efforts might profitably be extended to microscopic examination of a thin section . 
As to the examination of stones in a soil profile , I would repeat my own rather stale and weary warning . 
Stones in a soil profile are those things that have failed to weather to form a soil . 
Do not ignore them but at least pay them less attention than the fine fractions . 
Let us suppose that we have succeeded in making a full assessment of a parent material . 
We are still left with many other factors which will ultimately influence the processes of profile formation . 
There are ( a ) the topography of the site which influences drainage , surface run-off and the chances of erosion , ( think of this in relation to the mass of debris left after the retreat of the ice sheet ) , ( b ) the climate within the developing profile — a composite of temperature , rainfall , evaporation and transpiration and drainage . 
( a ) and ( b ) indirectly influence ( c ) the kind of vegetation which can in turn check the processes of decay and leaching in some cases and in others hasten them . 
Sets of slides were then shown to illustrate the effect of : — ( 1 ) Altitude 
Parent Material : Silurian shale drift . 
( a ) At 1,2007 above sea level producing peat , peaty gley and gley podzolic and slightly podzolic profiles . 
( b ) At 2507 above sea level . 
Brown forest soil of good base status . 
( 2 ) Rainfall 
Common parent material sandy textured drift of mainly Carboniferous Limestone . 
Co . 
Roscommon , Ireland . 
458-508 mean annual rainfall 23 podzol . 
Co . 
Meath 308 mean annual rainfall , high base status , Brown Forest Soil . 
( 3 ) Vegetation 
Site Knightwood Inclosure , New Forest , Hampshire . 
Parent Material Barton Sand . 
Planted 1860 Oak 23 low base status , Brown Forest Soil . 
Scots Pine 23 Deep humus podzol . 
SOIL DEVELOPMENT ON DRIFT DEPOSITS OF THE WELSH BORDERLAND by D. MACKNEY 
Since little pedological investigation has been directed to drift deposits of the Welsh Borderland , outside certain areas in Shropshire and Cheshire , this discussion of soil development is centred on the Cheshire-Shropshire Plain . 
For the most part this plain is below 300 ft. , abutting to the west against the eastern uplands of Wales and in the south fringing the pre-Cambrian and Palaeozoic rocks of the south Shropshire uplands . 
This gently undulating , sometimes flat surface masks an extremely complex series of glacial deposits which are often very thick , so that only a few isolated ridges of Trias sandstone obtrude . 
The glacial events which have led to the formation of the Midland plain are controversial in detail , but some conclusions are universally accepted . 
The deposits which form the plain have been derived from the Palaeozoic rocks of Wales and the north , as well as from the underlying Triassic rocks . 
However it is probable that a good deal of the surface layers of drift have been affected by sorting and grading , which is presumed to have taken place during the withdrawal of the ice front , when melting released vast amounts of water . 
The evidence for this lies in the occurrence of glacial sands and gravels , as well as glacial clays , which are sometimes laminated . 
Throughout the region there are isolated basin sites which are thought to be remnants of old glacial lakes where water was trapped through the haphazard deposition of glacial debris . 
Many of these have since been filled by peat which presumably developed in Atlantic and Sub-Atlantic times . 
BROWN EARTHS IN BRITAIN 
For many years in Britain the brown earth group has been divided into high and low base status soils ; the sub-division has been arbitrarily made , and in some cases a pH of 6.5 in the B horizon has been accepted as a line of division . 
Since soils within the brown earth group , apart from limed soils and those marginal in affinity to calcareous soils , rarely have a pH of 6.5 in the B horizon the system is not perfect . 
When examining agricultural soils great confusion can result , for soils which are of low base status under semi-natural conditions can be induced to maintain the chemistry of high base status soils by liming and fertilizing . 
In parts of western Europe and eastern United States of America , where pedologists are concerned with soils in similar environments to Britain , two main sub-divisions of soils similar to our brown earths are recognised ( 1 ) acid soils with textural B horizons , i.e. , with B horizons at least partly formed by illuviated clay , ( in western Europe { Sol brun lessive2 and { Sol lessive2 ; in U.S.A. Grey-brown podzolic soil ) : ( 2 ) strongly acid soils without textural B horizons , ( { Sol brun acide , western Europe and U.S.A. ) . 
Obviously many more characteristics are required to define these sub-divisions , but these will be considered later . 
In Britain , on soil maps of our country we have used both grey-brown podzolic soil and { sol brun acide as descriptive terms for particular areas . 
However , since in the west Midlands , soils with textural B horizons are less well developed than typical grey-brown podzolic soils , advantage has been taken of the units used in western Europe . 
Here well developed soils with moder humus and textural B horizons are called { sol lessive2 and less well developed soils with mull humus , { sol brun lessive2 ; thus , the latter unit , can be properly used to describe soils in the Midlands . 
**f SOIL DEVELOPMENT 
It is possible to extract two important groups from the variety of soils which occur on the drift deposits of the Cheshire-Shropshire plain , and these can be used to illustrate the type of soil formation characteristic of the region . 
The two groups of soils exemplify relationships within an extremely complex region . 
( 1 ) { Sols bruns acides and podzolised soils associated with glacial sands and gravels . 
( 2 ) { Sols bruns lessive2s and surface-water gley soils associated with glacial clays . 
( 1 ) { Sols bruns acides and podzolised soils 
The glacial sands are highly siliceous , base poor parent materials , generally with less than 10 per cent . 
clay , and most frequently with less than 5 per cent . 
clay . 
The acid soils which have developed support a semi-natural cover of heath , or of deciduous wood-land consisting of oak and birch with some rowan and holly , and a bracken or heathy type of ground flora . 
Under deciduous forest the humus form is moder , with F and H layers of approximately equal thickness , and under heath the humus form is frequently difficult to assess due to periodic burning . 
Beneath these humus layers several types of profile may be found , but frequently the solum is freely drained , and shows little sign of development , being uniformly brown in colour apart from a slight colour ( B ) horizon — this typifies the { sol brun acide . 
In detail it is a strongly desaturated soil throughout , with single grain or weak crumb structures , or in more loamy materials very weak fine sub-angular blocky structures . 
There is no texture profile ; estimates for free iron do not indicate any iron B horizon , and clay ratios do not show any significant differentiation of silica and sesquioxide . 
The { sol brun acide is frequently associated in the landscape with soils showing signs of podzolisation , i.e. , with soils having iron and/or humus B horizons , and these may be found in different stages of development . 
The course of soil development appears to be { sol brun acide 23 podzolised { sol brun acide 23 humus-iron podzol 23 humus podzol ( Fig. 25 ) . 
A series of profiles examined at Delamere , north Cheshire , on glacial sands illustrates part of the development sequence ( Fig. 26 ) . 
Extensive areas in Delamere were planted with oak early in the 19th century , and more or less cleared in the early years of the first World War . 
Replanting consisted mainly of pine , though some open , degenerate , dry oak-birch woodland remains . 
The landscape unit drawn diagrammatically ( Fig. 26 ) is common on the Cheshire-Shropshire plain , and illustrates the gentle rolling relief , with a peat-filled basin . 
The podzolised { sol brun acide has the following characteristics : 
1 . 
Thin moder , sharply separated from the mineral soil . 
2 . 
Some superficial bleaching immediately below the organic layer . 
3 . 
An Ae horizon of approximately 9 ins. of dark yellowish brown ( 10YR3/4 ) sand in which there are numerous bleached sand grains . 
4 . 
A Bs horizon of 3/4 ins. indicated by the yellowish red ( 5YR5/6 ) colour . 
Hydrogen peroxide treatment of samples from the mineral horizons showed , when the organic matter was removed , that there is a well developed grey Ae horizon which gradually merges into the Bs horizon . 
The humus-iron podzol is considered to be a more mature profile for the Ae horizon is grey having lost most of its organic matter , and this is represented in a thin black horizon ( Bh ) overlying a strongly developed Bs horizon ( Figs. 25 and 26 ) . 
An ashy coloured residue is left after hydrogen peroxide treatment of the humus B horizon and this qualitatively suggests that it is low in inorganic iron ; however , chemical evidence from similar profiles indicates that a considerable amount of iron may be combined with organic matter in this layer , and this will be taken into solution by the hydrogen peroxide treatment . 
In the lowest position of the catena is the humus podzol ( Figs. 25 and 26 ) . 
It has the following characteristics : 
( 1 ) The humus form is transitional between mor and moder , though there is a marked pine needle litter . 
( 2 ) Strongly bleached , deep Ae horizon , though it is traversed by a complex series of flow bands of colloidal organic matter . 
( 3 ) A thick ( 6 ins. ) cemented black Bh horizon . 
( 4 ) There is no orange-brown Bs horizon ; the sub-soil consists of bleached sand , though here it is apparently affected by gleying . 
After hydrogen peroxide treatment of the horizons all are left completely bleached , confirming therefore , that there is no zone of iron accumulation within the profile . 
What are the factors which have operated in the differentiation of these soils ? 
Since climate has had an overall influence , and all the profiles are developed on glacial sands and gravels , it may be assumed that differentiation is chiefly due to site and/or vegetation , or to vegetation as it is affected by man . 
It is widely believed that podzolisation in lowland Britain is the result of the dominant role which heath ( Calluna ) assumes in the vegetation cover of deforested or abandoned land . 
From this accepted doctrine , however , there is a real tendency to believe that all podzols are formed under heath ; to see a podzol is to point to the role of heath , on the site now , or in the past . 
Work in western Europe in the last decade , and some confirmatory investigations in Britain , show podzolisation as a progressive development , starting under deciduous woodland and probably reaching maturity at the humus-iron podzol stage under Calluna , though in some cases heath may not be an essential part of the vegetation cycle . 
The occurrence of podzolised { sols bruns acides and podzols in close proximity at Delamere and elsewhere , is difficult to explain in terms of past vegetation without a pollen analysis of the profiles concerned . 
There are so many possibilities in the thousands of years in which vegetation has influenced soil development . 
In the case of the humus podzols which are found in general adjoining peat or certainly in the lowest position in the catena , it can be convincingly argued that development has been influenced by ground-water . 
The presence of ground-water has prevented the precipitation of the illuviated iron oxides , or due perhaps to a change in regional or local water levels , formed iron B horizons have been disrupted by waterlogging and gleying ; in either case the leaching of humus is not confined by the filtering effect of an iron B horizon and consequently a more deeply leached profile results . 
Using a solution of lead-210 in equilibrium with its daughters , supplied by the Radiochemical Centre , Amersham , a source was prepared and counted through a series of aluminium absorbers of increasing weight . 
The curve of observed activity plotted against absorber thickness is shown in Figure 2 . 
An aluminium absorber weighing 27 mgcm2 was used in the following experimental work although this was thicker than necessary and reduced the efficiency of the Geiger counter from about 15% to 11% . 
Reference standards were prepared by precipitating lead chromate from a hot dilute acetic acid solution containing a known quantity of lead-210 in equilibrium with its daughters . 
The calibrated solution of lead-210 ( about 10-2 { 15mcml ) was supplied by the Radiochemical Centre , Amersham . 
Lead chromate is accompanied by only about 75-85% of the bismuth-210 and therefore time must be allowed for radio-equilibrium to be restored . 
The presence of 75% of the activity of bismuth-210 is equivalent to ingrowth over two half-lives ( ten days ) . 
Therefore after a further forty days , the bismuth daughter will be within 0.1% of its final equilibrium value . 
If reference sources are required for use sooner than forty or fifty days after preparation , the lead-210 together with added lead carrier must be separated from the bismuth-210 daughter by ion exchange ( see Analytical Method , steps 4 , 5 ) before precipitating lead chromate . 
Knowing the time of separation and the activity of the lead-210 solution , the ingrowth of the bismuth-210 can be calculated . 
The absolute activity of the reference standards can be calculated from the known activity of the lead-210 solution and the chemical yield , but this calculation is unnecessary provided the same lead carrier solution is used to prepare the reference standards and for the analyses . 
Only the weights of the recovered lead chromate precipitates need be known because the concentration of the lead carrier solution cancels out of the algebraic equations . 
An effort was made to detect the presence of any radioactive impurities in the tracer by separating the lead-210 and the bismuth-210 by anion exchange . 
The { 15b-counting of the lead-210 fraction began within a few minutes of completing the separation . 
The ingrowth of bismuth-210 was followed for ten days and showed no abnormalities . 
Any impurity in the lead fraction must have been well below one percent . 
Some separated lead-210 was used to make reference standards and as a tracer in recovery experiments . 
There was no significant difference between these results and those obtained using the original lead-210 solution supplied by the Radiochemical Centre which we concluded was radiochemically pure . 
2.2 The Recovery of lead-210 tracer from solution . 
Rosenquist ( 4 ) showed that minute quantities of lead can be isolated from large volumes of solution by coprecipitating the lead with a strontium sulphate . 
Lead and strontium form mixed crystals so that the more insoluble lead sulphate is almost completely recovered even if precipitation of the strontium sulphate is incomplete . 
Using ten milligrams of lead carrier and six hundred milligrams of strontium per liter , more than 95% of added lead tracer was recovered in each experiment . 
Gravimetric recoveries were less in the presence of ethylenediamine tetra-acetic acid ( 10 ppm ) , Teepol ( 0.2 ml commercial Teepol per liter ) and Calgon ( 250 and 500 ppm ) , but always exceeded 70% . 
Radiochemical recovery of the tracer corrected for gravimetric recovery of the carrier averaged 97.5 14 0.5% in all cases where these additives were present . 
Excessive quantities of chloride also reduce the gravimetric recovery of lead . 
Up to 0.1 N. chloride ion ( 96% recovery ) the effect is negligible but becomes increasingly important thereafter : 0.3 NCl- ( 85% recovery ) , 0.5 NCl- ( 79% recovery ) , 1.0 NCl- ( 56% recovery ) . 
No more than ten milligrams of lead was used in order to ensure good separation on the ion exchange column and to make it possible to keep the lead in solution in small volumes of dilute hydrochloric acid . 
Absorption of the beta particles is also kept to a minimum but the accuracy and precision of weighing the precipitated sources suffers . 
All precipitates were weighed on a semi-micro balance which had been calibrated with a set of certificated weights from the National Physical Laboratory . 
Complete chemical exchange between the radio-lead and the added lead carrier is necessary if the analytical results are to be correct . 
In the preliminary experiments , the tracer was added to a liter of effluent and immediately coprecipitated with strontium sulphate from hot solution . 
Chemical exchange was complete under these conditions ; but when the tracer was added to alkaline effluent and allowed to stand for several days before the addition of lead carrier , the recovery of lead-210 was as much as five per cent low when corrected for gravimetric recovery of the carrier . 
Complete exchange was obtained by acidifying the effluent with five milliliters of concentrated nitric acid and boiling for more than half an hour before completing the coprecipitation . 
Boiling the effluent with more than 5 ml. of acid resulted in gravimetric recoveries which were too low to be tolerated . 
To ensure complete chemical exchange , one hour at , or very near , the boiling point is recommended in the analytical method . 
The presence and growth of algae in the alkaline effluent does not prevent the recovery of radio-lead under the prescribed conditions although some radioactivity remains on the algae until the metathesis has been completed by heating the mixed sulphates with three separate portions of dilute ( 1.25 normal ) sodium carbonate solution . 
The strength of the carbonate solution was chosen after experiments with lead tracer alone which indicated that less lead was lost than at other concentrations . 
The mixed carbonates are dissolved in 2N hydrochloric acid and fed to a column of anion exchange resin . 
The algae , if any was present in the effluent , is simply filtered out on top of the resin bed . 
2.3 . 
Separation of lead and bismuth by anion exchange . 
The anion exchange resin ( Amberlite IRA-400 , 60-100 mesh , chloride form ) is prepared by drying the commercial product and grinding it to pass the correct sieves . 
A small manual coffee grinder is useful as the resin can not be ground with a mortar and pestle . 
The sieved resin is washed repeatedly with distilled water to remove fines and then with hydrochloric acid to convert the resin completely to the chloride form . 
The 60-100 mesh resin is again washed with water to remove the acid and finally dried in air . 
The drying may be speeded up by heating in a low temperature ( 40°- 60° C. ) oven until damp dry . 
The final drying should be at room temperature with the resin protected against dust by a covering of filter paper . 
For each aliquot to be analysed , about 3.5 grams of air-dried resin is weighed out and slurried into a glass tube with 2N hydrochloric acid . 
The glass tube is 11 cm. long and 1 cm. in internal diameter . 
One end of the tube is drawn down to a fine tip and a B14 conical glass socket is fitted to the other end as shown in Figure 1 . 
The reservoir is a 50 ml cylindrical separating funnel with a capillary tap modified by the addition of a B14 cone to fit the glass column . 
The exact volume of the eluting agents must be found by experiment for each batch of resin using radioactive tracer ( lead-210 , bismuth-210 ) . 
A typical elution curve is shown in Figure 3 . 
Once these volumes have been established , the weight of resin used is also fixed . 
All available evidence indicates that the fractions containing lead and bismuth are free of cross contamination apart from the natural ingrowth of the daughters arising from the decay of lead . 
Polonium-210 remains on the column and does not interfere . 
Strontium does not form a chloro-complex and therefore passes through in the feed solution and the first wash . 
The resin is used for a single separation and then thrown away . 
In the first stage of the analysis , only the fraction containing lead-210 is collected . 
The lead is precipitated as the chromate , washed , slurried onto an aluminium counting tray , dried under an infra-red lamp , weighed , and set aside for five days while the bismuth-210 grows in . 
At the end of five days , bismuth-210 will have reached one-half of its equilibrium value and can be counted through an aluminium absorber sufficiently thick to stop the beta particles from lead-210 and the alpha particles from polonium-210 . 
Earlier beta counting is permissible but the sensitivity of the method is reduced ( See Fig. 4 ) . 
The presence of other lead nuclides may be demonstrated by observing the ingrowth of the bismuth activity and comparing the shape of the normalised curve with the curve in Fig. 4. using an arbitrary scale of activity proportional to the existing ordinate . 
During the first few hours the curve will be distorted if activity other than bismuth-210 is present . 
These bismuth nuclides may include : together with their lead parents . 
All but lead-212 will decay completely within six hours . 
The decay of lead-212 will distort the observed activity for four and a half days if it is present . 
Thereafter the normalised curve should follow Fig. 4 exactly . 
If it is essential to confirm that the beta activity is indeed due to bismuth-210 , or if much higher decontamination factors are required , the lead chromate is washed quantitatively with 2N hydrochloric acid into a centrifuge tube and dissolved in the presence of bismuth carrier . 
The solution is kept near the boiling point for fifteen minutes to assist chemical exchange . 
Chromate , which would interfere with the ion exchange separation , is reduced by adding a few drops of hydrogen peroxide . 
The ion exchange separation is repeated and the bismuth is eluted with 1N sulphuric acid . 
The bismuth fraction is diluted and phosphoric acid is added . 
The phosphate precipitation is repeated to remove contamination by sulphate or occluded sulphuric acid . 
If there is sufficient beta activity , the radiochemical purity of the Bi-210 may be checked by observing the decay curve . 
The removal of lead chromate from the aluminium counting tray together with the bismuth-210 prior to the second ion exchange separation has been checked by counting the trays . 
Not more than 0.2% of the bismuth-210 remains on the tray after the acid wash . 
This loss is acceptably small for an analytical step when no correction for carrier recovery is possible . 
The completeness of the chemical exchange between the bismuth-210 and the added carrier was also tested . 
Two samples of precipitated lead chromate ( lead-210 , bismuth-210 ) were counted and dissolved in nitric acid in silica basins . 
The contents were evaporated to dryness with bismuth carrier and then taken up in 2 N hydrochloric acid and the ion exchange separation completed . 
The bismuth was recovered from the eluate as the phosphate . 
Results did not differ from those obtained by the more convenient method of heating the dissolved chromates in 2 N hydrochloric acid for fifteen minutes . 
The more rigorous method of securing chemical exchange was unnecessary . 
2.4 Decontamination from other nuclides . 
Lead-210 when present in effluent is likely to be found only at very low concentrations . 
With a permitted maximum concentration of 10-12 curiesml it is one of the three most stringently controlled { 15b-emitting nuclides at the present time . 
Therefore it is essential that the radiochemical procedure for the assay of lead-210 shall provide for a high degree of decontamination from major fission products and other nuclides which are likely to be present in amounts greatly exceeding lead-210 so that these shall not be mistakenly reported as lead-210 . 
Table 1 shows the decontamination factors obtained experimentally for ten radionuclides , accompanied in two instances by radioactive daughters . 
The decontamination factor falls below 104 only for Ruthenium-106 and zirconium-95 with their daughters in the first stage , i.e. the lead chromate source containing the bismuth-210 daughter . 
When the second stage ( the bismuth phosphate source ) is completed , the decontamination factors are exceptionally high . 
3 . 
Results and Discussion . 
A known quantity ( approx. 1 x 10-2 { 15mc ) of lead-210 was added to 1-litre aliquots of different batches of typical low-activity effluent . 
The aliquots were allowed to stand for about seven days ( except where noted to the contrary ) before lead carrier was added and the analytical procedure begun . 
When we have a scalar effective mass me we may express t in the form **f 
The index s in the equation t = AE-s is therefore 1/2 . 
For a non-degenerate semiconductor with s = 1/2 we have from 13 10.6 equation ( 83 ) , **f 
since **f and **f . 
Thus we have **f 
The mobility { 15me when we have only lattice scattering by the acoustical modes of vibration is therefore given by **f 
This gives the well known T-3/2 law for the variation of mobility in pure semiconductors at high temperatures ; it is unfortunately not very well obeyed for most semiconductors since both anisotropy and other scattering mechanisms tend to modify the mobility to an appreciable extent . 
We defer the calculation of the constant a to 13 13.4.4. 10.10 Low-mobility semiconductors 
Although the theory of electrical conductivity which we have given seems to be applicable to metals and to normal semiconductors having a high electron and hole mobility , we may readily show that it can not be applied without serious modification to materials for which the mobility is low . 
There are many such materials which appear to have mobilities of about 1 cm2V sec . 
For such materials the relaxation time t would have a value of about 6 x 10-16 sec if we have me = m and a smaller value still if me < m. Now because of collisions the value of the energy can not be precisely stated for a time much greater than t so that , if { 15dE is the uncertainty in energy , we must have ( cf. 13 1.4 , equation ( 67 ) ) **f 
Thus if **f , **f . 
The allocation of energy levels in a band therefore becomes meaningless , particularly if the energy spread of the carriers , as in a non-degenerate semiconductor , is only of the order of kT . 
For a semiconductor like Ge , on the other hand , **f that the energy may be fairly closely specified . 
For low-mobility semiconductors the band theory of conduction must be abandoned and we must regard conduction by electrons as a form of field-assisted tunnelling between adjacent atoms of the crystal . 
This process has been discussed extensively by A. F. Joffe2 and has been applied by him to the study of liquid and amorphous semiconductors . 
The limitations of the band theory , particularly as applied to narrow bands with high effective mass have also been recently discussed by H. Fro " hlich and G. L. Sewell . 
The theory of conduction by " jumping " from site to site has also been used by N. F. Mott to discuss conduction by impurities in semiconductors at low temperatures , the so-called impurity band conduction . 
The full details of the theory of this type of conduction have not yet been worked out to anything like the same extent as for conduction in materials having a high electron or hole mobility . 
11 The Effective-mass Approximation 11.1 The quasi-classical approximation 
WE have shown in Chapter 8 that , to a high degree of approximation , an electron moving in a perfect crystalline lattice in an external field of force F may be regarded as a particle moving classically in the field , the particle having a tensorial effective mass ; the equations of motion were derived in 13 8.8 . 
These may be expressed in terms of the wave vector k or crystal momentum P by means of the vector equation **f 
This equation may be transformed into an acceleration equation , giving the rate of change of the " averaged " velocity **f , in the form **f 
where 1/Me represents the effective-mass tensor whose Cartesian components 1/mrs are given by **f 
When the energy E may be expressed in the quadratic form **f 
where the quantities Ars are constants , and Ars = Asr and the components of the effective-mass tensor are constants . 
The various simplifications of equation ( 2 ) which may be made when some of the quantities Ars are zero or equal have been discussed in 13 8.8 ; in particular , when **f so that the effective mass is a scalar me , the equation of motion reduces to the simple classical form **f 
We shall refer to this , and the more general form ( 2 ) , as the quasi-classical approximation . 
It should be clearly appreciated that these equations are in no sense based on classical mechanics — their derivation depends essentially on the quantum theory of electron waves in crystals as shown in 13 8.8 The term quasi-classical is used to indicate that their form is classical . 
Once they have been derived , however , they may be used to describe the motions of the conduction electrons in the crystal by treating the electrons as classical particles . 
In the derivation of equation ( 1 ) we pointed out that there were certain restrictions under which it could be applied . 
In particular , the force F must be " slowly varying " , i.e. it must change very slightly between neighbouring cells in the crystal . 
We have applied equations of this form to discuss the motion of electrons under external electric and magnetic fields and have found that this description leads to results in excellent agreement with experiment when the fields are not too strong . 
We have also used the idea of effective mass in 13 9.3.6 to discuss the motion of an electron in the Coulomb field of an impurity atom in a semiconductor . 
Here , however , we have a rather paradoxical state of affairs in that , while we regarded the electron as a particle of mass me , we used wave mechanics to derive the energy levels of the impurity centre , quoting the well-known result for a hydrogen atom . 
Indeed we may readily see that the quasi-classical approximation only holds provided the wavelength { 15le of the quasi particle is short compared with the distance over which the field varies appreciably ; this is the well-known criterion for the application of classical mechanics to the motion of a particle in a field of force . 
For the motion of a free particle of mass m in a field of force given by a potential function the classical equation of motion **f 
is replaced by Schro " dinger 's equation **f 
or more generally by the equation **f 
where H[p , r ] is the classical Hamiltonian expressed in terms of the momentum p . 
Equations ( 7 ) or ( 8 ) determine the stationary-state wave function ps associated with the energy E. Because of the similarity of equations ( 5 ) and ( 6 ) it would seem not unreasonable to replace equation ( 5 ) , when we are dealing with an " external " field of force in a crystal to which classical mechanics can not be applied , by an equation of the form **f 
where is the potential which determines the force . 
This is effectively what we have done in discussing the energy levels of an impurity centre in a semiconductor in 13 9.3.6 . 
We shall devote most of the present Chapter to proving that such an equation can indeed be used to describe the motion . 
Some thought will have to be given to the interpretation of the wave function ps . 
It is clearly not the same as the wave functions used to describe the motion of the electron in the perfect crystal ; as we shall see , it is not the whole wave function but may be interpreted as a slowly varying amplitude . 
The extension of equation ( 9 ) to the case when the effective mass is tensorial may be expected to follow in the same way as equation ( 8 ) is an extension of equation ( 7 ) , the Hamiltonian H being the sum of the energy of the electron in the crystal as a function of the crystal momentum P ( which we should expect to replace the momentum p of a free particle ) and the potential energy being derived from the external force . 
We might reasonably therefore expect the equation which determines the motion of an electron in a crystal under an external force to be **f 
where is the energy of an electron in the perfect crystal given as a function of the crystal momentum P. In terms the wave vector k , equation ( 10 ) may be written in the form **f 
where is the energy of electrons in the perfect crystal as a function of the wave vector k . 
For slowly varying fields it is well known that equations such as ( 7 ) and ( 8 ) give the same results as classical mechanics ; similarly , equations ( 9 ) and ( 10 ) will give the same results as the quasi-classical approximation when this is applicable . 
Equations ( 10 ) and ( 10a ) clearly reduce to equation ( 9 ) when we have a scalar effective mass me ; they represent a higher degree of approximation than equation ( 2 ) . 
So far , we have only given plausible arguments for their form ; we shall now proceed to derive them using the quantum theory of the motion of electrons in a crystal . 
11.2 Quantum theory of the effective-mass approximation 
The wave equation describing the motion of electrons in a crystal in a perturbing field of force may be derived in a number of ways . 
An elegant derivation , which also shows up well the physical principles involved , originally given by G. Wannier , has been developed by J. C. Slater , and we shall first of all follow this method of derivation . 
In order to use Wannier 's method we shall have to introduce some wave functions which he used and which are generally known as Wannier functions ; they are built up from the Bloch wave functions which we have already used in our discussion of the motion of electrons in a perfect lattice . 
These functions are particularly well suited to this kind of problem , whereas for many other problems the Bloch functions are to be preferred . 
As we shall see , the Wannier functions are localised , whereas , the Bloch functions are spread throughout the whole crystal ; the latter are therefore appropriate for the discussion of problems in which we do not require to specify the position of an electron closely , while the former are useful when discussing problems associated with a definite point in the crystal such as an isolated impurity centre . 
It was indeed in order to obtain a localised wave function that the Wannier functions were first introduced . 
We know that the Bloch functions defined by **f 
are solutions of the wave equation for the perfect crystal and hence that a wave function representing a solution of the wave equation may be expanded as a series of such functions . 
If we restrict the values of k to the first Brillouin zone there will be N such allowed values corresponding to each energy band , where N is the number of unit cells in the crystal . 
In order to obtain an exact expansion of the wave function we should require to use Bloch functions corresponding to all bands . 
However , when we have a substantial gap between the bands it appears that we may obtain , under certain conditions , a good approximation by using Bloch functions only from the band in which we are interested , and these we shall denote by . 
We then have for the expansion of the wave function ps **f 11.2.1 The Wannier functions 
The expansion given in equation ( 12 ) is not very easily interpreted physically if a number of coefficients are required to give an accurate description of the wave function representing the motion of an electron in the perturbing field of force . 
To overcome this difficulty Wannier ( loc. cit. ) introduced a new set of wave functions , derived from the Bloch wave functions , which have the property of being localised . 
Consider the wave function **f 
where the constants { 15an are at our disposal , the sum being taken over the N allowed values of k . 
In the first unit cell of the crystal we may choose the constants { 15an to make all the functions add . 
We shall assume that the Bloch functions are normalised for a volume V containing N unit cells , and we have already seen that they are orthogonal , so that we have **f 
In the definition of the Bloch functions there is an arbitrary phase term and we use the constants { 15an which may be written in the form exp ( i{15bn) to take out this phase term . 
Indeed we may assume that the Bloch functions are so defined that they add to give the maximum contribution in the first unit cell so that we may take **f for all values of n . 
All stages of Calanus , for example , seem to migrate on some occasions while any stage may not on others . 
Such data can not yet be rationalized . 
Where information is less extensive , however , it is possible to find some regularity in the observations . 
Thus in { Euphausia superba from the Antarctic , the metanauplii remain in deep water , the later larval stages migrate diurnally , and the adolescents stay permanently at the surface . 
The migrating stages all come from 100-250 meters , and the time of their arrival at the surface is directly related to their swimming capacity : 3rd ( oldest ) calyptopis from 1800-2200 hr ; 2nd , from 2200-0200 hr ; and 1st , from 0200-0600 hr . 
Similar ontogenetic differences are apparent in { Bosmina coregoni whose adults remain at the surface while the young migrate to and from a depth of 50 meters . 
Such permanent occurrence at the surface could of course be considered the extreme of a variable day depth . 
The effect of day depths upon the surfacing of various animals has been reviewed elsewhere . 
c . 
Anomalies . 
In spite of the variability of migrational behavior , some kinds of anomalies may be recognized . 
Vertical movement occurs in some forms apparently in the reverse manner to that commonly met . 
Such reversed migrations are known for { Acartia clausi , A. longiremis , Nyctiphanes couchii , Evadne sp. , Oithona nana , Daphnia lumholzi , Stages 4 , 5 , and adult of { Calanus finmarchicus , Diaptomus banforanus , and { Cyclops bicuspidatus . 
An echo-producing layer , which the authors think probably consists of euphausiids , has also been described as , in part , regularly moving in a reverse manner . 
Most of these records are well substantiated and involve whole populations rather than aberrant individuals . 
But normal movements have been reported also for the same species in the case of five of these examples and for other species in the same genera for the remaining { Evadne , Daphnia , and Diaptomus . 
Many forms sometimes migrate and on other occasions do not , but a few appear to remain permanently at one level . 
Considering the widespread incidence of migration in the groups concerned , these may be considered as anomalous . 
The most clearly substantiated case is that of the copepod { Anomalocera patersoni , which remains permanently at the surface . 
Among other copepods { Rhincalanus gigas , Calanoides acutus , Microcalanus pygmaeus , Oithona frigida , and { Centropages typicus are all reported as showing no migration . 
The predaceous cladoceran { Bythotrephes longimanus also remains at one level , about 10 meters down . 
In view of its well-known normal migration , the occurrence of { Calanus finmarchicus in the summer at the surface in bright sunlight may justly be considered anomalous . 
This phenomenon has nevertheless been recorded many times , and such surface Calanus may be present in enormous numbers , breaking the surface into small circular ripples like raindrops . 
Observed underwater , two zones of differing behavior were recognized : an upper one about 30 cm in depth , in which the Calanus swam up and down repeatedly , frequently bumping on the undersurface of the water , and a lower one of indeterminate depth in which animals swam directly up or down . 
It seems likely that a continuous interchange was taking place between the population at the surface and that in deeper water . 
A second group whose normal vertical migration is sufficiently well known to make daytime occurrence at the surface rank as anomalous is the Euphausiacea . 
There are numerous records of euphausiids swimming at the surface in bright sunshine , with particular mention of their shoaling behavior under these circumstances . 
2 . 
Mechanisms . 
The majority of vertical migrations undoubtedly result from active swimming although passive movement through the water has been suggested on various grounds . 
For example , transport in vertical currents resulting from temperature differences has been proposed ; differences in water viscosity after temperature changes have also been suggested as a cause of movement , and passive movement could possibly result from changes in the specific gravity of the animals as a result of feeding . 
Any or all of these mechanisms might apply under particular circumstances , but the evidence in favor of active swimming is overwhelming . 
Indeed , deep-living Calanus may even keep its level during the arctic night by active migration against such vertical water movements as do occur . 
The rapidity of some vertical movements has led to the supposition that the animals must have had passive assistance , but measurements of swimming speeds prove that even the most extensive and rapid vertical movement is within the capabilities of the animals performing it ( Table 2 ) . 
Evidence has been presented for a supposed randomness in the movement of plankton animals . 
If valid , this implies that migrations involve kineses rather than taxes ( Chapter 10 ) . 
However , the data cited in support of this idea comprise without exception observations made in the laboratory . 
A kinesis resulting in an upward movement by Daphnia has also been demonstrated in the laboratory at particularly low light intensities , but otherwise swimming in these experiments was directional in relation to the light source . 
Such observations as have been made in the sea indicate that the predominant movement of copepods is directional . 
Although a random movement may occur close to the surface , this results from the restriction imposed by the boundary itself . 
The speeds of ascent calculated for some forms in the sea make it further improbable that the mechanism of ascent is a kinesis ; a directional taxis would seem more probable . 
Downward movement may in some forms start as a passive sinking , especially when it occurs before dawn ; but this must almost certainly be replaced by the headfirst downward swimming observed in the field . 
3 . 
Initiating , controlling , and orienting factors . 
The primary dependence of diurnal migrations upon changes in light intensity is beyond doubt . 
Yet in spite of a great amount of work , the detailed causal relationship remains one of confused complexity . 
Loeb first suggested the importance of light as the governing factor but combined its influence with that of gravity . 
Later authors , in particular Rose , have proposed that light alone can provide an adequate mechanism if the animals have , and select by exploration , a zone of optimum light intensity . 
This view has been enlarged with a suggestion that both phototaxes and geotaxes may play a part in keeping animals near their optimum . 
Experimental work largely performed on Calanus , however , has failed to make clear the relative importance of light and gravity in this context . 
A plankton population held in glass tubes at a particular depth in the sea resolves itself into two components , one swimming up and the other down . 
The proportion swimming up increases with increasing depth . 
Experiments using light reflected up against gravity showed that here the reaction to light predominates . 
Yet other experiments in the dark showed that the population still segregated into one group swimming up and another swimming down . 
Hardy and Bainbridge have been able to remove the confusing experimental factor of a limited vertical range with their plankton wheel . 
Their tentative conclusion is that upward migration is generally a positive movement toward a source of low light intensities . 
Little upward movement can be obtained by blacking out during the day , except with Daphnia . 
Their results leave little doubt that downward migration is not sinking as the result of an inhibition of movement but is a strong , rapid , and direct downward swimming away from light . 
The complete absence of light does not generally result in a downward sinking but rather in station-keeping maintained by a characteristic hop-and-sink behavior comprising alternate phases of upward swimming and downward sinking . 
In Daphnia , migratory behavior results from the interaction of both phototactic and geotactic responses . 
Furthermore , the direction of phototactic movement is dependent upon the postural angle of the antenna and not the orientation of the body . 
A reversible photochemical system has been proposed to account for the photic responses , and this requires a minimal rate of change in light intensity to induce response ; but the rates of change in the sea may be too low for this . 
An important experimental advance has been made by Harris and Wolfe , who studied the behavior of { Daphnia magna in a tank filled with India ink suspension and illuminated by an overhead light of variable intensity . 
This technique has allowed for the first time sufficient change in intensity over limited distances for dependent behavioral changes to be seen in the laboratory . 
Despite a compressed time scale these authors have obtained an extraordinarily close simulation of migratory behavior in nature . 
A complete cycle of vertical migration can be demonstrated in a vessel 30 cm high . 
As well as strong naturally-characteristic individual variations , this includes a midnight sinking and a dawn rise . 
At high light intensities the animals keep station at their optimum by a vertical hop-and-sink behavior and this confirms earlier observations on station-keeping in { Balanus nauplii . 
At low light intensities this is replaced by a kinetic response independent of the light direction . 
The dawn rise is a manifestation of this . 
In complete darkness all movement is inhibited and a sinking results . 
Harris and Wolfe stress the importance of a sensory adaptation in the photoreceptor system when interpreting their results and suggest that animals in the sea could follow prolonged slight changes without being affected by rapid large changes . 
In imposing directionality upon the movement of vertically migrating animals , gravity must be second only to light . 
Preoccupation with the idea of kinetic movement and an overemphasis of the incidence of midnight sinking have led some authors to dismiss gravity as of no consequence . 
Yet it must in fact be of the utmost importance in many cases . 
Parker first proposed " geotropism " as one of the factors in vertical migration , and his ideas have since been enlarged by many authors . 
The continued ascent of crustaceans in total darkness , which seems substantiated in a good many instances , and the experimental evidence showing Calanus keeping station in the dark and Daphnia ascending , strongly imply an orientation dependent upon gravity . 
Pressure has been suggested as having some influence upon migration , especially of Calanus . 
But experiments expressly designed to test this have not revealed any change in the behavior of this species under pressures up to the equivalent of 20 meters depth . 
Striking results were obtained , however , with zoea and megalopa stages of Portunus and Carcinus . 
A high proportion of these swam up for periods of up to 3 hr when subjected to pressures equivalent to 5 , 10 , 15 , and 20 meters depth . 
These findings have since been confirmed in studies of Acartia and Centropages , the megalopas of { Carcinus maenas and Galathea as well as adults of the copepod { Caligus rapax , still without any success in eliciting a response from Calanus . 
There is as yet no morphological evidence for a pressure-sensitive organ in any of these forms , and the mechanism of perception is quite uncertain . 
The unequivocal demonstration of a sensitivity to pressure in some of the deep-migrating copepods or decapods would be a valuable contribution to the whole problem of vertical migration . 
But at the moment , light must remain the chief factor by which most forms may gauge depth . 
There is evidence that phytoplankton may have some effect on the vertical migration of crustacean zooplankton . 
Hardy first laid real emphasis on this possibility . 
Observations on the inverse distribution of plants and animals in the sea suggested that many forms must be prevented from coming up or must come up for only a short time in the presence of high concentrations of phytoplankton . 
There is some evidence possibly supporting this idea although this relates only to horizontal movement ; on this basis the concept of external metabolites as affecting animal-plant relationships in the sea has been developed by Lucas . 
But later laboratory experiments indicate that greater numbers of Calanus swim up in the presence of a variety of pure and mixed phytoplankton cultures than in unenriched water , only one culture , of Chlorella , depressing the number swimming up . 
The mechanism underlying this increase in upward migration has not been investigated , but probably reduction in light intensity by the plant cells is not the intermediate factor . 
In other instances this might however be effective : for example , blue-green algae in Lake Windermere may reduce the light intensity at 4.3 meters by more than 50% . 
This must surely affect the responses of animals . 
This resulted in units of much lighter weight than could be obtained with tubular constructions . 
The growth of the aircraft industry brought even greater emphasis to the need for lightweight compact heat exchangers . 
During the 1930's , the secondary surface plate-and-corrugation construction became established for aero-engine radiators , using dip-soldered copper . 
The air and engine-coolant passages were separated by flat plates . 
The air passages were packed with corrugated foil bonded to the primary plates to provide the necessary surface area for heat transfer . 
The narrower coolant passages were also packed with foil , chiefly to provide sufficient support for the flat plates to withstand the coolant pressure loadings . 
The introduction of the aluminium alloy dip-brazing process in the early 1940's was quickly taken up for aircraft heat exchangers and led to substantial weight reductions as compared with copper construction . 
This development coincided with the introduction of pressurized aircraft cabins and the demand for air-to-air cabin coolers . 
Although in this case the heat transfer coefficients on the two sides of the heat exchanger were of comparable magnitude , the use of secondary surface was still attractive , since the greater part of the surface area could be made up of fins only 0.006 in. ( 0.15 mm. ) thick . 
Furthermore , developments in the detail form of the fins made possible a reduction in the total surface area required as compared with the use of smooth continuous passages for the same thermal duty and pressure losses . 
The properties of compact form , low weight , and design flexibility thus developed found ready application on a much larger scale with the introduction of tonnage scale air separation plants . 
2.1 Methods of Construction 
The basic method of construction is both simple and extremely flexible . 
Figure 3 illustrates the arrangement of a single passage . 
This can be extended in length and width up to the limit of manufacturing equipment available . 
The corrugation is machine-formed , thus ensuring a high standard of uniformity in height and fin pitch . 
A number of such passages may be combined to give either a cross or a countercurrent flow formation , as shown in Figures 4 and 5 . 
The size and type of corrugation may be varied for each stream to suit the operating requirements and to provide a reasonable layout with minimum block volume and weight . 
Typical corrugations are shown in Figure 6 . 
The flow patterns may be further developed to provide multi-pass or multi-stream arrangements by the inclusion of suitable internal seals and distributors and the fitting of external header tanks , as indicated in Figures 7-10 . 
With the simple cross-flow layout in Figure 7 , the corrugations extend throughout the full length of each set of passages , and no internal distributors are required . 
This construction is appropriate when the temperature range in each stream does not exceed about one-half of the difference between the warm and cold inlet stream temperatures or , more generally , when the effective mean temperature difference in cross-flow is not significantly below the logarithmic mean temperature difference for countercurrent flow . 
On low temperature plants , this construction is sometimes useful for liquefiers , where the temperature changes little on the condensing side , and where a large throughput of low pressure gas as the warming stream calls for a large cross-section and short passage length . 
For higher duties , with temperature ranges in both streams up to 80 per cent or 90 per cent of the inlet temperature difference it is sometimes advantageous to use a multi-pass cross-countercurrent arrangement as shown in Figure 8 . 
Stream A flows straight through , while stream B is guided by means of internal seals and external tanks to make the required number of passes . 
The unit may thus be considered as comprising several cross-flow sections , assembled in counter-formation , such that the effective mean temperature difference approaches much more closely to countercurrent than to cross-flow conditions . 
This type of construction is used for gas-gas and gas-liquid applications . 
When very high thermal efficiencies of , say , 95-98 per cent are required , a pure countercurrent formation is invariably adopted . 
Typical layouts are shown in Figures 9 and 10 . 
The choice of headering is governed by several considerations , such as the operating pressures , the number of separate streams involved , and whether or not reversing duty is included . 
Figure 9 shows an arrangement suitable for two-stream steady duty , in which stream A is at comparatively low pressure . 
A more general solution is shown in Figure 10 . 
This is used if streams A and B are reversed periodically , the geometry of these streams being symmetrical to maintain constant flow characteristics . 
Additional steady streams may be included as C , D , or E to suit requirements . 
This type of arrangement is also used when dealing with high pressure streams in all channels . 
In all countercurrent flow units , suitable distributors must be provided in the end regions , such that the flow of each stream is spread uniformly across the whole width of each layer throughout the length of the main zone . 
This problem is of great importance not only to the proper performance of the heat exchanger but also on manufacturing and mechanical strength considerations . 
Further details are given in later sections of this review . 
The possibility of varying the geometry and type of corrugation in different layers has already been mentioned . 
For industrial applications , the height of corrugation normally lies in the range 0.15-0.47 in. ( 3.8-12 mm approx. ) , the thickness varies from 0.008 to 0.015 in. ( 0.2 to 0.38 mm. approx. ) , and the fin pitching varies from 10 to 15 or 18 fins per inch ( 3.9 to 5.9 or 7.1 fins per centimetre ) depending upon the type of corrugation . 
The resulting total surface areas lie from about 300 to 450 square feet per cubic foot of block volume ( 1,000 to 1,500 square metres per cubic metre ) . 
The free cross-sectional area ratios lie between 0.70 and 0.80 . 
Both the surface area and the free cross-sectional area must be suitably divided between the various streams . 
For instance , in a two-stream gas-gas heat exchanger , each stream may have a surface area of about 200 square feet per cubic foot of total block volume , with a free cross-section ratio of about 0.4 , while in a gas-liquid heat exchanger , the gas stream would have a surface area of about 300 square feet per cubic foot of total block volume , with a free cross-section ratio of about 0.6 . 
In general , the taller corrugations are used for gas streams , while those at 0.15 in. to 0.25 in. high are used for liquid streams and in condenser-reboilers . 
The use of plain continuous corrugations is chiefly limited to condenser-reboiler use , or to cases where the free passage of contaminating solids is desired . 
For most other applications , a reduction in the total surface area and block volume required can be achieved by the use of more complex types of corrugation such as the herringbone and multi-entry patterns shown in Figure 6 . 
These are discussed in more detail in later sections . 
The manufacture of the heat exchangers involves several distinct stages , beginning with the assembly and dip-brazing of individual blocks , i.e. tube plates , corrugations , and edge-seals only . 
Each block is thoroughly cleaned after brazing and subjected to preliminary leak tests before the fitting of header tanks by argon-arc welding . 
The block is then tested hydraulically to its full design test pressure on each stream separately . 
In the case of multiple assemblies , each block may also be submitted to flow tests on each stream prior to selective assembly to ensure uniformly balanced flow distribution throughout the whole assembly . 
Figure 11 shows a typical two-stream countercurrent block during manufacture , with header tanks fitted to one stream only . 
On completion , this type of block would be suitable for either steady or reversing operation . 
With existing brazing equipment , individual blocks are made up to 9 ft ( 2.75 m ) long with an overall cross-section of 17 in. x 21 in. ( 0.43 m x 0.53 m ) to give a total block volume of about 22 ft3 ( 0.62 m3 ) . 
By means of appropriate manifolding , a number of such blocks may be assembled together either in series or in parallel , or a combination of both , according to requirements . 
Two blocks are shown as a series arrangement in Figure 12 and sixteen blocks in parallel in Figure 13 . 
A more complex arrangement is shown in Figure 14 . 
This assembly contains three separate heat exchangers through which one stream is common on the low pressure side , while two of the high pressure streams are in parallel and the third high pressure stream in series . 
This complete assembly is welded up to form a single unit with flanged main connections and vents only . 
For multiple arrays it is generally preferred to assemble together a number of blocks and to weld up all the interconnecting pipework and manifolding , so as to limit the number of flanged joints on the plant . 
If aluminium pipework is used the flanged joints may be eliminated completely and the heat exchangers attached to the main pipework by site-welding . 
For very large assemblies , it may be necessary to split the design into several separate sub-assemblies suitable for transport and installation , and to connect these together at the erection stage either by site-welding or by flanged joints . 
2.2 . 
Mechanical Design 
Mechanical design aspects must always be considered from the outset , since these may well influence the general layout and internal construction and so affect the basis for performance assessment . 
For the operating pressures and conditions required , two major factors are the internal pressure loading on the corrugations and associated brazed joints , and those on the header tanks , together with any external pipework loadings . 
For low-to-medium steady operating pressures in the range 0-100 lbin2 ( gauge ) ( 1-8 kg/ cm2 ( abs ) ) , the mechanical design does not generally present any serious problems . 
For higher pressures and for reversing duty the mechanical design requirements become of increasing importance , particularly in relation to the size and arrangement of header tanks . 
The internal plate and corrugation construction is adequate for static test pressures at room temperature of 600-1,000 lb/ in2 ( gauge ) ( 42-70 kgcm2 ( abs ) ) , depending upon the type and thickness of corrugation . 
For low temperature applications the corresponding rated maximum operating pressures would be 250-450 lbin2 ( gauge ) for steady conditions , or 125-225 lbin2 ( gauge ) for reversing applications . 
For such pressures , however , it is necessary to limit the span of the header tanks in order to avoid excessive peripheral loadings in the plane of attachment to the block . 
This means either that the block cross-section must be kept small , or that small tanks , such as those shown in Figure 10 , must be fitted . 
The latter alternative is particularly suitable for reversing applications and for large scale steady operation . 
Internal distributors are necessary to spread the flow across the whole width of each passage , and these must be adequate to withstand the internal pressure loadings . 
When considering the installation of a heat exchanger assembly for low temperature service , due consideration must be given to thermal contractions both in normal service and under any abnormal circumstances which might arise . 
The method of mounting and the external pipework must be sufficiently flexible to allow for such movements without imposing excessive loads on to the assembly . 
This precaution is , of course , common to all low temperature installations . 
In normal operation relative movements within the assembly should not generally provide any serious problem since the balancing of flows which is so important on performance considerations ensures that the temperature patterns , and hence the contraction effects , are also uniform across any section of the assembly . 
Nevertheless , an adequate measure of flexibility is maintained between parallel assemblies to allow for any residual unbalance effects and for temporary effects which might arise during transient or abnormal operating conditions . 
2.3 Performance 
Performance design calculations for any type of heat exchanger depend upon the process requirements , i.e. flow rates , temperatures , and pressures of each stream , and upon the relevant heat transfer and friction factors for the type and arrangement of surface considered . 
The latter must generally be determined experimentally in the first instance . 
The broad subjects of heat transfer and heat exchanger design are well covered by McAdams and Jakob , while Kays and London give the results of extensive researches and experiments particularly related to compact forms of heat exchanger including various types of secondary surface construction . 
The erratic behaviour of thin metal films is well known and is the subject of an extensive literature , but as shown by the foregoing , a better understanding of film properties is beginning . 
Summarizing the Introduction , it can be stated that the anomalous electrical properties of films are principally due to their structural imperfections and to the thermodynamic instability produced when metal vapour is abruptly condensed to the solid phase . 
The changes of resistivity and temperature coefficient of resistance , which occur upon heating or ageing a film , arise from the re-ordering of the structure , the relief of high internal stresses and the further oxidation or gas absorption of the film . 
These changes are parallel to those occurring in fine resistance wires upon annealing after cold-working . 
However , the gas absorption and higher degree of lattice imperfection in vacuum-deposited films cause much greater variation of properties . 
There is an increasing amount of evidence that high stability resistance films can be obtained by correct annealing treatment and suitable protection . 
It is the purpose of this paper to describe a method of making reasonably stable resistance elements by the vacuum deposition of nickel-chromium alloy on glass and to discuss their properties in terms of the processing conditions . 
2 . 
Practical requirements Substrate 
The surface of the supporting substrate should be smooth and uniform , and both chemically and mechanically stable at temperatures up to about 350° C in atmosphere and vacuum . 
Any variation of surface smoothness gives a corresponding variation of film resistance value , because the film is thin enough to be greatly affected by the state of the surface . 
For example , a film of resistance as low as 10 { 15Osquare on a polished glass surface may be discontinuous when deposited under identical conditions on a finely ground glass surface . 
It is a characteristic of a film deposited from the vapour that the grains tend to grow on surface prominences , which trap the atoms first arriving there and act as centres for nucleation . 
Films as thick as 1000 A15 may be discontinuous when deposited on a coarse surface because large grains are formed which do not touch , and the thickness must be increased before conductivity is observed . 
Such films tend to be unstable because their conductivity depends upon contacts between large grains . 
The most suitable substrate materials are found amongst glasses and ceramics . 
Good results have already been obtained using glasses of high silica content such as Pyrex or Vycor . 
These are two of the few glasses unaffected by water vapour . 
Many other glasses , including some borosilicates , devitrify in contact with water , and their surfaces become powdery because small crystals of metal silicates are formed . 
Soda-lime glasses are not used because their surfaces are also chemically unstable . 
During flame polishing , when the glass is bombarded by thermally produced gas ions or ionic bombardment in a glow discharge , free sodium ions are active at the surface of the glass . 
They combine with water vapour from the gas atmosphere to form sodium hydroxide and deliquescent sodium silicate by reaction with silica in the glass . 
Some further reaction with the deposited film must be expected . 
Ceramics possessing good chemical and mechanical properties are available ; however , their surface smoothness is often variable because of the sintering process used in their manufacture . 
Glazing is not always a satisfactory solution to this problem because standard glazes are often based upon some of the unsuitable glasses already described . 
Very careful examination of surface smoothness is needed when choosing a ceramic material for the support of vacuum-deposited films . 
The temperature coefficient of linear expansion of metals is usually an order higher than that of glass or ceramics , and this factor partly contributes to the high internal stresses which have been observed in thin films . 
However , once the films have been annealed , the effect of the expansion of the base on the resistance of the film is very small , compared with the average temperature coefficient of resistance of films , and is insignificant when compared with that of bulk metals . 
The resistance alloy 
In the early stages of deposition of a metal film , aggregates of metal atoms ( nuclei ) are formed on the substrate . 
The number of nuclei is dependent upon the physical and chemical properties of the metal and substrate , and upon the rate of deposition . 
As the nuclei increase in size they grow together , eventually to form a continuous film . 
The second stage of growth is marked by the onset of electrical conductivity , and the rate of change of resistance with film thickness is very high . 
Unfortunately , the most useful resistance values coincide with this unstable region of thickness for many metallic conductors . 
The most successful high-resistance films have been made by depositing chromium and alloys of chromium with nickel , silicon , titanium , etc . 
For example , nickel-chromium alloys have a high bulk resistivity ( 80-130 mO cm ) and therefore films of this alloy are much thicker than films of the pure metals for the same resistance value . 
Films of resistance 400 { 15Osquare are at least 80 A15 thick , more or less continuous and are outside the very unstable region of thickness . 
Nickel-chromium alloys also have a low temperature coefficient of resistance in bulk , and are very resistant to chemical attack because of the compact protective oxide layer which forms in contact with an oxidizing atmosphere . 
The formation of double oxides having a spinel structure has been shown on nickel-chromium alloys under examination by electron diffraction , and this reason has been given to account for their high chemical stability . 
Evaporation conditions 
The lowest values of temperature coefficient of resistance and the best stability are achieved in films deposited under conditions favouring oxidation . 
During deposition the substrate is heated to relieve the internal stress in the film , but this treatment can also increase the rate of oxidation . 
The residual gas atmosphere in the chamber of a kinetic vacuum system is highly oxidizing due to the high proportion of water vapour at the normal working pressure ( 10-4 mm Hg ) . 
Assuming that the partial pressure of water vapour is only 10-5 mm Hg , then it is calculated approximately that 5 x 1015 molecules cm-2 s-1 strike the substrate surface . 
If the rate of deposition of chromium metal is about 3 A15 s-1 , then ten water vapour molecules strike the surface for every chromium incident atom . 
Thus there is sufficient oxygen ( in the form of water vapour ) available at the source for the film to be highly oxidized at normal rates of deposition . 
Oxidation also occurs after the chromium atoms have left the vapour source , giving rise to the familiar gettering effect . 
The fall in pressure can readily be observed on the vacuum gauge . 
Thus the first few atomic layers deposited during the gettering period are highly oxidized , and when the chamber has been " cleaned up " the deposit is more metallic . 
After evaporation ceases , the deposited film remains open to oxidation . 
Thus the deposited film is inhomogeneous and approximates to a sandwich layer of oxidemetal/ oxide , in which the two outer layers are more highly oxidized than the inner layer . 
The exact state of oxidation of the deposited film is unknown and a further effect of oxidation can be observed upon baking in air . 
The final resistance change upon annealing may then be positive or negative , because the decrease attributed by Vand to lattice transformation may be greater or less than the increase due to further oxidation . 
Heat treatment and protection 
Heat treatment carried out during or after deposition serves three purposes : 
( 1 ) high internal stresses in the film are relieved ; 
( 2 ) some defects in the crystal lattice are removed , thus improving the heat-stability ; 
( 3 ) a protective oxide layer is completed , making the film less subject to external atmospheric attack . 
In practice , it has been found advisable to heat the substrate in vacuum before deposition to a temperature of at least 300° C. A further heating period in air for 30 min at 300° C completes the annealing of the film . 
The electrical properties of resistance tapes and wires are stabilized by annealing and by cyclic baking in air or hydrogen . 
This treatment reduces the strains and dislocations set up during the drawing of the wire . 
Thus the treatment required by a vacuum-deposited film is similar . 
Baking during and after deposition re-orders the crystal lattice , and improves the resistance stability with time , also forming a compact oxide surface layer . 
Several fast baking cycles carried out in air hasten the changes of resistance up to 300° C , which become smaller with each successive cycle . 
3 . 
Experimental work Evaporation technique 
The preparation of nickel-chromium resistance films was carried out in a vacuum deposition plant having a 12 in. diameter chamber equipped with pumps capable of reducing the residual gas pressure in the vacuum chamber below 10-4 mm Hg in 5 minutes . 
Provision was made for two h.t. lead-through electrodes ( for cleaning by positive ion bombardment ) , three electrodes for the evaporation source and several smaller electrodes for connecting the radiant heater , thermocouple , and resistance monitor . 
The evaporation source was heated by electron bombardment ( Fig. 1 ) . 
This source consisted of a stainless steel supporting block ( forming the anode ) on which was mounted a 1/4 in. diameter special ceramic hearth 1/4 in. high . 
Nickel-chromium wire ( 22 s.w.g. ) was fed through a stainless steel guide tube to the centre of the hearth . 
The feed mechanism was mounted at the side of the hearth , and allowed the wire to be fed either continuously or to be intermittently operated by a handwheel outside the vacuum chamber . 
The nickel-chromium wire was bombarded by electrons emitted from a small hot filament of 0.020 in. diameter tungsten wire ( forming the cathode ) , supported 1/8 in. above the top of the hearth . 
The cathode heater supply was obtained from a 8 v , 100 A transformer with secondary winding insulated from earth and primary for 15 kv . 
The anode and cathode were connected across a suitable h.t. supply , having a maximum power of 1.5 kw at 3 kv ; the anode was held at earth potential and the cathode at negative 3 kv . 
The top of the hearth was hollowed to enable the wire to melt and form a bead from which evaporation could take place . 
Substrates and workholders 
Special jigs were made to hold flat specimen plates of Pyrex , soda glass and ceramic . 
During each evaporation , the resistance of one plate was monitored by connecting the end terminals to an external circuit for resistance measurement . 
A simple ohmmeter was used for monitoring the resistance value during evaporation . 
The accuracy of the measurements was only of the order 14 2% , but the results were used only to indicate the approximate value of the resistance during evaporation . 
A bridge method of measurement was used to determine accurately the resistances of the slides , and is described more fully later . 
The workholder consisted of a simple jig constructed so that only 1/8 in. at each end of the slides was masked by the clamp , and these were placed next to the monitor plate . 
The workholder was supported 4 in. above the evaporation source by means of a tripod . 
A radiant heater , dissipating 750 w at 110 v , was mounted above the workholder to raise the temperature of the substrate to 300° C before evaporation . 
The temperature of the substrate was measured by means of a chromel-alumel thermocouple placed inside the vacuum chamber with its junction resting on the top face of the workholder . 
The thermocouple was connected to an external meter calibrated to read degrees Centigrade , covering a temperature range from 0 to 500 in divisions of 10 degrees . 
A special chamber assembly was constructed for deposition of films on cylindrical formers and , for monitoring their resistance , a static flat glass slide was used . 
By experiment a simple relationship between the resistance of the static plate and the resistance of the cylindrical formers was obtained , thus enabling the evaporation to be roughly monitored . 
Contacts 
The method of making contact to the deposited film influenced both the accuracy with which the film could be measured and the ultimate stability . 
Rutherford in Manchester by J. E. GEAKE Manchester College of Science and Technology 
It is now 50 years since Rutherford , working in Manchester , conceived the idea that the atom had a small concentrated nucleus , and from this idea sprang the whole of our present-day knowledge of atomic structure and our exploitation of its consequences . 
This great landmark in physics was celebrated by holding the Rutherford International Jubilee Conference early in September . 
It was appropriate that the Conference should be held at Manchester University because , although Rutherford did valuable work at Cambridge and at McGill , it was his Manchester period which produced the most important results , and the discoveries with which his name is mainly associated . 
It was also appropriate that there were two parts to the Conference — a commemorative session in which some of the surviving members of Rutherford 's Manchester team took us back by their reminiscences to those great days of the past , and also a full-scale conference setting out the present state of our knowledge of the nucleus . 
To keep up with a rapidly-changing subject such as this , one must not spend too long looking backwards . 
Of those closely associated with Rutherford in Manchester , Marsden , Darwin , Chadwick , Andrade and Niels Bohr were all present , and it was greatly regretted that William Kay , Rutherford 's laboratory steward and personal assistant , to whom he acknowledged a great debt , did not live to be present at these celebrations ; he died in Manchester only a few months ago . 
The main commemorative session of the conference consisted of the reminiscences of Sir E. Marsden , Sir Charles Darwin and Professor Andrade , and this was followed by a ceremony at which honorary degrees were bestowed . 
During the week , delegates saw something of the local Derbyshire scenery , visited Jodrell Bank and A.E.I. at Trafford Park , were received by the Lord Mayor at a lavish reception in Manchester 's impressive Victorian Gothic Town Hall , and rounded off the week at a special concert given by Sir John Barbirolli and the Halle2 Orchestra — the source of another of Manchester 's claims to renown . 
Concurrently with the Conference an exhibition of things associated with Rutherford was held — photographs , letters , models and , most interesting of all , some of his actual apparatus , including the piece said to have been his " pet " — the superb piece of glass-blowing by Baumbach which made possible the spectral identification of { 15a-particles as helium . 
The letters on view gave some interesting glimpses into the organization and economics behind the scene . 
There was Schuster 's letter offering to hand his chair over to Rutherford ( then at McGill ) , Rutherford 's answer making careful enquiries about the financial arrangements for research , and Schuster 's detailed reply saying how he spent his annual grant for teaching and research ( all £450 of it ! ) and by how much it was safe to overspend without getting into trouble . 
Rutherford was satisfied , and came in 1907 , and thus began the work in " Tom Tiddler 's field " , which was how Rutherford referred to one of the most celebrated research groups in the history of physics . 
Rutherford owed a considerable debt to Schuster for handing over to him a well organized and relatively well equipped laboratory and teaching department . 
While the glory of discovering the nucleus falls to Rutherford , it was entirely owing to Schuster that the work was done in Manchester . 
As early as 1906 Rutherford , then at McGill , had realized , from the observation that an { 15a-particle beam was spread out slightly by passing through a mica sheet , that there must be surprisingly large electric fields within atoms , but it was not until 1911 that the idea of the nucleus was finally conceived . 
A trivial defect in an { 15a-beam tube , which was cured empirically by inserting brass washers to confine the beam , suggested that { 15a-particles were reflected by metals . 
Rutherford suggested to Marsden , a second-year student ( in those days undergraduates were given small research projects as part of their training ) , that he should follow this up . 
After some initial difficulties , because the available { 15a-particle sources were too weak , Marsden eventually obtained a stronger source and did the experiment which is seen in retrospect to be one of the most profitable ever carried out . 
He directed a beam of { 15a-particles at metal foils , and observed the range of angles at which they came off . 
The result was staggering ; although most of the particles were only deflected slightly , a few were turned through large angles , and a very few came almost back along their tracks . 
As Rutherford said later , it was as if one fired 15 in. shells at tissue paper , and found that occasionally they bounced back ! 
Marsden told Rutherford what he had observed , Rutherford questioned him about the experiment to convince himself that it was all right , and that was all for several weeks , until a Sunday evening in the Autumn of 1911 . 
Rutherford had invited several of his research workers to supper in his house at Withington , as he often did , and while they were chatting after supper Rutherford suddenly came out with his first ideas about the atomic nucleus ; before they went home he asked one of them , Darwin , to check his hasty derivation of the scattering law to be expected when { 15a-particles were deflected by point nuclei . 
They even discussed , on that first evening , the idea that , if the nucleus were not quite a point , departures from the law at close approach could yield information about nuclear structure . 
Although Rutherford did not live to see powerful enough scattering experiments performed , this is now the basis of modern methods of investigating the structure of nuclei and nucleons . 
In the months that followed Geiger and Marsden carried out more sophisticated scattering experiments than the one which had revealed the effect , and actually measured the angular distribution of the scattered { 15a-particles . 
The results confirmed Rutherford 's scattering law and therefore the validity of the assumptions he had made in deriving it , and led in 1913 to a group of three papers which laid the foundations of nuclear physics . 
The commemorative session of the conference produced reminiscences about several of Rutherford 's group in Manchester ; of Moseley whom Sir Charles Darwin ( who worked with him ) described as the hardest-working person he had ever known , and who was an expert in finding a meal in Manchester at 3 a.m. ; of Niels Bohr who was a very comforting theoretician with great skill in bridging the gap between startlingly new theoretical concepts and classical ideas ; of Robinson , a keen music-hall addict — and indeed of the music-hall origin of the correct intonation to Rutherford 's nickname of "Papa " . 
While these reminiscences of the physics of 50 years ago were appropriate and entertaining , it was right that most of the time at the conference should be concerned with the physics of the present . 
There were nearly 200 contributed papers , and for those who want a detailed picture of the present state of nuclear physics these papers will shortly be published as a 750-page volume . 
The conference sessions , however , consisted of the presentation of invited papers , each intended to summarize a different aspect of the subject . 
Thirty years ago Rutherford said , " It is my personal conviction that if we knew more about the nucleus , we should find it much simpler than we suppose . 
I am always a believer in simplicity being a simple fellow myself . " 
The subject at present seems a long way from this simplicity ; parts of the conference seemed to be in a foreign language , and at one point there were so many rival theories that they were referred to by reference numbers . 
Perhaps we need another Rutherford . 
The main topics reviewed included nuclear forces , nuclear structure , and the interactions with outside particles from which most of the evidence for nuclear properties is obtained . 
There was also a paper on the limitations and possibilities of the instruments for nuclear investigation , and another , rather off the main line , on cosmological dating by nuclear methods . 
It has long been understood that the attractive forces between nucleons ( the neutrons and protons which comprise nuclei ) were somehow concerned with the interchange of a particle ( the { 15p-meson or pion ) between them . 
There has also been evidence that sometimes two pions are in transit between the interacting nucleons at the same time , and the possibility of this occurrence modifies the force to be expected ; although the theory of this process is still an unsolved problem , models describing the resulting behaviour have been proposed . 
What has only recently been confirmed — in fact it was announced at this conference — is that occasionally three pions at a time are involved . 
These three pions may actually be joined together transiently as a compound particle during the interchange process ; indeed , theoreticians have been invoking a compound particle of this type for some time . 
There now seems to be evidence for its existence . 
A nuclear model which has been surprisingly long-lived and successful is the shell model , which was first proposed 25 years ago . 
This assumes nucleons to occupy energy levels , obey quantum-number selection rules , and group themselves into closed shells in a manner analogous to the electrons outside the nucleus . 
This theory was given a new lease of life by adding the concept of nucleon spin , which undergoes coupling with the nucleon " orbital " motion . 
The presence of any nucleons in addition to the numbers which comprise closed shells will tend to distort the otherwise spherical shape , but these distortions were ignored in the approximate treatment of the problem . 
If there are only a few nucleons more ( or less ) than complete shells the mean distortion is indeed small , but the theory has been extended to include vibrations about this mean shape . 
With larger numbers of extra nucleons , mid-way between the numbers comprising complete shells , the nucleus is much more distorted , and rotational modes become important . 
With these larger numbers of extra nucleons it is no longer practicable to treat them singly and only their collective behaviour is considered . 
The way nucleons are arranged in a nucleus , and especially in the surface regions of heavy nuclei , is another topic of current interest . 
Some workers consider that nucleons tend to be found singly or in pairs in the nuclear surface , while others believe that there is more than a random chance of their being found in groups of four , although the grouping may be of a very transitory nature , the particles perhaps remaining associated for 10-22 of a second or so . 
Indeed , it is known that if a single particle , say a neutron , hits a nucleus it may result in the ejection of an { 15a-particle ( an assembly of 2 protons and 2 neutrons ) . 
However there was a vigorous argument at one session of the conference as to whether this { 15a-particle existed in the nuclear surface and was knocked out by the neutron , or whether the incident neutron simply collected three more particles and itself became part of the resulting { 15a-particle . 
The evidence seems to be in favour of the former idea — that the four particles were already associated before ejection . 
Soon after Rutherford came to Manchester he and Geiger , using Geiger 's new { 15a-particle counting techniques , were able to make the first measurements of the half-lives of radioactive elements . 
Nearly 20 years later , when Aston measured the relative abundances of the isotopes in lead ( the end-points of radioactive decay series ) from a lead-uranium ore , Rutherford realized that this , combined with his half-life measurements , could yield estimates both of the age of the earth ( i.e. the time since solidification ) and of the time since the actual formation of the heavy elements . 
Rutherford 's results increased the estimated time-scale for the Earth 's development by a factor of more than 10 over the currently accepted estimates due to Kelvin , and this advance produced the newspaper headline " Doomsday Postponed " . 
Apart from Rutherford 's assumption that the amount of 235U initially formed was at the most equal to that of 238U , modern cosmochronologists would agree with him . 
It is now believed that 235U was produced initially in greater abundance than 238U , and this , plus minor changes in the accepted values of other constants , pushes the estimated time since the formation of the heavy elements ( loosely called the age of the galaxy ) up from Rutherford 's estimate of 3.4 x 109 years to about 20 x 109 years . 
Statistically the three-parameter 1,000 mb forecasts for these 20 cases are much better than the two-parameter forecasts and are about the same as the C.F.O. forecasts . 
The 1,000-500 mb thicknesses and the 500 mb heights are much better forecast by the three-parameter model than by either C.F.O. or the two-parameter model . 
The thermal winds are also forecast better with the three-parameter model than with the two-parameter model . 
There is little to choose between the C.F.O. and three-parameter model forecasts of the 500-200 mb thicknesses and thermal winds , but the C.F.O. 200 mb forecast is rather better than that produced by the three parameter-model . 
The forecasts of the 200 mb contours and 500-200 mb thickness produced by extrapolation from the two-parameter model were , not unexpectedly , worse than those produced by the other two methods . 
It should be noted that C.F.O. do not produce forecast charts of the 500-200 mb thickness , and that the values attributed to them have been obtained by subtracting their 500 mb forecasts from their 200 mb forecasts . 
b ) Examples of forecasts 
The numerical forecasts using the three-parameter model based on data for 00 GMT 26 February 1959 and 5 May 1959 are shown in Figs. 1-8 . 
These two situations were chosen because the former forecast produced a large r.m.s. error at 500 and 200 mb and was not one of the better forecasts , whereas the latter was typical of one of the good forecasts . 
A depression centred ESE of Newfoundland at 00 GMT 26 February 1959 ( Fig. 1 ( a ) ) moved rapidly NE and deepened 12 mb in the following 24 hr ( Fig. 1 ( b ) ) . 
The axis of the high-pressure ridge in mid-Atlantic also moved rapidly NE and was lying from Iceland to the northern North Sea at 00 GMT 26 February 1959 . 
The smaller depression originally west of Ireland filled and its associated trough was orientated N-S over Eastern Norway . 
The numerical forecast dealt quite well with the main depression although the movement and deepening were not quite sufficient . 
The trough associated with the warm front and the preceding ridge were over-intensified and were not moved sufficiently north-eastwards . 
The weak trough over Norway was quite adequately forecast . 
Pressure was forecast to be about 8 mb too high in and to the west of the Bay of Biscay , the result of spurious anticyclogenesis . 
An inspection of the 1,000-500 mb thickness charts indicates that the numerical forecast distorted the thermal pattern in the region of the depression much more than actually occurred , and this was one of the worse thickness forecasts of the series . 
This is a typical error of this model since the geostrophic wind used for advection of the thickness lines is much greater than the actual wind in regions of cyclonic curvature , and the advection is overdone . 
Fig. 2 shows that the rapid movement of the 500 mb trough from east of Newfoundland to mid-Atlantic with the formation of a closed circulation was quite well forecast , although the trough was moved too rapidly in the south . 
Pressure was forecast to be too high between 10° and 20°W , a result of spurious anticyclogenesis . 
Fig. 3 indicates that the 200 mb forecast gave much too high pressure in mid-Atlantic . 
The movement of the western Atlantic trough was quite reasonably forecast in middle latitudes but was moved too rapidly in the south . 
This rapid movement in the south was almost certainly associated with the strong gradients produced by the spurious anticyclogenesis . 
The vertical motion charts are shown in Fig. 4 and are quite consistent with the forecast positions of the synoptic features . 
The pattern for the 600-200 mb layer is similar to that for the 1,000-600 mb layer , but the magnitudes of the vertical velocities measured in mb hr-1 are less in the 600-200 mb layer than in the bottom layer . 
If the vertical velocities had been computed in cm sec-1 the magnitudes in the two layers would have been more similar . 
The numerical forecast based on the 00 GMT data for 5 May 1959 was one of the better numerical forecasts . 
An anticyclone moved eastwards from mid-Atlantic to the British Isles , and two shallow depressions in the vicinity of Newfoundland amalgamated and moved into the entrance to the Denmark Straits . 
These features were quite well forecast ( see Fig. 5 ) , although the central pressure of the depression was not quite right . 
The eastward movement of the Atlantic thermal ridge was forecast to be a little less than actually occurred , and a cold trough forecast about 50°N 20°W did not materialize . 
Fig. 6 indicates that the movement and development of the troughs and ridges at 500 mb were forecast very well . 
The 200 mb forecast ( Fig. 7 ) was also successful , especially near Portugal and in the vicinity of the British Isles . 
However , the forecast position of the 200 mb trough near Greenland was not correct . 
The vertical motion patterns in Fig. 8 are consistent with the synoptic features forecast in Figs. 5 to 7. 7 . 
CONCLUSIONS 
The forecasts based on the three-parameter model are significantly better than those based on the Sawyer-Bushby two-parameter model for the 20 situations investigated . 
The extra degree of freedom allowed in the new model does not give rise to such vigorous over-development as in the two-parameter model , and although spurious anticyclogenesis still occurs it is not usually so intense as previously . 
Knighting and Hinds ( 1960 ) showed that the incorporation of a stream function into the two-parameter model gave a significant improvement in the results , and it is quite likely that the introduction of a stream function into the present model would produce a further improvement . 
The three-parameter forecasts of the 500 mb contours and the 1,000-500 mb thicknesses are statistically better than those produced by C.F.O. , but there is little to choose between the corresponding forecasts for the 1,000 mb contours and the 500-200 mb thicknesses . 
At 200 mb the C.F.O. forecasts are slightly better than the three-parameter model , probably because no allowance is made in the numerical forecasts for the presence of a portion of the stratosphere below 200 mb . 
The accuracy of the 200 mb numerical forecasts seemed worse on days of a low tropopause over a significant part of the area than on days when the tropopause was nearer 200 mb . 
ACKNOWLEDGMENTS 
The authors wish to thank the Director-General of the Meteorological Office for permission to publish this paper . 
A graphical method of objective forecasting derived by statistical techniques By M. H. FREEMAN Meteorological Office , Dunstable Manuscript received 18 January 1961 ) SUMMARY 
The objective forecasting technique described consists of a composite diagram from which the forecast value of the predictand can be read directly , given the values of the predictors . 
Each section of the diagram combines a new predictor with an estimate of the predictand obtained from the previous sections . 
The isopleths in the diagrams are obtained by fitting a curved surface ( involving powers and cross-product terms of up to the fifth order ) to the basic data by a " least squares " procedure . 
Only terms which are significant at the 5 per cent level are retained in the regression formulae so produced . 
At each stage the predictor to be selected is that which contributes most to the combination so far chosen . 
The method was used to forecast visibility ( as one of 32 code figures ) at London Airport three and six hours ahead . 
When it was tested on two winters ' independent data , correlation coefficients of 0.89 and 0.83 were obtained for the 3-hr and 6-hr forecasts , respectively . 
During the same period the figures for the normal subjective forecasts made at London Airport were 0.87 and 0.74. 1 . 
INTRODUCTION 
An objective method of forecasting may be described as one which calls for no judgment on the part of the forecaster . 
Given the same initial data any person using the method will produce the same forecast . 
Numerous objective techniques have been described by workers in the U.S.A. , but objective forecasting has received much less attention in Great Britain . 
Swinbank ( 1949 ) , Craddock and Pritchard ( 1951 ) , and Saunders ( 1952 ) all produced methods of forecasting fog which were partly objective , but some of the predictors used had to be forecast subjectively . 
Most objective techniques depend on the production of either formulae or diagrams , and both methods have been subject to various weaknesses which the system to be described attempts to overcome . 
Many of the earlier systems produced forecasts in terms of only a few categories , e.g. , fog , fog in patches , or no fog ; for aviation forecasting a forecast of visibility in yards or miles is required . 
Formulae may be deduced from physical principles , but more often they are devised by statistical processes to produce regression equations . 
These have almost always contained only linear terms whereas more complicated relations may be required . 
In the graphical methods the lines on the diagrams often had to be drawn subjectively and it was not easy to tell whether the best lines had been drawn or not . 
In many systems the choice of predictors to be used had to be made subjectively . 
Rigorous statistical methods were used in developing the present method , the computations being made on a Ferranti Mercury Computer at Meteorological Office , Dunstable . 
The problem chosen for investigation during the development of the objective forecasting technique was the important one of forecasting visibility at London Airport . 
The system which was devised consists of a composite diagram such as that illustrated at Fig. 1 . 
The pecked line on the diagram indicates its method of use . 
The top left-hand section is entered with the appropriate value of the first predictor and successive turns are made at the appropriate isopleths of each of the other predictors , the forecast being read from the scale on exit . 
2 . 
VISIBILITY PREDICTION DIAGRAMS FOR LONDON AIRPORT 
The particular problem specified was to forecast visibility at London Airport for 0900 and 1200 GMT using 0600 GMT data and for 1800 and 2100 GMT using 1500 GMT data ( i.e. , a 3-hr and a 6-hr forecast morning and evening ) . 
The winter period , November to January , was selected and forecasts were to be given to the nearest 100 yards up to 1,000 yd and at 200-yd intervals up to 2,000 yd . 
This requirement and the desirability of having an approximately logarithmic scale of visibility led to the use of the visibility code shown in Table 1 . 
The selection of the parameters to be tried as predictors was one of the most important parts of the investigation . 
Anything which physical principles suggested might be relevant was included , and the advice of experienced forecasters at London Airport was sought . 
Most of the parameters tested are listed in Table 2 . 
Many were extracted directly from the London Airport registers but some had to be specially computed . 
The geostrophic winds over London Airport were measured from surface charts at the Central Forecasting Office , Dunstable . 
The wind shear was defined as the ratio of the surface wind speed to the geostrophic wind speed . 
Computed pressure gradient was a complicated parameter obtained from pressures and pressure tendencies at four neighbouring stations . 
The lapse rates were obtained as the difference between the surface temperature at London and the temperature 50 mb ( or 25 mb ) above the surface at Crawley ( or Larkhill for the early years ) . 
The hydrolapses were similarly defined using dewpoints instead of temperatures . 
Data for the eleven winters November 1946 to January 1957 ( 1,012 days in all ) , were recorded on specially printed Paramount edge-punched cards and were used in the development of the objective forecasting technique . 
Data for the three following winters were used to obtain an independent check on the efficacy of the system . 
To assist in selecting the more promising predictors each parameter x was correlated in turn with the visibility to be forecast z . 
A polynomial of the form **f was fitted to the data by the method of " least squares , " successively higher order polynomials being tried until further terms gave no further reduction in the r.m.s. error ( SE ) . 
The correlation coefficient r was calculated from the formula **f where SD was the standard deviation of the visibility to be forecast . 
Generally the highest Jurassic rocks are only exposed near the eastern end of the Vale , as the Aptian and Albian transgress westwards on to older Jurassic strata . 
Thus at Dinton , basal Wealden is preserved beneath the local Aptian , but by Tisbury Gault rests on Portland Beds , on Kimmeridge Clay around Shaftesbury and East Knoyle and by Penselwood Hill , five miles west of Mere , Albian rests on Oxford Clay . 
( b ) Brief History of Previous Work 
The great variety of formations exposed within the Vale of Wardour has attracted geologists since early in the nineteenth century and there are many descriptions by many writers . 
Lady Bennett provided Sowerby ( 1818 ) with some of the earliest ammonites described from the Portland Beds of Chicksgrove ( south ) quarry , and also referred to the Tisbury Star Coral ( { Isastraea oblonga ) . 
The first comprehensive account was that of Fitton ( 1836 ) . 
He noted the sandy nature of the Chilmark building stones , found Purbeck dirt beds and discovered a cycad trunk near Tisbury . 
He observed the Hastings Sands ( Wealden ) above the Purbeck Beds near Dinton and separated a sandy bed below the Gault which was later assigned to the Lower Greensand . 
Fitton also realised that the Wardour fold was asymmetric , with steeper northern dips , and included a section diagram with his account . 
In 1856 there appeared the first one-inch Geological Survey maps of the area which had been surveyed by Bristow . 
In 1877 Blake & Hudleston gave the first comprehensive account of the Corallian outcrop in north Dorset and were able to link up the north Dorset succession with that of the type locality at Weymouth . 
They described the apparent northward thinning of the Upper Corallian . 
They also noted the increasing number of rolled corals in the upper beds in the same direction , and commented on the false-bedded Todber Freestones . 
Three years later this was followed by a study of the Portland Beds within the Vale of Wardour . 
In this paper they established , among other facts , that the Upper Freestone Building Stones fifteen feet thick in the Chilmark Ravine are reduced to a two-foot band , crammed with { Camptochlamys lamellosus at Chicksgrove and Oakley , within only one and a half miles . 
The nature of the junction with the overlying Purbeck has been much discussed since then , and is still not settled . 
In 1881 W. H. Hudleston led the first Geologists ' Association excursion to the Vale of Wardour and in the same year the Reverend W. R. Andrews ( 1881 ) , then resident at Teffont , published the first account of the presence of the Middle Purbeck marine Cinder Bed in the Vale of Wardour . 
In 1894 this was followed up by a comprehensive description of the whole Purbeck sequence ( Andrews & Jukes-Browne , 1894 ) , based on the Dorset ostracod divisions , but this was disregarded by Woodward ( 1895 ) when writing his Survey Memoir . 
By 1900 the Geological Survey completed the six-inch mapping for the New Series one-inch map , Sheet 298 , which includes that portion of the Vale of Wardour east of Tisbury . 
In the accompanying memoir ( Reid , 1903 ) he firmly established the presence of both Wealden and Lower Greensand between the Gault and Jurassic beds . 
He also records seeing the Tisbury Star Coral { Isastraea oblonga , already recorded by earlier writers , but in position of growth . 
This was observed in what must have been a temporary section , where a lane forks off the road from Tisbury to Fonthill , three-quarters of a mile north-west of Tisbury Square . 
On the other hand , Reid adhered to Woodward 's interpretation of the Purbeck succession and discounted the unconformable Wealden boundary suggested by Andrews & Jukes-Browne . 
The latter writer ( Jukes-Browne , 1903 ) added further material on the Purbeck-Wealden boundary and it appears that Reid 's mapping followed Woodward 's Purbeck divisions , and needs some revision to fit in with the palaeontological divisions now used . 
In the same year ( 1903 ) as the memoir appeared , there was a second Geologists ' Association excursion to the Vale of Wardour ( Blackmore &Andrews , 1903 ) , and by 1904 Jukes-Browne had completed his survey of the Cretaceous rocks ( 1900-4 ) , which includes descriptions of sections west of the area dealt with in the sheet memoir , some of which do not appear to have received any attention since . 
Jukes-Browne included a quarter-inch map , in his Cretaceous Rocks , Part 1 ( 1900 ) , showing the Mere Fault , but no detailed mapping had been done . 
In the fifty years since 1904 there have been only a few further references to this interesting area . 
In 1933 Dr. Arkell gave an admirable summary of the Jurassic rocks ; he followed up the earlier observations on the dissimilarities between the Chilmark-Tisbury building stones and the Dorset counterparts , and attempted to disentangle the confused ammonite nomenclature of the Portland Beds . 
He placed , tentatively , but almost certainly rightly , the main Tisbury and Lower Chilmark building stones in the upper part of the Portland Sands of the Dorset coast , only retaining the oolitic upper Chilmark building stones within the Dorset Portland Stone . 
This will entail the remapping of the Wardour Portlandian to fit into the new classification . 
( See also Arkell , 1935 , for correlation table . ) 
( House , 1958 . ) 
In 1938 F. H. Edmunds added a contribution to the physiographical evolution of this area which accompanied the fourth Geologists ' Association 's Field Meeting to the area . 
The next year , J. F. Kirkaldy ( 1939 ) refers to the thin Lower Greensand below the Gault that crops out round the Vale , and also south of Shaftesbury , but he was unable to determine the zonal position of either outcrop . 
Outside the Vale of Wardour proper , the Warminster Greensand beds at the base of the Chalk Marl have received attention from Jukes-Browne in 1896 , 1900-4 and 1901 , and from Scanes , jointly with Jukes-Browne , in 1901 , and with Pope-Bartlett in 1916 when , in the latter year , both authors led the third Geologists ' Association excursion . 
All the earlier Warminster Greensand accounts have been fully summarised by Edmunds ( 1938 ) for the fourth Field Meeting in the area of the Geologists ' Association in 1937 . 
It now seems clear that the fossils from the Warminster Greensand are Cenomanian in age and the majority did not come from Warminster itself but from Maiden Bradley and Mere . 
Nevertheless , the Warminster name has been adopted for these beds , whereas today the best available section is at Dead Maid Quarry , Mere . 
Also included in Edmunds ' account ( 1938 ) is the first contribution on the Mere Fault which was the present author 's starting point for detailed mapping . 
Edmunds estimated the Mere Fault to have a northerly downthrow of about 600 feet near Charnage Quarry . 
He shows the fault to be reversed , passing just to the south of Mere , and downthrowing Lower and Middle Chalk against Kimmeridge Clay . 
Wooldridge &Linton ( 1955 ) have given the whole area prominent attention in their comprehensive survey of the Structure , Surface and Drainage of South-East England . 
They regard the three east-west lines of downland ridges comprising ( a ) The Great Ridge-Mere White Sheet Hill ridge , and ( b ) The Barford Down-Berwick St. John White Sheet Hill ridge , and ( c ) the Melbury Beacon , Win Green-Coombe Bissett Down ridge as type examples of the remnants of the Mid-late Tertiary Peneplains . 
Also they regard the Wardour drainage as now adjusted to structure through two cycles of erosion and that the bulk of this area lay outside the furthest advances of the Pliocene Sea . 
At Whitsun in 1954 this writer led the fifth Geologists ' Association Field Meeting over the Vale of Wardour and the Mere Fault country from Shaftesbury . 
The Field Meeting report ( Mottram { 6et al. , 1957 ) included some of the more interesting localities visited from which the palaeontological records were obtained by various people , as well as brief references to the Mere Fault at West Knoyle , Charnage , Mere , Wolverton and Penselwood Hill , visited by the Association during the excursion . 
( c ) Tectonic Summary of the Wardour Anticline 
The tectonics of the Wardour fold have not been described in detail previously , but much is self-evident from the New Series one-inch map , Sheet 298 , which shows the Vale of Wardour as far west as Tisbury and Ridge . 
The Wardour Anticline has an amplitude of about 1200 feet so that around Tisbury the Cenomanian base must have risen to about 1000 feet above present O.D. The fold has steeper northerly dips than those on the southern limb , which are everywhere from 3-5° south ( see Fig. 3 , Section 1 ) . 
The northerly dips gradually steepen westwards and west of the Fonthills a 10-15° NNW. dip can be seen in planus Zone chalk on the roadside from Tisbury to Hindon . 
The accompanying map to this paper ( Fig. 3 ) shows how the northern limb continues to steepen westwards past East Knoyle to where the Mere Fault begins at West Knoyle . 
North-west of East Knoyle , around Windmill Hill , the Green and Upton , there is quite clearly a local roll displayed by the Upper Greensand outcrops . 
These double back eastwards from Windmill Hill to Milton before resuming their north-west trend along Haddon Hill . 
Also the Gault base rises above the 600-foot contour west of Upton , so in this small and interesting upland area north-west of Clouds House there is a periclinal fold , pitching east , riding on the main northern limb of the Wardour fold ( see Fig. 3 , Section 2 ) 
In general the Jurassic rocks are nearly conformable to the overlying Cretaceous , but these are local variations in addition to the steady westward Cretaceous overstep . 
The Jurassic rocks within the Vale of Wardour are affected by a series of gentle rolls , trending north-west to south-east , which disappear under the transgressive Lower Greensand and Gault without affecting them . 
The Portland Beds , exposed in the Chilmark Ravine , are brought up by a shallow anticline and this is flanked to the south-west by a shallow syncline which brings the Wealden down to river level again near Sutton Mandeville . 
The next undoubted flexure affects the Portland Beds south-east of Knoyle Corner , but is only partly preserved beneath the transgressive Gault above , and appears on the map ( Fig. 2 ) . 
Around Tisbury itself the numerous Portlandian quarries show a variety of dips . 
Some apparently can be ascribed to false bedding . 
This was seen in 1940 and 1941 in the temporary opening of a shallow quarry between road and railway 500 yards north-east of Hazeldon Farm ( 936381 ) . 
False bedding was also seen in 1949 in a new track section south of Court Street . 
However , in other pits , the dips appear to point towards the valleys . 
Some of these exposures show considerable gulling , like those that can be seen in Tisbury West Quarry on the Newtown Road , and still being worked . 
This gulling recalls the cambered structures described in the Midland Ironstone field and in the Oxford region by Hollingworth , Taylor & Kellaway ( 1944 ) and Arkell ( 1947a ) respectively . 
It appears from notes on Reid 's 1900 six-inch maps in the Geological Survey Library , that much , presumably Lower , Greensand debris still remains on the Purbeck outcrop around Lady Down and on the Portland outcrop north-west of Tisbury . 
This writer was able to map two definite outliers of Lower Greensand on Lady Down and around Vicarage Barn , as shown on Fig. 1 . 
The Lower Greensand , forming these two outliers , is thin , as the silage pit , four feet deep , reached the base of ferruginous sands , which also contained occasional small quartz pebbles . 
Lumps of a very dark and hard ferruginous sandstone , recalling a tropical laterite , can also be found with ironstained Purbeck slabs in the surrounding arable fields . 
This thin veneer-like Lower Greensand outcrop north-east of Tisbury suggests that the present Wardour Jurassic surface round Tisbury may be , in part , an exhumed pre-Lower Greensand erosion surface . 
This is supported by finding further quartz pebbles and chert debris in arable fields on the Portland outcrop north-east of the cross-roads ( at 924293 ) on the Tisbury to Newtown road . 
This is south of where Reid mapped the Lower Greensand being overstepped westwards by Gault near the " Beckford Arms " . 
It is possible therefore that the existing post-Jurassic material on the Portland Beds is the ultimate remains of the combined residue of Lower Greensand and basal Gault hereabouts . 
Across the Nadder Valley over the ground north-east of Wardour Castle the Portland dip slope disappears under rounded swells of Lower Greensand and Gault above , before the land rises up towards the Upper Greensand escarpment behind . 
These results are perhaps rather unexpected in view of the obvious difference in shape between these two structures . 
Measurements showed that the surfacevolume ratio of the connectives was about 3.5 times greater than that of the relatively massive terminal abdominal ganglion . 
The point of contrast between the effluxes from the terminal ganglion and from the whole nerve cord used in the previous investigation was the apparent absence , in the case of the isolated ganglion , of a final slow phase of sodium loss in a region of low radioactivity . 
In the previous study ( Treherne , 1961b ) this phase was tentatively identified with the breakdown of the normal sodium extrusion mechanism in the isolated nerve cord when separated from its tracheal supply . 
Thus according to this hypothesis it could be postulated that in the present experiments the isolation of the ganglion resulted in a less serious interference with the normal metabolism so that the breakdown of sodium extrusion did not occur until later at a very low level of activity beyond the limits of this technique . 
The present results have shown that , as in the whole abdominal nerve cord ( Treherne , 1961b ) , the rate of loss of sodium was apparently an active process which was slowed down by the presence of 2:4-dinitrophenol at relatively low concentration . 
Similarly the extrusion of sodium in the terminal ganglion was reduced in the potassium-free solution , demonstrating a linkage of potassium influx with sodium efflux . 
The rate of efflux of sodium ions from the terminal abdominal ganglion was not significantly affected by the removal of about 50% of the connective tissue and cellular sheath . 
On the basis of these results it must be concluded , therefore , that the rate-limiting process in the efflux of sodium measured by this technique was not the transfer of ions across the cellular perineurium . 
In addition it follows from this that the diffusion of sodium ions through the connective tissue sheath must also have occurred relatively rapidly , a result which had been previously predicted ( Treherne , 1961a ; Wigglesworth , 1960 ) . 
The rate-limiting process measured in these experiments must , therefore , be associated with some components of the central nervous system lying at a deeper level than the perineurium . 
Perhaps the most obvious possibility is that the efflux of 24Na measured in these experiments was , in fact , the result of the transfer of sodium ions across the cell membranes of the underlying tissues . 
In this case the similarity of the t0.5 between the connectives and the terminal ganglion becomes explicable , for under these circumstances the efflux might be expected to be independent of the surfacevolume ratio of the whole organ . 
The results described above do not , of course , give any definite information about the nature of the processes involved in the passage of ions across the perineurium . 
However , the fact that the presence of dinitrophenol and potassium-free solution appeared to have slightly less effect on sodium efflux in the desheathed preparations might suggest that this layer of cells perhaps plays more than a passive role in the ionic regulation of the central nervous system of this insect . 
The addition of poison to , or the omission of potassium ions from , the external solution has been shown to produce a fairly rapid slowing down of sodium extrusion from the abdominal nerve cord . 
The fact that the rate-limiting process is not , apparently , the penetration of the superficial perilemma implies that these changes in the chemical composition of the bathing solution are quickly transmitted to the deeper layers of the central nervous system . 
This conclusion is perhaps rather unexpected in view of the appreciable delay in the breakdown of normal electrical activity obtained when the insect nervous system was exposed to solutions of high potassium concentration ( Hoyle , 1953 ; Twarog & Roeder , 1956 ) . 
In some previously published accounts on the entry of 42K and 24Na into the intact abdominal nerve cord of Periplaneta ( Treherne , 1961a , c ) an attempt was made to calculate the fluxes of these ions between the haemolymph and the central nervous system . 
These ionic movements were calculated with the conventional equations used to describe fluxes in cells and tissues . 
This procedure involved the assumption that the rate-limiting process was the transfer across the superficial boundary and that the movements within the underlying layers occurred rapidly so that the labelled ions were effectively well mixed . 
The present results have shown that these assumptions represented an oversimplification and consequently the calculated values have little significance . 
It is hoped that in a future investigation the fluxes taking place between the central nervous system and the haemolymph can be calculated for this more complex system . 
SUMMARY 
1 . 
The rate of loss of 24Na from the terminal abdominal ganglion of { Periplaneta americana L. has been studied by measuring the decline in radioactivity associated with an isolated preparation maintained in flowing physiological solution . 
2 . 
The rate of sodium efflux was substantially reduced in the presence of 0.2 mM.l. dinitrophenol and in potassium-free solution . 
3 . 
The extrusion of 24Na was not significantly affected by the removal of the fibrous and cellular sheath surrounding the ganglion . 
The rate-limiting process in the efflux of sodium measured in the experiments was not , therefore , the transfer of ions across the nerve sheath , but an extrusion from tissues lying at a deeper level in the central nervous system . 
THE KINETICS OF SODIUM TRANSFER IN THE CENTRAL NERVOUS SYSTEM OF THE COCKROACH , { PERIPLANETA AMERICANA L. BY J. E. TREHERNE A.R.C . 
Unit of Insect Physiology , Department of Zoology , University of Cambridge ( Received 15 June 1961 ) INTRODUCTION 
Some previous investigations have shown that the exchanges of sodium and potassium ions between the haemolymph and the cockroach central nervous system occurred relatively rapidly ( Treherne , 1961a ) and appeared to be effected by a mechanism involving an active extrusion of sodium ions ( Treherne , 1961b ) . 
More recently it has also been shown that the measured efflux of sodium ions was not significantly affected by the removal of substantial portions of the cellular and fibrous nerve sheath ( Treherne , 1961c ) . 
It was concluded from this that the rate-limiting factor measured in these experiments was not the transfer of ions across the perilemma but the extrusion of sodium from the underlying tissues of the central nervous system . 
Thus any rate-limiting movements of ions across the perilemma occurred too rapidly to be measured by the techniques used in the previous investigations . 
In the present experiments , therefore , an attempt has been made to measure the rapid component of 24Na exchange by determining the rate of loss of radioactivity obtained on washing isolated nerve cords and single connectives and ganglia for relatively short periods in successive volumes of physiological solution . 
METHODS 
The experiments described in this paper were carried out using the abdominal nerve cords of adult male { Periplaneta americana L. In these experiments the nerve cords were made radioactive by soaking them for varying periods in a solution containing 24Na ( 0.1-0.5 mc.ml . ) . 
With short loading periods ( 20 sec. - 5.0 min. ) the isolated ligatured nerve cords were soaked in the oxygenated physiological solution ; for longer loading periods ( 5-20 min. ) the nerve cords of decapitated individuals were perfused with the radioactive solution as described in a previous paper ( Treherne , 1961c ) . 
The ligatures were tied with threads pulled from 15 denier nylon stockings . 
The composition of the radioactive solution used was that given by Treherne ( 1961a ) . 
On removal from the radioactive solution the ligatured nerve cords were carefully blotted and then washed for varying periods in successive 0.2 ml. amounts of inactive solution of the same composition . 
The amount of 24Na remaining in the nerve cord at varying times was determined from the measured radioactivity of the washings . 
The radioactivity measurements were made with a Mullard MX 123 G.M. tube linked to a 100 c . 
Panax scaler . 
Some preliminary measurements were made to estimate the extent of any " inulin space " in the central nervous system . 
This was done by soaking ligatured isolated nerve cords for 1 hr. in a 3.0% solution of 14C-labelled inulin ( 3.0 mc.g. ) made up in physiological solution . 
The nerve cords were then washed for 25 sec. and the 14C-inulin was extracted by soaking them for 24 hr. in the physiological solution . 
The washing time of 25 sec. used was found to be the minimum period necessary to remove 97% of the radioactivity from the surface of a nerve cord exposed to 14C-inulin for 1 sec . 
These values are thus likely to be minimum estimates of the " inulin space " of this organ for some radioactivity must have leaked from within the nerve cord during the washing procedure . 
In a limited number of cases the rate of loss of 14C-labelled inulin was determined by washing the ligatured isolated nerve cords in successive volumes of the physiological solution as for the 24Na efflux experiments . 
RESULTS 
The results illustrated in Fig. 1 show the decline in radioactivity of some isolated abdominal nerve cords , previously soaked in the solution containing 24Na , when maintained in an inactive solution of the same composition . 
In all cases semi-logarithmic plots of the results for varying loading times appeared to follow a complex course initially , eventually assuming an exponential form after a period of between 160-200 sec . 
It was found possible to separate a fast component from the curves for the loss of 24Na from the nerve cords by subtraction from the initial values lying above the line extrapolated to zero time . 
The separation of an efflux curve into fast and slow components with data plotted semi-logarithmically with respect to time is shown in Fig. 2 . 
The fast component illustrated in Fig. 2 was complex initially , but assumed after a few seconds a simple exponential form with a half-time ( t0.5 ) of approximately 33.0 sec . 
The half-time for the slow component was , in this case , 260 sec . 
The escape of 24Na from the isolated abdominal nerve cords was also measured in the presence of 0.5 mM.l. 2:4-dinitrophenol . 
The poison was added to the physiological solution during the initial loading period with the 24Na and was present at the same concentration in the inactive solution during the subsequent efflux experiments . 
Previous results ( Treherne , 1961 b ) have shown that there was a slight delay period of a few minutes before the poison affected the rate of extrusion of sodium from the nerve cords . 
In the present experiments , therefore , the nerve cords which were loaded with 24Na for only short periods ( less than 5 min. ) were pretreated with 0.5 mM.l. dinitrophenol to maintain a constant exposure to the poison of 5 min. before the efflux experiments were commenced . 
Fig. 3 shows the escape of 24Na from a poisoned preparation loaded with 24Na for 10 min . 
In this experiment the fast component was not abolished by the presence of the poison , in fact t0.5 in this case was 33.0 sec. , which was the same as that for the normal preparation illustrated in Fig. 2 . 
In this particular experiment the slow component for 24Na efflux was , however , much reduced as compared with the normal preparation . 
The effects of 0.5 mM. / l. 2:4-dinitrophenol on the escape of 24Na from the isolated nerve cords are summarized in Table 1 . 
The results clearly indicate that the presence of the poison affected the slow phase of sodium loss but not the initial fast component . 
The total activity of the 24Na in the slowly exchanging fraction was estimated by extrapolation of the slow component to zero time . 
Fig. 4 illustrates the estimated radioactivity of the slowly escaping fraction at varying times after exposure to the solution containing 24Na . 
These data would appear to show that the poison had little effect on the rate of accumulation of the radioactive ions in the slowly exchanging fraction . 
The results are , however , too few to judge the equilibrium level of radioactivity as between the normal and poisoned preparations . 
The escape of 24Na from isolated ligatured fragments of the central nervous system was studied in some experiments . 
The loss of radio-sodium from the terminal abdominal ganglion and from the connective between the fourth and fifth abdominal ganglia was found to occur as a two-stage process as for the whole abdominal nerve cord . 
A control serum known to contain a weak anti-D antibody is included in each batch of tests ; only if this gives a macroscopic positive with the D positive and a clear negative with the D negative cells should the rest of the test be read . 
Comment . 
This is a very sensitive and useful technique which is unlikely to fail to detect any Rh antibodies . 
It is recommended that it should always be used as a routine antibody detection method . 
Occasionally sera are encountered which give pan-agglutination with trypsinised red cells . 
The antibody responsible for the pan-agglutination can usually be quite easily removed by incubating the serum with an equal volume of the patient 's own trypsinised red cells . 
The absorbed serum can then be re-examined for the presence of specific antibodies with the standard trypsinised cells . 
No. 16 . 
Lo " w's papain technique for antibody detection 
Equal volumes of the serum to be tested , papain and a 2 per cent suspension of red cells are placed in a precipitin tube , taking care to adhere strictly to the order : ( a ) serum , ( b ) papain , ( c ) red cells . 
It is also important that the serumpapain mixture should not be allowed to stand on the bench for more than about 5 minutes before the red cells are added . 
It has been noted that the best results are obtained if the red cells are allowed to sink through the fluid during the incubation period . 
Therefore the contents of the tubes should not be mixed up at the initial stage . 
The test is read after precisely one hour 's incubation , controls of known D positive and D negative cells with a weak incomplete anti-D being included with each batch of tests . 
Comment . 
This is a good and efficient technique and is excellent for the detection of Rh antibodies . 
In fact anti-D antibodies may be detectable when they are not apparent by any other technique , even the Indirect Coombs . 
It does , however , give positives when certain other antibodies are present so that care must be taken in the establishment of the specificity of any antibody detected by this method . 
Titration of Rh Antibodies 
Technique No. 17 . 
Saline . 
Serial dilutions of the serum are made in saline as in technique No. 6 ( or if desired techniques Nos. 7 or 8 ) and incubated at 37°C for 2 hours with standard D-positive red cells ( 2 per cent suspension ) in saline . 
The tests are read taking the usual precautions against breaking down the agglutinates . 
The results are recorded as for ABO titres . 
( See Plates 6 and 7 . ) 
Technique No. 18 . 
Albumin . 
The serial dilutions of the serum are made in AB serum and the standard cells are suspended in 30 per cent bovine albumin . 
In all other respects the method is identical with technique No. 17 . 
Technique No. 19 . 
Albumin Addition . 
Serial dilutions are made in AB serum . 
After 1 1/2 hours ' incubation an equal volume of bovine albumin is added without disturbing the cells . 
After a further 30 minutes ' incubation the tests are read in the usual manner . 
Technique No. 20 . 
Indirect Coombs Technique . 
Serial dilutions of the serum are made in saline using double unit volumes ( 0.06 ml. ) in the cell-suspension tubes . 
Four volumes of a 5 per cent suspension packed washed D-positive red cells are added to each tube . 
From this point the procedure is exactly as in technique No. 14(a) . 
Technique No. 21 . 
Trypsin . 
The serial dilutions of serum are made in AB serum and warmed to 37°C before the addition to each tube of an equal volume of trypsinised D-positive red cells . 
The tests are incubated for 1 hour and read by tapping the tubes and examining the contents macroscopically and if necessary microscopically for agglutination . 
Technique No. 22 . 
Papain . 
The serial dilutions are made as for technique No. 18 , after which one volume of Lo " w's papain is added to each tube . 
This is followed immediately by an equal volume of a 2 per cent suspension in saline of D positive red cells . 
The tubes are incubated for exactly one hour and then read , first tapping the tube twice gently before examining the contents macroscopically and if negative , microscopically . 
Interpretation of Results 
Sera are usually tested by at least two techniques . 
In the testing of Rh negative women antenatally , for instance , it is recommended that the saline ( technique 12 ) albumin ( technique 13 ) and trypsin ( technique 15 ) or papain ( technique 16 ) techniques are used in parallel . 
Any reaction obtained , however weak , indicates that further tests are necessary to confirm the presence of an antibody and to establish its identity . 
If the serum of a D negative individual agglutinates the D positive but not the D negative control cells , there is a high probability that the serum contains anti-D , but the specificity should be confirmed by testing against several more examples of D-positive and D-negative red cells . 
If a pattern of reaction is obtained other than that expected for anti-D , the serum requires a more detailed investigation ( Table 14 ) ; this is usually undertaken by a specialist serological laboratory . 
Moreover it must be realised that a serum behaving like anti-D in the above tests may in fact be a mixture of Rh antibodies . 
Rather less than half the Rh antibodies found in Rh negative persons are mixtures of anti-D and anti-C , a much smaller number are anti-D plus anti-E and a very few are mixtures of all three antibodies . 
A knowledge of whether or not a particular anti-D is mixed with anti-C or anti-E is usually unimportant clinically , but if the serum is required for Rh typing purposes its exact content must be known . 
It is dangerous to use for typing purposes a serum containing anti-C or anti-E in addition to the anti-D , for by this means certain individuals who are in fact D negative may be falsely classed as D positive . 
cells which contain C without D will show the presence of anti-C in an anti-C plus anti-D mixture while which contain E without D cells will detect anti-E in an anti-E plus anti-D mixture . 
Therefore , while the testing of a suspected anti-D against about 3 D positive and 2 D negative red cell samples followed by titration is adequate for normal purposes , a far more detailed investigation of the serum must be made ( probably by a specialist laboratory ) if it is required for Rh typing . 
It is , of course , possible as in example 4 ( Table 14 ) that the antibody belongs to one of the other blood group systems such as Kell , Duffy , Kidd , Lutheran , etc . 
For a description of these another textbook , such as An Introduction to Blood Group Serology , must be consulted . 
Antibodies related to these systems can only be identified by a laboratory possessing a panel of red cells extensively " genotyped " to cover them . 
CHAPTER 8 THE CHOICE OF BLOOD FOR TRANSFUSION AND DIRECT MATCHING METHODS 
BLOOD transfusion has developed so rapidly in the last twenty years that it comes as something of a shock to realise that its history goes back into the remote past . 
In ancient thinking the words " blood " and "life " were almost interchangeable and many endeavours were made to transfer the healthy life blood of a young man to the aged and infirm . 
In most cases this was done by the recipient drinking the blood ; the results were of course , rather disappointing ! 
As early as the sixteenth century it was realised that the transference should be from blood vessel to blood vessel , but it is not known whether such an exchange was in fact performed . 
Harvey 's discovery of the circulation of the blood in the early seventeenth century gave a new impetus to the interest in transfusion and Lower actually kept alive dogs , which had been exsanguinated , with blood from other dogs , transferred by connecting the carotid artery of the one to the jugular vein of the other by means of quills . 
The success of this venture led to attempts to transfuse Man . 
Animals ( sheep and lambs ) were used as donors , but the experiments were discontinued when the fourth recipient died . 
It is interesting to note that this patient had three transfusions in all , the first symptomless , the second showing typical symptoms of a haemolytic transfusion reaction and the third resulting in the patient 's death . 
During the latter half of the nineteenth century experiments started again , sometimes using animal blood , sometimes human , but the results were so often serious or even fatal that transfusion was abandoned . 
Then in 1901 Landsteiner discovered the ABO blood group system and realised immediately the importance of his discovery . 
It was not until some fifteen years later , however , that it was universally accepted that blood grouping and direct compatibility tests were a necessary prelude to transfusion . 
It was then realised that if the recipient had agglutinins active at 37°C in his serum and the transfused blood had the corresponding agglutinogen , the blood would be destroyed { 6in vivo and a haemolytic transfusion reaction would result . 
The possibility of the destruction of the recipient 's red cells by transfused antibody was not considered to be a real danger because of the dilution factor . 
For this reason , up to about 1940 , group O blood was considered safe for transfusion to all groups and was called Universal Donor Blood . 
Nowadays it is realised that transfusion with homologous blood , i.e. blood of the same type as the recipient , is to be preferred , not only because the transfusion of antibodies may be dangerous , but also because the number of potential donors is doubled ; an important point when the demand for blood is steadily increasing . 
The titre of anti-A and anti-B antibodies in most donor blood is not dangerous so that in emergency , one pint of group O can be given with little risk , but in massive transfusions of group O blood to patients of other groups the quantity of antibody transfused becomes considerable and may even result in the destruction of almost all the recipient 's own red cells . 
In particular , it has been shown that exchange transfusion of infants suffering from haemolytic disease should be performed with blood of the infant 's own ABO group . 
The discovery of the ABO blood groups was , however , merely the beginning . 
Today many blood group systems are known , by means of which some hundreds of types of blood can be differentiated . 
Should they all be taken into consideration in choosing blood for transfusion ? 
It is obvious that they can not be and except in special cases only two systems are in fact considered , ABO and Rh . 
When blood is transfused there are many dangers present , of which two are directly concerned with the antigen content of the transfused blood , the first being that of sensitisation , the second that of incompatibility . 
In the first case the recipient does not possess the antigen found in the transfused blood nor the corresponding antibody , but the transfusion acts as a sensitising dose so that antibodies are produced in response to the transfusion or to a subsequent stimulus by the same antigen . 
Blood for transfusion can not be chosen so as to exclude every possibility of sensitisation but fortunately most of the blood group systems are not strongly antigenic in Man and can usually be disregarded . 
The main exception is the Rh system , and here the problems of sensitisation must be faced . 
In the ABO system ( where antibodies occur naturally ) and in other systems whenever atypical antibodies active at 37°C have been formed the problem is not that of sensitisation but of incompatibility . 
A consideration of the two systems , ABO and Rh , gives an idea of the factors involved and how best to arrive at the objective , the safe transfusion of blood . 
The ABO blood group system is still the most dangerous . 
This is because the antibodies are naturally occurring and over 95 per cent of all recipients will have anti-A and/or anti-B in their serum . 
On the other hand ABO blood grouping is a straightforward procedure and the simplest of direct matching techniques will detect any incompatibility . 
Most of the mistakes which occur are clerical rather than technical . 
3 RESULTS Classification of the Population 
EVERY person living in the village who was over the age of five years had been asked to supply a specimen of urine , and to answer a questionnaire ( Table 2 ) . 
The very young children were not tested because apart from any practical difficulties , the florid manifestations of diabetes at this age seem to make it unnecessary , though in any subsequent survey we should like to include this age group . 
2,071 males and 2,034 females were tested which makes an 81% response of the population over the age of five years . 
Details of thirty-three previously diagnosed cases of diabetes were collected from the general practitioners ' and clinic records , one of these was a boy under the age of five so that the total examined is therefore 4,105+1 . 
As far as can be determined the 19% of non-cooperators were not different in age or other environmental factor from the rest , and in calculating rates , it has been assumed that they are a random sample of the whole population . 
However , in testing the significance of possible aetiological factors , further consideration has been given to this and any affect of selection has been excluded as rigorously as possible . 
The normal portion of the population , in whom no glycosuria was found at the time of examination has been used as a control group . 
Only those discovered to have glycosuria were asked to undergo a glucose tolerance test as the known diabetics had been previously verified and were already under treatment . 
It is found that the blood sugar curves we obtained show a gradual rise in continuous sequence from the normal to the diabetic , and three arbitrary divisions have been made , and , because a true glucose method of blood sugar estimation was used , the levels considered important are 160 mgm% at 1 hour , 140 mgm% at 1 1/2 hours , and 120 mgm% at 2 hours ( Conn 1958 ) . 
These levels were taken to divide the intermediate and lower blood sugar curves , and it is of interest that this level separates the cases of transient or intermittent from those of constant glycosuria . 
As there is no universal agreement about the actual lower levels of blood sugar in diabetes the appearance of the whole curve was noted , and particular attention was paid where it had not returned to the fasting level at two hours . 
Thus our grouping of the examined population is classified as follows : — 
A. The unaffected population or control group of 3,916 persons . 
B. Known diabetics , 33 . 
C. Glycosurics , 167 . 
The glycosurics in turn are subdivided according to their blood sugar curves ( Diagrams 1 and 2 ) . 
a . 
Latent diabetics , with high type of curve , 25 . 
b . 
Intermediate . 
In 42 cases the blood sugar levels rose to , or only just above 160 mgm% at 1 hour , 140 mgm% at 1 1/2 hours , 120 mgm% at 2 hours . 
c . 
Transient or intermittent glycosurics with low or normal blood sugar levels , 75 . 
d . 
A group of 25 glycosurics on whom no test was performed . 
It is estimated that the total percentage of known diabetics in Ibstock is between 1.3% and 1.4% . 
If we can take Ibstock to be a random sample of the general population of Britain , the 95% confidence limits for the average incidence in Britain are 1.0% and 1.6% , but , in fact , it is possible that it is not exactly comparable and the limits should be wider . 
It is interesting to note that this range includes the results found in other similarly conducted surveys of whole population groups ( Table 4 ) . 
Discussion of the Abnormal Groups The Known Diabetics ( Diagram 4a ) 
The thirty-three previously diagnosed diabetics form a somewhat artificial group owing to the duration of their disease and its treatment , and because they knew they were diabetic when they answered the questions . 
Wherever this could bias a result in testing the significance of any factor , this group has been excluded . 
On the other hand , the others did not know the result of the tests at the time of answering the questionnaire , and this makes these results of particular statistical interest . 
In considering the known cases diagnosed and under treatment at the time of the survey , twenty-nine were already on the general practitioners ' lists , but during the year , they found three more men and the boy under five years old , all of whom had indisputable symptoms and signs , thus a total of nine males and twenty-four females are put to their credit . 
These cases have all been examined at the diabetic clinic of the Leicester Royal Infirmary although they were not all traced until the end of the survey . 
We think it is most improbable that any previously diagnosed diabetic is now unrecorded so that the percentage figure for known cases , when estimated on the whole population of 5,406 , = 0.61% . 
In diagram 3 an attempt has been made to indicate the extent of the assumed diabetic problem in this small community before any search had been made for the latent cases . 
It shows the distribution of the known diabetics according to their age and year of diagnosis . 
Superimposed are the diabetics known to have died in Ibstock since 1940 , which has been taken as a base line because it was the year in which the living case of longest duration was diagnosed . 
It will be noticed that there are now no diabetics living in Ibstock who were diagnosed after the first two cases for another four years . 
Some may have left the village ; there are three deaths recorded during this time , but the possibility is that , as these were war years and food rationing was in force , the elderly , mild and obese diabetics might have been sufficiently controlled by increased activity and less food to have remained latent and symptom free , and even free of glycosuria . 
Since 1951 the average number of new diabetics diagnosed has been four { 6per annum and these have all presented with symptoms . 
The Latent Diabetics ( Diagram 4b ) 
Out of the newly discovered glycosurics , 25 persons — 11 men and 14 women — show the frankly diabetic type of glucose tolerance curve ( Diagrams 1 and 2 ) . 
Estimated on the examined population of 4,105 , this gives the percentage for latent diabetes in Ibstock as 0.67% . 
No history of thirst , polyuria nor loss in weight was given and these people were unsuspected by themselves or their doctors . 
No physical examination of the complete group has been achieved owing to the reluctance on the part of the individuals to attend the diabetic clinic for the purpose , but the general practitioners have marked their record cards with coloured indicators so as to keep them under their particular scrutiny . 
They have also allowed the health visitor for diabetics in the County of Leicestershire to call and give any necessary dietetic instruction and to institute a regular follow up service of urine testing and weighing . 
This group of latent diabetics were all over forty years of age , most were considerably over weight ; none have yet required regular insulin treatment . 
Intermediate Group of possible Pre-diabetics ( Diagram 4c ) 
Abnormal glucose tolerance curves were obtained in forty-two of the glycosurics examined , and although not reaching the characteristic levels used for diagnosing diabetes , they correspond to the criteria put forward by Conn ( 1958 ) . 
The lower limits of the group were defined by the blood sugar levels of 160 , 140 , 120 mgm% at 1 , 1 1/2 , and 2 hours respectively , and with the exception of three cases this level separated the constant from the transient glycosurics . 
The upper levels naturally merge into the lower diabetic curves . 
It will be shown later in the analysis of certain factors that this seems to be an important group of probable pre-diabetics . 
The younger people show this change as well as the older and there was a considerable excess of young men , 30m : 12f . 
Although it was a practical impossibility to perform cortisone glucose tolerance tests ( Conn 1958 ) , ( Fajans and Conn 1959 ) , in this group of people at the time of the survey , it is an investigation which might be of great value , as it would also be to perform serial glucose tolerance tests at for example , one or two year intervals . 
The general practitioners have again tagged the medical record cards of these people with a different coloured indicator so that at any attendance at the surgery the possibility of diabetes is remembered and any significant data noted . 
It should be of interest to see if this amount of clinical supervision will alter the natural effect of time and have a preventive action . 
Transient or Intermittent Glycosuria ( Diagram 5a ) 
In the group of glycosurics with normal glucose tolerance tests , the age range was 5 to 81 ( Table 3 ) . 
There were 48 males and 27 females . 
There were only three cases of constant glycosuria which satisfy the stricter definition of renal glycosuria , i.e. , the constant passage of glucose in the urine at normal or sub-normal blood sugar levels . 
Transient glycosuria with normoglycaemia may indicate transient lowering of renal threshold as is commonly found in pregnancy , and it may be that as with pregnancy there is an increased liability to the development of diabetes . 
It seems wise to keep an open mind and to follow up these cases with urine and possibly blood sugar estimations at a later date to measure the true significance of this finding . 
It should also be recalled that the faintest change in colour of the Clinistix was taken as positive . 
Glycosurics on whom no Glucose Tolerance Tests were performed ( Diagram 5b ) 
Twenty-five glycosurics , for one reason or another , were not subjected to blood sugar examination . 
It is probable that three were diabetic ; one of whom , a woman , died of coronary artery occlusion before the test could be arranged . 
Case 205 f . 
Her husband was found to be diabetic in the survey and a clinical impression suggested that this was a case of conjugal diabetes . 
Case 1082 f . 
Short and stout , utterly refused further tests . 
Case 1568 f . 
Minimal glycosuria , pregnant and left Ibstock . 
Case 2081 f . 
Recently discharged from mental hospital . 
Case 3112 f . 
Glycosuria found during an attack of influenza . 
On re-testing she was sugar free . 
Case 3352 f . 
On re-testing no glycosuria was found . 
Case 3458 f . 
Urine only faintly positive . 
Her doctor reported that she was " a hermit type " and unlikely to co-operate . 
Case 3429 f . 
Aged 82 and too old and feeble to be troubled . 
Case 118 m . 
Paranoid schizophrenic , difficult and dangerous . 
Case 133 m . 
Aged 81 . 
Too old and frail . 
A second specimen of urine was negative . 
Case 1088 m . 
Refused to lose time from work . 
Case 1286 m . 
Improvident and careless ; wife is a severe diabetic . 
Case 1666 m . 
Mother diabetic , but he did not wish to be off work for the morning . 
Case 1672 m . 
He and three sons gave a history of investigation for " renal glycosuria " 25 years ago . 
It is probable that the remaining men were not prepared to give up time from work to come for the test . 
Changes since the Survey 
Since the field work finished , two diabetics have returned to live again in Ibstock where they were originally diagnosed , both in 1951 . 
A boy who was 2 1/2 years old at onset had been staying at a residential home for diabetic children in the south of England as his home environment was not good . 
The other is a woman who was diagnosed at the age of 51 . 
Her mother was diabetic and she is short and stout and does not require insulin . 
Three new diabetics were diagnosed by their doctors in 1959 , two of whom had been tested in the survey . 
A man of 25 developed diabetes in the acute form and requires insulin . 
A woman of 54 who was negative in the survey but now requires to be dieted strictly . 
The third , an obese woman , had previously refused to be tested or she might well have come under treatment sooner . 
These changes have been mentioned to show the continuity of the pattern of the condition we are examining but have not , of course , been taken into account in the statistical sections as they would introduce bias . 
SECTION 2 X RAYS : HALF-VALUE THICKNESS RANGE 1.0-4.0mm of Cu ( 200-400 kV ) CLOSED-ENDED APPLICATORS Compiled by R. G. Wood , M.Sc. , F.Inst.P. , A.M.I.E.E. , and W. H. Sutherland , B.Sc . 
The Royal Infirmary , Cardiff and M. Cohen , Ph.D. , A.R.C.S. , A.Inst.P. , The London Hospital , London , E.1 
The tables published in the corresponding section in Supplement No. 5 were compiled by Clarkson from measurements made by a number of hospital physicists in Great Britain . 
In common with other tables derived from a number of sources , they suffered from the disadvantage that several of the conditions ( e.g. thickness of applicator end-plate ) to which the data referred were not closely defined . 
Furthermore , if smoothing of survey data is based on values calculated by an empirical formula to fit the figures available , some inconsistency will inevitably remain since no formulae have been found which ensure smoothness in each of the three ways in which depth-dose data can be plotted ( see below ) . 
It was therefore decided to replace the survey data with tables derived from a single centre , thus bringing this section into line with the two other sections of this Supplement concerned with low and medium energy radiation . 
The new tables have , however , been compared with data made available from a number of other centres , and with the tables for diaphragm-limited fields in Section 3 . 
SOURCE OF DATA 
The present tables are based on water-phantom measurements made in Cardiff by Wood and Sutherland using an ionization chamber of external diameter 3 mm so arranged that its centre could approach to 1.5 mm from the applicator end-plate with no intervening tank wall . 
As an independent check an experimental comparison of this technique with that of The London Hospital ( Oliver and Kemp , 1949 ) was carried out in 1955 in conjunction with Cohen . 
Measurements were made on the same X-ray set using alternately a Kemp ionization current comparator with a chamber of external diameter 6 mm ( Kemp , 1945 ; Kemp and Banfield , 1957 ) , and the apparatus of Wood and Sutherland . 
This comparison showed that when allowance was made for small differences near the surface , no significant disagreement existed between the results obtained by the two techniques . 
The final measurements of percentage depth dose from which the tables were derived were made on a Westinghouse Quadrocondex machine under the following conditions : The measurements were made with a series of square " Fulfield " applicators of 50 cm F.S.D. , the ends being closed with flat Perspex of thickness 1/8 inch ( approximately 3 mm ) . 
Strictly , the data refer only to these applicators , but for clinical purposes the tables may be used for any applicator of similar design provided the thickness of the end-plate is the same and it is made of similar material . 
The effect on the data of using applicators of different design or end-plate thickness will be considered further in a separate publication . 
No measurements were made for zero area , but this information is provided in Section 3 . 
SMOOTHING AND EXTRAPOLATION OF DATA 
Smoothing of the experimental data , for square fields , was carried out graphically by plotting ( 1 ) individual depth-dose curves on loglinear paper , ( 2 ) percentage depth dose versus square root of area on linear paper for individual depths , and ( 3 ) percentage depth dose versus half-value thickness on linear paper for individual depths . 
Values for depths from 16 to 20 cm were obtained by extrapolation . 
This is justified since the logarithmic plots of depth dose are straight lines from 10 cm downwards . 
The whole table for 2.5 mm of Cu H.V.T. was obtained by interpolation , while that for 4.0 mm of Cu H.V.T. was obtained by extrapolation . 
For the latter purpose guidance was provided by some additional experimental data from the Royal Victoria Infirmary , Newcastle upon Tyne , but owing to the uncertainties of extrapolation this table must be regarded as somewhat less reliable than the others . 
DATA FOR RECTANGULAR FIELDS 
Johns and his colleagues have used the data for square fields to calculate tables for a series of rectangular areas , using Clarkson 's ( 1941 ) method , with the help of the digital computer of the University of Toronto . 
Depth doses for the primary radiation were assumed to be the same as those given in Section 3 . 
The computed values of percentage depth dose were smoothed graphically , by methods ( 1 ) and ( 3 ) above , prior to tabulation . 
Some of the rectangular fields included in these tables are different from those given in Section 3 , since it is intended that the data in this section shall correspond to the applicators most commonly used in Great Britain . 
Data for circular fields and for other rectangles may readily be computed by the equivalent field method ( see Appendix A ) . 
COMPARISON WITH PREVIOUS TABLES ( SUPPLEMENT No. 5 ) 
In this context deviations of the new tables from the old are expressed as percentages of the local dose . 
( 1 ) In the range 1.5-3.0 mm of Cu H.V.T. , for areas of 100 cm2 and above , the new tables agree with the old to within 3 per cent on average , with occasional divergencies up to 6 per cent . 
On the whole the new values are lower than the old , except when both area and depth are large . 
( 2 ) In the range 1.5-3.0 mm of Cu H.V.T. , for areas less than 100 cm2 , the new values are significantly lower than the old , confirming the findings of Cohen ( 1955 ) . 
The average differences amount to 5 to 7 per cent , but at some depths reach 10 to 12 per cent . 
( 3 ) At 1.0 mm of Cu H.V.T. the new values are lower than the old for all areas , the average difference being 4 to 5 per cent . 
COMPARISON WITH DATA FROM OTHER CENTRES 
In addition to the data from Cardiff covering the range of qualities from 1.0 to 3.0 mm of Cu H.V.T. presented in the tables , recent measurements at some qualities have been made at the Royal Infirmary ( Bradford ) , Western General Hospital ( Edinburgh ) , Lambeth Hospital ( London ) , Christie Hospital ( Manchester ) and War Memorial Hospital ( Scunthorpe ) . 
These measurements have been intercompared , revealing close agreement between the various centres , provided allowance is made for differences occurring in the first 2 or 3 cm by matching at some arbitrary depth , say 5 cm . 
These differences are partly real , arising from the use of applicators of different design , but mainly only apparent , arising from variations in the methods of assessing the surface dose . 
In view of the very small diameter of the chamber used and its close approach to the surface it is thought that the values tabulated represent a very close approximation to the variation in dose near the surface . 
COMPARISON WITH DATA IN SECTION 3 
The depth-dose data in this range of qualities measured by Johns and his colleagues in Saskatchewan are presented in Section 3 . 
The Canadian measurements were made with open applicators of special design ( see Introduction to Section 3 ) and differ from the British data in that there is no scatter component from the walls or end of the applicator . 
The two sets of data have been compared after applying the method of transformation suggested by Johns , Fedoruk , Kornelsen , Epp and Darby ( 1952 ) , making use of data for the range of depths 0 to 1 cm kindly supplied privately by Miss Fedoruk . 
Agreement is obtained within experimental error provided an appropriate equivalent water thickness , which allows approximately for the effects of both the end-plate and the applicator walls , is used in place of the nominal thickness of the applicator end-plate . 
The equivalent water thickness ( for Fulfield applicators , 1/8 inch flat Perspex end-plates ) is independent of area , but varies with H.V.T. as follows : 
Since the equivalent water thickness of the end-plate alone is approximately 3.8 mm , it is seen that the allowance which must be made for the scatter contribution from the applicator walls is substantial . 
Thus the simple correction factors for the end-plate only , measured by Johns , Hunt and Fedoruk ( 1954 ) , are insufficient for applicators of the type considered in this section . 
SURFACE BACK-SCATTER FACTORS 
These are taken from the survey values published by Greening ( 1954 ) , which were based on measurements made at 11 centres with seven different types of X-ray generator . 
SECTION 4 GAMMA RAYS : CAESIUM 137 TELETHERAPY UNITS Reviewed by J. E. Burns , M.Sc. , A.Inst.P. , Westminster Hospital , London , S.W.1 SOURCES OF DATA 
At the time the work on this section had been completed , there were to the knowledge of the reviewer , seven caesium units which were in clinical use , four in England and three in North America . 
Data were obtained from six of these centres : Addenbrooke 's Hospital ( Cambridge ) , Royal Marsden Hospital ( London ) , Royal South Hants Hospital ( Southampton ) , Westminster Hospital ( London ) , Ontario Cancer Institute ( Canada ) , and Alice Lloyd Radiation Therapy Centre ( Michigan , U.S.A. ) . 
ENERGY OF RADIATION 
The caesium source at Michigan was manufactured at Oak Ridge National Laboratory ; all the other sources were manufactured by the United Kingdom Atomic Energy Authority . 
It is well known that one of the main difficulties in the preparation of caesium 137 is to obtain freedom from contamination by other radioactive materials . 
Thus sources may differ in their degree of contamination , and the effective quality of their radiation may be different . 
It is of importance , therefore , to know whether the data given here , being mainly from British sources , applies also to sources manufactured elsewhere , in particular to American sources . 
Comparing the data received from the caesium unit at Michigan , it appears that it probably does apply . 
The half-value thicknesses from the five British sources were reasonably consistent , varying from 5.3 mm to 5.7 mm ( mean 5.4 mm ) in lead , from 10.6 mm to 11.0 mm ( mean 10.8 mm ) in copper , and from 7.8 to 8.0 cm ( mean 7.9 cm ) in water . 
Comparing the American source , the percentage depth doses differ from the average ( see later ) by no more than 141 1/2 per cent of the local dose , the half-value thickness in lead is in good agreement , 5.35 mm , but the half-value thicknesses in copper and water are rather higher , 11.25 mm and 8.35 cm respectively . 
Using the calculated attenuation coefficients of White Grodstein ( 1957 ) , the average half-value thicknesses of the British sources have been used to calculate the effective photon energy of the radiation . 
These are as follows : and can be compared with the accepted value of 0.66 MeV for caesium 137 g rays . 
BACK-SCATTER FACTORS 
Data were received from four centres , and a smoothed average of values was taken . 
Individual values of back-scatter factors differed from the average by not more than 1 per cent . 
In estimating the dose-rate at the maximum level from the dose-rate in air , it should be remembered that variations of air dose with area are at least as great as ( and are additional to ) the variation of back-scatter with area . 
The values will of course depend very much on the collimator system of the unit . 
For the only unit for which information is available , the dose-rate in air at the normal working S.S.D. increases by 15 per cent from a 4 x 4 cm field to a 16 x 16 cm field ; as the back-scatter factor varies by 4 1/2 per cent over the same range , the skin dose will vary by a total of 20 per cent . 
PERCENTAGE DEPTH DOSES 
Owing to the fact that caesium sources are usually several centimetres long it is necessary to define the term source-skin distance ( S.S.D. ) for these units . 
The definition of S.S.D. adopted for this section is the distance of the skin from the front of the source container . 
Four of the six centres had already chosen this definition for their own units . 
The other two centres were using different definitions but when their values for S.S.D. were converted to the more common definition their percentage depth doses showed improved agreement with those from the first four centres . 
On the basis of the general definition , the S.S.D.s at which measurements were taken were as follows : 
For the purpose of comparison , all percentage depth doses were converted to 40 cm S.S.D. using the method described by Johns , Bruce and Reid ( 1958 ) and Burns ( 1958 ) ( see Appendix B ) ; 40 cm was chosen as being midway between the extremes , so as to minimise any errors that the method of conversion may introduce . 
Asphyxia as the most important cause for death in drowning was still widely accepted until World War 2 , when research in the United States was initiated to see what could be done to save the lives of pilots who had been forced to land in the sea . 
Swann ( 1951 ) was chosen to conduct a large series of investigations and it is mainly due to his work and those who have followed that the modern view of drowning has emerged . 
He was able to show important differences in the mechanism of drowning in fresh and salt water , using dogs . 
In fresh water drowning large amounts of water entered the lungs and were absorbed with great rapidity into the circulation , giving rise within a very few minutes to rapidly fatal heart failure in ventricular fibrillation , this the result of the grossly diluted blood entering the heart muscle . 
The gross and rapid dilution of the blood in freshwater drowning was clearly demonstrated by Swann and at only 3 minutes after submersion the blood was found to be diluted with an equal volume of inhaled water ; it is therefore not surprising that death occurs rapidly in these circumstances . 
In sea water drowning Swann showed that water was rapidly withdrawn from the blood into the lungs by the inhaled sea water , concentrating the blood and giving rise to a more gradual heart failure without the ventricular fibrillation that occurred in fresh water drowning . 
The gross and rapid concentration of the blood in sea water drowning was well demonstrated in that after only 3 minutes ' submersion the blood had lost some 40% of its water . 
In addition , large amounts of the salts in sea water passed in the reverse direction into the blood to cause further disorganization of the blood chemicals ; it is again not surprising that death occurs rapidly in these circumstances . 
Swann also showed the resuscitation was usually successful with drowned dogs when heart failure had not occurred : once heart failure and falling blood pressure had occurred survival was most unlikely , even though irregular heart beats and respirations might occur for some minutes afterwards . 
He was also able to show that this lethal heart failure often occurred as early as 2 minutes after complete submersion , particularly in fresh water , explaining the higher mortality in this type of drowning . 
THE MODERN VIEW 
The experiments on animals suggest that the mechanism of drowning in humans would depend on whether it occurs in fresh or salt water . 
In fresh water drowning in humans we would expect a rapid death within a very few minutes , partly due to asphyxia , but mainly due to sudden heart failure brought about by the explosive absorption of large amounts of water into the circulation . 
In salt water drowning in humans we would also expect a rapid death , partly due to asphyxia and partly due to rapid concentration of the blood . 
In drowning in other waters the mechanism would probably depend on whether the saline concentration in the water was greater or less than in the body . 
It should , however , be emphasized that death often occurs within 6 minutes and almost invariably with 10 minutes of becoming totally immersed , and that many of the cases removed from the water whilst still alive are doomed to die within a few minutes from the devastating changes which have already taken place , no matter whether the water was fresh or salt . 
This knowledge explains the very high mortality rate in drowning . 
There are , however , a small number of cases which are rescued from water before large amounts of water have apparently been inhaled , due to very rapid rescue , shock , reflex inhibition of the heart or persistent spasm of the air passages , preventing or restricting inhalation of water . 
It is in these cases that artificial respiration would offer the greatest chance of recovery . 
These are presumably cases in which there has not been time for the gross disturbance of body fluid which has such grave effects in most cases of drowning . 
But in the vast majority of cases , drowning is not a simple asphyxia due to obstruction of the air passages and lungs by water but is a complicated process in which violent disturbances of the body fluids and chemicals make the situation so much worse for the individual concerned . 
This is the modern view of drowning and , although much is still not understood , it is now worth considering other important aspects , particularly the signs and symptoms , prognosis , resuscitation and prevention of drowning , as well as forensic problems relevant to dead bodies removed from water . 
SIGNS AND SYMPTOMS 
Drowning is rarely witnessed but the ordinary course of events is apparently as follows . 
The swimmer remains on the surface until he is exhausted and then the course in swimmers and non-swimmers is similar . 
The drowning person sinks and rises a number of times in the water and inhales a little water into the air passages , but this is prevented from entering his lungs by coughing and glottic spasm . 
( Rarely he may die at this stage from shock , reflex inhibition of the heart , from pre-existing heart disease or from almost pure asphyxia due to unrelenting glottic spasm ) . 
He continues to rise and sink in the water , shouts for help , coughs and chokes , but does not inhale much water into his lungs . 
With increasing asphyxia due to glottic spasm he loses consciousness and cough reflex , sinks and inhales large amounts of water . 
It is in this stage that the lethal exchanges of water occur . 
Oxygen reserves become severely depleted within 6 minutes and within 10 minutes heart and respiration almost invariably cease . 
Death occurs , the body sinks and remains submerged until putrefaction and gas formation bring it to the surface some days later . 
The symptoms of drowning vary from one case to another , from sensations of tranquillity to utmost distress . 
The following two cases are quoted by Polson ( 1955 ) . 
In the first case ( originally reported by Cullen , 1894 ) the sensations of a woman rescued from drowning at sea are particularly interesting . 
Self-preservation was dominant in her mind at first and there was great distress as she saw others swimming away from her . 
She experienced only acute suffering as described in her own words : " I sank and gasped involuntarily , then all other senses were overpowered by the agonizing scorching pain which followed the rush of salt water into my lungs . 
From that moment I was conscious only of that burning suffocation and the intense desire that others might know what had become of me . 
Except for that one thought my brain was dulled " . 
She complained of roaring in her ears and redness before her eyes . 
She was unconscious when rescued by her husband within 3 minutes of the time she first became submerged . 
But the experience of Admiral Beaufort , also quoted by Polson ( 1955 ) , who was partially drowned when a boy and rescued within 2 minutes , were those of painless tranquillity and thoughts of his previous life . 
In another case , a boy of 15 years was accidentally submerged in the River Derwent ( News Chronicle , August , 1960 ) for an uncertain period . 
He was rescued and recovered following artificial respiration . 
Of his experiences he stated : " I was sure I was dead , I just remember sinking . 
Whilst under the water I had a terrible dream that I was going on a train to Heaven . 
I never expected to wake up again . " 
It is , however , unlikely in any of these three cases who lived to tell the tale that substantial amounts of water had been inhaled . 
PROGNOSIS AND RESUSCITATION 
The prospect of survival following drowning must , of course , depend on many factors — the fitness of the subject , the duration of immersion and the amount of water inhaled being most important . 
The person with heart disease may die from sudden shock the moment he falls into cold water and it is not unusual for such subjects to be found dead in their own warm domestic baths , there being no question of drowning . 
In fit persons the prognosis depends on the length of asphyxia and the amount of water inhaled . 
In general , those who have been submerged a short time stand a better chance of survival in that oxygen reserves may not have been completely exhausted and spasm or shock may have prevented or restricted the inhalation of water into the lungs . 
But when large amounts of water have been inhaled it is most unlikely that recovery will occur , although the heart may continue to beat ineffectually for several minutes after rescue . 
It should be stressed again that the time required to inhale these lethal amounts of fluid is very short indeed , especially in fresh water drowning where explosive absorption of water from the lungs into the circulation may cause fatal ventricular fibrillation in as little as 2 minutes after commencing to breathe water . 
The course of events in sea water drowning is almost as rapid and thus the time available for rescue and resuscitation is pitifully short in those who have passed beyond the phase of glottic spasm into the second phase in which substantial amounts of water are inhaled . 
The prospect of recovery for those who have probably inhaled only a little water is better but there is here no time for delay in attempting resuscitation for irrecoverable changes can occur in a few moments . 
There is no time to examine the victim , no time to loosen clothing or clear the airway — these matters must be left until artificial respiration by any recommended method has been commenced . 
In theory artificial respiration should be continued in all cases until regular spontaneous breathing has occurred or death is certain . 
The question asked most often is : " How long should artificial respiration be continued in the absence of signs of recovery ? " 
Answers vary greatly but most would agree that 15 minutes ' artificial respiration should be given before an examination is made and this process repeated for at least 1 hour before attempts are finally abandoned ( Donald , 1955 ) . 
It is occasionally stated that successful resuscitation may take place when the drowned individual has been submerged for prolonged periods . 
Bates in 1938 , reporting six cases of recovery from alleged drowning with submersion up to 35 minutes , stressed the need for artificial respiration to be continued until the body had cooled substantially or the early signs of { 6rigor mortis were present . 
Present knowledge of the mechanism of drowning throws grave doubt on the accuracy of such prolonged periods of submersion with subsequent survival . 
Taylor ( 1956 ) regards recorded cases of recovery after submersion for more than 7 or 8 minutes as wholly unreliable unless this has been intermittent or incomplete as might occur in the air pockets of upturned boats . 
It is theoretically possible that submersion in extremely cold water might on rare occasions chill the body so rapidly that vital organs are protected from the effects of lack of oxygen ( as is now practised surgically ) , allowing survival after periods of submersion which would ordinarily be lethal ( Donald , 1955 ) . 
The possibility that life had been preserved by some rare chance would indicate the need for at least some attempt at resuscitation in all bodies freshly recovered from water , as is the current practice . 
When recovery occurs following drowning it is usually ultimately complete , without evidence of significant residual damage to the lungs ( Rushton , 1960 ) , heart or brain , though a period of observation and treatment will be required for some days to guard against complications . 
The individual who has survived fresh water drowning may show evidence of severe destruction of red blood cells due to excessive absorption of water , with resulting temporary kidney damage and staining of the urine by red blood pigment , as in Rath 's case ( 1954 ) quoted by Bowden ( 1957 ) . 
There may be cardiac failure due to alteration in the blood volume brought about by the absorption or withdrawal of fluid from the circulation and gross congestion and oedema of the lungs may occur within a few hours and cause death when recovery was expected . 
Pneumonia may also occur early due to the inhalation of substantial quantities of dirty and infected water . 
Haemophilia Complicated by an Acquired Circulating Anti-Coagulant : A Report of Three Cases MICHAEL HALL The Radcliffe Infirmary , Oxford 
A CIRCULATING anticoagulant may arise in patients with haemophilia and Christmas disease or may appear sporadically in normal people ( Lewis , Ferguson and Arends , 1956 ; Verstraete and Vandenbroucke , 1956 ; Hougie , 1955 ; Nilsson , Skanse and Eydell , 1958 ) . 
The anticoagulant has been studied by various workers , who suggest that it prevents the reaction between antihaemophilic globulin ( AHG ) and Christmas factor by destroying AHG ( Hougie and Fearnley , 1954 ; Bersagel and Hougie 1956 : Biggs and Bidwell , 1959 ) . 
The presence of an anticoagulant may , therefore , account for the failure of some patients to respond to treatment with AHG-containing material . 
Recognition of the presence of an anticoagulant , even in very small amounts , is therefore important and a method for its detection and assay has recently been described ( Biggs and Bidwell , 1959 ) . 
Since the management of these patients may be difficult three cases are described . 
The laboratory methods used for the haematological investigations were those of Biggs and Macfarlane ( 1957 ) , with the exception of the inhibitor assay which was by the method of Biggs and Bidwell ( 1959 ) . 
The human AHG was prepared and supplied by the Lister Institute of Sterile Products . 
CASE REPORTS CASE 1 
This patient ( R. I. No. 80047 ) , aged 23 years was admitted on May 23rd , 1958 . 
He had a family history of haemophilia , one younger brother being affected . 
He was first recognized as haemophilic at the age of 2 years when he bled profusely following circumcision . 
Since then he had been admitted to hospital on many occasions with various bleeding episodes , mainly haemarthroses and haematomata . 
As a result of the former , he had been admitted to the Nuffield Orthopaedic Centre in September 1956 , with a flexion contracture of the right hip , but this had responded well to treatment . 
On the present occasion he was admitted to the Nuffield Orthopaedic Centre for a similar reason , but within a day or two of admission developed severe right-sided abdominal pain which was associated with tenderness , pyrexia and vomiting . 
Since the diagnosis of acute appendicitis was raised , he was transferred to the Radcliffe Infirmary . 
On examination he looked pale and ill , and his right knee and hip were flexed . 
There were guarding and tenderness in the right iliac fossa and right groin , with tenderness high on the right posterior rectal wall . 
There was anaesthesia in the distribution of the right femoral nerve . 
Blood pressure was 115/70 . 
The haemoglobin was 11.4 g. per 100 ml . 
A diagnosis of a right-sided retroperitoneal haematoma was made and he was treated with analgesics , transfusions of fresh plasma and blood . 
In spite of this , bleeding continued and the haemoglobin dropped to 7.7 g. per 100 ml . 
His general condition was weaker and he appeared jaundiced . 
The lack of response to the transfusion treatment was unusual and some routine laboratory tests , in which a sample of the patient 's blood had been used as a control , suggested that an inhibitor of AHG was present . 
He was then treated with 2200 plasma equivalents of human AHG intravenously . 
This produced a characteristic and severe reaction , but failed to halt the bleeding process and he developed a haematoma of the upper chest wall and right side of the neck . 
The following day he complained of dysphagia and difficulty in breathing , and a chest X-ray showed evidence of mediastinal extension of this haematoma . 
Haematological investigation had by this time shown the presence of an inhibitor , the level being 33-50 units per ml. ( 1 unit of inhibitor is the amount which will destroy 75 per cent of added AHG in 1 hour ( Biggs and Bidwell , 1959 ) ) . 
With this level of inhibitor no amount of AHG-containing material , either animal or human , was likely to be effective in halting the bleeding process . 
The only possible way of reducing the level of the inhibitor seemed to be by exchange transfusion . 
Therefore , an exchange transfusion equivalent to twice the blood volume was performed . 
The inhibitor level fell to 5.9 units per ml. and the clotting time to 23-30 minutes . 
To take advantage of the improved circumstances , two doses of animal AHG , equivalent to 3200 ml. and 3300 ml. of fresh plasma were given . 
The effect was to reduce the clotting time to 6 3/4 minutes and the inhibitor level to 5.0 units per ml. , and a trace of AHG was measurable . 
The following day two further doses of animal AHG , equivalent to 3000 ml. and 8000 ml. of fresh plasma , were given . 
The clotting time was reduced from 60 minutes to 15 minutes and the inhibitor level to 3.9 units . 
No plasma AHG level was , however , obtained . 
There was a marked improvement in general condition following the exchange transfusion , and the jaundice and haematomata disappeared . 
Dysphagia disappeared after about 24 hours . 
Pain in the abdomen and groin lessened and he gradually became able to straighten his leg . 
A mild pyrexia developed after the exchange transfusion and there were signs of pneumonia in the right side of the chest . 
He was treated with tetracycline , 500 mg. 6-hourly , and improved . 
Hydrocortisone at a daily dose of 200 mg. was given in the hope of preventing further formation of anticoagulant . 
He was able to get up and sit in a chair . 
The only troublesome complication was persistent bleeding from the "cut down " site through which the cannula had been inserted . 
This necessitated the transfusion of 20 pints of blood , but was eventually stopped by repeated packing of the wound with Calgitex ribbon gauze soaked in Russell 's viper venom . 
The cannula was left { 6in situ for several days following the exchange in case of emergency , but was finally removed on June 12th , when nearly all bleeding had stopped . 
Further intermittent oozing continued for 10 days after this and another seven pints of blood were transfused . 
On the night of June 14th his temperature rose abruptly and in the next 72 hours reached 104° F. No obvious cause was discernible for this , though he had a tender haematoma on the upper outer aspect of the left forearm which had resulted from a venepuncture . 
Blood cultures remained sterile : a swab taken from the " cut down " site in the right arm grew a penicillin-resistant { Staphylococcus aureus but this wound did not appear infected . 
The pyrexia was , therefore , ascribed to the blood transfusions and absorption of blood . 
However , the administration of hydrocortisone was discontinued , and penicillin was given at a dose of 125 mg. t.d.s . 
and sulphamethoxypyridazine at 0.5 g. daily . 
The swinging pyrexia continued , the haematoma increased , brawny oedema developed , and there was oedema of the hand ; by June 28th the haematoma was obviously infected and was pointing over the lateral condyle of the humerus. 100 ml. of bloodstained pus was aspirated and the abcess was therefore incised . 
{ Staph. aureus resistant to penicillin , aureomycin and tetracycline was cultured from the pus . 
Management was now directed to the treatment of the staphylococcal infection , and of the bleeding diathesis . 
As can be seen from Fig. 1 , various antibiotics were given in full dosage and between July 13th and 26th the administration of chloramphenicol , 500 mg. 6-hourly , and intravenous Furadantin , 30 ml. per litre of normal saline b.d. , appeared to have controlled the infection . 
But relapse ensued on July 27th and a blood culture grew { Staph. aureus resistant to penicillin , tetracycline and erythromycin , but still sensitive to Furadantin and chloramphenicol . 
A similar organism was also grown from the pus from the left elbow . 
The patient was now desperately ill . 
Intravenous penicillin was given at a dose of 12 million units per 100 ml. of normal saline 6-hourly with Benemid , 0.5 g. 6-hourly by mouth . 
Penicillin blood levels as high as 32 units per ml. were obtained ; there was no dramatic fall in temperature but the general condition and appetite improved . 
By August 18th he was so much better that the administration of all antibiotics was discontinued . 
The haematoma of the left forearm produced two sloughing discharging areas , one posteriorly and one anteriorly , both of which had superabundant granulations protruding from them . 
These shrank considerably and eventually healed ( Fig 2 ) . 
During this period continual blood loss occurred from the incised abscess and from the anterior slough . 
Treatment was difficult because there were few veins into which needles or metal cannulae could be inserted . 
To allow time for veins to recanalize , polyethylene cannulae had to be inserted through larger veins into the femoral , subclavian and the superior caval veins . 
The patient bled profusely from these " cut down " sites and it was not possible to control bleeding by pressure , Stypven or Calgitex gauze while the cannulae were still { 6in situ . 
These procedures , though necessary , only aggravated the transfusion problem and a large volume of blood had to be transfused ( Fig. 1 ) . 
By this time the patient was debilitated , but felt much better , and was able to take a 3000 calorie diet . 
His pyrexia settled after 4 weeks , when a haematoma of the anterior abdominal wall developed and he complained of vomiting and of pain in the left groin . 
The haemoglobin fell and a further blood transfusion was given . 
In the middle of September melaena began and became more frequent and more fluid . 
Further deterioration ensued . 
A large haematoma appeared in the left groin and thigh and became grossly infected . 
By October 8th large fluid stools containing almost pure blood were passed . 
In spite of further blood transfusions he died in coma on October 9th . 
During admission he received 270 pints of blood . 
Necropsy report ( R.I.P.M. No. 771/58 . 
Dr. W. C. D. Richards ) 
At { 6post-mortem examination a large infected cystic haematoma was found in the retroperitoneal tissues on the right side of the abdomen . 
This involved the psoas , { quadratus lumborum and iliacus muscles . 
A similar haematoma on the left side had ruptured into the colon . 
The haematomata contained turbid brown fluid and masses of brown altered blood . 
On the left side the iliac haematoma communicated with a large infected haematoma of the thigh . 
Both ureters were surrounded by the fibrous tissue forming the anterior wall of the abdominal haematomata , the pelves of the kidneys being slightly dilated . 
The liver ( 3020 g. ) and spleen ( 850 g. ) were both enlarged . 
Microscopically the liver , spleen and iliac lymph nodes showed siderosis and there was amyloidosis of the spleen and liver . 
The liver was fatty . 
Masses of Gram-positive cocci were present in the blood clot filling the haematomata . 
Inflammatory granulation tissue lined the inner surface of the haematomata . 
CASE 2 
This patient ( R. I. No. 42050 ) , aged 43 years , was admitted on May 5th , 1958 , for weight reduction prior to extensive dental extractions . 
His haemophilia had been recognized for many years and numerous haemorrhagic episodes of variable severity and duration had occurred , many necessitating hospital admission . 
A bruising tendency had been noticed 14 days after birth and he had suffered prolonged haemorrhage after biting his tongue at the age of 2 years . 
There was a family history of obesity , but not of haemophilia . 
On examination he was obese , weighing 16 st. 9 1/2 lb . 
There was evidence of old haemarthroses involving both knees , both elbows , the right ankle and left shoulder . 
There was severe dental caries of both upper and lower teeth and it was decided that root remnants would have to be extracted . 
An 800 Calorie diet was begun and Dexedrine spansules mg. 15 mane , Saluric , 0.5 g. b.d. and potassium chloride , 1 g. twice daily were prescribed . 
His weight dropped to 15 st. 6 lb . 
At first , a few superficial bruises were the only haemorrhagic manifestations . 
Active physiotherapy to the knee was given with considerable improvement . 
After about 6 weeks several deep painful haematomata developed at various sites . 
On July 17th 10 roots and carious teeth were extracted from the upper jaw under general anaesthesia . 
His subsequent progress is summarized in Fig 3 . 
Before operation a polyethylene cannula was inserted into a forearm vein to a distance of 33 inches so that the tip should lie in a major vessel . 
( Venography later showed that the tip of the catheter was in the right ventricle ; the catheter was , therefore , withdrawn until the tip lay in the superior { vena cava . ) 
Statisticians and electrical engineers are familiar with an analogous uncertainty between time and frequency in the analysis of time-series , and this obviously suggests the query : can a frequency n be associated with an energy E ? 
Physicists appeal to the relation E = hn , where h is Planck 's constant , but quite apart from the qualms expressed by Schro " dinger ( 1958 ) about this relation , it is at least arguable that the frequency n is as fundamental in it as the energy E. I can therefore sympathize with ( though I am sceptical of ) the proposals by Bohm and de Broglie for a return to the interpretation of ps in terms of real ( deterministic ) waves ; I do not think these proposals will be rebutted until the statistical approach has been put on a more rational basis . 
Interesting attempts have been made by various writers , but none of these attempts so far has , to my knowledge , been wholly successful or very useful technically . 
For example , Lande2 keeps to a particle formulation , whereas it is the particle , and its associated energy E , which seem to be becoming the nebulous concepts . 
Let me refer again to time-series theory , which tells us that the quantization of a frequency n arises automatically for circularly-defined series — for , if you will allow me to call it this , periodic " time " ( more precisely in a physical context , for the angle variables which appear in the dynamics of bound systems ) . 
A probabilistic approach via random fields thus has the more promising start of including naturally two of the features of quantum phenomena which were once regarded as most paradoxical and empirical — the Uncertainty Principle and quantization . 
This switch to fields is of course not new ; the real professionals in this subject have been immersed in fields for quite a while . 
However , I am not sure that what probabilists and what physicists mean here by fields are quite synonymous , and in any case it is the old probabilistic interpretation in terms of particles that we lay public still get fobbed off with . 
It would seem to me useful at this stage to make quite clear to us where , if anywhere , the particle aspect is unequivocal — certainly discreteness and discontinuity are not very relevant . 
Here I must leave this fascinating problem of probability in quantum mechanics , as I would like to turn to its function in the theory of information . 
( 3 ) The concept of information 
Information theory as technically defined nowadays refers to a theory first developed in detail in connection with electrical communication theory by C. Shannon and others , but recognized from the beginning as having wider implications as a conceptual tool . 
From its origin it was probably most familiar at first to electrical engineers , but its more general and its essentially statistical content made it a natural adjunct to the parts of probability theory hitherto studied by the statistician . 
This is recognized , for example , in an advertisement for a mathematical statistician from which I quote : " 
Applicants should possess a degree in statistics or mathematics , and should if possible be able to show evidence of an interest in some specialized aspect of the subject such as , for example , decision theory , information theory or stochastic processes . " 
It has not , I think , been recognized sufficiently in some of the recent conferences on information theory , to which mathematical statisticians { 6per se have not always been invited . 
The close connection of the information concept with probability is emphasized by its technical definition in relation to an ensemble or population , and indeed , it may usefully be defined ( cf. Good ( 1950 ) , Barnard ( 1951 ) ) as - log p ( a simple and direct measure of uncertainty which is reduced when the event with probability p has occurred ) , although the more orthodox definition is the " average information " - { 15Sp log p , averaged over the various possibilities or states that may occur . 
It is also possible to extend this definition to partial or relative information , in relation to a change of ensembles or distributions from one to another . 
With this extended definition of - log p/p7 , where p7 relates to the new ensemble , the information can be positive or negative , and as the logarithm of a probability ratio will look familiar to statisticians , although it should be stressed that the probabilities refer to fully specified distributions , and the likelihood ratio of the statistician ( made use of so extensively by Neyman and E. S. Pearson ) only enters if the probabilities p and p7 are interpreted as dependent on different hypotheses H and H7 . 
For example , if p7 is near p , differing only in regard to a single unknown parameter th , then **f 
where is R. A. Fisher 's information function , under conditions for which this function exists . 
Formally , the concept of information in Shannon 's sense can be employed more directly for inferring the value of th . 
To take the simplest case shorn of inessentials , if we make use Bayes 's theorem to infer the value of a parameter { 15thr which can take one of only k discrete values , then our prior probability distribution about { 15thr will be modified by our data to a posterior probability distribution . 
If we measure the uncertainty in each such distribution by - { 15Sp log p , we could in general expect the uncertainty to be reduced , but we can easily think of an example where the data would contradict our { 6a priori notions and make us less certain than before . 
This seems to me to stress the subjective or personal element in prior probabilities used in this way , and my own view is that the only way to eliminate this element would be deliberately to employ a convention that prior distributions are to be maximized with respect to uncertainty . 
In the present example this would imply assuming a uniform prior distribution for { 15thr , and ensure that information was always gained from a sample of data ; it is somewhat reminiscent of arguments used by Jeffreys in recent years for standardizing prior distributions , but I think it important to realize that such conventions weaken any claim that these methods are the only rational ones possible . 
Whether or not the information concept in this sense finds any permanent place in statistical inference , there is no doubts of its potential value in two very important scientific fields , biology and physics . 
This claim in respect to biology is exemplified by the Symposium on Information Theory in Biology held in Tennessee in 1956 ; and while we must be careful not to confuse the general function of new concepts in stimulating further research with the particular one of making a particular branch or aspect of a science more precise and unified , the use of the information concept in discussing capacities of nerve fibres transmitting messages to the brain , or coding genetic information for realization in the developed organism , should be sufficient demonstration of its quantitative value . 
As another illustration of the trend to more explicit and precise uses of the information concept in biology , we may consider the familiar saying that life has evolved to a high degree of organization , that in contrast to the ultimate degradation of dead matter , living organisms function by reducing uncertainty , that the significant feature of their relation with their environment is not their absorption of energy ( vital of course as this is ) , but their absorption of negative entropy . 
An attempt to measure the rate of accumulation of genetic information in evolution due to natural selection has recently been made by Kimura ( 1961 ) , who points out that a statement by R. A. Fisher that " natural selection is a mechanism for generating an exceedingly high degree of improbability " indicates how the increase in genetic information may be quantitatively measured . 
While his estimate is still to be regarded as provisional in character , it is interesting that Kimura arrives at an amount , accumulated in the last 500 million years up to man , of the order of 108 " bits " , compared with something of the order of 1010 bits estimated as available in the diploid human chromosome set . 
He suggests that part of the difference , in so far as it is real , should be put down to some redundancy in the genetic coding mechanism . 
With regard to physics , I have already mentioned " negative entropy " as a synonym for information , and this is in fact the link . 
Again we have the danger of imprecise analysis , and the occurrence of a similar probabilistic formula for information and physical entropy does not by itself justify any identification of these concepts . 
Nevertheless , physical entropy is a statistical measure of disorganization or uncertainty , and information in this context a reduction of uncertainty , so that the possibility of the link is evident enough . 
To my mind one of the most convincing demonstrations for the need of this link lies in the resolution of the paradox of Maxwell 's demon , who circumvented the Second Law of Thermodynamics and the inevitable increase in entropy by letting only fast molecules move from one gas chamber to another through a trap-door . 
It has been pointed out by Rosenfeld ( 1955 ) that Clausius in 1879 went some way to explaining the paradox by realizing that the demon was hardly human in being able to discern individual atomic processes , but logically the paradox remains unless we grant that such discernment , while in principle feasible , at the same time creates further uncertainty or entropy at least equal ( on the average ) to the information gained . 
That this is so emerges from a detailed discussion of the problem by various writers such as Szilard , Gabor , and Brillouin ( as described in Brillouin 's book ) . 
( 4 ) The ro5le of time 
I might have noted in my remarks on quantum theory that , whether or not time is sometimes cyclic , it appears in that theory in a geometrical ro5le , reminiscent of time in special relativity , and not in any way synonymous with our idea of time as implying evolution and irreversible change . 
It is usually suggested that this latter ro5le must be related to the increase of physical entropy , but when we remember that entropy is defined statistically in terms of uncertainty we realize not only that evolutionary time itself then becomes statistical , but that there are a host of further points to be sorted out . 
Let me try to list these : 
( a ) In the early days of statistical mechanics , at the end of the last century , Maxwell 's paradox was not the only one raised . 
Two others were Loschmidt 's reversibility paradox , in which the reversibility of microscopic processes appeared to contradict the Second Law , and Zermelo 's recurrence paradox , in which the cyclical behaviour of finite dynamic systems again contravened the Second Law . 
It should be emphasized that , while these paradoxes were formulated in terms of deterministic dynamics , they were not immediately dissipated by the advent either of quantum theory or of the idea of statistical processes . 
For I have just reminded you that time in quantum mechanics is geometrical and reversible ; and stationary statistical processes based on microscopic reversible processes are themselves still reversible and recurrent . 
The explanations of the paradoxes are based , in the first place , on the difference between absolute and conditional probabilities , and in the second , on the theory of recurrence times . 
The apparent irreversibility of a system is due to its being started from an initial state a long way removed from the more typical states in equilibrium and the apparent non-recurrence of such a state to the inordinately long recurrence time needed before such a state will return . 
( b ) So far so good — but this conclusion applies to a system of reasonable size . 
We conclude that microscopic phenomena have no intrinsic time-direction , at least if this can only be defined in relation to internal entropy increase ( cf. Bartlett , 1956 ) . 
This is consistent with theoretical formulations in recent years of sub-atomic phenomena involving time-reversals . 
( c ) We have also to notice that while the entropy of our given system will increase with external or given time , this relation is not reciprocal , for , if we first choose our time , a rare state in our stationary process will just as likely be being approached as being departed from . 
The proportions between the mean and these z values are 0.4732 and 0.2734 respectively . 
The proportion between z1 and z2 is therefore 0.4732 - 0.2734 = 0.1998 . 
This is the same as the proportion between z1 = - 1.93 and z2 = - 0.75 , since the curve is symmetrical . 
4.16 As well as occurring in the equation of the normal and other curves , the mean and variance parameters have another valuable property . 
This is the fact that they are additive . 
If we have two populations , with means { 15m1 and { 15m2 , and we add the variate values of these populations in pairs , we find that the mean of the sum ( { 15m1+2 ) is the sum of the means ( **f ) or **f 
The mean difference between pairs of population values is the difference of the means of the separate populations , i.e. **f 
These simple properties are not , in general , possessed by medians , modes , or other position parameters . 
4.17 A similar property exists for variances , but in this case we must take account of the correlation between the two sets of data which are to be added or subtracted . 
The extent of correlation is expressed by the correlation coefficient r ( Greek letter rho , pronounced " roe " ) . 
This coefficient is positive when high values of one variate are paired with high values of the other , and similarly for low values ; it is negative when high values of one variate are paired with low values of the other , and it is zero when there is no systematic linear relationship between the variates . 
The coefficient r can take all fractional values between + 1.0 and - 1.0 ( for further discussion of r see Chapter 9 , particularly 9.4 ) . 
We may now state that the variance of a sum ( { 15s21+2 ) is **f 
A similar property holds for the variance of the differences between two correlated populations given as **f 
If it happens that our two populations are uncorrelated ( r = 0 ) , then the last terms in equations 4.10 and 4.11 vanish ( i.e. 2{15rs1 { 15s2 = 0 ) and the sum or difference of the variates has a variance equal to the sum of the separate variances , or , **f 
These additive properties are not in general possessed by the other measures of dispersion that have been discussed . 
4.18 The data already used in Table 4 . 
A are written out in full in Table 4 . 
C , which illustrates how the above five formulae work . 
Here , the individual values of X1 and X2 are put opposite one another so that r = 3/4 . 
The values of X3 and X4 are put together so that r = 0 . 
The actual means and variances of the sums and differences of X1 with X2 and X3 with X4 , may be compared with the results of using the above formulae . 
**f 
These results agree with those calculated in Table 4 . 
C. The reader should notice that in this table , **f . 
4.19 Measuring Scales and Parameters . 
All the parameters we have discussed may be justifiably used with measurements on a ratio or interval scale . 
Nominal scales , by definition , do not justify the calculation of any position or dispersion parameters , since in such scales there is no dimension or singleness of direction involved . 
In nominal scales , events are numbered to show they are the same or different from other events , i.e. the numbers reflect qualitative , not quantitative characteristics in the data . 
An ordinal scale does reflect quantitative features of the material measured , i.e. a dimension or singleness of direction , but it does so by inconstant units of unknown size . 
The numbers which constitute an ordinal scale may vary by fixed and known amounts ( such as in ranking ) , but this in no way implies that the objects measured by these numbers also change by fixed amounts . 
The lack of isomorphism between number intervals and object intervals in ordinal scales of all types , makes the addition and subtraction of ordinal measurements illegitimate . 
Addition and subtraction of numbers signifies an imaginary movement over certain intervals . 
If these numerical intervals do not correspond to object intervals , addition or subtraction of the numbers may lead to false conclusions about the objects they are supposed to represent . 
Since addition and subtraction of ordinal measurements are not legitimate , the calculation of means is not justified , and the use of medians , which do not require the addition of X values , is more permissible . 
4.20 An illustration of the type of error which means of ordinal scales may engender , will clarify the above discussion and bring to light some further relevant considerations . 
Imagine a set of objects A , B , C , ... which differ from one another by equal amounts of some variable . 
Let the " true " interval scale , measuring these objects , be represented by the italic numbers 1 , 2 , 3 , ... 
If all knowledge of the interval sizes is denied us , we may construct a standard ordinal scale , which may be represented by normal numbers , 1 , 2 , 3 , ... 
The relation between the " true " and the ordinal numbers might be — 
Relative to the interval scale , this ordinal scale is stretched at B , F , H , I , J , M , and N , and compressed between O and P. If we measure the objects ACK and CDE on our ordinal scale , the means of these two groups of objects are each equal to 3 , i.e. the mean object is D for both sets . 
Yet the positions of the two sets of objects are different when measured on the " true " interval scale , which yields means of 5 and 4 respectively , i.e. objects E and D. The point being made here is not that the numerical values of the means differ from one scale to another , but that the two scales yield different conclusions about the similarity between the two groups of three objects . 
The mean Centigrade temperature of a set of objects will be numerically different from the mean Fahrenheit temperature , yet both means will refer to the same object , because these scales are interval scales . 
The ordinal scale means of objects DEO and AGP are 5 and 6 , while the interval scale means agree at the value 8 . 
This illustrates the error converse to that already given , the ordinal scale producing a difference where none exists . 
4.21 Means and Medians . 
The medians of the ordinal measurements of the first two groups given above are and . 
This observation shows that means and medians do not necessarily agree in the conclusions they yield . 
The interval scale means show that CDE sits to the left of ACK , ordinal scale means make both groups equal in position , and now , ordinal scale medians place CDE to the right of ACK . 
Which of these conclusions is correct ? 
The truth is that the first and last are both correct , though they disagree ! 
This apparent paradox is resolved when we note that means refer to the interval properties of objects and medians to their ordinal properties . 
If only order is known , medians will yield conclusions which are correct so far as order is concerned . 
If intervals are known , these supersede simple order , and means will yield conclusions which are correct relative to this improved knowledge . 
Note that the medians of both the interval and ordinal measurements of ACK and CDE agree in selecting objects C and D. We may say that a mean is a strong parameter which requires known intervals and if applied to a weak scale ( ordinal ) may yield false conclusions . 
A median is a weak parameter and if applied to a strong scale ( interval or ratio ) will yield a result comparable to that obtainable from any weak equivalent of this scale . 
Finally , we should note that the numerical size of a difference between means of interval or ratio scale data is an indication of the extent to which the data differ in position , but the numerical size of a difference between medians of any data is not an indication of the extent of difference . 
4.22 Variances and Semi-interquartile Ranges . 
The argument against ordinal scale means can be extended to the use of variances on ordinal scale data . 
Is there any dispersion parameter which may be legitimately used on ordinal measurements ? 
The obvious candidate for this role is the semi-interquartile range , but although this is a parameter concerned chiefly with order , it is unsatisfactory . 
The semi-interquartile ranges of two sets of ordinal results might show them to be similar ( or different ) in dispersion , but the use of some other order parameter ( e.g. half the distance between the top tenth and the bottom tenth of the data ) might show them to be different ( or similar ) , and we have no reason for choosing one kind of order parameter rather than another . 
We shall not pursue this argument further , except to say that dispersion is almost synonymous with distance and the distance between objects is something about which ordinal scales tell us very little . 
To seek a dispersion parameter for ordinal scale data is to ask from the scale more than it is able to tell us . 
4.23 A Mechanical Analogy . 
We may imagine a variate X to be represented by a horizontal uniform rod of negligible mass which is marked off in the units of X. Each individual in the population can be represented by a small weight . 
We can now attach these weights to the uniform rod at the points which represent their variate value . 
The resulting assembly will resemble a histogram turned upside down . 
An illustration is given in Fig. 4 . 
A. In this illustration , each individual f is represented by a weight hung from its value of X. If we try to find that point on the rod which will balance the whole assembly , we discover it as m . 
In other words , the mean of a distribution is its centre of gravity . 
When the apparatus is hung from its centre of gravity , we may give one end of it a little push . 
This will set it spinning or rotating about the point of suspension . 
The amount of spinning it does depends on how spread out the weights are along the rod . 
If the weights are clustered closely around the centre of gravity , it will be highly stable and swing very little . 
If they are spread out along the length of the rod , it will be unstable and swing a great deal . 
The stability of the apparatus is given by { 15s2 . 
In other words , the variance of a distribution is its moment of inertia . 
4.24 Short Cuts in Calculating . 
We have already learned that frequency distributions provide easier arithmetic than a set of disorganised measurements ( 4.5 ) . 
There are techniques which make calculation still less laborious , and these may well be discussed here . 
In calculating the mean of a set of data , we must add all the values of the variate and divide the total so obtained by N. When the variate values are large numbers ( such as age in months ranging from 120 to 145 months ) , addition is laborious and , consequently , liable to error . 
A short cut which reduces the size of the values to be added is to accept a central value arbitrarily ( A ) before we begin the calculation and write all variate values ( X ) as deviations ( x7 ) from this . 
The mean of the data can then be found from **f 
This formula derives from the fact that the sum of the deviations of a set of numbers from their mean ( { 15Sx ) is zero ( 4.8 ) . 
It follows that if { 15Sfx7 = 0 then A = m , and we have chosen the mean as our central value by accident . 
If { 15Sfx7 is positive , then the A chosen must have been smaller than m . 
If { 15Sfx7 is negative , then the A chosen was larger than m . 
4.25 The major difficulty encountered in calculating the variance or standard deviation of data , is that if m is , say , 74.98 , then all deviations from this value must involve two places of decimals . 
Squaring numbers containing two places of decimals is a tedious matter . 
This difficulty can be circumvented by using the deviations from A mentioned above . 
The formula for the variance then becomes — **f 
and the standard deviation is **f 
The reason we subtract the correction term **f is that the sum of squares of deviations from a mean , is smaller than squares about any other point . 
Peierls ( 7 ) has gone into details , but his treatment , he admits , is non-rigorous . 
As Dolph ( 8 ) points out , the promised justification of this has never appeared . 
Schwartz ( 9 ) , in a very important and powerful paper , treats the Sturm-Liouville case ( and also certain singular cases ) , but only as a special case of a long and complicated function-theoretic argument . 
Keldysh ( 10 ) has also given a linear-operator approach to the problem . 
Altogether , there does seem a case for a direct justification of Peierls 's work that does not depend on function-theoretic arguments , and this is particularly so when it appears that , without any great complication , it is possible at the same time to make a contribution to the singular case in which the range of x remains finite but becomes discontinuous at one or other or both of the end-points . 
This contribution does not seem to be covered by the existing function-theoretic arguments . 
The problem we shall consider is the following . 
We take the equation **f 
where may be complex but is continuous except at r = 0 , and where **f exists . 
We suppose that l is a positive integer or zero . 
The reader will readily verify that the analysis is not restricted to those values of l , but this is the case of practical importance . 
( The equation is the well-known equation that arises when a three-dimensional equation with spherical symmetry is solved by the method of separation of variables . ) 
The boundary conditions we impose are ( 1.3 ) , for some b 0 , together with the requirement that be . 
This , as the analysis shows , is sufficient to define an eigenvalue problem , except in the case l = 0 , when we have to impose a further condition of the type ( 1.2 ) at a = 0 . 
Despite this , the case l = 0 is similar enough to the case l 0 , so that we can safely restrict ourselves to l 0 . 
The case l = 0 , with continuous , is just the Sturm-Liouville case , which therefore comes out as a particular case of the argument . 
We shall examine the eigenfunctions associated with this eigenvalue problem . 
As usual , an eigenfunction is a non-trivial solution of the equation ( 1.4 ) which satisfies the boundary conditions . 
In the self-adjoint case , the set of eigenfunctions would be complete , i.e. any reasonable function could be expanded in a series of them . 
In the non-self-adjoint case , we shall see that in general this no longer holds , but that the set of eigenfunctions can be made complete by adding to it certain other functions which , though not eigenfunctions , are related to them . 
( Their precise form will be found in 135 . ) 
I shall refer to these additional functions as adjoint functions . 
The problem can be extended to the case in which r = b is also a discontinuity of , of the same type as at r = 0 . 
It will not be necessary to discuss in detail this extension , but it will be clear that the same general conclusions hold on the completeness of the set of eigenfunctions and adjoint functions . 
I have limited myself to proving completeness , but , at least in certain cases , much more can be proved . 
For example , in the Sturm-Liouville case , a very straightforward adaptation of ( 1 ) [ Ch. 1 ] shows that not only is the set of eigenfunctions and adjoint functions complete , but also that , if is any function of , then the eigenfunction expansion of ( an expansion which , of course , includes adjoint functions ) converges under Fourier conditions to . 
This analysis does not seem to extend to the singular cases considered in this paper . 
2 . 
If **f , then ( 1.4 ) has solutions **f , of which **f is . 
If we then write ( 1.4 ) in the form **f 
we see that it is formally equivalent to the integral equation **f . 
Our first objective is to prove that , for **f , and all **f sufficiently large , the solution of ( 1.4 ) that is is , apart from a multiplicative constant , **f , 
where denotes a term small where **f is large , uniformly for r in , and where **f . 
We do this by investigating ( 2.1 ) . 
Let **f . 
Then **f 
for all r , l , where A denotes various positive constants . 
Let **f . 
Then , if **f , ( 2.1 ) gives **f 
since **f exists , the term denoting a quantity which tends to zero as **f . 
Also , if **f , **f 
where **f . 
But , for **f , we have **f . 
For , for all z , **f , 
so that **f . 
The required estimate for follows from this by using the asymptotic expressions for **f . 
Substituting this estimate in ( 2.2 ) , we obtain **f 
The first of the two integrals in the last line is **f since **f in the range of integration and **f . 
The second integral is **f , by a similar type of argument . 
( The second integral will not , of course , appear if **f . ) 
It thus follows from ( 2.1 b ) and ( 2.4 ) that , for **f , if **f is large enough , i.e. that **f . 
If we substitute this result back in the integral in ( 2.1 ) and re-estimate this integral on the same lines as has just been done , we emerge with ( 2.1 a ) . 
Thus any solution of ( 2.1 ) satisfies ( 2.1 a ) . 
That there is one ( and just one ) solution of ( 2.1 ) can be proved by the usual iteration process , of which the work above is effectively the first step . 
Then ( 2.1 ) can be differentiated back to show that the solution is a solution of ( 1.4 ) . 
We have thus found a solution of ( 1.4 ) that is . 
If we denote this solution by , then any other solution apart from a constant multiple of is given by a constant multiple of **f , 
and knowing now the behaviour of near r = 0 , we can readily verify that is not solution is therefore ( apart from a multiplicative constant ) unique . 
We remark finally that , since **f is an integral function of l , the process of solving ( 2.1 ) by iteration shows that **f is also an integral function of l . 
3 . 
We now consider the solution which satisfies ( 1.4 ) and the boundary conditions **f . 
As in ( 1 ) [ Ch. 1 ] is an integral function of l . 
The Wronskian of { 15f , ch is independent of r and so may be written as , and **f will be an integral function of l . 
Further , the vanishing of is a necessary and sufficient condition for { 15f , ch to be multiples the one of the other , i.e. for l to be an eigenvalue . 
For large values of **f , **f 
( The asymptotic behaviour of **f is obtained by differentiating ( 2.1 ) with respect to r and proceeding as before . ) 
Hence , for large values of **f , the zeros of must be near the zeros of **f , which are , of course , independent of . 
Further , for large **f , the zeros of are simple . 
This is best seen by writing **f 
where C is a circle with centre l , and by using the asymptotic expression ( 3.1 ) for to give an asymptotic expression for . 
It is then clear that values of l near the zeros of **f do not satisfy = 0 . 
We now construct the function , where **f , 
and . 
This is a meromorphic function of l , having poles at the zeros of . 
It will be our object in the next section to show that , if is such that all the residues of = 0 almost everywhere . 
4 . 
If all the residues vanish , becomes an integral function of l . 
Let us suppose that we can prove ( as we shall do ) that we can find a sequence of circles **f , with **f , such that is bounded on the circles , with the bound possibly dependent on r , but independent of n . 
Then , by Liouville 's theorem , is a constant , independent of l . 
Suppose then that . 
It follows by differentiation that **f , 
with the result holding at least almost everywhere . 
By varying l , we have = 0 almost everywhere . 
It remains to prove the boundedness of , with r fixed , but **f , on the circles **f . 
Since we are concerned only with results " almost everywhere " , we may exclude r = 0 . 
The differential equation is thus non-singular in the interval [ r , b ] , and we can appeal to ( 1 ) [ equation ( 1.7.8 ) ] to get an asymptotic form of for sufficiently large **f . 
In fact , we have **f , 
where A denotes various positive constants independent of l . 
From 132 we have , again for fixed r and sufficiently large **f , **f 
Finally , if we choose the sequence **f to be such that **f , 
we see that **f 
on each of the circles **f , and so , on those circles , for n sufficiently large , we have from ( 3.1 ) that **f 
If we now substitute ( 4.1 ) , ( 4.2 ) , ( 4.3 ) in the definition of , and use Schwarz 's inequality to estimate the integrals , we see readily that , on the circles **f , is bounded with bound independent of n . 
5 . 
From this , we can deduce the completeness of the eigenfunctions and adjoint functions . 
Before we do this , however , we must examine the nature of these eigenfunctions and adjoint functions . 
In the real self-adjoint case , it is well known that the zeros of are real and simple , and , if { 15ln is such a zero , is a multiple of , so that we may write **f . 
Then , near l = { 15ln , the singular part of is **f . 
Hence the residue at l = { 15ln is **f , 
and this vanishes for all r if and only if the Fourier coefficient of with respect to the eigenfunction vanishes . 
The argument remains valid even in the non-self-adjoint case provided that { 15ln is a simple zero of . 
However , there is no longer any guarantee that the eigenvalues of will be simple , and counterexamples are easily provided . 
Suppose now that { 15ln is a zero of order p of has a residue of the form **f 
where the are constants depending on the derivatives of at l = { 15ln and whose precise value will not concern us . 
Now can be written in the form **f , 
and we know that = 0 . 
Hence **f , 
and interchange of the order of differentiation gives that **f 
is independent of r . 
If we repeat this process with higher differentiations with respect to l , we obtain finally that **f 
is independent of r for s = 0 , 1 , ... , p-1 . 
This implies that , for these values of s , **f 
so that ( 5.1 ) can be expressed as a linear combination of the p functions **f , the coefficients being homogeneous linear combinations of the p expressions **f , 
or , what is the same thing , homogeneous linear combinations of the p expressions **f . 
For the residue to vanish it is therefore sufficient that all the Fourier coefficients of with respect to the p functions **f should vanish . 
Hence , if all the Fourier coefficients of , then all the residues of vanish , and so , as already proved , = 0 almost everywhere . 
This shows , by application of a standard theorem , that the system of eigenfunctions and adjoint functions , where the adjoint functions are **f , 
is complete . 
The question does arise whether the adjoint functions are indeed necessary for completeness , or whether on the contrary they themselves can be expressed as linear combinations of the eigenfunctions , and so be eliminated from the expansion of an arbitrary function . 
It is a standard theorem in the theory of orthogonal functions that all the eigenfunctions and adjoint functions are necessary if they form an orthonormal set , and we shall prove that they are substantially orthonormal in 13 6 . 
What we shall actually prove ( and it is clear that this will be sufficient ) is 
( 1 ) that all the eigenfunctions and adjoint functions associated with an eigenvalue { 15ln are orthogonal to all the eigenfunctions and adjoint functions associated with an eigenvalue { 15lm , where **f ; 
( 2 ) that the eigenfunctions and adjoint functions associated with an eigenvalue { 15ln of multiplicity p can be expressed by a non-singular transformation as linear combinations of p orthonormal functions . 
It should be remarked that the number of multiple eigenvalues is at most finite , and so the number of adjoint functions is at most finite . 
A PERMUTATION REPRESENTATION OF THE GROUP OF THE BITANGENTS W. L. Edge 
1 . 
The group G of the bitangents has been studied in two recent papers ( [ 3 ] and [ 4 ] ) . 
It was represented in [ 4 ] as a subgroup of index 2 of the group of symmetries of a regular polytope in Euclidean space of dimension 6 , in [ 3 ] as the group of automorphisms of a non-singular quadric Q in the finite projective space [ 6 ] over F — the Galois Field . 
The culmination of [ 4 ] is the compilation , for the first time , of the complete table of characters of G , and Frame uses this table to suggest possible degrees for permutation representations . 
Such representations , of degrees 28 , 36 , 63 , 135 , 288 are patent once the geometry of Q is known ; but Frame , having observed that there is a combination of the characters that satisfies the several conditions known to be necessary , had proposed also 120 as a possible degree . 
As there is no guarantee that the set of necessary conditions is sufficient , and as no representation of G of degree 120 seems yet to have appeared in the literature , a description is here submitted of one that is incorporated with the geometry of Q. 
Q consists , as explained in [ 3 ] , of 63 points m ; 315 lines g ( all three points on a g being m ) lie on Q , while through each g pass three planes d lying wholly on Q ( in that all seven points in d are m , and all seven lines in d are g ) . 
These three d form the complete intersection of Q with E , the polar [ 4 ] of g . 
There are , and it is intended to construct them , 120 figures F ; each F includes all 63 m together with 63 d , one d being associated with each m — having m for its focus as one may say . 
Those g in d that pass through its focus may be called rays ; all three d containing a ray belong to F , their foci being those three m that constitute the ray , so that , there being three rays in each of 63 d , there are 63 rays in F. The plane of any two intersecting rays is on Q , and the third line therein through the intersection is a ray too . 
None of the 72 d extraneous to F includes a ray ; of those d that pass through a g which is not a ray only one belongs to F , the other two being extraneous to F. 
Although such a figure as F may not have been previously described it has been encountered , so to say , by implication , being obtainable when Q is regarded as a section of a ruled quadric S in [ 7 ] ; one has then only to take , on S , those points that are autoconjugate ( i.e. incident with their corresponding solids ) in a certain triality . 
That such points make up a prime section of S is known ( see 5.2.2 in [ 5 ] ) , and that there are 63 of them accords with putting k = l = 2 in 8.2.4 of [ 5 ] ; 8.2.6 then says that , of 63 m , 32 lie outside the tangent prime T0 to Q at a given point m0 while 8.2.5 says that there are 63 rays , or " fixed lines " in Tits ' phraseology . 
2 . 
Let d , d7 be any two of the 135 planes on Q that are skew to one another ; they span a [ 5 ] C and , being skew , belong to opposite systems on K , the Klein section of Q by C. 
Through any line g of d passes another plane of K which , belonging to the opposite system to d , is in the same system as d7 and so meets d7 at a point m7 ; moreover , the points m7 so arising from g in d concurrent at m lie on g7 , the line of intersection of d7 with the tangent space [ { 15dg7 ] of K at m . 
The plane , other than d7 , on K that contains g7 is [ mg7 ] . 
So there is set up a correlation between d and d7 ; each point of either is correlative to a line of the other . 
If m in d and m7 in d7 each lie on the line correlative to the other their join is on K. There are 21 such joins ; through each point m of d there pass three , lying in the plane joining m to its correlative g7 , and likewise there pass three coplanar joins through each point m7 of d7 . 
Since K consists of 35 m there are 21 , which may be labelled temporarily as points m , that lie neither in d nor in d7 ; through each m passes one transversal to d and d7 ; these 21 lines , one through each m , are the joins mm7 of points each on the line correlative to the other . 
Through each point on K pass nine lines lying on K ; if m is in d three of them lie in d while another three join m to the points on its correlative g7 ; there remain three others , so that 21 g on K meet d in points and are skew to d7 . 
Another 21 meet d7 in points and are skew to d . 
There are also among the 105g on K seven in d , seven in d7 , 21 transversal to d and d7 ; there remain 28 , which may be labelled g* , skew to both d and d7 . 
These 28 g* may be identified as follows . 
Take any g in d ; the solid that joins it to any g7 through its correlative m7 in d meets K in two planes through mm7 , m being that point on g to which g7 is correlative . 
But there are four lines g7 in d7 that do not contain m7 ; then the solid [ gg7 ] meets K in a hyperboloid whereon the regulus that includes g and g7 is completed by g* . 
As there are seven g in d , and four g7 in d7 not containing the correlative m , the 28 g* are accounted for . 
There being three m on each g* , but only 21 m in all , one expects there to be four g* through each m ; this is so . 
For let the transversal from m to d , d7 meet d in m , d7 in m7 ; through m , and in d , are lines g1 , g2 other than the correlative g to m7 ; through m7 , and in d7 , are lines g17 , g27 other than the correlative g7 to m ; each solid **f 
meets K in a hyperboloid whereon a regulus is completed by a g* through m . 
3 . 
Take , now , one of these g* : the transversals from its three m to d , d7 form a regulus whose complement includes g in d and g7 in d7 , neither g nor g7 being correlative to any point on the other . 
The correlative m in d of g7 is conjugate to every point of g and , by the defining property of the correlation , to every point of g7 ; so , likewise , is the correlative m7 in d7 of g . 
Hence the polar plane j0 ( [ 3 ] , 136 ) of [ gg7 ] with respect to Q contains both m and m7 ; there is one remaining point m* of Q in j0 , and it lies outside C — for to suppose that it belonged to C would put the whole of j0 in C , whereas the kernel of Q , which is in j0 , is outside C. Now there are 63-25 = 28 points m* on Q that are not on K ; thus each m* is linked to a g* , and m*g* is a plane d on Q. 
There are three planes on Q through any line thereon ; if this line is a transversal m{15mm7 from one of the 21 m to d and d7 two of these planes are on K , while the third contains a quadrangle **f with its diagonal points at m , m , m7 . 
The tangent prime to Q at any vertex of this quadrangle contains m{15mm7 and meets d , d7 in lines belonging to a regulus completed by g* through m . 
Thus four concurrent g* are linked with coplanar m* whose plane , containing the transversal to d and d7 from the point of concurrence , lies on Q but not on K. 
4 . 
Choose now , from among the 315 g on Q , the 21 transversals of d , d7 and those , three through each m* , that join m* to those m on the g* that is linked with it . 
Each such join contains two m* , the g* that are linked therewith both passing through m ; hence , under this second heading , the number of g selected is **f . 
So 63 g are chosen : call them rays . 
Through each m on Q pass three rays , and they are coplanar . 
If m is m* this is manifest from the prescription of choice , as it is too if m is in d or d7 . 
If m is m the rays are , say , **f and lie in that d through m{15mm7 that is not on K. So 63 d are chosen from among the 135 on Q ; each contains three concurrent rays . 
Call the m wherein the rays concur the focus of d . 
Through any g there pass three d ; if g is a ray these d are those having the m on the ray for foci . 
The points of d other than its focus m are foci of those other d which belong to F and contain m ; if d , d7 in F are such that the focus of d7 is in d then the focus of d is in d7 . 
Whenever two rays meet the third line through their intersection and lying in their plane is a ray too . 
It is these 63 d , with the 63 rays and foci , that constitute the figure F. 
Each d in F contains , as well as three concurrent rays , a quadrilateral of g that are not rays ; thus , by four in each of 63 d , the 315-63 = 252 g that are not rays are accounted for . 
Through each such g pass two planes on Q in addition to d , but they are extraneous to F. The 135-63 = 72 extraneous planes may be labelled d ; the planes above denominated by d and d7 are in this category . 
No g in d is a ray and only one of the planes on Q that pass through it belongs to F whereas , were g a ray , all three would do so . 
5 . 
Label the m in any of the 72 d by **f 
they lie on g that can be taken as **f 
Through each such g there is a single d belonging to F ; label the foci of these d , none of which can lie in d , respectively **f 
Then those d whose foci are in d join its points to the respective triads **f 
Thus the join of every pair of points 17 is on Q and , there being no solid on Q , the points 17 lie in a plane d7 whose lines consist of the triads 27 . 
Each of the 72 d has , it is now clear , a twin d7 coupled with it by F. The correlation between d and d7 is shown by 1 and 27 or , alternatively , by 17 and 2 . 
Those d that pass one through each line of d7 have for their foci the points of d correlative to these lines ; if d passes , say , through 17 37 57 its focus is the point 5 common to those d whose foci are 17 , 37 , 57 . 
Since , by the construction in 134 , d and d7 determine F uniquely there are x/36 figures F where x is the number of pairs of skew planes on Q. To calculate x note , in the first place ( using d now to signify a plane on Q whether it be in F or extraneous thereto ) , that each d is met in lines by 14 others , two passing through each g in d . 
Note next , to ascertain how many d meet a given d0 in points only , that the 15 d through a point m of d0 project , from m , the figure of 15 g in [ 4 ] passing three by three through 15 points ( [ 2 ] , 131313-15 ) . 
This is a very much over-simplified example , but it may serve to emphasise the point that common criteria of adaptation often contradict each other . 
A common antecedent to symptoms of stress in the individual is violent change in the environment and , in the particular instance of stress conditions and behaviour that I will be discussing , overt and drastic changes are not far to seek . 
Africa is in a stage of turbulent transition . 
The last hundred years have brought great changes in the life of its tribes and of its tribesmen . 
As I have mentioned , a fertile source of human stress is the clash between the demands of the individual and those of his society . 
This conflict must be the more severe when the two aspects are not geared together , functionally , as they tend to be in any rigid pre-literate tribal system where the conformity of the individual to a very stable pattern of expected behaviour is ensured by the traditional methods of child rearing . 
Tonight I will be considering some aspects of life in Zululand and change has been as violent here as elsewhere on the continent . 
The modern Zulu is neither purely traditional African nor purely Western in his attitudes , aspirations and behaviour . 
He is a displaced person and his society is a displaced society . 
In effect , there are few readily identifiable social norms for any specific action and I think that it is this fact that makes the investigation of stress disorder in Zululand so difficult and yet so potentially illuminating . 
The situation is an excellent example of Durkheim 's anomy , social disorganization at all levels — " norms " are hard or impossible to find and the psychologist can not , for long , hold many preconceptions . 
As , to most of you , the background will be unfamiliar I must spend a little time in giving a very short account of the social situation then ( say 1850 ) and now . 
In the nineteenth century the Zulu people were the pastoralist and agriculturist conquerors of a very large area of Southern Africa . 
There was more than enough land for their needs . 
The men were warriors whose chief domestic duty was the tending of the cattle — an occupation strictly taboo to women . 
The women did the hard work on the lands . 
The state was a pyramidal patriarchy with the Zulu king , the secular and religious " father of his people " , at the apex . 
The men remained at their homesteads except when they were required for military service , and all legal and ritual authority was vested in the males of the nation . 
Most marriages were polygynous and based upon a system of bride-price , and the Zulu woman was at the bottom of the social pyramid . 
While the behaviour of all members of the society was strictly circumscribed by law and custom , this was especially true of the young married woman , living under the strict tutelage of her husband 's mother . 
She even had to modify the very speech that she used in order to avoid any words containing the root sound of the name of her father in law . 
The extended family was always present , which helped greatly in the rearing of children ; children that were of vital importance to the nation for not only did they ensure continuity of the clan and the adequate care of the parents when they died and became ancestral spirits , but they were also economically profitable , a girl child fetching , on marriage , some ten head of cattle ( highly prized on both economic and religious grounds ) from the prospective bridegroom . 
Fertility in women was thus an attribute of paramount importance . 
In any marriage without issue the woman was , almost invariably , regarded as the sterile partner . 
In only two ways could women ever assert power in any public fashion . 
On one day in the year they were allowed to dress as men , tend the cattle , drink beer in a masculine fashion , sing obscene songs and beat any man found outside the huts . 
Also any woman , if possessed by the spirits of the dead ancestors , could become a diviner — usually called in lay description " a witch-doctor " . 
During the period of her emergence into this ro5le the possessed person ( ninety per cent of diviners were and are women ) became very ill , showing gross symptoms of mental disturbance , — in our society the label " psychotic " would probably be applied — and then often recovered to take up her profitable and public duties as a diviner of the causes of harm in the society such as illness or the results of bewitchment . 
To the people , a kind of Harley Street consultant . 
So much for a very brief summary of the position as it was . 
What of the analogous situation today ? 
There is no longer a Zulu King , the temporal and spiritual head of his people . 
Tribal authority has been taken over , in all really effective aspects , by the white man . 
The tribal lands have been drastically restricted in area . 
In order to make ends meet some eighty per cent of all men of working age ( between sixteen and fifty ) have to be away from home for some ten months in each year , working hundreds of miles away in the mines and factories of the white man . 
The Zulu extended family has , usually , been broken up , and the traditions and regulations of the tribe are becoming a dead letter . 
Many Zulu have become Christians , abandoning , at any rate nominally , the worship of the ancestors . 
Polygyny is rare , and becoming rarer . 
Poverty and malnutrition are rife ; infant mortality is some 350 per 1000 live births . 
Both tuberculosis and venereal disease have become common disorders — the latter exacerbated by the promiscuity engendered by the migrant labour system . 
What of the Zulu woman in all this ? 
She will still work in the fields though they can not produce enough food for herself and her children . 
She will have to tend the cattle , an unthinkable action in the indigenous situation . 
She is still subject to the control of her mother in law . 
She is less likely to be pregnant and to bear a live child ; conception is more improbable with her husband away for a large part of the year and here too venereal disease rates are of relevance . 
On average , she will have had two or three years of Western education . 
Even if she has been to school for a much longer time she may not be allowed to work in the distant towns . 
The transvestite ceremony of the one day in the year has fallen into desuetude , but the Zulu woman can still become a diviner and there are as many of these — probably more — than there ever were . 
Here , then , we have a classic picture of general social stress as it has usually been conceived . 
It is obvious that the Zulu woman could be affected at many levels of her functioning by the pressures inherent in the general situation , and many theorists would argue that some new forms of pathological behaviour were to be expected or , at least , that one would expect an increase in the rates of known types of mental disorder in the population . 
Has either of these possibilities come to pass ? 
This is an extremely difficult question to answer but , possibly rashly , I am inclined to say " yes " . 
About 1897 the crying began — umHayizo or isiPoliyane — it goes under different names . 
But none of these names , as far as I can ascertain , had appeared in the language before this date . 
There is no mention of this very specific behaviour in the written records of travellers , missionaries or lexicographers , though other aberrant forms of behaviour such as spirit possession had been named and described from 1820 onwards . 
The people themselves date the symptoms from 1897 , " after all our cattle had died in the greatest rinderpest epidemic " . 
But why should simple " crying " be regarded as pathological ? 
It is , in fact , anything but simple and ordinary . 
A Zulu woman may suddenly begin to cry out { " Hayi ! 
Hayi ! 
Hayi ! " or { " Zza ! 
Zza ! 
Zza ! " or to make guttural grunting screams . 
She may keep this up for hours , days , even weeks on end , ceasing only during sleep . 
By our standards this looks , and sounds , most peculiar and most earlier observers unhesitatingly adjudged it pathological . 
Various ethnologists , doctors and missionaries stated that the crying was directly caused by : epilepsy ; alcoholism and the breakdown of the old social order ; abnormal sexual habits ; forbidden or unfulfilled sexual wishes ; " gain by illness " ; the use of love charms by men ; even " Hamletism " . 
Once a " reason " for the behaviour had been stated no further investigation was , generally , felt to be necessary but there are implications of a stress situation in most of the hypotheses advanced . 
Observers tended to assume that the crying was a discrete reaction — a single and separate bit of behaviour in its own right . 
At any rate , using interviews , questionnaires and a projective test ( asking my subjects to tell stories about pictures which were illustrative , I hoped , of the " stress points " of the culture ) I spent some years trying to find out about this very clear cut kind of behaviour . 
I hope that some of my findings may serve to illustrate various levels of adaptation , the possible utility of some apparently " maladaptive " symptoms , and to demonstrate that this pattern of behaviour is anything but discrete and that it has a logic of its own as an integral part of the personality of the screamer . 
Firstly it emerged that while some ten per cent of men reported that they had suffered occasional attacks , almost exactly half Zulu women showed a history of the crying fits . 
This fact emerged on three separate occasions from random samples totalling some thousand women . 
This made the use of a quantitative criterion for normality ( is it more normal to scream than not to scream ? ) unprofitable , and I went on to examine related phenomena to try to establish the nosology and aetiology of the condition . 
Using as a control group those women who had no history of such crying I found , on a statistical basis , that the crying was not linked with " hysteria " as I had thought likely , but that it was highly significantly associated with a history of such classical symptoms of anxiety as precordial pain , sweating hands and feet , apparently "causeless " fear etc . 
The screaming represented an immediate reaction to fear . 
The subject felt overpowering terror , the physical sensation of which was localised between the shoulder blades , and cried out . 
This could be precipitated by many different stimuli in the environment , a snake , a clap of thunder , a sharp word or even , subjective and very common , " a feeling of anger " . 
In effect , what I was investigating was probably a sudden discharge of anxiety in the form of an immediate , but prolonged , fear reaction . 
Here , too , the interesting finding appeared that the cryers were , if anything , less prone to most symptoms of conversion hysteria than were the controls . 
There seemed a possibility that this relative immunity from hysterical blindnesses , paralyses etc. was connected with the crying fits as this was a central difference between the two groups ; the categories of cryers and controls having been established after all the questions had been asked , on the basis of whether the reply to the question " Have you ever had crying attacks ? " was positive or negative . 
But there was one exception to this freedom from hysterical conversion . 
Women with a history of pseudocyesis , common in the area , and itself a classical symptom of conversion hysteria , were practically all to be found in the crying group . 
This was of particular interest for two reasons . 
Firstly it was an exception to the relative lack of proneness to conversion shown by the screamers , and the reasons for this exception thus seemed worthy of close investigation . 
Secondly , in terms of the literature , such pseudo-pregnancy has often been regarded as the result of a strong but unavailing wish for a child , especially when the woman is under strong social pressure to produce a baby — the obstetrical history of some Queens of England where an heir to the throne was required is a case in point . 
Piaget stresses that children can not visualize the results of the simplest actions until they have seen them performed , so that a child can not imagine the section of a cylinder as a circle , until he has cut through , say , a cylinder of plasticine . 
As always for Piaget , thought can only take the place of action on the basis of the data that action itself provides . 
While experience and general cultural opportunities are of great importance in helping the child to develop his concepts of space , it must not be forgotten that genetic causes , and temperament , play important roles too , especially the former . 
It has long been known that ability to manipulate shapes in the mind is present by 10-12 years of age , independent of measured intelligence . 
Further , girls possess this ability to a lesser degree than boys , and it is likely that their inferiority in this respect is in part due to the differing kinds of activities in which they engage . 
It was suggested , too , by El Koussy in 1935 , that the ability depended on the capacity of the individual to obtain , and the facility to utilize , visual spatial imagery . 
El Koussy 's point of view has recently received a little support from the work of Stewart and Macfarlane Smith ( 1959 ) using the electroencephalograph . 
Piaget would certainly admit that imagery supports spatial reasoning and geometrical thought , but is not in itself sufficient . 
CHAPTER NINE Concepts of Length and Measurement 
BEFORE children come to school they are likely to hear many expressions used by adults and older children in relation to length and measurement . 
For example , most children hear their mothers speak of yards of material , or — less often — their fathers speak of feet of timber , or of the distance to the station or nearby town . 
More frequently , however , they hear of comparisons rather than the names of actual lengths , such as " This is longer than that " , or " That is higher than this " . 
These expressions are associated with many experiences ranging , maybe , from the length of nails to the height of mountains . 
Likewise a child hears terms like " near " and " far " in relation to nearby or distant towns . 
Again , from his play , or through watching the activities of grown-ups , he learns that a piece of string may be made shorter by cutting a piece off , or a stick made shorter by breaking it . 
Likewise he learns that sticks and ropes may be joined to other sticks and ropes and so made longer . 
Later we shall say a great deal about the view of the Geneva school regarding conceptual development in relation to length and measurement . 
It is sufficient to say here that it is out of these pre-school and out-of-school experiences , and out of infant school activities such as take place in the " free choice " period , that the child comes to understand the quality of longness or length — that is , the extent from beginning to end in the spatial field . 
During these experiences the child moves from visual , auditory and kinaesthetic perceptions , and actions to concepts . 
In activities involving counting a child may be asked to count the number of steps he has to take to cross the classroom . 
Another child will be found to take a different number of steps . 
Or , the lengths of short objects may be measured by the foot — the distance from heel to toe — or by the span from little finger to thumb when the hand is stretched as far as possible . 
From a variety of similar exercises the teacher can help her children to understand the need for a fixed unit of length for measuring purposes . 
Of course , mankind has had exactly this problem of establishing fixed units , and a little history of measurement is an enjoyable and stimulating piece of work for older junior pupils . 
By the upper end of the infant 's school the faster learners will be ready to be introduced to one of the agreed units of measurement , viz the foot . 
Lengths of wood or hardboard , or plain foot rulers without end pieces or sub-divisions — which can be purchased — are given to the children , and they are instructed to measure various lengths and record their answers in a notebook . 
In the early stages they should be set to measure the lengths of lines drawn on the blackboard or floor , or to measure the length of pieces of string , paper , etc , all of which are cut to an exact number of feet in length . 
Later , they can be set to measure the length of other objects in the environment to the nearest foot , so that if an object is nearly 3 feet long it is recorded as a full 3 feet . 
It is good , too , to let children estimate lengths before they measure , in the hope that it will lead to estimation with increased accuracy . 
With experience and maturity the pupils naturally become dissatisfied with a ruler that permits measurement to a foot only , for there are so many bits and pieces left over . 
This is the moment to introduce the inch , and a foot stick or foot ruler with inch marks on it . 
At the same time have work cards available on which there are lines drawn to an exact number of inches , or lengths of string and paper similarly cut for the pupils to measure . 
The next step is the measurement , to the nearest inch , of objects in the environment ; the children ought frequently to express their answer as , say , 1 foot 3 inches and as 15 inches , for this will help them to understand the relationship between two units used in the measurement of length . 
Soon they will be found to be ready for a wall scale by means of which they can measure each other 's height . 
This is an activity that creates great interest , since personal dimensions and growth are of great consequence to most children . 
Next we come to the yard and yard stick ; a necessary unit when measuring longer distances . 
It is helpful to have some rulers divided into 3 feet with alternate sections , say , red and white , and a second set divided into 36 inches , with alternate inches of different colours . 
After comparing these with the whole foot , and with the 12-inch ruler previously used , the teacher should show that the yard ruler or stick is comparable with the length of her stride . 
By means of graded exercises similar in type to those described for feet , and feet and inches , we hope to get the child to the stage where he can measure a length as , for example 2 yards 1 foot 9 inches . 
The ordinary foot ruler with end pieces , and fractions of an inch up to 1/10 or even 1/16 inch , can be introduced when pupils are ready for it , but with the very slow learners simplified rulers may have to be used throughout the junior school . 
So far , activities and experiences that presuppose that the concepts of length and measurement are possible for children have been dealt with . 
Have we , however , any clues as to the first beginnings of these concepts ? 
Are there any conditions which are necessary before understanding of length can take place at all ? 
The Geneva school led by Piaget has carried out many interesting experiments in this field to which we now turn . 
THE VIEWS OF THE GENEVA SCHOOL ON THE DEVELOPMENT OF CONCEPTS RELATING TO LENGTH AND MEASUREMENT 
Piaget , Inhelder , and Szeminska ( 1960 ) have outlined the views on the way in which the child comes to understand length and measurement . 
In one of the experiments reported early in their book they study his spontaneous measurement . 
The experimenter showed the child a tower made of twelve blocks and a little over 2 feet 6 inches high — the tower being constructed on a table . 
The experimenter told the child to make another tower " the same as mine " on another table about 6 feet away , the table top being some 3 feet lower than that of the first table . 
There was a large screen between the model and the copy but the child was encouraged to " go and see " the model as often as he liked . 
He was also given strips of paper , sticks , rulers , etc , and he was told to use them if his spontaneous efforts ceased , but he was NOT told how to use them . 
The following stages were observed : 
( a ) up to about 4 1/2 years of age there was visual comparison only . 
The child judged the second tower to be the same height as the first by stepping back and estimating height . 
This was done regardless of the difference in heights of the table tops ; 
( b ) this lasted from 4 1/2 - 7 years of age roughly . 
At first the child might lay a long rod across the tops of the towers to make sure they were level . 
When he realized that the base of the towers were not at the same height , he sometimes attempted to place his tower on the same table as the model . 
Naturally , that was not permitted . 
Later , the children began to look for a measuring instrument , and some of them began using their own bodies for this purpose . 
For example , the span of the hands might be used , or the arms , by placing one hand on top of the model tower and the other at the base and moving over from the model to the copy , meanwhile trying to keep the hands the same distance apart . 
When they discovered that this procedure was unreliable , some would place , say , their shoulder against the top of the tower ( a chair or stool might be used ) and would mark a spot on their leg opposite the base . 
They would then move to the second tower to see if the heights were the same . 
The authors point out that in their view this use of the body is an important step forward , for coming to regard the body as a common measure must have its origin in visual perception when the child sees the objects , and in motor acts as when he walks from the model to its copy . 
These perceptions and motor acts give rise to images which in turn confer a symbolic value first on the child 's own body as a measuring instrument , and later on a neutral object , e g a ruler . 
( c ) from 7 years of age onwards there was an increasing tendency to use some symbolic object ( e g a rod ) to imitate size . 
Very occasionally a child built a third tower by the first and carried it over to the second : this was permitted . 
More frequently , though , he used a rod that was exactly the same length as the model tower was high . 
Next , the child came to use an intermediate term in an operational way ( i e in the mind ) , this , of course , being an expression of the general logical principle that if A=B , and B=C , A=C . 
Children were found to take a longer rod than necessary and mark off the height of the model tower on it with a finger or by other means , so as to maintain a constant length when transposing to the copy . 
But , this transference is only one aspect of measurement ; the other aspect which must be understood is sub-division ; for only when this , too , has been grasped can a particular length of the measuring rod be given a definite value , and repeated again and again ( iteration ) . 
In the final stage it was found that children could also use a rod shorter than the tower , and it was applied as often as was necessary ; so that the height of the model tower was found by applying a shorter rod a number of times up the side . 
For the authors , then , the concept of measurement depends upon logical thinking . 
The child must first grasp that the whole is composed of a number of parts added together . 
Second , he must understand the principles of substitution and iteration , that is the transport of the applied measure to another length , and its repeated application to this other . 
( 7 ) Equilibrium in the Hydraulic Press . 
An all-glass 50 c.c. hypodermic syringe , the piston of which could be loaded with different weights , was connected to a length of narrow glass tubing . 
Alongside was an exact duplicate of the apparatus so the subject could work with two liquids of different densities at the same time . 
One liquid was tap water tinged very slightly red , and the other was concentrated salt solution tinged very slightly blue . 
( 8 ) Equilibrium in the Balance . 
The balance arm ( and the associated supporting framework ) was made from Meccano strips . 
By this means the distance of the weights from the fulcrum could be quickly obtained . 
The weights were cut so that the weight plus attached hook weighed 2 , 5 , 10 or 20 g . 
( 9 ) Projection of Shadows . 
( 10 ) Correlations . 
Each of forty postcards had the head of a girl drawn on it . 
The shape of the face , hair style and colouring differed for each girl , but the hair and eyes were coloured as indicated in the book . 
Inhelder and Piaget give no stages earlier than 3A , but the writer laid down criteria for 1 , 2A and 2B stages . 
Subjects 
Our population consisted of 34 average and bright primary school pupils ; 14 average and bright preparatory school pupils ( aged 8-11 years ) ; 39 grammar school pupils ; 50 secondary modern school pupils ; 50 comprehensive school pupils ; 10 training college students ; 3 able adults whose ages ranged from 25 to 32 years of age ; thus making 200 subjects in all . 
In the comprehensive and secondary modern schools approximately equal numbers were drawn from the top and bottom streams of each year group . 
General technique 
Each subject was examined , individually , on four experiments , with everyone taking the experiment involving the combinations of colourless chemical liquids ( no. 5 ) . 
After the subject had been introduced to the materials , and after some general discussions and sometimes free experimentation , he was asked to perform certain standard tasks and asked certain standard questions . 
The subject 's actions were noted and his replies recorded verbatim . 
Details of the exact procedure used in each experiment may be obtained from the writer . 
It must be stressed , however , that the experimenter was quite free to vary the procedure by asking supplementary questions , or by prompting , or by experimenting slightly differently , if he thought it would be helpful . 
In brief our procedure was semi-structured and this is the best that one can do if the clinical approach is to be combined with some degree of standardization of procedure . 
The subjects were asked " to think aloud " as much as possible . 
Usually Inhelder and Piaget give details of three stages of thinking ; stages 2 and 3 usually being subdivided further into " A " and " B " stages . 
After examining our protocols it was thought better to subdivide the Inhelder and Piaget stages still further , and we usually used nine stages , viz : 
1 ; 1-2A ; 2A ; 2A-2B ; 2B ; 2B-3A ; 3A ; 3A-3B ; 3B . 
In this way we were , in our opinion , able to classify our protocols within the framework provided by the authors . 
Each protocol was studied by the writer and by the experimenter independently , and given a rating on the scale of stages . 
The results were compared and after discussion a final rating was given to each protocol . 
The assessment of some of the protocols was not an easy matter , and we can not be sure that the more difficult ones were always rated correctly , although the ratings of these are not likely to be more than one stage out in the nine-stage scale that was usually used . 
In the experiment involving invisible magnetization the authors give a stage 3 only , not stages 3A and 3B , and we have kept to this . 
3 . 
RESULTS 
A number of tables are now given showing how the different groups performed on the various experiments . 
All our results are included . 
It is important to know to what extent the level of thinking of our subjects remained the same throughout the four experiments that each one undertook . 
To determine this we used Kendall 's coefficient of concordance W , which specifies the degree of association between a number of sets of rankings . 
First , the rank of each subject was calculated , separately for each of the four experiments . 
W was then calculated from formula 9.16 given by Siegel ( 1956 ) , p. 234 ; this allows for tied observations . 
Furthermore , if the total number of cases concerned is N , and N 7 , we may find the probability of any value as large as an observed W , by calculating xe2 = , with d.f . 
= N-1 , where k is the number of sets of rankings ( Siegel , 1956 , p. 236 , formula 9.18 ) . 
Accordingly xe2 was calculated for each W and the probability associated with so large a value of xe2 was found by referring to Siegel ( 1956 ) , Table C , p. 249 . 
Table 11 shows the values of W , and the probability of finding an associated xe2 as large , Pxe2 , for the differing groups of experiments and subjects . 
Even if there is a substantial degree of association between the level of thinking displayed by our subjects on each of the four experiments , it is necessary to determine if the experiments ( coupled with the manner in which the protocols were assigned to stages by Inhelder and Piaget ) were in fact drawn from the same population of experiments . 
For example , it could be that a particular experiment was rather easier or more difficult for one reason or another . 
Accordingly the Kruskal-Wallis one-way analysis of variance by ranks was used , as this test will decide if a number of different samples are drawn from the same population . 
The test assumes only that the variables studied have an underlying continuous distribution , and that ordinal measurement is possible for each variable . 
These conditions are fulfilled in the case of our data . 
First , the total number of subjects at each stage on each of the four tests was calculated , and the rank of each subject found from the single series that resulted . 
Thus H , the statistic used in the Kruskal-Wallis test , was calculated from formula 8.3 given by Siegel ( 1956 ) , page 192 , as this allows for tied observations . 
Since in our case there were four samples , and the number of subjects in each sample is greater than five , H is distributed approximately as xe2 with d.f . 
= k-1 , where k is the number of samples . 
Once again the probability of finding a xe2 as large as H was found by referring to Siegel , Table C , page 249 . 
Hence Table 11 shows also the probability of finding a xe2 as large as H , PH , for the differing groups of experiments and subjects . 
The results of the remaining ten training college students were not analysed in this manner on account of the smallness and homogeneity of the sample . 
The four experiments which they undertook were : Chemical Combinations , Pendulum , Invisible Magnetization , and Equilibrium in the Balance . 
Reference to the values of PH in Table 11 shows that the experiments in the first , second and fifth groups may be regarded as random samples drawn from the same population of experiments . 
In the third and fourth groups , however , PH < 0.01 indicating thatone or more experiments in each group cannot be so regarded. Experience gained in examining the subjects indicated that the Projection of Shadows , and Correlations experiments found in the third and fourth groups , respectively , were likely to be responsible for this . 
Consequently the remaining three experiments in each of these groups were subjected to the Kruskal-Wallis test ; and for each of the two groups of three experiments the value of H so obtained was such that PH 0.05. 4 . 
DISCUSSION 
The following discussion deals principally with the educational implications of the study , and in order to be succinct the findings are grouped under a number of points . 
( 1 ) The main stages in the development of logical thinking proposed by Inhelder and Piaget have been confirmed . 
It seems that the authors are correct in suggesting that it is only rarely that average to bright junior school children reach the stage of formal thinking . 
The ablest of the secondary modern and comprehensive school pupils certainly attain the stage of formal thought , but not all the older grammar school pupils always do so . 
There is a suggestion that ill-digested snippets of knowledge , mental set , and expectancy , are affecting thinking more in the students than among the school pupils . 
The student with the poorest performance was aged 19 years , and on the four experiments her replies were classified at the 2A , 2B , 2B and 2B-3A stages . 
She had obtained a pass in Art at G.C.E. " A " level . 
However , the least able of the secondary modern and comprehensive school pupils certainly remain at a low level of logical thought even at 15 years of age , and many of these do not seem to pass beyond the 2A-2B stage of thinking . 
This is a finding the authors do not mention , and it leads one to suspect that the school population in Geneva which they examined consisted of able children . 
( 2 ) By getting each subject to undergo four experiments and analysing the results by means of a non-parametric statistical technique , it has been possible to show that there is a considerable agreement between the levels of thinking that the subjects display in the four experiments . 
Moreover , the value of the coefficient of concordance W declines as the population becomes more homogeneous with respect to mental age . 
Naturally there is no exact correspondence since the experiments and "intelligence " tests do not measure exactly the same thinking skills . 
Among the preparatory and grammar school pupils , W = 0.89 , and among the primary and grammar school pupils W = 0.81 ( Table 11 ) . 
In these groups the Mental Ages of the pupils ranged from 8 years to well above 15 years ( the M.A. usually accepted for average adults ) , whereas in the primary school group alone , for which W = 0.52 , the mental ages would range from 8 to 13 or 15 years . 
The authors give no evidence on this issue , but one would certainly expect some such stability of thinking skills if their general theory is correct . 
Again the Kruskal-Wallis test gave reasonable grounds for assuming that eight of the ten experiments may be regarded as samples drawn from the same population of experiments . 
The Correlations experiment is too easy for secondary , but not for primary pupils , compared with the other eight experiments ; while the Projection of Shadows test placed too many subjects at stage 2B . 
( 3 ) The majority of our protocols show much the same kind of reasoning as those of Inhelder and Piaget , and support many of their statements . 
For example , the authors maintain that , at the level of formal thought , the child comes to the Projection of Shadows experiment assuming proportionality from the start . 
Below is a copy of part of the protocol of a boy aged 13 years 3 months . 
" What happens to the shadow as you move the ring up and down the scale ? " 
" Nearer the wall smaller , further away bigger . " 
" Use two rings of different size , and move them until their shadows are exactly the same size , that is , they cover each other exactly . " 
Places the 5cm. diameter ring at 20 cm. from light , and 10 cm. diameter ring at 40 cm . 
" Why do the rings have to go in these positions ? " 
" Well 10 is twice 5 , and 40 is twice 20 . " 
After placing three rings of different diameter correctly in position he is asked to place four rings of different diameters in position so that their shadows coincide . 
He places 5 cm. ring at 10 cm. from light , 10 cm. ring at 20 cm. , 15 cm. ring at 30 cm. , and 20 cm. ring at 40 cm. from light . 
" Tell me exactly what you have done about the position of the rings . " 
" Well 5 is 10 cm. from torch , 10 is twice as big so it goes at 20 cm. , 15 is half as big again so it goes at 30 , and 20 is twice 10 so it goes here at 40 . " 
Unfortunately , Story does not break down her data for monocular viewing according to whether T- and I-figures were on the same or opposite sides as the eye used so that this prediction would only apply to half the trials she reports . 
Nevertheless , there is no sign of this trend in her results for monocular viewing . 
( 3 ) The effects to be expected due to the different spatial positions of the two eyes should be even more striking when the distance between shape and eye is less than in Story 's experiment , and when the I-figure is shown to one eye and the T to the other : although these conditions have often been used in experiments on FAE no effects of this sort have been reported . 
( It might , however , be worth looking for them in future experiments. ) ( 4 ) Finally , although Story suggests that the different visual angles subtended by the figures at the retinae might be the explanation of the effects obtained under binocular viewing , she does not show in detail how these effects would be predicted by the geometry of the situation , and it is difficult to see how the effects found could in fact be produced in this way . 
Nevertheless , the suggestion is an interesting one and could be followed up by experiments in which the figures are placed closer to the eye and conditions of alternating monocular viewing are employed . 
It is possible that the reason why the A-effect is obtained only when both eyes are used is that binocular vision itself provides a cue to the distance of the figures and thus to their relative apparent sizes ( v. below ) : thus , the fact that the effect only occurs with binocular viewing does not necessarily conflict with the hypothesis that under some conditions the FAE may be determined by apparent size , and indeed can be interpreted within the framework of this hypothesis . 
Size of circles 
If smaller circles than those used by Sutherland are employed , the A-effect does not occur ( Day and Logan , 1961 ; Terwilliger , 1961 ; McEwen 1959 ; Oyama , 1956 ) : the usual result under these conditions is that the T-circle looks smaller than C whether I is nearer or further away . 
( It should be noted that Terwilliger did not obtain this result : when the retinal size of T and I was the same , he found no change in the apparent size of T. ) This effect is also found when T and I shapes are the same distance away as one another ( Day and Logan ( 1961 ) , cf. also Ko " hler and Wallach ( 1944 ) ) . 
Day and Logan make the interesting suggestion that this shrinkage may resemble a time error effect though they do not discuss the details of how this might occur . 
Unfortunately , from what is known about time errors , one might expect the opposite effect with small circles . 
When a series of stimuli are being judged , there is usually a point in the middle of the series where ( after practice ) there is no constant error : above this point , time errors tend to be negative , below it , positive . 
We shall call this point the " adaptation point . " 
Subjects will have an adaptation point at the start of an experiment and it will usually be shifted in the course of the experiment : now when a small circle is shown as I-figure this should shift the adaptation point downwards . 
If it shifts it downwards further for that part of the visual field on which the I-figure is shown than for other parts , we would expect the T-figure to be judged larger than the C-figure : the T-figure is less far away from the adaptation point at that part of the visual field than is the C-figure from the adaptation point at its part of the visual field . 
Day and Logan obtained exactly the opposite result to this . 
Thus , there is some difficulty in applying this type of explanation , though the correspondence between the change in direction of the FAE with different sized circles ( found by Day and Logan ) and the change in direction of TE ( found by Watson , 1957 ) is very suggestive . 
Nevertheless , Day and Logan 's work does make it difficult to interpret the A-effect as due to differences in apparent size because of their finding that when large circles are used and both are far away , the T-circle appears larger than the C. Outline and filled-in circles 
Day and Logan show that the A-effect occurs with outline circles but not with filled-in circles : it is hard to see what explanation could be offered for this at present . 
Further discussion 
One very ingenious recent experiment has demonstrated in a most convincing way that an FAE determined wholly by apparent size does occur under certain conditions : Gregory ( personal communication ) has shown that if the apparent size of a figure is made to shrink continuously while the retinal size remains the same , when the shrinkage in apparent size is stopped suddenly there is a dramatic increase in the apparent size of the figure . 
This phenomenon is very striking and is seen by all observers . 
Since this shows that a FAE determined by continuous change in apparent size can occur , the question arises of why it is so difficult to demonstrate the effect with static figures . 
There are three possible answers to this . 
( 1 ) It may be that just as with FAE due to retinal size , the effect through apparent size only occurs if the difference between the apparent sizes of the T- and I-figures is optimal ( cf. the distance paradox ) . 
If this is correct , we would only expect to obtain a FAE due to apparent size under limited conditions . 
This suggestion could be tested experimentally by keeping one circle a constant size and distance and varying the size and distance of the other keeping retinal size equal . 
We would expect an effect due to apparent size to occur only within a limited range of size and distance of the other figure . 
In Gregory 's experiment , because the apparent size of the inspection figure changes continuously , these changes are bound to straddle the point which would be optimal for producing the effect . 
( 2 ) The conditions of the experiments performed with static figures are such that there may be a temptation to judge in terms of retinal size : it is known that when two shapes of different real size are aligned side by side , subjects tend to make judgements in terms of retinal size ( Joynson and Kirk , 1960 ) . 
It would be interesting to test for the occurrence of the A-effect , using for T- and C-figures two shapes of the same physical size but different retinal sizes at different distances away from the observer and not aligned opposite one another . 
The T-circle could be kept the same retinal size as the I , and the C-circle would be a different retinal size : subjects would be asked to compare the real size of T- and C-figures . 
These experimental conditions should tend to favour judgements in terms of apparent physical size rather than apparent retinal size . 
( 3 ) It may be that apparent size only influences FAE when the apparent size has changed continuously , i.e. where there has been an apparent movement effect : if established this would be an important finding since it would reveal a difference in the mechanisms underlying apparent movement and judgements of apparent size ( v. below ) . 
This could only be established by a thorough investigation of the static A-effect along the lines set out in ( 1 ) and ( 2 ) above . 
THEORETICAL CONSIDERATIONS 
The work of Hubel and Wiesel ( 1959 ) suggests a new theoretical approach to FAE problems . 
In order to see the experiments described above in perspective , it may be worth setting out briefly what this approach is : it has suggested itself independently to a number of workers in the field , and Papert is currently engaged on testing some of its implications . 
It must be stressed that a new approach is necessary since the sort of theory espoused by Ko " hler and Wallach ( 1944 ) and by Osgood and Heyer ( 1952 ) is unable to account for many of the phenomena of FAE . 
They both assume that inspection of a contour results in any contour subsequently falling near the second contour being seen as displaced away from it : the amount it is displaced is said to depend upon the distance separating the two contours on the retina , and there will be a point at which displacement is maximal . 
Three instances of well attested phenomena which this theory is unable to explain will be quoted . 
( 1 ) In Figure 1 , if the I-line is fixated , the T-line should appear as shown ( P ) : displacement should be small where I and T lie near together gradually increasing to a maximum and then decreasing . 
In fact T is seen occupying the position of line A. ( 2 ) Similarly when a curved line is shown , and a straight line used as I-figure , the straight line should appear like line P in Figure 1 ( b ) but in fact appears like line A. ( 3 ) The theories are unable to account for the after effect of seen motion . 
Both theories under discussion assume that the FAE occurs before any analysis of the stimuli is undertaken . 
Hubel and Wiesel have demonstrated by recording from single cells that in the cat considerable analysis of the stimulus on the retina occurs at or before the level of the striate cortex . 
In particular they present evidence to show that in the striate cortex there are cells whose response is determined by the orientation of lines on a given part of the retina ; i.e. the orientation of lines is coded in separate fibres at this level of the cat visual system . 
If we assume that there are cells with similar receptive fields in human beings we have a very simple explanation of the effect shown in Figure 1 ( a ) : inspection of a line in one orientation will result in heavy firing of the cells maximally responsive to lines in this orientation , and to some firing of cells maximally responsive to lines in neighbouring orientations . 
If any adaptation occurs in these cells as a result of prolonged firing , when a T-contour in a slightly different orientation to the I line is exposed on the same part of the retina , the cells fired maximally by it will be ones which are normally maximally responsive to contours in orientations lying further away from the orientation of the I-figure . 
It is reasonable to suppose that the orientation in which a contour is seen will depend upon the balance of firing in cells representing contour orientation : the firing in any one cell will be determined partly by the contrast of the contour with its background , etc. , but such effects would be balanced out if the ratio of firing in all cells sensitive to orientation in a given region of the retina were computed . 
If there are also cells sensitive to curvature of a line a similar mechanism would explain the sort of finding depicted in Figure 1 ( b ) . 
As yet there is no physiological demonstration of the existence of such cells . 
Hubel and Wiesel have , however , found cells which respond differentially according to the direction in which a stimulus is moved across the retina . 
If direction of movement is coded in single cells in human beings , adaptation in these cells might clearly underly the after-effect of movement . 
Once again the direction in which something is seen to move might depend upon the ratios of firing in cells sensitive to movement in different directions , and after prolonged movement in one direction a stationary image would produce less firing in the cells which had just been stimulated than normally , hence apparent movement in the opposite direction would be seen to occur . 
This explanation of FAE is based on sound physiological evidence and is so simple that it seems highly convincing . 
It does not , however , explain mere displacements in apparent spatial position occurring as a FAE : for this phenomenon , the Osgood and Heyer type of explanation appears reasonably plausible . 
This explanation in fact fits well with the explanation outlined above since Osgood and Heyer argue that the position at which a contour is seen itself depends upon ratios of firing in different cells . 
It is wondered if such a boy requires inspiration which might be got by tactful film teaching in the classroom . 
Indeed it might be questioned what he does learn at school . 
His untidy , dirty , badly spelled and careless paper does not indicate much attainment . 
Further information about viewing tastes comes out in the last two questions of the paper where the young people were asked in what way they preferred cinema to television and { 6vice versa . 
Again it is not easy to tabulate these written answers but they do fall into a fairly regular pattern . 
Unfortunately 26% do not answer the question . 
23% merely say they do not prefer television to cinema without any explanation and a small number 13% that they do not prefer cinema to television . 
Most of the reasons of those who prefer the cinema have already been discussed — the colour , the stars , the choice , the company and so on . 
The television supporters have other reasons . 
These are not all concerned with the content . 
23% , almost equally boys and girls , prefer to do their viewing in the comfort of their own homes . 
10% of the boys and 13% of the girls prefer television because they do not have to wait in a queue and have a cold journey home in a bus after the show . 
They do not get cold and wet and " even if the TV programme is not so good you feel better on a miserable night . " 
11% of the young people like TV because it is cheaper , at least so far as they are concerned . 
They are pleased to switch it off when they do not like the programme or change to the other channel . 
2% prefer to do their viewing at home because the atmosphere is not so smoky nor so stuffy . 
Others rising to 3% of the 18-year-old boys prefer television as they do not require to " dress up to go and see it . " 
Five secondary 15-year-old girls say the same . 
A 17-year-old girl civil servant , however , comments that cinema " is not so compelling as TV and being away from the home it does not make you lazy . " 
Another 17-year-old at secondary school says , " TV makes you lazy — most people become too lazy to make the effort to go to the cinema . " 
Another 15-year-old says , " My parents know the cinema is better but they ca n't be bothered going out and the TV gives them something to look at . " 
A small number of 15/16-year-old boys who have recently started work say that TV is " all right for Sunday when you ca n't get into the pictures . " 
This attitude only appears with a small percentage , about 1/5% of the boys and not at all with the girls . 
Other reasons for preferring TV other than the content of the programme are numerous . 
A 16-year-old secondary schoolgirl says , " At a cinema you can not do what you want , lie on the floor , get up when you like , shout at the people you do n't like but you can with TV . " 
This freedom in viewing is implied in a number of answers . 
A 14-year-old girl puts it , " You get peace and quietness to do what you like , " and an 18-year-old boy gets satisfaction , " You can blast at the stupid things seen and know you will not be put out . " 
A 15-year-old says , " There is peace and tranquility at home — you can leave and study when inclined . " 
Another 15-year-old boy probably explains this when he says you can " turn it off or go and do something else without feeling you have wasted money . " 
Television is blamed by a secondary schoolboy as "anti-social and leads to unfriendliness . " 
A girl of the same age also thinks " TV is anti-social . " 
This aspect is also mentioned by a number of others who repeat the objections that have often been made about radio controlling the home , when the family have to be quiet when one member is listening . 
Perhaps the most unexpected reply in this section came from a junior secondary boy of 15 , "Our rented TV was removed by my request six weeks before the exams in March . " 
A considerable number , although having TV in the home , " prefer watching TV in a cafe or at my mate 's house " or " in the girl 's home — it is cosier . " 
A few older boys translate this into , "It 's friendlier seeing TV with a pint in the pub . " 
Others find television useful as background to other activity . 
A 14-year-old boy confesses , " You can neck and kiss your girl in peace when dad and mum go to the pictures . " 
Another , aged 15 , finds " fireside comfort with a girl when family is out . " 
At 17 a boy claims , " It is warmer at home especially if you are in alone with the girl . " 
Another aged 14 with a dirty paper says , "I only watch TV when my parents have gone out so I can get peace to watch TV and my smoke . 
I really prefer cinema so that I can get out of the house and get rid of my moaning family . " 
Although they do not come into the enquiry proper it is interesting that two 19-year-old members of a boys ' youth club prefer TV because "you can sit back with a pie and a pint . " 
One feels sympathy for the 15-year-old girl who likes TV but goes to the cinema for " peace and quiet compared with noise at home . 
— There are six children at home . " 
Actual tastes in television viewing have already been discussed in the section on favourite TV programmes . 
The western is popular with both sexes and all ages . 
Sports play a large part in boys ' viewing . 
On the whole it is difficult to know who chooses the programme to be viewed . 
Two secondary girls of 15 would rather go to the cinema to see what they like . 
" You do n't have to watch what your parents want , e.g. boxing for 2 1/2 hours or some hopeless advertising programme . " 
" Because your young brother wants to see a stupid quiz programme you have to look as well . " 
Boys in different schools say , " You do n't have the family quarrelling about which channel to go on . " 
Two others say , " You do n't have to watch what younger children want or what parents want . " 
A number of 14/15-year-olds seem to like the serials on television but it is not clear whether they actually mean plays , dramas or novels too long for one evening and therefore continued for a number of weeks or whether they mean a series in which the same characters appear each week . 
" I like to be kept in suspense with serials , " has to be balanced by , " I just long to know what Dixon will solve next week . " 
A considerable number of girls like television dramatisation of novels . 
A few girls mention that TV occasionally gives opera and ballet performances . 
" I would never get a chance of seeing great ballet otherwise , " says one 15-year-old secondary girl . 
Several , of course , include ballet and opera among the types of film they would like to see in the cinema . 
Some add to this " but of course the public would not go . " 
Television music comes in for considerable praise and some of the musical settings are admired . 
" TV music interludes and background music are more enjoyable than that heard in the cinema . " 
" Settings for B.B.C. celebrity recitals help you to understand it better . " 
The commonest favourable criticism of television is that it provides so many programmes of an educational and instructional nature . 
" I like to see how things are made , " says a 15-year-old boy . 
Several secondary schoolgirls comment that Panorama and such programmes help them to " understand some of the things we hear about at school . " 
News programmes are popular . 
Indeed it seems that some boys make the news broadcast a break in their homework . 
An 18-year-old shorthand typist likes newsreels . 
" I would show newsreels . 
The decision banning the newsreel in the cinema is from my point of view absolutely wrong . 
Many people depended on it . " 
" It is marvellous seeing and hearing from famous people what you would n't know anything about if it was n't for TV , " says a 17-year-old student . 
The immediacy which is usually claimed for TV does not seem to be a point in its favour for young people except with sports programmes . 
A girl civil servant of 17 likes TV for showing " older films that we would like to see but were in circulation when we were too young to appreciate them . " 
The nature programmes of TV like Look , Zoo Quest , Safari , etc. , all have those who like them and look forward to them . 
" What a pity the nature programmes can not be in colour . 
The commentator speaks of the beautiful reds and greens but we just see black and white and grey . " 
For this reason we find a considerable number preferring the Disney series of nature films and asking for more . 
Another section of the young people like the dancing programmes . 
The White Heather Club receives more votes than The Kilt is my Delight and the more formal country dance items . 
Rock'n'roll programmes have a good following of the younger age groups and the various stars who have programmes receive votes . 
Tony Hancock is the most popular and Terry-Thomas the least . 
Magicians and illusionists seem to intrigue but some of the variety acts are described as " corny . " 
Plays are more popular with girls than with boys . 
4 . 
Summary and Conclusion 
The tastes of adolescents seem to be affected by their intelligence and their school education . 
There would appear to be great opportunity for teachers and others to inspire their young charges in the junior secondary school and in further education establishments to appreciate what they see at the cinema or on the television screen . 
There seems also a need for such inspiration in youth organisations of all types , not excluding those which have some form of religious background . 
Although the need is not so evident in the case of children attending senior secondary schools whose parents appear to a greater extent to influence their choice of cinema and television programme , nevertheless inspiration in the best types of visual material is just as necessary as instruction in literary , art and musical appreciation . 
The majority still look at films and television for entertainment . 
They seek to enjoy themselves . 
Family pictures are required , appealing to the higher instincts of the young people . 
Too many existing films are condemned by the young people themselves for their appeal to the baser nature of man and the makers and exhibitors are criticised for handling them . 
It is clear that the enormous sums of money spent on advertising films and their stars influence many young people in their choice of picture , but it is encouraging that the young people are not much influenced by the films or by the advertisements to lead a life other than that which happens to be theirs . 
A problem exists for the censor in looking after the morals of the adolescents . 
An " X " certificate assures a good house , according to the young people . 
The majority look at the category of a film before attending the cinema ( Table 5 ) . 
It is a matter for serious examination how so many under-age are able to see " X " films . 
Perhaps the regulations are not strict enough : perhaps they are too difficult to implement . 
Perhaps too many cinemas in a city are showing too many " X " films : perhaps the film makers are failing to produce universally suitable films in the numbers required for the existing houses . 
The cinema is still a popular place of entertainment for adolescents . 
About the same number attend once per week as attended thirty years ago , although fewer attend oftener ( Table 4 ) . 
The star and the type of film are the principal attractions for attending the cinema in 1960 ( Table 6 ) . 
Information about the films is obtained more from newspaper reports than from film magazines ( Tables 7 and 8 ) although nearly half the adolescents do not bother about either . 
Comedy films are most popular at all ages with crime and detection films in second place ( Table 10 ) . 
Small shops supply all the staple foods , and general stores offer a variety of household goods . 
Cheap clothing and furniture stores advertise goods on the instalment plan , and here also numerous shops devoted to repairs and to the sale of second-hand articles are to be found . 
This area has some of the oldest and lowest buildings in the parish , and one cheap cinema . 
Its north-easterly tip abuts on the market of San Ildefonso whose parish was once an annexe of San Marti2n , and it is full of busy taverns . 
4 . 
Fuencarral : forms part of the municipal quarters of Mun4oz Torrero , San Luis , Jardines and Carmen . 
A predominant business and commercial activity marks this area of banks , offices , the central Telephone Exchange , and the type of shop which deals in manufactured goods such as radios , typewriters , office-equipment and shoes . 
Dozens of tailors squat over their sewing in the upper storeys of old buildings and the side streets are studded with craftsmen 's workshops and the comfortable family type of restaurant , notable for its kitchen rather than its prices . 
5 . 
Luna — Desengan4o : belongs in parts to the municipal quarters of Estrella , Mun4oz Torrero and San Luis . 
This is the least definable area of all since its limits link up and merge with all others . 
Most of its buildings are residential , but the four churches it contains also make it the centre of ecclesiastical influence . 
The population of Madrid has trebled in the last fifty years and continues to grow in an increasing proportion ; in 1958 it was estimated at 1,887,000 . 
This rise owes much to migration from the country districts , especially those of the south because of the fall in real wages . 
Even in Madrid 's own province the gain at the expense of the country areas was nearly 2,000 in 1956 . 
Within the city itself , the birth rate has dropped by almost one-third over the same fifty years and , as in all the primate cities , was below the average of 23.43 per 1000 inhabitants in 1953 . 
Urbanization in Spain generally is distinctly correlated with a fall in reproductive rates . 
In San Marti2n the parish church declares that it is in contact with some 5,000 homes , but admits that the total population of the parish fluctuates between 25,000 and 30,000 . 
As the average size family is four or five , the overflow is taken up by approximately fifty hotels and 150 pensiones ( boarding houses ) . 
Density figures of 847 ( 12 square metres per inhabitant ) show that the housing problem is acute , and San Marti2n is , in fact , expanding upwards in the form of higher buildings . 
In the narrow back streets one commonly finds old houses whose bulging walls have been shored up by heavy timbers , often stretching beyond the pavement on to the road surface . 
When these finally topple the landlord is only too pleased , for the rents of pre-Civil War tenants have been controlled and tenancy secured . 
Although he must find alternative accommodation for his old tenants it need not be in the same area ; the loftier the new building , the higher the new rents , so that the previous occupier often has to move out of the parish . 
Thus , the demographic changes induced by the double decline in births and deaths are linked to an increasingly rapid change in the composition of the parish population . 
Money is ruthlessly finding its own level in housing , and as the wave of wealth sweeps from the Gran Vi2a to trickle away into insignificance in the poorer areas of Pez , so those who can not enter the economic swim are driven farther away from the centre of the city and their traditional parish . 
Two of the highest buildings in Europe now tower over the parish from the Gran Vi2a area . 
These skyscrapers , full of offices , flats and hotels , are also a home from home for Americans who administer their military bases in Spain under the pact of 1952 ; they supply much employment to the local parishioners . 
The new pattern evolving , therefore , may roughly be explained in terms of a correlation between the height of the building and the income group and the degree of density of population in the parish . 
The two opposing poles of this correlation are the Gran Vi2a and Pez areas , ten minutes ' stroll apart . 
There are no detached or semi-detached houses in this built-up parish ; and no front or back gardens . 
Buildings form part of blocks whose rear may overlook communal courts . 
These are either mere wells criss-crossed with washing-lines from window to window , or more spacious ones used for commercial purposes , such as scrap-iron storage yards . 
A sense of neighbourhood is , therefore , enforced by the number of families crammed together in one building whose ground-floor tenant usually acts as porter and general informant . 
A certain privacy is ensured for households who have separate access to common landings or to a staircase , but the entrance is invariably overlooked by a porter 's window . 
Yet this modicum of privacy is being invaded by the increasing clamour for accommodation . 
More and more " apartments " are being created out of old reception rooms or spare bedrooms . 
Humorists publish exaggerated cartoons in which even a large wardrobe or piano have been sub-let to the desperate homeless . 
Few families are owners of the houses they live in , but many more have a long-term lease of the floor on which they reside . 
Some of the ancient three-storeyed mansions , now converted into flats , have separate entrances and staircases for the use of owner and tenants . 
Four-storeyed buildings of grey stone , with attics jutting out of red-tiled roofs , and railed balconies at the French windows of each floor , are still the most common in the residential areas . 
Some of the tenement-houses have roof-terraces , access to which is usually a bone of contention . 
Only the more modern and higher buildings have central heating and originally-planned bathrooms . 
On the hot summer nights the side streets are full of the chairs and stools of family groups until the cool breezes of early morning . 
For the privilege of living in this parish a working-class father in the older houses may pay as little as the equivalent of one United States dollar a month — a controlled rent ; but this is probably a sixteenth of his weekly income . 
Rents which are uncontrolled may be as high as 2,000 pesetas a month or more . 
The sanctity of the home throughout Spain has never encouraged the casual Anglo-Saxon habit of " dropping-in " for unexpected visits . 
For a family of six , cramped in four rooms in Madrid , the enforced proximity of the neighbours scarcely permits the degree of self-imposed isolation which it would obviously prefer . 
Even if it could get on the depressingly-long waiting lists of the State , Syndicate or Church housing projects in the suburbs , a typical family would be reluctant to move from the familiar parish area ; meanwhile it regards with a resigned surprise the restoration of ancient castles , and derives a mocking pleasure from the splendidly unfinished ministries and monuments begun by a display-minded regime . 
The feeling of belonging to the parish as an ecclesiastical unit consists in being a feligre2s — a parishioner inscribed in the parish register . 
This entitles him to take advantage of the essential sacraments of baptism , marriage and extreme unction , and of the religious associations , charities and their services . 
Official status as a vecino in the district is acquired by a minimum of six month 's residence for all Spaniards of 21 or more , or for those of 18 or above who are legally living apart from their parents and are inscribed in the electoral census as heads of households . 
The municipal Padro2n is the civil register of those liable to pay taxes within the Centro district . 
All those listed therein are required to carry an identity card with photograph and , if qualified for social insurance benefits , to acquire on marrying a Family Book from the so-called Ministry of Grace and Justice . 
The difference between membership of the ecclesiastical and civil units can not be considered wholly in terms of the voluntary and the compulsory . 
Except for an insignificant percentage of Protestants , there is religious conformity within the parish , and social and religious obligations often dovetail ; for religion is not yet merely a personal affair , and the parish still exerts certain controls . 
These will be discussed in the next chapter , where an examination of the political structure of both Church and State will reveal the authority and influence each wields . 
The aim of this chapter has been to paint the background and landscape of the Madrid picture . 
The subsequent pattern that will emerge will not be the comparatively regular one of the pueblo but , rather , a jigsaw of interlocking social relationships which merge their various forms and colours . 
2 THE AUTHORITIES AND THE WORLD AROUND 
AN AUTHORITARIAN triad composed of mayor , police and priest , similar to that found in the village , exists in the city but in a more impersonal form , which only adds weight to its authority . 
It helps to create awareness of community among all who share a common mode of living in the district and parish , divisions which are themselves part of a nationally imposed political structure . 
For not even the rural parish is an autonomous , integrated whole wherein everything that happens is functionally interdependent , and the urban parish is much less so . 
San Marti2n is at the heart of the nation 's government ; and interaction between the superstructure of the capital as a whole and the local parish unit becomes clear only when the institutionalism of authority in general is examined . 
It is not my task here to go deeply into the historical causes of the existing system , or to evaluate the political structure . 
A distinction must , however , be drawn between that which is traditional and enduring and that which is the result of current political necessity . 
When , in the sixteenth century , the country quickly fell under a bureaucratic absolutism pride was lost in the provincial fueros , in municipal liberties , and in the rights of the Cortes of Castile . 
Imperialism , Parry says , killed the best political thought in Spain . 
Later , as an aftermath of the Napoleonic wars , the pendulum of government swung from reaction to counter-reaction . 
The political instability and internal strife reflected by the ninety-eight changes of Cabinet between 1834 and 1912 — a period which saw revolutions , regents , pretenders , new monarchs , the First Republic , military coups , a Restoration , and the humiliating loss of the last of Spain 's New World possessions — made the populace apathetic and destroyed its little faith in government . 
This is very quickly revealed in the parish by the reluctance to discuss the past , except that during which Spain was dominant in world affairs . 
Past experience has not apparently deterred this people 's search for heroic leaders rather than for an abstract political ideal ; the comparative success of two dictatorships and the failure of the Second Republic in this century might be adduced in support of this view if one were concerned with political theory . 
Government in Spain continues to rest on the three institutions of an hereditary monarchy ( rejected by two short-lived republics ) , the parliament of the old Castilian Cortes , and an extensive Civil Service , with a permanent staff except for its highest officials . 
Spain is at the moment a kingdom without a king . 
The Franco regime has committed itself to the maintenance of the monarchy as an institution by the 1947 Law of Succession and the Referendum of the following year . 
Meanwhile the regime , in its own words , is " a representative , organic democracy in which the individual participates in government through the natural representative organs of the family , the city council and the syndicate " . 
Of these three organs one — the family — has continued to participate through the parish in the election of another — the city council of Madrid — since the fourteenth century . 
Syndicalism can be considered as a twentieth-century edition of the mediaeval gremios or trade guilds , which were themselves linked to both the family and the parish by their religious activities and the practice of spiritual sponsorship . 
It grew in the cities , not in the country areas , and was closely associated with anarchism in the past before the Falangists and Catholics made it " respectable " in its current form of national verticalism . 
In Pul Eliya these obligations are still imposed upon the holder of any gamvasama plot whether or not he chooses to lay claim to the title of Gamara1la . 
As shown in Map E ( p. 152 ) each of three ba1ga has one elapata , one { elapat panguva , one gamvasama and four ordinary pangu . 
According to Ievers the elapata , the { elapat panguva and the gamvasama should all belong to the Gamara1la , but this represents only an ideal initial situation . 
When detailed Pul Eliya records begin in 1886 the pattern had already diverged widely from this ideal . 
In that year , in each of the three ba1ga , the gamvasama , { elapat panguva and elapata were in different hands . 
Nevertheless the theoretical association of the elapata with the { elapat panguva provides yet another example of the principle of " fair shares " . 
Since the elapata constitutes the end of the field it therefore carries with it the obligation to build and maintain the whole of the end fence . 
This is about ten times more fencing than attaches to any ordinary panguva strip . 
Because of this extra fencing obligation the owner of an elapata is excused from the duty of carrying out tank repair work . 
But the { elapat panguva has no such privilege . 
Thus the idea behind the doctrine that the elapata and the { elapat panguva should always be owned by the same individual is simply to ensure that no one wholly escapes from the unpleasant obligation of carrying out tank repair ra1jaka1riya duty . 
This was felt to be particularly important since in the event of a breach in the bund all villagers must be equally responsible . 
In a comparable way , while the owner of an elapata and the owner of a gamvasama must both pay for the building of watch huts , the latter , as Gamara1la , escapes the ra1jaka1riya duty of night watchman . 
But , unlike the owner of the elapata , the gamvasama owner must do his share of bund repair ra1jaka1riya along with the other shareholders . 
In Pul Eliya this carefully differentiated system of rights and obligations has been rigorously maintained even though the status of the Gamara1la as a specialised class of individual is no longer formally recognised . 
The rights and duties attach to the land itself , not to the individuals who own it . 
CONTEMPORARY PRACTICE IN PUL ELIYA 
So much then for the theory behind the tenure of land in Pul Eliya Old Field . 
Now let us consider the actual state of affairs as it existed in 1954 . 
According to present-day Pul Eliya tradition the Old Field originally contained 18 pangu , six for each ba1ga , but at some unspecified date in the past two extra pangu were added to the Pahala ba1ga by reducing the amount of land allocated to the Pahala elapata . 
The circumstances which brought this change about are not now remembered so I was fortunate that among the few nineteenth-century documents relating to Pul Eliya which still survive there are two tax returns which appear to confirm the tradition . 
The Village Vel Vida1ne still submits annually to the revenue administration a return purporting to show the exact amount of land cultivated throughout the village and the precise ownership of each plot . 
Today this return is compiled for the purpose of crop statistics , but its form is just the same as that of the paddy tax census of the 1870-90 period . 
It is , therefore , easy to correlate surviving tax census documents with the layout of the modern field . 
Table 4 has been drawn up from this documentary evidence to show the relationship between the 1954 Old Field holdings ( Upper Field ) and those of the years 1889 , 1890 . 
This table is analysed in detail in section B of the present chapter . 
The detailed analysis shows that the 1889 list is drawn up according to a scheme of 18 pangu ; the 1890 list on the other hand fits the present-day arrangement of 20 pangu . 
The story of the " two extra pangu " must therefore be correct and the alteration must have occurred shortly before 1890 . 
Because of this satisfactory fit of documentary evidence with oral tradition I feel confident that Map E ( which " fits " the present-day arrangement of strips to an "original " system of 18 pangu and three elapata ) is justified and correct . 
" Originally " the field consisted of 3 ba1ga ; each ba1ga comprised a 40-fathom elapata and 6 pangu ; each panguva comprised 10 fathoms in the Upper Field and 10 fathoms in the Lower Field . 
Such discrepancies as now exist result from the fact that shortly before 1890 two fathoms from panguva four of the Pahala ba1ga together with 22 fathoms from the Pahala elapata were reclassified as forming " two extra pangu " . 
Since that date the Pahala ba1ga has been deemed to consist of 8 pangu as opposed to the 6 pangu in each of the other two ba1ga . 
The principal effect of this reclassification has been to alter the type of ra1jaka1riya obligation falling on owners of these plots of land . 
Details are given at pp. 207 f . 
" BETHMA " 
The arrangement of the irrigation channels together with Vel Vida1ne 's assumptions concerning water allocation for the different parts of the field have the following implications : 
( 1 ) The Upper Field consists of two equal parts — the north half of the field and the south half of the field . 
( 2 ) The Lower Field is half the area of the Upper Field . 
Thus the field as a whole is divided into three supposedly equal areas , each of which contains the same number of strips of the same width , owned in the same way . 
One-third of every holding falls into each of the three main parts of the field . 
This symmetry has important consequences . 
The North Central Province institution of bethma has received frequent comment . 
This is an arrangement whereby the shareholders in a field which is short of water may agree to cultivate only a proportion of that field and then share out the proceeds among themselves . 
The theoretical procedure , as recently described by Farmer is as follows : " 
The village has an admirable system , known as bethma , under which , if the whole extent of the paddy field can not be cultivated for lack of water , as many of the tracts as can be irrigated are divided , regardless of their ownership , between the peasants in proportion to their several holdings , and thus cultivated as a compact block with minimum waste of water ( Farmer , 1957 , p. 558 ) . " 
The earliest reference to bethma in this form is an administration documents of the 1861-4 period . 
I have studied these entries with care , but they are unfortunately ambiguous . 
It is evident that the Government Agent of that date imagined that the system was supposed to work in the way that Farmer has described , and he on several occasions records the fact that he had ordered reluctant villagers to carry out bethma division in this way . 
But it seems to me probable that this form of bethma was the unintended invention of the British Government Agent himself ! 
At the present time different villages seem to work bethma in different ways , and there is no way of ascertaining which , if any , of these methods is the ancient traditional system . 
But what is quite clear is that the Pul Eliya method is very much simpler than that described by Farmer . 
Furthermore it is bethma which provides the ultimate justification for fragmenting each individual holding in the complicated way I have described . 
For Pul Eliya the system is as follows . 
If the villagers are to cultivate rice in the Old Field during the Yala ( AprilSeptember ) season they will decide from the start either to cultivate the whole of the field or two-thirds of the field ( that is , the whole of the Upper Field only ) or just one-third of the field ( that is , the northern half of the Upper Field only ) . 
No pooling of proceeds or reallocation of holdings is necessary since the land is already divided up in such a way that each shareholder works the whole or two-thirds or one-third of his total holding as the case may be . 
In my limited experience this is the most common form of bethma in all this area . 
The ideal scheme described by Ievers , in which the total field is divided into two or more tracts ( pota ) , corresponds to the actual facts for all the villages in the Pul Eliya area . 
It is invariably the case that every strip or holding in the upper tract has a corresponding strip or holding in the lower tract , though the precise manner in which this is effected is not always the same . 
This fragmentation of individual holdings is always directly associated with the local practices regarding bethma . 
The relative size of the different tracts ( pota ) is such that when the water is scarce cultivation of the upper tract only , or of half the upper tract divided longitudinally , serves as a bethma . 
Farmer 's description , which is the orthodox one , implies that individual Sinhalese farmers get on so well together that they can readily agree to a reallocation of land in times of water scarcity . 
I can only say that this does correspond to my experience ! 
CULTIVATION AREAS 
Before proceeding , we may note one further feature of the Tax Lists ( Table 4 ) . 
For the years 1889 and 1890 the areas of each individual holding are given in seed quantities ( P = pa12la ; L = la1ha : where 1 pa12la = 10 la1ha ) . 
But in the 1954 Plot List areas are given in acres . 
The numerical totals at the bottom of the table are in each case nearly the same ; the 1889/90 Tax Lists show that the upper part of the Old Field had a sowing area of about 48 pa12la , the 1954 returns show the same field as having an area of just short of 48 acres . 
The latter figure exaggerates the facts by about 50 per cent . 
The coincidence of numbers is no accident . 
The administration 's requirement that the Vel Vida1ne 's crop returns should show cultivation areas in acres rather than in seed quantity dates from the early days of this century . 
The villagers , however , still reckon land areas in terms of seed sown and have no satisfactory method of converting one scale into the other . 
In making out his annual returns the Vel Vida1ne now works to a simple rule of thumb . 
Sinakkara land and badu land has been surveyed by government officials and hence the true acreage of such holdings is known and is entered accordingly . 
For the Old Field on the other hand , all that is really known is that it contains 20 pangu . 
Now when the Old Field was originally surveyed in 1900 , the whole field was shown to be just over 40 acres . 
It thus became established that in Pul Eliya " 1 panguva " equals " 2 acres " and this tradition has stayed . 
Today when working out the allocation of labour obligations for the purpose of ra1jaka1riya duty every 2 acres of sinakkara land and badu land counts as 1 panguva . 
In this way it was argued that at the beginning of 1954 there were 52 pangu in Pul Eliya in all . 
Of these 20 were the Old Field pangu and 32 were represented by 64 acres of sinakkara and badu land . 
( Cf. 48 pangu ( Table 5 ) plus plots 124 , 151-2 ( Table 6 ) . ) 
The quite erroneous acreages shown in the 1954 Plot List for the plots in the Old Field were arrived at by reversing this argument . 
Every 6 pangu in the upper tract of the Old Field are reckoned as 12 acres . 
This leaves out of account both the elapata of the Upper Field and the whole of the Lower Field . 
Consequently by the time the Vel Vida1ne has completed his returns so as to show an acreage figure for each plot he has about 20 acres too many . 
Pul Eliya village , like all other villages in the area , has been submitting these bogus crop returns annually ever since the beginning of the century , and the same type of error has persisted throughout . 
For Pul Eliya the return for " area cultivated " has never been less than 15 per cent in excess and has often been over 50 per cent in excess . 
PARENTS ' EXPECTATIONS OF THE JUNIOR SCHOOL F. Musgrove Purpose and Scope of the Survey 
In May and June 1960 a survey was made of attitudes to and expectations of the school among parents of children in the last two years of two junior schools in a Midland City . 
Children of this age ( 10 and 11 years ) were chosen on the assumption that parental interest and curiosity would be at their height , and views on education most fully developed , in this period immediately preceding secondary selection . 
One junior school ( A ) is situated on a large municipal housing estate of subsidised houses ; the children in the top two years numbered 310 . 
The school has a " progressive " headmaster ; teaching and school organisation are informal and there is no excessive concentration on the "three R's " . 
The other junior school is smaller and there were 104 children in the last two years . 
It serves an expensive residential area of owner-occupied houses . 
It is a Church of England school favoured by well-to-do Anglican parents of the district . 
It is far more formal in its teaching and organisation , and places more emphasis on the " three R's " , than school A. 
The two schools were chosen because of the marked social contrast in the areas they serve . 
A random sample of one in four names was taken from the school registers with a view to interviewing the parents of these children . 
The homes of 26 children in school B were approached and interviews were carried out in 22 ; the homes of 62 children in school A were approached and interviews were carried out in 50 . 
An important feature of the survey was the separate interviewing of husbands and wives . 
On the estate ( Area A ) 42 couples were interviewed , five wives whose husbands were either unavailable or refused interview ; and three husbands whose wives were either unavailable or refused interview . 
Thus one or both parents of 50 children ( 22 boys and 28 girls ) were interviewed — 47 mothers and 45 fathers , a total of 92 parents . 
In the middle-class district ( Area B ) 18 couples were interviewed and , in addition , four wives whose husbands were not available . 
Thus one or both parents of 22 children ( 14 boys and 8 girls ) were interviewed : 18 fathers and 22 mothers , a total of 40 parents . 
Altogether 132 parents in the two areas were interviewed , representing 72 children ( 36 boys and 36 girls ) . 
The parents in Area A were predominantly working class : 47 of the 50 children came from homes where the head of household was in the Registrar-General 's Occupational Classes 3-5 . 
In Area B the parents were predominantly white-collar , professional middle class : 19 of the 22 children were from households where the head was in Occupational Classes 1 and 2 . 
The following table gives the percentage distribution of occupational classes in the two groups , in the City ( 1951 Census Report ) and in the country . 
The overlap between the two groups within the city is very small . 
Parents in Area A were on average younger than parents in Area B : 
The average size of family was larger in Area A than in Area B : 3.2 and 2.5 children respectively . 
The author was assisted in the interviewing by 14 local teachers who were known to him for their interest in problems of educational sociology and who had , in a number of cases , previous interviewing experience and training in field work . 
The team worked throughout under the direction of the author who designed and directed the project . 
Six families were randomly allocated to each member of the team . 
Preliminary meetings were held to discuss the content of the interviewing schedule , to clear up any possible ambiguities in the wording and purpose of each item , and to standardize procedure at the interviews and in the recording of interviewees ' responses . 
All members of the team were clear that they should record as fully as possible all answers that were given and any additional information or opinion that was volunteered : that although some questions might simply be answered " yes " or " no " or " do n't know " , any elaboration , qualifying comment or reasons given should also be noted . 
All interviewers were to emphasize to the parents that the interviews were unofficial and that answers were not only entirely confidential but anonymous . 
A copy of the schedule used in the interviews ( excluding " classificatory questions " regarding age , number of children , occupation , etc. ) will be found in Appendix A. 
The interviews provided evidence of parents ' expectations on three scores : ( a ) relating to children 's behaviour , ( b ) relating to academic and scholastic training , and ( c ) relating to the curriculum . 
Parents ' Expectations of the School in the Sphere of Behaviour Training Emphasis on the Responsibility of School or Home 
Parents were asked whether they expected the school to guide their child 's behaviour as well as teach " school subjects " , and those who answered " Yes " were asked to state what kinds of behaviour they expected the school to encourage . 
Interviewers were asked to make a full recording of elaborations and qualifications to answers to the first part of the question ( 5a ) so that responses could be classified and placed on a five-point scale ranging from strong emphasis on the home 's responsibility at one extreme to strong emphasis on the school 's at the other . 
The following are the five groups into which all answers were sorted : 
1 . 
Answers which gave the school an emphatic responsibility for children 's behaviour , e.g. , " Certainly the school should teach children how to behave — that 's what school 's for " ; " Definitely yes — it 's the school 's job to teach manners , etc . " 
2 . 
Answers which emphasized the school 's importance but also mentioned the need for parental assistance , e.g. , " The school is responsible for behaviour to a great extent , but not entirely " and " The school has a big responsibility , as well as the parents . " 
3 . 
Answers which stressed the equal partnership between home and school , e.g. , " Fifty-fifty partnership " ; " Home and school should share the responsibility equally " ; " Home and school complementary " and " School 's job in school hours , parents ' job otherwise " . 
4 . 
Answers which emphasized the home 's responsibility but also mentioned the need for some support from the school , e.g. , " It 's mainly the parents ' responsibility but the school should help " and , " To some extent — but this is mainly the responsibility of the home and parents " . 
5 . 
Answers which placed the responsibility for behaviour emphatically on the parents ( requiring of the school no more than that it should not undermine parental influence ) , e.g. " It is definitely the parents ' job to guide behaviour " ; " Definitely no : the school ca n't do everything and should stick to its job , which is teaching " subjects " " ; and " Teachers should teach — behaviour is the parents ' responsibility " . 
The two areas were sharply distinguished in their answers : in Area A , 27.7 per cent . 
gave answers which fell into categories 3 , 4 or 5 , whereas 57.5 per cent . 
in Area B did so : 
There was no tendency for parents in either area who stressed the home 's responsibility for behaviour to have fewer children than the average : in Area A , 20 parents stressed the home 's responsibility as against the school 's and their average number of children was 3.1 , while the average for the area was 3.2 ; in Area B , 23 parents stressed the home and their average number of children was 2.5 , the same as for all the families in the area . 
There was no tendency for working wives in either area to stress the school 's responsibility more than non-working wives . 
In Area A , 75 per cent . 
of the mothers were in full-time or part-time work , in Area B , 14 per cent . 
were at work . 
Twenty-five per cent . 
of the mothers in Area A who were not at work ( 4 out of 12 ) stressed the home 's responsibility ( categories 3 , 4 or 5 ) , but so did 22.8 per cent . 
( 8 out of 35 ) of mothers who went out to work . 
In Area B , all three working mothers stressed the responsibility of the home as against the school , and 58 per cent . 
( 11 out of 19 ) of the non-working mothers . 
The difference in expectations between the two areas reflects their different social class composition . 
When the same social levels in the two areas are compared the differences disappear . 
In order to obtain social groups large enough for comparison , Occupational Classes 1 and 2 are combined to form the " Middle Class " and Occupational Classes 3 , 4 and 5 to form the " Working Class " . 
In Area A , three out of five middle-class parents placed emphasis on the home , in Area B , 22 out of 34 . 
There was no significant difference between the two areas within the middle class . 
On the estate , 17 working-class parents emphasized the home and 70 emphasized the school ; in the contrasted area one working-class parent emphasized the home , and five the school . 
There was no significant difference between the two areas within the working class . 
On the other hand , there was a highly significant difference between the two areas when social class was not held constant . 
On the estate , 20 parents emphasized the home and 72 the school , in Area B , 23 emphasized the home and 17 the school . 
Although in working-class Area A a far higher proportion of parents than in middle-class Area B emphasized the school 's responsibility for behaviour-training , a far higher proportion claimed explicitly to direct or influence their children 's behaviour in three main directions : towards their teachers , towards their friends , and in their choice of friends and associates : 
Claims to give explicit direction and guidance on behaviour were significantly greater in working-class Area A than in middle-class Area B : in the former Area 188 claims ( out of a possible 276 ) were made on three criteria ; in the latter only 53 ( out of a possible 120 ) . 
The difference between the areas is significant at the 0.001 level . 
The reasons for this marked difference between the areas was apparent in the answers given by the respondents : parents in the middle-class area were sufficiently confident of their children 's behaviour that they felt no need to instruct them on their relationship with teachers and friends , and they felt sufficient confidence in the social composition of the school and the locality that they saw no need to guide their children in the choice of friends . 
This was clear from many of the answers given to questions 7a and 7c . 
The interviewees were not asked why they did or did not advise their children about whom to play with or whom to avoid : the question could be answered simply " Yes " or " No " , yet one-third of the parents who said that they did not tell their children how to behave with other children volunteered the explanation that this was " unnecessary " and a similar proportion of those who said they never told their children not to play with certain other children elaborated their answer by saying there was no need to do so in this school and/or district : " No : the children at this school are nice children " and " No : it is unnecessary around here " . 
The marked difference , then , between directing and non-directing parents is a function of area and not of social class . 
The greater tendency among parents of Area A to direct behaviour reflects their lack of confidence in the social contacts available to their children . 
Behaviour which the School should encourage 
The greater emphasis in working-class Area A on the school 's responsibility for behaviour-training does not necessarily reflect a lack of concern for parental duties : the school is often given the job of directing behaviour because , it is felt , only the school can do this effectively . 
The reason often volunteered for assigning so much responsibility to the school was that the children would "take more notice of teachers " than of parents . 
The anxiety over children 's disobedience towards parents is reflected in answers to the question : " What kinds of behaviour do you expect the school to encourage in your child ? " 
Parents who expected the school to guide behaviour were asked to particularize . 
Out of the 77 parents in Area A who gave such particulars of the attitudes , virtues , and qualities of personality which they wished the school to develop , 70 per cent . 
showed a concern for various forms of unruly or anti-social behaviour . 
The Vale has a population of about 13,000 people . 
Most of them live in scattered farms , hamlets and villages . 
There are also two small market towns in the area , each with about 1,500 inhabitants . 
Most of my detailed enquiries have been carried out in one of these towns and in three adjoining rural parishes , in one of which I live with my family . 
A certain number of my informants live in other parts of the area . 
In addition , a private census of the whole Vale population , carried out in 1960 , has provided a good deal of basic information about each individual inhabitant and the composition of each household . 
Although a rural and predominantly agricultural area , no part of the Vale is more than 12 miles from major industrial and urban centres . 
Many of the people who live in the Vale work outside it and travel to and fro each day to earn their livings in adjacent urban areas . 
Most Vale people also have kin ties with people who live in these areas and in other parts of South Wales with whom they maintain effective social relations . 
A larger number of Vale people who do not work in the urban areas nevertheless visit them fairly regularly to see friends and relatives who live there or who are in hospital there , to shop or go to the cinema , and for such recreational purposes as to attend football matches and greyhound races . 
About 40 per cent of the adult population of the Vale consists of people who were born outside it and have lived in it for less than 15 years . 
The majority of such comparative newcomers were born in other parts of South Wales , mostly in places in the counties of Glamorgan and Monmouthshire which lie within 25 miles of the borders of the Vale . 
Many of them have close relatives still living at their places of birth or previous residence with whom they maintain frequent and intimate contact . 
The most important sources of employment for those Vale people who earn their livings within its borders are agriculture and forestry , stone quarries and cement works , and the building industry . 
A large number of men and women are employed in different capacities by public bodies such as the County and Rural District Councils , the Fire Service , and local electricity and water undertakings . 
There is also a large Royal Air Force station in the Vale which provides employment for a number of locally resident civilians . 
Further sources of employment are public and private transport and communication services , the distributive trades , and a number of small industrial concerns in the two Vale market towns , among which are an asbestos factory , a printing works and three firms of agricultural engineers . 
2 
Most of the material concerning kinship in the Vale was obtained by standard anthropological procedures : the collection of genealogies , unstructured interviews with individual informants , and participant observation . 
Certain data on particular aspects of kinship behaviour were provided in the course of a study of the attitudes to mental disorder of the relatives of psychiatric patients . 
I have also had access to a wealth of documentary material , most of it unpublished . 
After a time , however , I found myself able to make increasing use of direct observation to supplement verbal information . 
Participation in the life of the locality and growing familiarity with the details of kinship connections made it possible to observe social relations between kin taking place in a wide variety of contexts and to compare behaviour between kin with behaviour between non-kin in similar situations . 
In collecting material from informants I have tried as far as possible to relate statements regarding kin ties to the individuals concerned rather than to married couples , elementary families or households . 
In the field situation this is not , of course , as easy as it sounds . 
Data on kinship are often obtained from two or more informants simultaneously . 
The discussions and arguments between them which such inquiries tend to provoke often compensate for the resultant difficulty in comparing knowledge of kin and quality of relationship with them revealed by individual members of the same domestic unit . 
This emphasis on the kinship universe of the individual rather than the domestic unit arose from certain apparent differences between men and women , between spouses , and between parents and children in degree of recognition of extra-familial kin ties and in their functions in various contexts . 
I have also attempted to collect material on the interconnectedness of kin ties by interviewing and observing different members of the kinship universe of individual informants . 
The difficulties of doing so seem often to be directly related to the degree to which an individual 's kinship network is what Bott describes as " close-knit " , in which there are many relationships , independent of the individual concerned , among the component units of his kin universe . 
In many " families " there is generally at least one person who is acknowledged by most other family members to be the expert on genealogical connections . 
The existence of such recognized experts is particularly common among " families " long settled in the area , other members of which tend to rely on them for details of genealogical connections and to refer the investigator to them when approached for kinship information . 
Firth refers to such experts as pivotal kin , " relatives who act as linking points in the kinship structure " and who " hold more threads of genealogical connections in their heads than anyone else " . 
I prefer to differentiate between experts and pivotal kin , and to reserve the latter term for those individuals who act as connecting relatives , irrespective of whether they are also experts . 
The significance of pivotal kin as connecting links is usually greater if they are also experts , as is often the case . 
But many pivotal kin are elderly men who , in general , know less about kinship connections than their daughters or nieces ; and it is often found that individuals remain pivotal kin after their death . 
Not only do their graves sometimes form the pivot round which kin ties tenuously revolve , but the dead are often used by living informants as foci from which genealogical connections stem . 
This is particularly the case when the dead person lived to a great age or had high prestige for some reason among his kindred or in the locality . 
Most pivotal kin who are also experts are elderly women who , from their personal knowledge of dead kin of previous generations , maintain links of information and social contact between their own and their siblings ' descendants and the descendants of their parents ' and grandparents ' siblings . 
In theory , and often in practice , this means that such women carry in their heads kinship knowledge of six generations depth and extending laterally among consanguineal kin as far as the grandchildren of second cousins . 
When economic and other social factors reinforce relatively remote kinship connections , the lateral extension among consanguineal kin may go further : the grandchildren of pivotal kin may recognize as cousins of unspecified degree the descendants of the pivotal kin 's second or third cousins . 
The same factors often lead to knowledge of , and contact with , affines being very extensive . 
There are many individuals in the Vale who are able to identify between 200 and 500 living and dead relatives , about the majority of whom they can provide at least such information as sex , marital state , place of residence and occupation . 
Most of these individuals are people long settled in the area , by which I mean people who , in the main , were born in the Vale and one or both of whose parents , and often whose grandparents , were also born there . 
By contrast , there are other individuals who show a very much more restricted range of kin recognition of the order of about 50 relatives in all . 
Some of these individuals have always lived in the area but most of them are relatively recent immigrants , that is , adults who were born outside the Vale , often in urban areas , and who have only moved into the locality since 1945 . 
In both instances , in spite of the great differences in size of the average kinship universe , it is rare for the depth of generations over which kin are recognized to exceed seven or to be less than four . 
Again , while the number of kin with whom an individual may have some kind of periodic contact tends to vary with the size of the kinship universe , the number of kin with whom an individual has frequent and intimate contact is usually little different for those with large kinship networks from those with small . 
Degree of physical mobility is only one of a number of interdependent social factors which act directly or indirectly to influence the size of an individual 's kinship universe . 
These factors are also related to the amount of contact the individual has with his extra-familial kin and to the differentiations he makes among them ; the most important are occupation , economic resources , ownership of property and degree of social mobility . 
In some cases religious affiliations and level of education also seem significant . 
The decisions which an individual makes in choosing how far to observe or disregard in any particular set of circumstances the sentiments , obligations and expectations which are involved in the recognition of extra-familial kin ties appear to be influenced by the interplay of such factors as these . 
It is within the framework provided by them that idiosyncratic preferences operate . 
The same factors also tend to affect the degree to which marriages reinforce already existing ties of kinship and affinity and , among certain sections of the population , the scarcely less significant ties between kith , that is , between friends and neighbours of approximately the same perceived social status . 
Indeed , kith may be described as consisting of those who are an individual 's potential affines . 
The multiplicity of roles which every individual fills both successively in his lifetime and simultaneously at any given time is a sociological truism which needs no labouring . 
In any attempt to study the functions of kinship in a highly complex society it is nevertheless all too easy to lose sight of the importance for social behaviour of role-relationships other than those based on kin ties . 
Any analysis of a system of social relations necessarily involves the overemphasis , for heuristic purposes , of lines of demarcation between particular aspects of behaviour . 
In fact it is often very difficult for the observer to disentangle the kinship network of an individual from the wider social network of which it forms a part . 
This is most clearly seen in the case of farmers and their families who , together with those whose occupations are largely dependent on agriculture and who come , in many cases , of local farming stock , form one of the significant sections of Vale society . 
At the same time it is possible to demonstrate the importance of the social factors mentioned earlier in relation to the structure and functions of extra-familial kin ties . 
Among farmers the degree of physical mobility is relatively low . 
Although most farmers in the Vale are tenants , holdings relatively rarely become vacant other than through the death or retirement of the tenant , when it is the traditional policy among landowners and their agents to give preference among applicants for the new tenancy to the sons of the previous tenant . 
The vast majority of farmers are the sons and grandsons of farmers and most farmers ' wives are the daughters of farmers . 
Those children of farmers who are socially mobile tend to maintain close links with their relatives who are still farming . 
There is a high degree of interconnectedness in the kinship and social networks of farmers ; there is also considerable variation between individual farmers in the recognition of extra-familial kin ties , according to the age of the individuals concerned , the stage of development in its life-cycle reached by the elementary family to which they belong and the social context of contacts between them . 
The result is that it is often almost impossible to know whether social relations between individuals in particular instances should be classified as taking place between kin or between non-kin . 
The reticent users were asked simply , as described above , to state the methods they had ever used and the stage in family building when they started these practices . 
They were not asked for further details in view of their original reluctance to admit to practice . 
In this attempt to elicit contraceptive histories , attention was directed towards minimising any embarrassment . 
The relevant questions were put at the end of the questionnaire to allow time for the interviewer to gain the informant 's confidence and the list of contraceptives included both medical and colloquial names for the various contraceptive methods . 
The use of the card with its numbered list prevented the informant from having to mention the methods by name . 
In the event interviewers found little difficulty with these birth control questions ; reports from supervisors suggest that once an informant had embarked on the questionnaire , he or she co-operated to the end . 
Only 17 refused to say whether or not they had ever practised any form of birth control , and a further 20 informants , who were found to have taken some action to control conception , refused to indicate the methods they had used ; one commented : " I think it is a very private matter and would rather not discuss it . " 
This bears out the American study experience : only 10 of the 2,713 wives who were interviewed were unwilling to answer the questions about their attempts to avoid conception ; this was less than the refusal rate for their questions about income and the usual refusal rate for income questions in other sample surveys . 
Despite the apparent ease of the interview situation and the low refusal rate on these birth control questions , possibilities for error and reticence exist . 
As mentioned in Part 1 of this paper , nearly half the informants were interviewed in the presence of relatives , friends or children ; although it seems that the presence of these people did not seriously affect the response to questions on contraceptive practice , they may occasionally have been an inhibiting factor , even though informants were not required to mention methods by name . 
Also , although the informants seemed to understand the terms on the card showing the list of contraceptives , it is possible that incorrect answers were given by a few who only knew a different colloquial name for the method used . 
The following analysis shows that a large majority of the informants only ever used one contraceptive method or group of methods simultaneously ; however , it is possible that a few informants , weary at this stage in a long interview , may not have taken the trouble to outline their whole contraceptive history and only mentioned the method they considered the most important . 
Lastly , the interviewers , though skilled and experienced at questioning diverse people on a wide range of topics , were not specifically trained as those engaged in the Lewis-Faning and the American study had been for this almost clinical aspect of the inquiry . 
DIFFERENTIAL RESPONSE BY MALE AND FEMALE INFORMANTS 
One or more of the above may account for the surprising finding that , in every cohort and social class , birth control practice was mentioned more often by men than by women . 
Some 74 per cent of the male informants married since 1930 reported practising contraception in their first marriages against only 65.1 per cent of the female informants . 
The questions had been designed ( see p. 122 ) to obtain each couple 's contraceptive practice and not just the action taken by the informants alone , and hence similar results were anticipated from male and female informants . 
Perhaps this was a naive expectation , since psycho-sexual factors , particularly in this culture may tend to inhibit women on the subject and possibly in turn lead men in some cases to overstate their practices . 
A complete understanding of this differential sexual response is obviously impossible , but a clearer examination of the method of questioning suggests some explanation and makes possible an assessment of the significance of this finding on the validity of the results on birth control methods . 
Questioning on family planning opened with an inquiry about attitudes . 
Q. 182a : " Many married couples do something to limit the size of their families and to control when their children come . 
How do you feel about this ? " 
Replies showed that male informants married since 1930 fully approved of birth control more frequently than female informants ; in all 68.9 per cent of the men against 63.9 per cent of the women , but the differences were especially marked amongst those married in the 1940s , where 72.2 per cent of men approved against only 60.2 per cent of women . 
This questioning on personal attitudes was followed by the enquiries about practice described above . 
Response to the first question shows the main sex differential ; 57.5 per cent of the male informants married since 1930 answered positively ( in our terminology declared themselves to be avowed users ) as against 47.2 per cent of the female informants ; this differential operated in all cohorts and classes , but , as with the attitude question , was more marked in the 1940-49 cohort ( 62.1 per cent of male informants to 46.1 per cent of female informants ) and particularly amongst the skilled manual and other manual workers in this cohort . 
It was only when informants had declared their use of contraception in this way that they were asked the methods they had used and were shown the full list of appliance and non-appliance methods . 
At this stage the same proportion of each sex reported using only non-appliance methods including withdrawal , but the female informants reported less use of appliance methods . 
Closer examination revealed , as was to be expected , that as many female informants as male informants had reported use of the cap ; hence the difference lay essentially in reports of the sheath . 
We had expected the difference to lie in reports of " male " methods since it seems possible that some female informants who disapproved of birth control might quite reasonably have denied practice if their husbands were responsible for the methods used , and particularly as the request for information on the couple 's methods was not specifically repeated in the wording of the question on methods used ( Q. 188 ) ; but we thought this difference would show up more in the proportion reporting withdrawal . 
However , in all cohorts as many women as men married since 1930 had , by this stage in the questioning , reported the practice of withdrawal . 
But perhaps , and Freedman and Whelpton mention this possibility , women responded to the positive suggestion of " husband is careful , withdraws " and some reported this method when in fact their " careful " husbands had used the sheath . 
It will be remembered from p. 123 ( Q. 186 ) that all those denying birth control practice were shown a numbered list of non-appliance methods and asked to state , by number which , if any , they had used . 
In some of the cohorts and classes where the sex differential in the proportion of avowed users was most marked some of the leeway was made up by a greater proportion of women admitting to the use of these non-appliance methods ( in our terminology declaring themselves to be reticent users ) , particularly in the 1940-49 cohort where a further 21.1 per cent of the female informants became reticent users as against only 16 per cent of the male informants ( the proportion for the " other manual " group showed an excess of 10 per cent for women over men ) . 
It should be remembered here that for these informants this was the first time they had been shown a list of methods and also that this list only included non-appliance methods . 
Interestingly , at this point , more women than men mentioned use of withdrawal and significantly more in the seriously affected 1940-49 cohort , supporting the theory that some of the sex differential on avowed use was due to the failure of women to report practice when their husbands had taken the contraceptive action . 
Also , since these informants were confined to non-appliance methods , it is possible that some women reported withdrawal when in fact their husbands had used the sheath . 
The combined answers of the avowed and reticent users together give us the total extent of eventually admitted birth control practice . 
This shows a steady differential in all cohorts including the 1940s , of approximately 10 per cent more admitted practice for male informants than females ; the difference lies , particularly in the 1940-49 cohort in the proportion of male and female informants reporting use of appliance methods . 
From the probably genuine sex differential in personal attitudes to contraception , through the intensive , carefully worded but perhaps too closely defined method of questioning , some female informants may have failed to reveal their birth control practices , particularly where their husbands were responsible for the contraceptive measures , and others may have recorded " husband is careful " , i.e. withdrawal , when in fact he used the sheath . 
In assessing the significance of this , particularly in relation to the analysis of patterns of contraceptive practice to follow , it seems most relevant to examine the effect on the internal consistency of the all user group , and more particularly the avowed user group . 
Here we find that the differential response by male and female informants has not seriously disturbed the balance of methods reported by the two sexes . 
Amongst the all user group the proportions reporting any appliance method and using only non-appliance methods show an unbalance for the sexes only in the 1940-49 cohort , and even these differences are barely significant at the 5 per cent level . 
The pattern for the avowed users is even better ; in all cohorts and classes the frequency of methods reported by male and female informants is similar . 
Since the analysis of birth control methods and contraceptive histories is concerned essentially with the patterns of methods reported by the users and particularly the avowed users , we have felt it justified to continue the analysis of birth control methods for all informants , male and female combined . 
The above poses obvious questions about the completeness of the data to follow . 
Undoubtedly the results understate the actual extent of practice and probably the use of some methods ; nevertheless , this is a first attempt to get at the birth control experiences of a national sample and the findings appear to be consistent in their trends , and at least point to changes over time in contraceptive behaviour , even if they do not provide an absolutely complete history of birth control experiences throughout the population . 
USE OF DIFFERENT BIRTH CONTROL METHODS 
The informants who admitted to the practice of birth control , whether at once or after probing , indicated the various contraceptive methods they had used during their married lives . 
Many reported that two or more methods had been used , either simultaneously or in succession , so the number of reports of methods exceeds the total of users . 
To show the extent to which the various methods are used and their changing popularity over the period , Table 1 treats each method separately and gives the proportion of users reporting each method . 
It also contrasts the Marriage Survey with the American study . 
Table 1 shows the overwhelming importance among Marriage Survey users of the two male methods : the sheath is reported by almost half these users and withdrawal by 44 per cent . 
The next most popular method is " safe period " but it is only reported by 16 per cent of the informants , followed by cap ( 11 per cent ) and pessary and gels ( 10 per cent ) . 
Comparison of the three cohorts shows some changes . 
There is a significant trend away from withdrawal and towards the cap ; the increase in the proportion of sheath users is not quite significant . 
The American data can be compared with the Marriage Survey totals column . 
Although the sheath is the most popular method in both countries , the frequency of other methods is significantly different . 
Withdrawal , Britain 's next most frequently adopted method , is used by only 15 per cent of the American sample , and instead there is greater reliance on the " female " methods : cap , safe period and douche . 
In Britain there are nearly twice as many reports of the use of " male " methods as " female " ( 92.8 per cent to 48.2 per cent ) , whereas in the U.S.A. the proportions are reversed . 
Hogben 's paper is thus of some value as a counsel of scientific caution , but adduces no fundamental objections to the theory . 
In the preceding pages an attempt has been made to clarify the issues and gain some idea of the influence of genetic factors in one aspect of language , the sound structure . 
This has been taken broadly , and the sound-producing apparatus and its results , whether in the individual , the group , or the population , the complement of sounds of a language and of the languages of a population , and the changes in a sound complement , have all been considered . 
Each of these should have a genetic component . 
The development , structure and functioning of the vocal apparatus are clearly determined in part by genes , and hence the nature and the limits of the continuum of sound production possible to this apparatus must be likewise . 
And following from this , in the last analysis , any vocal sound produced by an individual , whether in speech or not , and if in speech , whether significant or not , will be of the nature that it is , in part at any rate , because of the particular genetic composition of that individual . 
Similarly the complement of sounds used by a group in the vocalisation of its language and the total complement of sounds used by the various groups of a population in the vocalisation of their languages will be of their characteristic natures , in part , because of the particular genetic composition of that group or population . 
And it would seem that genetic factors must play some part in changes in a sound complement . 
This is not only in the sense that the intermediate stages in any case of sound change must have some genetic component , but also in the sense that the motivations which induce a community of speakers to make the change derive from those speakers , and hence axiomatically reflect , to some extent , their genetic composition . 
The most important of these motivations has been taken to be the tendency to economy of effort , a tendency which is known to be operative in a wide range of human activities , and which itself must be largely genetic in its determination — there is after all no difficulty in imagining its evolution in a species under conditions of natural selection . 
But even those changes which seem to be mainly the result of cultural influences of one sort or another will have a genetic component . 
The speakers of a dialect borrow , imitate , or learn sounds from other dialects , partly , perhaps , as I have suggested above ( p. 205 ) in accordance with their own preferences , but mainly , it is usually assumed , because of their impulses to conform with what seems a desirable norm . 
Such impulses will in theory also have a genetic component . 
They vary , as is common knowledge , from individual to individual and they doubtless vary also , in terms of mean values , from group to group . 
The result of this investigation has been to develop in more detail the hypothesis of genetic influence in the sounds of language , particularly with regard to the extent of its field of operation and to the nature of the way in which this influence is exerted . 
For the reasons given , it seems that the existence of a genetic component of language as such is { 6a priori to be accepted ; the question which remains then is whether the further hypothesis of the extent and the nature of the genetic influence such as has been outlined in the preceding pages is valid . 
The answer to this must primarily depend on the success with which it is considered that this hypothesis may be applied to and shed new light on the observed data of the subject , and suggest further constructive work . 
There can be no doubt of its applicability to a considerable amount of the material in linguistics and its ancillary disciplines . 
It can be applied to the individual and to the particular rate , method , and accuracy of his acquisition of his sound complement , to the uniqueness of this , and to its aberration from the group mean . 
It can be applied to the group , to the mean of the group rate and method of acquisition , to the uniqueness of the group sound complement , and to the relations between overlapping groups and their dialects . 
Further , it can be applied to the population , to the uniqueness of the total sound complement of a population , to the widespread similarities in the sound complements of its various constituent groups , and to the particular distributions of the sounds and sound features of that total sound complement . 
It also provides a basic factor in the causation of phonetic change , clarifying the nature and the role of the tendency to economy of effort in this phenomenon , and offers an explanation of many of its observed characteristics , including some , such as the parallel developments in related languages spoken by related peoples , or the long continued drifts in a sound complement , which have been peculiarly resistant to explanation in the past . 
And it suggests a number of lines of investigation which should be fruitful in the further development of the subject . 
Some of the most obvious of these may now be considered briefly in turn . 
GEOGRAPHICAL DISTRIBUTION OF SOUND FEATURES 
The most obvious and important linguistically is the geographical distribution of sounds and sound features . 
The cases discussed in this book have been discovered largely by trial and error , and an adequate series of maps of the distributions of the main types of articulations is a prime desideratum . 
Besides articulations in the strict sense , it would seem likely that there may be much of interest in the distribution of such features as type of syllabic structure , liaison and juncture phenomena , the restrictions on occurrence of specific sounds and sound types — practically all the languages of Europe from Dutch to Russian , for example , permit no voiced plosive in word final position — and so on . 
And further , among less detailed phenomena , the establishment of the distribution of languages with lexical tone would seem valuable in this connexion . 
At the moment we have very little idea of the distributions of such features , and the lines of research which they may suggest . 
The historical development of such distributions opens a new field in that the appearance of a specific sound type in one language need not be an event which is solely the result of conditions internal to that language ; it may be related to the occurrence of sounds of similar type in other languages , of the same or different family , in the same region . 
I have suggested in a previous article ( Brosnahan , 1959 ) , for instance , that the development of affricate articulations in the Old High German consonant shift is part of a larger , but geographically limited phenomenon , a remarkable development of affricates over the last two thousand years and centred in the area now occupied by the Western Slavonic languages , Hungarian and Albanian . 
Our understanding of language and the deeper-lying factors in its development is likely to be very greatly extended by investigation along these lines . 
A further possibility is the comparison and mapping of acoustic features or characteristics of representative samples of different languages . 
With modern methods of recording , it is not difficult to devise techniques to determine , say , the mean distribution of energy over the range of frequencies used in speech . 
Such mean distributions should vary from language to language with differences in their sound complements , and with differences in the relative frequency of occurrence of specific types of articulation . 
The mapping of such distributions may also be informative in bringing to light unexpected correspondences at the sound level among different languages . 
THE MECHANISM OF HEARING 
This leads to another field of investigation . 
The discussion of the vocal apparatus in this work has been confined to that of the sound-producing mechanism . 
But it is not unreasonable to expect that the capacities of the sound reception mechanism may also have exerted some influence on the development of the sound aspect of language . 
It is true there is little evidence that the auditory distinctiveness of specific sounds has much effect on their selection in a sound complement ( p. 12 f. above ) but other possibilities exist . 
The capacity of the ear and its mean sensitivity to different ranges of acoustic frequency are likely to vary from group to group and population to population of the earth 's surface in accordance with differences in the genetic composition of the peoples involved , and it is not impossible that the general or average " set " of a language in the frequency scale shows some sort of correlation with this capacity . 
A case that springs to mind in this connexion is that of languages with lexical tone , and an investigation into audiograms of speakers of these languages and comparison with those of speakers of other types may be of interest . 
Some possible indications of a close connexion between vocal language and the hearing mechanism have been found . 
The mechanical resolving power of the cochlea with regard to frequency , measured as the extent of the shift of the point of maximum response along the cochlear partition for a given ratio of frequency change , is practically independent of frequency in most animals . 
In the human ear , however , this resolving power is relatively low up to about 300 cycles per second and then shows an abrupt increase , reaching a relatively high value by 1,000 cycles per second ( von Be2ke2sy and Rosenblith , 1951 ) . 
Since the range of frequencies most important for intelligibility seems to be that above 1,000 cycles per second , it is tempting to regard the human variation from the pattern in other animals as the result , at least in part , of adaptation in the course of evolution to these important frequencies of human vocal communication . 
If language or its forerunners has exerted such influence on the phylogenetic development of the hearing mechanism , it is not unlikely that this mechanism has also exerted some influence on the frequencies of language . 
THE ACQUISITION OF SPEECH 
A field in which the influence of genetic factors is likely to be more easily recognised is that of the acquisition of a sound complement in the process of learning to speak . 
A real need is more work of the nature of that done by Irwin and his associates covering adequate numbers of children and carried out by investigators with standardised techniques , to determine in detail the norms of this acquisition in other communities and with other languages . 
Besides their importance in demonstrating the influence of the heredity of the group , such norms would be of considerable value in pediatrics and child development generally as well as in speech therapy . 
They may be expected to vary , not only on the grounds of genetic theory , but also in accordance with our existing knowledge of child development : thus , for example , the recent investigations by Geber and Dean ( 1957 ) have indicated that the general development of young East African children is some months ahead of that of European children of corresponding ages . 
Another field here , which would seem to be very important , but which as far as I know has hardly been touched , is the environment in which the child acquires its sound complement . 
Though some information is available as to the nature and frequency of the sounds which the child produces , no attempt seems to have been made to determine the nature and the frequency of the sounds which the child hears at this period of its life . 
Difficult though such research may be to plan and execute , it should not be neglected . 
It may well be that some correlation will be found between the nature of the stimulus from the environment and the nature of the child 's development , and this must be considered in assessing the role of the genetic component in the process . 
Investigation of this topic may also be of value by giving precision to the conception of the representative sample of the sound complement , which , it was suggested above ( p. 140 ) , could be taken as the actual norm of the group in the experience of the individual . 
THE GRAMMATICAL INTERPRETATION OF RUSSIAN INFLECTED FORMS USING A STEM DICTIONARY by J. McDANIEL and S. WHELAN , National Physical Laboratory , Teddington , England INTRODUCTION 
THE NPL Russian-English automatic dictionary is organised on a stem-paradigm basis wherein there is for most nouns and adjectives a single entry for all their inflected forms and for most verbs only one or two entries . 
This is in contrast to the full-form type of dictionary organisation wherein each inflected form of every word has a separate entry . 
The decision to organise our dictionary on this basis was made so as to be able to accommodate it on the magnetic tape store available to us on the ACE digital electronic computer of our laboratory and , further , to minimise the look-up time per word on the computer without complicating the look-up procedure too much or investing too much programming effort in its compilation . 
The word content of the dictionary initially is to be 15,000 words from the Harvard University Automatic Dictionary . 
Our dictionary will have an average of about 1.5 entries per word , whereas a full-form dictionary would have about ten times that average . 
The operation of our stem-paradigm dictionary involves two extra processing steps as compared with the full-form type dictionary . 
Firstly , words referred to the dictionary are reduced to their stems so that they may be matched against the corresponding dictionary stem entries and , secondly , after matching of stems , that part of the referred word split off to give the stem requires interpretation to determine its grammatical significance for that stem . 
The first process is known as affix-splitting and consists of matching the end of a referred word against a list of recognised affixes having grammatical significance . 
The process is fully described in a companion paper to this . 
We shall refer to the results of these papers where necessary . 
The second process , affix interpretation , is the subject of this paper . 
The extra grammatical properties of the referred word revealed by affix identification , in addition to those identifiable in the stem of the word are as follows , for nouns , adjectives and verbs : — NOUNS : — Number and case ADJECTIVES : — Number , case , gender , short or long form VERBS : — Person , number , tense , gender , mood , voice , and , for participles only , case and short or long form . 
Of course , not all combinations of these properties can occur . 
The majority of pronoun forms are treated like adjectives . 
The remaining pronoun forms and all indeclinable words are referred to full-form type dictionary entries , and do not participate in affix identification , although they undergo the splitting process . 
Affix interpretation is necessary for all stem type entries as its results form the basis of systems of syntactic analysis designed to improve a word-for-stem type " translation " of Russian into English . 
Rules of English inflection , insertion of prepositions and auxiliaries , suppression of Russian equivalents and variations of word order will all require the affix interpretation results . 
2 . 
PRINCIPLE OF INTERPRETATION 
THE splitting process consists in matching the endings of text words against a list of affixes , and splitting off any matched affixes , so that the interpretation problem may be stated as the problem of giving a grammatical significance to each of these recognised affixes when they are found . 
Now some of the affixes will have varying significance depending on the stem from which they have been split . 
For instance , one of the affixes in the list is -A , and this can have five different interpretations : — 
1 . 
Genitive singular when split from some masculine noun stems . 
2 . 
Genitive singular and nominative plural when split from some other masculine noun stems and from neuter noun stems . 
3 . 
Nominative singular when split from feminine noun stems . 
4 . 
Feminine short form when split from adjective and participle stems . 
5 . 
Present Gerund when split from verb stems . 
So for these ambiguous affixes ( they are mostly noun affixes ) it is necessary to check the stem type from which the affix has been split before giving the grammatical significance . 
There is a further check , on the validity of a given split , which can be conveniently made during interpretation . 
This is to check that the matched dictionary stem includes the split-off affix in the declension or conjugation intended to be associated with it in the dictionary compilation stage . 
We call this check reconciliation of stem and affix , and it is necessary because of the occurrence of stem homographs and also because of the possibility of a text word whose true stem is not entered in the dictionary being falsely split and the resulting stem matching with a dictionary stem . 
We combine interpretation and reconciliation in one operation , making use of a paradigm indicator associated with each stem , and one or more role indicators associated with each affix . 
By speaking of the paradigm of a stem , we mean that set of our recognised affixes , all of which combine with that stem to form valid inflectional forms of one Russian word . 
Thus each stem entry in the dictionary contains a computer word , known as the paradigm indicator word ( PIW ) , which indicates by a binary pattern the paradigm of that stem . 
There are three different formats for the PIW for noun , adjective and verb stems . 
The verb format is used for two types of verb stems , but in each case it represents a different set of endings . 
This was only necessary in practice because one computer word ( the ACE word is 48 binary digits ( bits ) long ) is not long enough to represent all the verbal affixes . 
We shall consider the noun format of the PIW as a specific example . 
The word is divided into fields , one for each of the case and number combinations of nouns . 
Accusative plural is excluded , as its endings follow those of nominative plural or genitive plural depending on the animation of the noun . 
In each field , a bit position is associated with each affix that conveys the significance of that field with a noun stem . 
The noun format is shown in Figure 1 . 
( ♯ is our symbol for the null affix ) . 
In the accusative singular field , only the feminine affixes are shown , the masculine and neuter affixes being implicit from the nominative singular , and genitive singular fields and the animation marker in bit position 43 . 
We could have repeated the masculine and neuter , nominative and genitive singular endings in the accusative singular field , but this would have required more bit positions than are available in an ACE word . 
So simply by indicating the animation of a noun stem , we can restrict the paradigm format to within one ACE word . 
The PIW for a particular noun stem is formed in general by inserting a binary digit 1 in the bit position corresponding to the appropriate affix in each field . 
For example , consider the stem entry and PIW resulting from the Russian word whose nominative singular is STOL ( table ) . 
The stem entry will be STOL — and the set of affixes which give all the inflected forms of STOL is♯ , { 11A , U , E , OM , Y , OV , AM , AKH , AMI . 
The PIW will thus have " ones " in positions 1 , 11 , 15 , 19 , 21 , 26 , 32 , 37 , 39 and 41 . 
The absence of a " one " in bit position 43 indicates the inanimate nature of the stem and hence implicitly indicates the accusative singular and accusative plural endings . 
A stem which takes alternative affixes in a given field will have " ones " in the bit positions of both affixes e.g. the stem VOLOS ( hair ) has the alternative affixes Y and A in the nominative plural form . 
Where a stem is not common to all inflected forms of a word , only those fields to which that stem applies will have a " one " in them e.g. the stem BRAT- ( brother ) applies to the singular inflected forms only ( 1 , 11 , 15 , 19 , 21 , 43 ) while the stem BRAT'- applies to the plural forms ( 29 , 33 , 36 , 38 , 40 , 43 ) . 
The formats for adjectives and verbs are shown in Figure 2 and in principle are similar to the noun format . 
They all have more fields than the noun format , but have much less variety of affixes within each field . 
The two verb formats have identical fields , but mostly different affixes in those fields . 
They include fields for participle affixes , but the affixes in these fields are only the participle stem-building affixes . 
However , as participle adjectival endings follow a perfectly regular pattern , they need not be explicitly stated in the PIW . 
Nearly all nouns and adjectives will require only one stem and PIW to represent all their inflected forms . 
Approximately 2/3 of Russian verbs will need only one stem , most of the rest requiring two stems , and only the irregular verbs more than two . 
The PIW are compiled by the computer from data sheets ( dictionary entry forms ) one of which is manually completed for each word to be entered into the dictionary . 
There is a different data sheet for each of several broad classes of noun declension , so as to limit the linguistic decisions to be made in completing the sheets , but all noun data sheets refer to the one standard format for the noun PIW . 
There are similar data sheets for adjectives and the two types of verbs , in these cases only one type of data sheet per format , because of the lesser variety of inflection . 
With the provision of a PIW in each stem entry in the dictionary , the problem of interpretation of an affix which has occurred on a given stem as a text word , is resolved into spotlighting the occurrences ( if any ) of that affix in the PIW for that stem and noting the fields ( grammatical properties ) in which they occur . 
This is most easily done by having , for that affix , a masking pattern containing a " one " bit corresponding to each occurrence of it in the PIW format . 
Then , by performing a " logical and " operation between this mask and the PIW of the given stem , the result will contain a " one " bit in each field where that affix has significance for the given stem . 
Of course , if the result was zero , this would mean that the affix and stem were incompatible i.e. the stem did not combine with the affix in any meaningful inflection . 
This situation may arise with stem homographs and with words whose true stems are not yet compiled into the dictionary and are falsely split . 
In the latter case the PIW would not contain the falsely split affix . 
The masking pattern referred to above we call the role indicator word ( RIW ) for the given affix . 
Some affixes have significance with more than one of the PIW formats , and for these there will need to be more than one RIW e.g. I has significance for and appears in each of the four PIW formats , so it will have four RIW . 
In order to be able to match the appropriate RIW to a given PIW in an interpretation , the format types are given a type number ( digits 47 and 48 ) and the RIW which relate to these types are given the corresponding type no . 
There are identical I and E verb RIW for each of 10 verbal affixes { 11 ( U , JU , I , J , ' , JTE , 'TE , A , JA , ENN ) and so we save some space in storing the RIW by having only one verb RIW for each of these 10 and indicating its dual utility . 
Let us consider two examples of interpretation of noun forms AVTOMOBILI and NEDELI , which would be matched against the dictionary stems AVTOMOBIL- and NEDEL- respectively , with I as the affix to be interpreted in both cases . 
The PIW for the noun stem AVTOMOBIL- and the noun type RIW for I would be as shown in Figure 3 . 
The " logical-and " of these two computer words would give a " one " bit in position 28 only i.e. in the nominative plural field . 
The PIW for NEDEL- is also shown in Figure 3 and the result of " anding " this word with the RIW for I would be a " one " bit in positions 14 and 28 i.e. in the genitive singular and nominative plural fields . 
By the former view the categories are common by definition and { 6a priori , by the latter empirically and by reason of a more or less similar semantic range { 6a posteriori . 
But while many modern linguists would subscribe to the latter view there remains still a common core of syntactic terms , common by definition among those making use of them , not from any content or semantic meaning , but from the method of establishing them within each language . 
Terms like Nucleus , Expansion , Cohesion , Endocentric , and Exocentric are general ( though not necessarily universal ) categories , by reason of the common operations by which sentences in a language are compared and classed together as regards the formal inter-relations of their components . 
These operations and the criteria employed need not be in detail the same between any two linguists , but the overall operational similarity in their use is obvious . 
" General syntax " thus allows two possible interpretations , and different answers may be given to the question of generality on each of the two . 
( 4 ) What is the relationship between syntax and morphology ? 
To some extent the answer to this question is conditioned by one 's answer to question ( 1 ) above . 
If the morpheme , not the word , is the minimal unit of syntax , the role of morphology , no longer concerned with syntagmatic word structure , is correspondingly reduced ; and there are those who say that the distinction between these two traditional parts of grammmar is of little value today . 
But assuming that the distinction is maintained one may ask which is to be analytically prior : in which domain do we establish the majority of the principal categories first ? 
Are syntactic structures set up to explain the use of the morphological form classes , or are form classes dependent on their role in syntactic structures for their grammatical significance ? 
This question may be , and has been , answered either way irrespective of the degree to which logic or " meaning " are admitted as criteria in grammatical analysis ; in traditional terms it involves the relative priority of such class concepts as noun and verb as against such as subject and predicate . 
( 5 ) What is meant by " structural " syntax ? 
" Structural " is an epithet few linguists would deny of their work today , as it carries connotations of up-to-dateness and scientific thinking , however varied its applications may be . 
" Structural " is , in fact , consistent with a number of otherwise divergent approaches to language . 
Trubetzkoy 's phonology as well as Pike 's or Trager and Smith 's phonemics is structural ; morphological analyses based on the " meanings expressed " by the forms can be worked out structurally , and equally the purely formal morphemic analysis of Harris is structural . 
Semantics can , at least in part , be treated structurally on the lines of the de Saussure-inspired "field theory " , or on the statistical models suggested by Wells and others , and Firth 's theory of context of situation , framed so as to cover the whole of the semantic analysis of utterances as far as this can fall within general linguistics , is essentially structural . 
Applied to general linguistics as a whole , " structural " has a fairly definite comprehensive meaning , namely that the elements and categories of linguistic statement and analysis are established and explained by reference to their relations with one another within the system or systems of the language concerned , rather than as units of an aggregate each carrying its own independent formal constitution or value . 
Applied to syntax , perhaps , the term adds less than to the other levels of linguistic analysis . 
In a sense syntax has always been structural , as it has concerned the relations of the parts of sentences to each other , whether as exponents of the logical constituents of propositions in the traditional view , or as the expression of the psychological components of " Judgments " , or , in formal terms , as the elements of a number of patterns to which sentences of a particular language can be shown to conform . 
These considerations are all pertinent to the reading of Tesnie3re 's recently published extensive work on syntax . 
His E2le2ments , in manuscript at the time of his death in 1954 and now published with an explanatory preface by J. Fourquet ( pp. 3-7 ) , arose from his dissatisfaction , especially from the teacher 's point of view , which is constantly kept to the fore , with traditional grammar and its preoccupation with morphology as the basis of grammatical instruction and the learning of languages . 
For Tesnie3re syntax is the centre of grammar and the proper foundation for grammatical categories like word classes , morphology being the study of some of the markers of such categories and of the syntactic functions of words in the sentence ( Chapters 15-6 ) . 
In language description syntax is the heart of the grammar , not something added at the end to explain the uses of the morphologically different forms . 
This emphasis on syntax , or sentence structure , in grammar , rather than on word form , morpheme shapes , and paradigms , is to be welcomed , and is in agreeable contrast to an excessive devotion to purely morphological problems among some modern linguists as well as more old-fashioned ones . 
Tesnie3re shares with the more rigidly formal American linguists a reaction against tradition , but as Fourquet remarks he owes little to their work , and his theories are , more perhaps than with most writers , his own . 
One may , however , ask whether he has gone far enough in rejecting traditional ideas , and whether despite his insistence on the autonomy of syntax ( p. 42 ) he has not , in fact , retained certain of them that look like convenient { 6points d'appui for his theory but themselves lack a secure basis in language itself . 
Tesnie3re 's syntactic theory is general in the first sense mentioned above ; language expresses thought ( p. 12 ) , and grammatical categories are { ide2es ge2ne2rales and { classificateurs of the innumerable { ide2es particulie3res ; they may vary from language to language and are not identical with the { cate2gories de la pense2e which are said to be the same for all men ( how do we know this ? ) , but have close links with them and often coincide , and always { rele3vent de la se2mantique ( Chapter 24 ) . 
An example of this kind of grammatical approach is found in the way Tesnie3re defines the various types of subordinate clause ( causal , final , conditional , concessive , etc. , Chapters 254-65 ) by their meanings , and then exhibits examples of the " same " types differently realized in different languages ( e.g. Chapter 243 , 137 ; 259 , 1315 ; 262 , 1323 ) . 
Though he elaborates his work mainly with reference to written French , with a bias towards the language of literature , and his illustrations are drawn largely from European languages ( note that all the American-Indian languages are lumped together typologically ! , p. 33 ) , he regards the basic elements of his syntax as universal . 
Words as written are the units he works with , but he recognizes the difficulties of word delimitation and the occasional inadequacies of traditional orthographic divisions ( Chapter 10 ) . 
Where what he considers to be the same sort of syntactic process ( e.g. a translation , see below ) is carried out in one language by a separate word and in another by an affix , he does not for that reason analyse it differently ( p. 361 ) . 
Tesnie3re 's syntax is based on the noeud , and sentences consist wholly of noeuds hierarchically arranged , the minimal sentence being a single simple noeud . 
Sentences set out in such a way as to reveal their " nodal " structuring are called stemmata , and abstract stemmata ( { phrases virtuelles , Chapter 33 ) represent sentence types with the lexical differences of the component words ignored . 
Sentences in familiar languages are usually based on a verbal noeud , but other noeuds ( nominal , adjectival , and adverbial ) are possible as entire sentences , especially in conversational discourse ( p. 15 ) . 
Stemmata represent the sentence structure , and the " real sentence " syntactically ; speaking a language is transforming it into a linear succession of words , and conversely understanding is recovering the sentence structure from such a succession ( Chapter 6 ) . 
The following examples illustrate , ( a ) and ( b ) a single noeud , and , ( c ) a hierarchy of noeuds in a stemma ( pp. 14-15 ) : 
Subordination , the dependence of the governed on the governor , represented by its occupying a lower line in the stemma , is fundamental , since the noeud is defined as { un re2gissant qui commande un ou plusieurs subordonne2s ( Chapters 2 , 3 ) , though the concept does not appear to be fully defined . 
Adjectives depend on nouns , and adverbs on verbs or adjectives , and { tout subordonne2 suit le sort de son re2gissant ( p. 14 ) , just as in Bloomfieldian terms words are grouped into endocentric constructions because they behave syntactically like their head component . 
But Tesnie3re also subordinates " subject " nouns to verbs , as is seen in the examples cited above , where parle governs Alfred as well as Bernard , and so on . 
We are not told why ; is it because in some languages ( e.g. Latin ) the verb by itself can form a complete sentence ( cantat , of which { vir cantat is an expansion ) ? 
In French chante is not a complete sentence of the same type as { Alfred chante , but { il chante is , and such a sentence , wherein il is a { mot vide and a mere indice , is regarded as a single semantic unit ( nucle2us ) , though a noeud of head and subordinate ( Chapter 22 , cp. stemma 33 , p. 56 ) . 
If this is the argument , it is not made clear by Tesnie3re . 
Words are divisible into the categories of " full " ( pleins ) and " empty " ( vides ) on semantic grounds , full words bearing a separate meaning , empty words only a grammatical use ( Chapter 28 ) . 
This is familiar ground , and it is hard to see how the distinction can be rigorously carried through ; " having an independent meaning " is probably equivalent to the fact that a gloss can be given by a native speaker to the word in isolation , and this is likely to be a matter of degree rather than of a binary division into two classes . 
Tesnie3re follows the fullempty division with the more formal division of { mot constitutif and { mot subsidiaire ( Chapter 29 ) , the former being able to constitute the head of a noeud , while the latter can only appear as a subordinate member of one . 
The divisions fullempty and constitutivesubsidiary are nearly though not quite coextensive in membership ( p. 57 ) . 
Although the fullempty division is the less satisfactory of the two , it is this that is used subsequently in word classification , and within full words four classes ( each of which can be the head of its own noeud ) are recognized and distinguished by their class meanings ( { contenu cate2gorique , Chapter 32 ) : 
Defined thus these classes are general , but not universal , because , astonishingly , we read that the nounverb distinction is predominantly European , and that the majority of other languages show only nominal noeuds as the basis of their sentences , and " conceive of process as a substance " ( p. 61 ) . 
{ Mots vides are either " junctives " , joining grammatically equivalent words and word groups together , or " translatives " , which convert the grammatical class of one word into that of another or convert a sentence or word group into the grammatical equivalent of a single word . 
Thus and and but ( traditionally coordinating conjunctions ) are junctives ; prepositions are translatives converting nouns into adverbs ( " first degree translation " , pp. 386-7 ) , and the traditional relative pronouns and subordinating conjunctions are translatives of the second degree ( conjunction + verbal noeud = adverb , relative pronoun + verbal noeud = adjective ) . 
Translation ( in Tesnie3re 's sense ) , which may be marked by separate { mots vides ( translatifs ) , by affixes or word form changes , or be unmarked , is what gives languages their universal suppleness and utility ( Chapter 153 ) , and its importance in grammar is emphasized throughout the book . 
In fact approximately the second half of it is devoted to the theoretical exposition and copious exemplification of the various types of translation , and includes double ( and triple and upwards ) translations , as when , for example , a de-adjectival noun or nominal expression is adverbialized ( e.g. French ( trancher ) { dans le vif , pp. 474-5 ) . 
The four classes of full words always preserve their class meanings and their consequent grammatical status , and an apparent atypical use ( e.g. adverb with a noun head , { un homme bien , un vin extra , { 15owi pa2lai a2nthropoi , Chapter 197 ) is explained as a translation adjective to adverb without overt mark ; conversely , morphological form , if in apparent contrast to syntactic function , has no effect on classification ( in French { touttoute in sentences like { elle est toute honteuse , p. 184 , is an adverb irrespective of its concordial variability of gender form ) . 
The theory has a great sweep about it : language is no conglomerate of single words , but a whole with meaningful division , a super-{6Gestalt : conceptual fields shape the raw material of experience and divide it up without overlapping , like the pieces in a completed jig-saw puzzle . 
The individual field , in its turn , is a mosaic of related words or concepts , the individual word getting its meaning only through distinguishing itself from its neighbours , and the field again being divided up completely and without overlapping . 
The concepts in a field , in short , form a structure of interdependent elements . 
A word-form may change without there being any change in the structure of the field , in Sprachinhalte ; for instance , in the Romance languages , the continuants of Lat. coxa replaced those of Lat. femur , weakened by a homonymic clash , without there being any change in the structure of the semantic field . 
Any change in the limits of a concept , on the other hand , will involve a modification of the value of the other concepts in the same field , and of the words which express those concepts . 
Trier sought to illustrate the validity of his hypothesis from his analysis of the intellectual vocabulary of Old and Middle High German . 
The most-quoted example is that of a comparison of a particular field in about A.D. 1200 with the corresponding one in about A.D. 1300 . 
At the beginning of the 13th century , the structural ensemble of the Middle High German " field " of knowledge was based , he maintains , on the co-existence of three key terms — { kunst , list and wi5sheit ( very roughly " art " , " artifice " and " wisdom " ) ; at the beginning of the 14th century , the key-words were { kunst , wizzen and wi5sheit . 
There had not , however , been a simple substitution of wizzen for list which continued to be used in a somewhat different sense : what had occurred was a re-organization of the linguistic structure of the field , and above all of the Weltbild or " world-picture " which the latter reflected . 
In 1200 , the term kunst was applied to courtly skills , and list to non-courtly ones , to techniques and skills other than those of the knightly class . 
Thus , courtly bearing towards adversaries was a kunst in a knight ; so was the art of writing poetry ; so were the liberal arts of rhetoric and music in so far as they contributed to the training of the ideal knight ; on the other hand , astronomy , botany , medicine and all the crafts of the artisan were liste . 
The difference between kunst and list was , however , not as clear-cut as that suggests ; whereas skill at arms was a kunst in a knight , it was only a list in a man at arms : i.e. , these branches of knowledge were not appraised objectively , but socially . 
This gulf between courtly and non-courtly at the level of material knowledge was transcended at the spiritual level : the term wi5sheit embraced kunst and list , and much else besides , being applied to all kinds of knowledge , divine as well as human . 
There was therefore a close interlocking of concepts within a field of knowledge conceived synthetically ; kunst and list were co-determined in their senses by the links which united them within the wider sphere of personal and divine wisdom . 
The key-terms of the later field did not form a mystic trinity of this type : there was merely a duality between kunst and wizzen , wi5sheit being on quite a different level from them . 
Kunst was used to describe certain branches of knowledge , in rather the same way as in modern German — in opposition to wizzen , which was applied to knowledge in general and to technical skills and abilities in particular , but without any social connotation . 
The disappearance of the earlier duality between kunst and list signified from the spiritual point of view the abandonment of an ethico-social attitude towards the scientific and technical : it had become possible to talk of what a man knew or could do , without a " social " appraisal of him as well as of what he was doing . 
Wi5sheit was no longer used as a semi-alternative for either of the other terms , nor as a synthetic term embracing them both . 
Material knowledge ( kunst and wizzen ) had been removed from the sphere of wi5sheit , which , as spiritual and religious wisdom , had moved to a different plane . 
The use of the terms showed a drastic change in the conception of knowledge , which had been divided up in a more analytical and abstract way . 
Whereas in 1200 no truly objective appraisal of knowledge was possible ( it could not be divorced from its social and/or religious connotations ) , in 1300 , spiritual or theological knowledge was dissociated from worldly skills , and the contrast between courtly and non-courtly attainments had been eliminated . 
Trier saw this re-arrangement of the field as reflecting the disintegration of the earlier " catholic " conception of knowledge . 
Trier 's theories have been strongly criticized as well as praised , in particular by Dornseiff and Scheidweiler in the 1930 's and early 1940's , and by W. Betz and Els Oksaar in the 1950's ; W. von Wartburg and S. Ullmann , as I have already mentioned , have criticized certain aspects of them , while remaining generally favourable . 
It is inevitable that I repeat some of the arguments used against Trier by other scholars , but I hope to make a few new points . 
Basically , Trier 's field theory depends on the validity of several hypotheses about the nature of language and of thinking and the relationship between the two : firstly , that the whole vocabulary is organized , as he believes , within closely-articulated fields which fit into each other and delimit each other in the same way as the words within the individual fields , without any overlapping ; and secondly , that the single word gets its meaning only through distinguishing itself from its field neighbours . 
The latter follows to some extent , but not , I think , completely , from the first postulate . 
Both points are valid , if they are valid , for any language at any period . 
Let us take the second point first because it can be dealt with more briefly . 
Whatever the validity of the oppositional approach in determining linguistic units such as phonemes and morphemes , it seems doubtful whether word-meanings are based on oppositions between words in the same conceptual field . 
This idea of the element only deriving its meaning from the system as a whole has to be qualified so much that it really ceases to have much point : e.g. , I can know the Russian for " to walk ( habitually ) " without knowing the Russian verbs for " run " , " hop " , " skip " , or " jump " ( habitually or otherwise ) . 
W. Pfleiderer makes the point that a child 's first properly used word means something to it , but it does not know any fields . 
It certainly seems that when learning a language one fortunately does not have to learn the whole before knowing the parts . 
If it be then argued that one can not know the system properly without knowing the whole , I should reply that it depends what one means by both properly and by whole . 
Is the whole of the English vocabulary that which is known to or used by that abstraction , " the man in the street " , or that which is " deposited " in the New English Dictionary , plus Eric Partridge 's Dictionary of Slang and a few other works of that type ? 
Nobody knows all the words in those works , i.e. , knows the whole of the system in that sense ; is it then the vocabulary used by the " man in the street " , whoever he may be ( with his 2,500 words , or whatever it may be ) ? 
The newspapers are full of complaints about the inability of school-leavers ( or students , or civil servants ) to " use English properly " . 
At one level , this means that the members of these groups do not express themselves as accurately or as elegantly as their critics do , or think they do . 
At another level , as a statement about English-speakers , it is rather like saying , " only 2 per cent of the population have normal teeth . " 
Take any obscurish word — since I have mentioned teeth , let it be the term " orthodontics " . 
As the name of a branch of dentistry , it comes ( I assume ) into the same field as " teeth " , and if we assume the validity of the hypothesis , the two help reciprocally to delimit each other 's meaning , they are part of the structure of the field — but only for those who know the word , or for everybody ? 
In either case , only a tiny proportion of the English-speaking population of the world is using the term " teeth " with an appreciation of its full value — which is absurd . 
Similar arguments can be brought against the main postulate — that closely-integrated conceptual fields , expressed in linguistic ones , cover the whole field of experience ( and of the vocabulary ) without gaps and without overlapping . 
Is this generally true of the way the vocabulary is organized in the consciousness of the individual — let alone of a vast and heterogeneous group of individuals ? 
Basically , the theory is one about the way the mind works — and as such , would be better tackled by psychologists than by linguists . 
Things are not made any easier by the fact that Trier does not make an absolutely clear division between his conceptual and his lexical " fields " : he does not always separate them at all , but when he does , he seems to indicate that conceptual divisions are expressed in linguistic ones , and not , as has been somewhat more plausibly maintained , that the structure of a language and the vocabulary " transmitted " to a given individual to some extent determine his modes of thought . 
What evidence is there to support the view that the vocabulary is organized in the manner suggested by Trier ? 
There are Trier 's own analyses which are open to a number of criticisms : as Scheidweiler points out , Trier himself makes statements about the use of words which seem to run counter to his own theories . 
For instance , on p. 150 of his { 6magnum opus , he speaks of a completely unarticulated field of " the positive assessment of value " ; he tells us that the famous terms kunst and list are applied interchangeably by the author of the Pilatus , and so on . 
There is no uniformity in the usage of different authors : it is true that Trier speaks of transition conditions under which the field becomes fluid ( " { das Feld zuna " chst einmal in ein sta " ndiges Fliessen gera " t " ) , but in that case , Scheidweiler comments , the whole period investigated by Trier must have been one of transition . 
From his own examination of the texts used by Trier , Scheidweiler finds it impossible to support the former 's conclusions about the values of the terms kunst and list , while with regard to wi5sheit he points out that the term Weisheit is still used in Modern German with the sense of " knowledge " in such phrases as " { ich bin mit meiner Weisheit zu Ende " , "er besass keine umfangreiche Buchweisheit " , " woher hast du deine Weisheit ? " and so on . 
Trier would probably counter by saying that he was concerned with conceptual fields and that his view could not be disproved by the survival of lexical fossils . 
This would perhaps be a valid argument , but the extent of the disagreement between Trier 's findings and Scheidweiler 's goes far deeper , and seems to justify caution with regard to Trier 's findings . 
Trier himself , judging by his various qualifications and his references to " transition states " found the evidence less clear-cut than he might have desired . 
In Scheidweiler 's opinion , usage in mediaeval German texts provided no support for any theory that words or concepts were organized in " fields " without overlapping : even the same author used the same words with totally different meanings , and so forth , in a way that we should find intolerable ( Scheidweiler quotes examples ) . 
One of his general conclusions is that these early texts are an unsuitable testing-ground for such a theory because of the lack of precision in the use of terms in mediaeval times . 
It seems to me that that judgement damns the theory for the wrong reason . 
Lack of precision in the use of terminology can not indefinitely be explained as the product of " transition " from one world-view to another , one system to another : the fact that lasting imprecision exists itself seems to disprove Trier 's hypothesis . 
Plato envisaged the need for an examination system not essentially different from ours . 
Of his potential " Guardians " he wrote : " 
We must find out who are the best Guardians .... 
We shall have to watch them from earliest childhood and set them tasks .... 
We must also subject them to ordeals of toil and pain and watch for [ their ] qualities . 
And we must observe them when exposed to the test ... put them to severer proof than gold tried in the furnace .... 
If we find one bearing himself well in all these trials ... such a one will be of the greatest service to the commonwealth as well as to himself . " 
The purpose of Plato 's tests was to be of service to the commonwealth as well as , and more than , to the individual . 
He held that social life depended on specialization of function and he believed that each person was best fitted by congenital constitution and education for a particular role . 
Education not only helped to train a person for his particular function , it also revealed native constitution : response to education predicted capacity for future achievement . 
The educational system was inevitably also a selection system , and Plato 's tests were only more refined instruments of screening than the educational process itself . 
This dual function of educational systems — to educate and to assign people to roles — is a perennial source of difficulty . 
Both functions are necessary , but it is not easy to carry them out together , and the temptation is to welcome one and to reject the other . 
Dr. Wiseman refers in his foreword to those who , rightly valuing education , reject the necessity of selection , and take up the position he condemns as " therapeutic extremism " . 
Plato may be accused of having gone to the other extreme , for it seems that having selected his Guardians he has little interest ( in the Republic ) in the education of the rest . 
The American public school system has accepted the function of education and on the whole rejected that of selection : selection is left to the college and the university , to the M.A. and the Ph.D . 
stage rather than to anything resembling the " 11-plus " and the G.C.E. In England 11-plus selection has been deplored because of its adverse effects on education in the primary school . 
A distaste for the selection function may be discerned also in the Crowther Report 's desire , on behalf of secondary schools , to make the G.C.E. a school-leaving and " qualifying " examination and to dissociate it from the selection of university students . 
Distasteful though the function of selection may be , however , it is one which the educational system can not escape , for as Plato pointed out educational achievement is not only the means to , but an indispensable index of capacity for , service to the commonwealth . 
The screening function has not been pressed upon educational systems with equal insistence at all times and in all places . 
In so far as social and vocational roles are predetermined by race , caste , or family , the assessment of the abilities of the individual is of less significance . 
The possibility of selection on the basis of individual differences presupposes some degree of social mobility , and it is arguable that it is at times and places where social mobility is greatest that the interest in examinations and tests has been strongest . 
Mr. Morris has noted that Imperial China , with its dictum " Employ the able and promote the worthy " , developed a highly complex system of examinations , whereas in the comparatively closed society of medieval Europe the interest in examinations was limited and sporadic . 
Bentham , intent on widening and improving recruitment to the Civil Service , was characteristically interested in examinations . 
The development of public examinations since the 1850's has been closely connected with the extension of elementary , secondary , technical and university education and of access to the crafts and professions . 
The more recent institution of the Diploma in Technology and the work of the Associated Examination Board are obviously related to the increasing esteem which technical skills and abilities command . 
Plato in fourth century Greece noted ( with disapproval ) the similar upward mobility of craftsmen and its connection with an interest in qualifications — with philosophy if not with the doctorate of it : " 
Philosophy ... is dishonoured by unworthy interlopers ... when any poor creature who has proved his cleverness in some mechanical craft sees here an opening for a portentous display of high-sounding words and is glad to break out of the prison of his paltry trade and take sanctuary in the shrine of philosophy . 
For as compared with other occupations , philosophy , even in its present case , still enjoys a high prestige . " 
Values in educational achievement change . 
Plato valued philosophy and despised crafts that enslaved men ; we value technologists more than philosophers ; but whatever kind of specialist one has most use for one seeks to select and promote ; and the greater the freedom to rise the more one uses tests and examinations to refine the screening function which the educational system performs . 
It is because democratic ideals and economic needs at the present time put a premium on the emergence of ability that we are specially interested both in education and selection . 
As new kinds of " service to the commonwealth " are demanded , new kinds of education have to be established , or old kinds have to be adapted ; and examinations at once define and support them . 
It is often said that examinations maintain standards in education ; it should not be overlooked that they sometimes help to create them . 
The Diploma in Technology not merely preserves standards , it sets objectives and stimulates the effort to achieve them . 
The reform of university examinations in the nineteenth century did not preserve standards , it helped to establish higher standards of education for service to Church and State . 
Examinations defined standards which supported the development of secondary education for girls in the same century and that of the maintained grammar schools in the twentieth century , and if they did not create sixth forms in these they at least stimulated their growth . 
The examination of general studies is helping to produce a situation in which such studies have a greater chance of survival in the sixth form . 
It is the value systems of the commonwealth which likewise confer on examinations their force as incentives to learning . 
Plato alone — and he in theory only — removed the economic incentive to learning . 
His Guardians were to be motivated in their arduous studies by disinterested service to the commonwealth : " They alone of all the citizens are forbidden to touch and handle silver or gold . " 
It is hardly to be supposed that the incentives he proposed would appeal strongly to the candidate in 11-plus , G.C.E. or university examinations : " Whenever we find one who has come unscathed through every test in childhood , youth , and manhood , we shall set him as a Ruler to watch over the commonwealth ; he will be honoured in life , and after death receive the highest tribute of funeral rites and other memorials . " 
It may be true that pupils do not always have clearly in mind the long-term advantages of passing examinations , and that it is rather the teacher or parent who is moved by them . 
Even so the incentive which is felt by the pupil through them is derived ultimately from the demands of the commonwealth for particular kinds of developed ability : the examination merely focuses these demands . 
The pupil 's educational values are at least indirectly those of the society in which he will find his role . 
It may be suspected that the G.C.E. candidate , for example , has a shrewd idea of the relative values of passes in English Language , Scripture Knowledge , Physics and Art . 
The trends in the number of entries for G.C.E. examinations to which Dr. Petch draws attention suggest a quick appreciation of the social and economic evaluation of different studies . 
The most radical method of increasing social mobility so far devised has been the use of intelligence tests . 
The education system educates and selects , but as we have seen the two functions are not easily reconciled . 
If selection can interfere with education , so can education , or the lack of it , interfere with selection . 
It has long been recognized that there are " mute inglorious Miltons " — mute and inglorious because uneducated and { 6a fortiori unselected . 
In twentieth-century England there may be few who have not had the opportunity of education , but opportunities have varied ; and as parents , teachers and communities can not be equalized opportunities are long likely to vary . 
Yet democratic ideals and the economic need to exploit the scarce commodity of talent alike impel us to seek out ability even where it has not been fully developed by education . 
No reputable psychologist has claimed that he can measure some pure hypothetical " intelligence " which has not been affected by environment and education , but psychologists have been highly successful in constructing tests which are less affected by differences in educational opportunity than are most tests of educational attainment . 
The psychologists ' success has naturally been looked upon with disfavour by those who could command educational opportunity though not intellectual capacity . 
Their tests have also been the object of abuse from those who believe that a person is made by collective society and who can not on ideological grounds accept that the individual ( or for that matter wheat ) has any characteristics which he does not owe to society . 
Neither group objects to selection or to selection tests : each merely wishes to select persons who meet his own specifications , which are not solely in terms of the qualities of the individual . 
It is to be hoped that the uninformed and doctrinaire attacks on the judicious use of intelligence tests will be stoutly resisted . 
They are not a panacea , but they can be highly competent instruments for use in the open society . 
It is significant that , as Dr. Wiseman points out , such tests first became widely acceptable in the American army in the First World War , when it was acceptable that military rank and function should depend on individual rather than social , economic or racial differences . 
Tests and examinations are instruments which a free and open society has need of . 
It must be admitted that selection on the basis of the abilities of the individual has been criticized by not illiberal persons . 
There are dangers in the selection of the able but badly educated . 
T. S. Eliot has suggested in effect that an e2lite may have intelligence but lack culture . 
The emergence of angry young men may be taken to support his argument . 
He probably underestimates , however , the assimilative power of education . 
Men do not remain young , or necessarily angry , and their children , faced with fewer obstacles to selection , may be more open to the influences of culture . 
The evidence in the Crowther Report shows that the first generation of the more educated seeks still more education for its children , so that culture as it were accumulates at compound interest . 
The selected have also been depicted as a " meritocracy " . 
One can sympathize with the guilty feeling that it is in some ways distasteful that some people should be endowed with greater gifts than others . 
It might have been better if it were true that all men are equal — though it would detract from the interest of , for example , the Olympic Games . 
The facts being what they are , however , it is incumbent on the objectors to " meritocracy " to say what alternative they would propose — aristocracy , plutocracy , caste , nepotism , party membership , or what ? 
Until a rational non-escapist alternative is offered , the only way seems to be to make intelligence tests , examinations and other instruments of selection as effective as possible for their purposes , while minimizing as far as possible any harmful effects they may have on the main function of the educational system , that of education . 
There is no denying that the inevitable process of selection can have deleterious effects on the more essential process of education . 
At every stage of the educational process where selection becomes prominent , the latter affects the former , usually in some respects to its disadvantage . 
Dr. Wiseman has discussed in particular the educational effects of 11-plus selection , where the problems have been recognized and fully debated . 
Nevertheless , during the sixteenth century several factors were to be instrumental in establishing those secure foundations on which the brilliant scientific achievements of the succeeding century could be built . 
First among these factors was a more emphatic appeal for acceptance of that philosophical outlook which has been so favourable to progress in science , namely , recourse to observation and experiment , and substitution of rationality for authority . 
In 1536 Peter Ramus ( 1515-1572 ) started the revolt against Aristotle 's tyranny with his M.A. thesis at Paris University that " all that Aristotle has said is false " . 
Marcellus Palingenius Stellatus voiced the same sentiment in his { Zodiacus vitae ( Venice 1531 ) in which he affirmed : 
" { 1Whatever Aristotle saith , or any of them all , I passe not for : since from the truth they many times doe fall . " 
In 1560 Barnaby Googe published his English translation of this work which contained , amidst a mass of characteristic moralising , references to the vacuum , light , the elements , heat , motion , etc . 
His translation was widely read as a textbook in Elizabethan grammar schools . 
The scientific attitude is also discernible in the writings of Leonard and Thomas Digges . 
From passages in the Pantometria ( 1571 ) it would appear that Leonard Digges , of University College , Cambridge , was conversant with the principles of the telescope . 
In his Dedicatory Epistle to the Stratioticus ( 1579 ) Thomas Digges , who also studied at Cambridge , mentions 
" { 1having spent many of my yeares in reducing the Sciences Mathematicall from Demonstrative Contemplations , to Experimentall Actions .... " 
Dr. John Dee ( 1527-1608 ) , of St John 's College , Cambridge , likewise sings the praises of { Scientia Experimentalis in his Preface to an English translation of Euclid ( 1570 ) . 
In 1550 Dee read public lectures on Euclid 's elements " { mathematice3 , physice3 , et Pythagorice3 " in the College of Rheims . 
His audience became so large that many had to listen at the windows . 
Dee also wrote on mechanics , perspective and on " burning mirrors . " 
The brilliant achievements of Galileo , of Stevin , of Gilbert and of others were the fruits of putting into practice of this " modern " experimental scientific attitude . 
The creation of the science of dynamics as we know it today is principally due to Galileo ( 1564-1642 ) , Professor of Mathematics at Pisa and Padua Universities . 
He pointed out that all bodies fell at the same rate and that the distance covered by falling bodies varied as the square of the time . 
He showed that the path of a projectile was a parabola , and he understood centrifugal force . 
He gave precise definitions of momentum , velocity and kinetic energy . 
It was he who formulated the principle of the parallelogram of forces , and he was familiar with what later came to be known as Newton 's first two laws of motion . 
Besides discovering the isochronism of the pendulum , he showed that the time of oscillation varied as the square root of its length . 
William Gilbert ( 1540-1603 ) , " the father of the magnetic philosophy , " was the author of that great textbook of magnetism and electricity , the " { De Magnete , " which was published in London in 1600 . 
His contempt for the methods of the schoolmen crops up everywhere in this book . 
He is full of the importance of experimentation , as for instance , when he warns that 
" men of acute intelligence , without actual knowledge of facts , and in the absence of experiment , easily slip and err . " 
Gilbert was the first to use the now familiar terms " electric force " , "electric attraction " , magnetic "pole " , etc . 
By the time of the sixteenth century considerable industrial and commercial expansion was taking place , and this resulted in a greater demand by the rising middle classes for a more utilitarian education biased towards science and mathematics , for substitution of a more realistic approach to life for the aloofness of the cloister . 
The increasing tempo of the new economic world could no longer afford to dispense with mechanics , hydrostatics , optics , navigation , etc . 
It was in order to cater for the needs of a society growing increasingly more conscious of the vital part that science could play in technology that Gresham 's College was founded in London in 1596 for gratuitous instruction in the seven liberal arts and sciences . 
The celebrated physicist Robert Hooke was Professor of Geometry here for a time . 
Lectures were given at the College — which , incidentally , was the first home of the Royal Society — till 1768 , when they were delivered at the Royal Exchange until 1841 , the year when the present Gresham College was erected . 
It was for precisely the same reason that during the second half of the century a new type of school , or academy , came into existence to give a wider education , including practical mathematics and physics , than that provided by the conservative public and grammar schools whose sole preoccupation was with the classics . 
Sir Humphrey Gilbert ( 1539-1583 ) proposed the erection of such an Academy in London in 1572 . 
By now the discovery of printing had come into its own and this led to the writing , in the vernacular , of numerous popular compendia of knowledge . 
The numerous editions through which many of these compendia and encyclopaedia went indicates the thirst of the people of those times for knowledge . 
The best known of these was probably the " Pearl Philosophic " ( " { Margarita Philosophica " ) of Gregorius Reisch , which was first printed in 1503 . 
The subjects of astronomy , natural philosophy , chemistry , optics , etc. , are treated in this encyclopaedia which was illustrated and intended as a textbook for young students . 
In his book on " Natural Magic " Giambatista Porta ( c. 1541-1615 ) dealt with such topics as optical experiments , mirrors , experiments on statics such as those of Nicholas of Cusa , and pneumatic experiments similar to those of Hero . 
An English edition of this book was published in London in 1658 . 
The Reformation , too , had an influence on the progress of science . 
The refusal to submit to a single spiritual authority carried over to other fields and helped to emancipate physics from Aristotle 's " tyranny " . 
In 1535 the students of St. John 's College were permitted to receive instruction from a lecturer in Natural Philosophy , who was to receive two shillings a week , half that sum being paid by the College and the other half by his audience . 
The Edwardian Code of July 1549 enjoined that disputations were to be held regularly . 
The disputations in mathematics , dialectics and in natural philosophy were to be held on Thursdays , Fridays and Sundays . 
We are given some idea of the nature of these university disputations from Izaak Walton 's life of Sir Henry Wotton ( 1568-1639 ) . 
He writes that Sir Henry : 
"{ 1about the nineteenth year of his age , he did proceed Master of Arts , and at that time read in Latine three Lectures { de Oculo : wherein he having described the Form , the Motion , the curious Compositione of the Eye and demonstrated , how of these very many , every humour and nerve performs its distinct office .... 
After these Observations he fell to dispute this Optique Question , Whether we see by the Emission of the Beams from within , or Reception of the Species from without . " 
By the visitation of 1549 a Reader in Natural Philosophy was provided for All Souls College , Oxford . 
In 1551 Michael Renninger ( or Rhanger , 1530-1609 ) was appointed to lecture on natural philosophy at Magdalen College , Oxford . 
The sixteenth century is significant for the publication of several educational treatises that paved the way for a new presentation of studies not only in the university curricula but also in that of the schools and which encouraged realism in education in distinction to scholastic formalism . 
The writings of Ramus , Francis Bacon , Sir Thomas Elyot , Rabelais , Vives and Melanchthon all catch a glimpse of the future reserved to scientific education , to a study of Nature by inductive speculation , to a study of things instead of the worship of words . 
For the traditional quadrivium Ramus would substitute mathematics , physics ( including astronomy ) , metaphysics and ethics . 
The textbook to be used in physics was his own treatise , " Studies in Physics , " which , in spite of his criticism of Aristotle , was based on the latter 's Physics , on Pliny 's Natural History and on Virgil 's Georgics . 
In the { De Tradendis Disciplinis ( 1531 ) Vives advocated the study of physics , even in the schools . 
But the subject still needed to be systematised and simplified before it lent itself to instruction of the young . 
Chapter 3 THE SEVENTEENTH CENTURY 
As a result of the genuine scientific curiosity of the true natural philosopher , of the curiosity of the gentleman of leisure in search of diversions , of the Puritans ' looking at the phenomena of God 's creation , and of the monetary interests of the manufacturer , the miner , the engineer , the alchemist , physics made great advances . 
Experimentation increased from a mere trickle into what was soon to become a flood ; in fact , so much so that science was in danger of being reduced " to a worship and idolisation of experiment as an end in itself . " 
The achievements of earlier physicists were crowned by the brilliant work of Galileo and Torricelli in Italy , of Guericke in Germany , of Huygens and Snell in Holland , of Mariotte and Descartes in France , and of Boyle , Hooke , Halley and Newton in England . 
Their advances marked the end of the era of doubt and confusion and proclaimed the birth of " modern " physics . 
Newton 's ( 1642-1727 ) " Principia " was published in 1687 in Latin and in this he defined mass , force , momentum , acceleration , etc. , clearly for the first time , and worked out his laws of motion . 
In 1668 Newton constructed the first reflecting telescope . 
Eight years earlier he had begun his experiments on the incidence of white light on a prism . 
Newton also investigated the colours of thin plates and coloured rings , the bending of light and the coloured fringes at narrow slits . 
His observations on double refraction in Iceland spar laid the foundations for the theory of the polarisation of light . 
In the controversy over the theory of light Newton threw his great authority on the emission theory , with the result that the wave theory of Hooke and Huygens was in abeyance for over a century . 
It was in 1658 that Robert Boyle ( 1627-91 ) invented his improved air pump with which he performed his classic experiments on the weight , pressure and elasticity of the air , and on the part played by air in respiration and in acoustics . 
Boyle encouraged study of experimental physics by writing ( in 1663 ) " { 1Some considerations touching the Usefulnesse of Experimental Naturall Philosophy .... by way of Invitation to the Study of it , " and by writing ( in 1664 ) " Experiments and Considerations touching colours " in which he deliberately gave a simple and popular outline of the subject in order to encourage more readers , including the fair sex . 
Boyle 's assistant , Robert Hooke , propounded his law — { ut tensio , sic vis — about 1658 . 
In 1666 he measured the force of gravity by the swinging of a pendulum . 
The fixing of the thermometric zero at the freezing point of water is due to him . 
In 1666 he demonstrated magnetic lines of force using iron filings and a small movable magnetic needle . 
In his Micrographia ( 1665 , p. 7 ) he advocated increased study of the new experimental physics in the place of " discourse and disputation , " since : 
" { 1These being the dangers in the process of humane Reason , the remedies of them all can only proceed from the real , the mechanical , the experimental Philosophy . " 
Remarkable advances were also made in applied science , e.g. the invention of a steam engine by Edward Somerset ( 1601-67 ) , second Marquis of Worcester , though the first practical steam engine was made only in 1698 by Thomas Savery ( 1650-1715 ) . 
Scientific instruments were now available on a large scale for the first time . 
Among these may be mentioned barometers , thermometers , telescopes , microscopes , the { 6camera obscura , lenses and prisms . 
A new profession — that of mathematical and scientific instrument maker — arose to supply the demands of the new experimental sciences . 
James Moxon , who lived on Ludgate Hill , was one such ; another was John Yarwell , who sold his scientific apparatus at " The Archimedes and Three Golden Prospects near the great North-Door in St. Paul 's Church-yard , London . " 
The advances in science and in applied science were largely the fruits of substituting observation and experiment for dogmatism and for the { a-priori methods of Aristotelian physics . 
First Investigation 
In the endeavour to sort out some of the intricacies of this problem the Foundation carried out two small investigations . 
A number of primary schools assisted in these studies and their help and co-operation is gratefully acknowledged . 
The first investigation was carried out in a Junior school in which the children were streamed by age — that is , they were grouped in classes according to age in the contributing Infant school and the Junior Headmaster accepted these groupings and maintained them throughout his school . 
In order to obtain a measure of performance , all the children in each of the four years of the Junior school were given , in the Spring Term 1959 , the Foundation 's Sentence Reading Test 1 . 
The median raw and standardised scores together with mean ages and age ranges of the four year groups are given in Table 1 . 
Class 5 was an exception to the rule of "streaming " by age since it contained all the poor readers from the 2nd year group . 
The standardised scores ( mean 100 , S.D. 15 ) contain an age allowance determined from the sample on which the test was standardised . 
The median standardised score for each year group was then used to determine what would be the expected median raw score for each class within the year group . 
This expected median raw score was then compared with the observed median raw score . 
If the classes had been grouped by age only — that is , within each class there was a full range of ability — then the observed and expected median raw scores should be approximately the same . 
Similarly , of course , the median observed standardised score for each class within a year group should be approximately equal to that for the year group as a whole . 
The results are given in Table 2 . 
In order to complete the analysis the children from Class 5 were distributed into Classes 3 and 4 according to their age . 
It will be seen from Table 2 that there was not a great deal of discrepancy between expected and observed scores for Classes 1 and 2 in the first year group . 
The observed scores for Class 3 , however , are well below expectation , while those for Class 4 are well above . 
The difficulty with Class 5 may have contributed to this discrepancy , but the same phenomenon occurs with the three classes in the 3rd year group and also with the two classes in the 4th year group . 
However , it will be seen that the age " streaming " is by no means exact — there is considerable overlap in the age ranges for each class in a year group . 
This was due to the presence of a few children only and therefore the results for the 3rd year group were re-calculated and the analysis confined to those children falling within a five month group in each class . 
The results are given in Table 3 . 
It is still clear from the figures in Table 3 that Class 8 is doing considerably better than their average age indicates and Class 6 not as well . 
A satisfactory explanation for these differences could not be found in any differential treatment of the various classes within a year group . 
That is to say , all classes within a year group in the school were treated as " parallel " and a careful balance of the teaching strength was always maintained . 
Indeed the only plausible explanation seemed to be one associated with the length of schooling . 
Information was obtained on this variable for most of the children in the 3rd year group and this showed that for the most part Class 6 had received 13 terms previous schooling and Class 8 , 15 terms . 
It must be made clear that this investigation was carried out in only one school and a relatively small number of children were concerned . 
However , the results showed that in a school where children were " streamed " by age , older children scored higher on the average on a reading test than might have been expected according to their age , while younger children did not perform as well . 
Furthermore , the findings were in the direction expected from the hypothesis that an extra term or two of schooling would result in improved performance . 
Second Investigation 
Following an article in an earlier issue of this Journal on the Effects of Streaming a number of primary school head teachers interested in this topic wrote to the Foundation expressing their willingness to co-operate in any relevant research . 
Although the problem of length of schooling was distinct from that of streaming , these schools together with others , readily agreed to participate in a further investigation which , it was hoped , would provide more definite evidence . 
Six Junior schools in all were asked to administer Sentence Reading Test 1 to all children in their four year groups , and to obtain for each child a record of the number of completed terms previous schooling up to the time of testing . 
A total of 1,604 children were tested and the relationship examined between reading performance and the number of terms previous schooling . 
Before considering any effect due to the age of the children , it was found that , within schools , there was a highly significant regression effect of raw scores on the reading test , on the number of terms previous schooling . 
Using this regression the expected mean reading scores for given lengths of schooling may be calculated and the results of this are given in Table 4 . 
Quite clearly reading test performance is affected by the length of previous schooling . 
After the effects of the age of the children has been eliminated , however , the regression of test score on length of schooling becomes statistically non-significant ( taking the usual 5% significance level ) . 
The predicted reading scores for different number of terms schooling after the elimination of the age effect are given in Table 5 . 
A comparison of Tables 4 and 5 shows that the change in score that may be expected for an increase of one term 's schooling has decreased from approximately 1.46 to 0.50 points of score , when age is eliminated . 
This second figure is no longer large enough to be described statistically as significantly different from zero . 
The regression analysis was also carried out on the results for each school separately . 
It was found that the regression of reading score on length of schooling remained statistically significant , after the elimination of age , in only one of the six schools . 
This was a large three-stream school which , for the most part , " streamed " by age within each year group . 
The regression for this school was found to be significant at the 5% level , while the results for the remaining five schools agreed with those obtained on the total . 
These results indicate that while length of schooling is obviously related to reading performance ( r = 0.539 ) there is such a close correspondence between length of schooling and age ( r = 0.979 ) that , to allow for age when considering test score also allows for differences in length of schooling . 
This analysis seemed conclusive enough ; there remained the possibility , however , that any residual effect from the length of schooling might only be apparent during the early years of the Junior school and that by carrying out analyses over all four years the effect was masked . 
These regression analyses were repeated , therefore , covering the first two and the last two years of the Junior school separately . 
Two schools were omitted from these calculations , since their data were incomplete . 
The first repeat analysis was carried out on the first and second years of the Junior school . 
Before the ages of the children were considered , it was again found that , within schools , there was a highly significant regression of raw reading score on the number of terms previous schooling . 
However , when the effect of the ages of the children was removed , it was found that no statistically significant regression remained . 
This regression analysis was also carried out on the first two years of each school separately , but the same result was found for each . 
Thus it is clear that variations in length of schooling have no residual effect on reading performance during the first two years of the Junior school once the effects of differences in age are allowed for . 
For the third and fourth years the regression of reading score on the number of terms previous schooling was also highly significant before age was considered . 
When the effects of age were eliminated , again the regression was no longer statistically significant . 
The repeat of the analysis for each school separately , however , gave results for two of the schools which agreed with those for the totals , but for the other two schools the number of terms previous schooling still had a significant effect on reading scores , even after the elimination of age . 
It will be recalled that most of the schools participating in the investigations were interested in the problem of streaming and in fact only one of the four schools in the last analyses was streamed by ability . 
In this school there was no residual effect of length of schooling . 
One other school practiced no streaming at all . 
It was a large school and except for one " fast " class in both the third and fourth years , in all other classes the children were grouped at random . 
This school also showed no residual effects of length of schooling . 
In the other two schools , however , streaming , not by ability but by age , was practiced and in both these schools the residual effect of length of previous schooling on reading performance was significant after the elimination of age . 
It is interesting to note that this result agrees with the first investigation reported above , in which the school concerned also streamed by age . 
Discussion of Results 
The number of schools participating in this investigation was fairly small and since the results seem to depend upon the type of streaming practiced in each school the findings must be reviewed with caution . 
There appears to be evidence , however , to suggest that under the usual circumstances pertaining in most schools , if due allowance is made for the age of each child when tested , then due compensation will also be given for any differences that might exist in length of previous schooling . 
Where the practice of grouping children into classes according to their age is adopted , the evidence from both investigations reported here suggests that even after due allowance is made for the age of the children , their reading performance still varies according to the length of previous schooling they have received , although this residual effect appears only to be noticeable during the latter part of the Junior school . 
The explanation of these results is not easy to find . 
The fact that this residual effect only appears in the latter part of the Junior school makes the hypothesis that it is due purely to length of previous schooling questionable . 
If the latter is to have an effect on test scores after age has been considered , then it would surely be more noticeable with younger children , that is , in the early years of the Junior school . 
It will be observed , however , that under these circumstances of " streaming " by age , the older children in a year group , who happen also to be those who have received a longer schooling , perform better than is expected of children of their age , while the younger children in the year group perform below the expectation for their age . 
The possibility must be considered , therefore , that the differential performance effect is not due to any differences in length of schooling , but to the fact that the children are " streamed " by age . 
Some evidence has already been obtained that one of the effects of streaming is to increase the " spread " of test performance . 
That is , under the circumstances of ability streaming , more high scores and also more low scores are produced than would be the case were the children not streamed . 
The suggestion here is that since older children of a year group will be doing more advanced work than the younger one , simply by reason of their age , an older stream will give the appearance of being " better " than a younger stream . 
A new type of ratepayers ' secondary school began to establish itself in the nineties . 
Not only this , but in London the School Board , ever short of good pupil-teachers , found itself at length in friendly competition with the T.E.B. in the field of teacher training . 
There were pupil teacher centres ; and a " college " in the Greystoke Place building off Chancery Lane began to undertake this work in a manner which the leader of the L.C.C . 
has in more recent times publicly described as illegal . 
On the same occasion he referred in quite different terms to the T.E.B. as taking " a wide and generous view of its duties " in its first plans for the London Day Training College . 
In this field , as in the initiatory stages of various other institutions destined to have a place in the life of London University , the Webb influence may be seen . 
The two powerful democratic agencies , the two Boards , were thus at various points in rivalry with one another for the custom of the teen-agers ; and in several spheres the School Board was undercutting the institutions supported by the Technical Education Board , of which Sidney Webb was the driving force . 
The dominion of the London School Board was at length overthrown as a result of a decision of the public auditor , strongly backed by the courts of appeal , that the Board had grossly exceeded its parliamentary powers in spending ratepayers ' money on evening and continuation work . 
In the uncomfortable atmosphere created by this challenge , all school boards now found themselves in hazard . 
Their friends had diminished in numbers , but they made up in the vigorous expression of outraged feelings for their growing sense of inferiority in face of onslaughts from Tory supporters of Church schools and in face of the criticisms of the social engineers playing earnestly with their one and two-tier models in the back rooms of the Fabian Society . 
One embarrassing complication which tested the pliable diplomacy of the Webbs arose out of the membership of the London School Board of their reforming associate Graham Wallas , passionately disposed as he was to defend it on the highest grounds of free-thinking principle . 
This old friendship with a fellow Fabian was for a long while in jeopardy . 
But Graham Wallas stood fast , whereas in this great struggle most of the School Board supporters , with their only staunch reserves in the rallying ground of the susceptible nonconformist conscience , were frequently in disarray because never quite sure whether they had all the hostile forces correctly identified . 
These forces were numerous enough , and even now after sixty years it is hard to find anyone whose sympathies can be enlisted for them against those who emerged with the battle honours and the consequent good press . 
The London School Board had been a gallant success against many odds from the beginning ( in 1871 ) , when Thomas Huxley drafted the first curriculum reform . 
And he and his colleagues were succeeded by a line of most able men and women of a quality which would bring outstanding distinction to the London County Education Committee today were they equipped with such talents . 
The School Board had undertaken to civilize one of the most backward and barbarous and misgoverned urban committees in Christendom ; it had carried through what Dr. Lowndes had aptly described as a silent social revolution . 
In the course of their constitutional development the school boards taught the country for the first time to use the machinery of a ratepayers ' democracy — a democracy of women as well as men — and moreover to use it in defence of public principles wider than the restraint of petty corruption . 
Their champions have been few . 
And all but the ugly name of the schools they administered has passed into oblivion . 
How far were the Webbs responsible for their demise ? 
That an { 6ad hoc education authority , with powers limited ( the Courts now declared ) to little more than instruction in the three Rs , must be an anachronism was becoming evident to all at the close of the nineteenth century . 
And it was undoubtedly the administrative triumph of the T.E.B. in so completely filling a new set of gaps in education that made the County Councils the final take-over claimants , as all-purpose authorities for the elementary and secondary sectors . 
Still , it would be wrong to suppose that the L.C.C . 
and the 0L.S.B had a war to the knife on their hands . 
Both were dismayed to see the national colouring their rivalry had assumed . 
The L.C.C . 
almost fell over backwards , repeatedly . 
It showed no greed for the rich inheritance , with its awful responsibilities , so different in their complexity from those offered by street markets and outfall sewers . 
Whilst this rather ugly chapter in national politics was unfolded , whilst the grinding of axes and the scuffles and squeaks of burrowing intriguers in the higher ranges of administration could often be heard above the sound of the Westminster traffic , the dominant wish of the county councillors in Spring Gardens was that somehow the face of the School Board should be saved . 
Matters first came to a head during the absence of Sidney and Beatrice on an extensive tour abroad . 
Garnett was successful in swiftly adopting a new Whitehall administrative provision which was now used to make the T.E.B. the grant-distributing authority for London of national Science and Art payments . 
This outraged the School Board , for , as Garnett astutely observed , it made his L.C.C . 
Board the effective authority for secondary classes . 
" The ball which had been set rolling ... did not stop " , he wrote later , " until the Education Acts ... had revolutionised ... administration ... throughout the country " . 
William Garnett and Robert Morant ( who drafted the Bill of 1902 and was rapidly promoted to become first permanent secretary of the new Board of Education ) have shared the same friendly biographer ; and it has long been known that these two men were at the centre of the network of political activity within which steps were taken to ensure that the ball went on rolling . 
What is much less clear is how far Sidney Webb was responsible for the direction taken by affairs in 1901 and 1902 , and how closely he worked with Morant , with whom he and Beatrice were of course later to quarrel over social insurance . 
Beatrice 's Diaries provide a certain amount of information and give us light on her views . 
Sidney had little or nothing to do with the incidents connected with the famous Cockerton judgment on the misuse of the school-board fund . 
But it is certain both that the Fabian tract 106 , The Education Muddle and the Way Out ( 1901 ) was essentially the fruit of Sidney 's thinking and that this tract and the lobbying pressures brought to bear by Sidney greatly influenced the drafting of the Education Bill . 
Tract 106 itself made the case first for local control of education , next for a unified control , and finally for the claims of the large all-purpose authority the form and frame of which existed since 1888 in the county and county borough councils . 
This important document ( largely penned by Webb ) in which a theory of educational administration is set out and related with the utmost assurance to the principle of the full development of every child 's faculties , is one of the few major texts on the subject which is available for profitable scrutiny by the student of the period . 
There has been a conspiracy of modesty about Sidney 's real claim to be the father of the Bill of 1902 ; and thus perhaps the ancestor of so many of our subsequent achievements and woes . 
Avoiding one counsel of the Fabian tract , that a few of the larger school boards might well be saved for limited purposes because of their superior efficiency , the Government came out for their abolition . 
In fact the argument for Sidney 's paternity for the measure of 1902 is in places weak , and even the word God-father would be unfortunate in the circumstances — though , if the voluntary schools were protected by angels , Sidney for reasons which do him credit was on their side . 
The idea of using the Education Bill of 1902 to aid denominational schools came to Sidney Webb before it came to Robert Morant , as Mr. Brennan has pointed out . 
Much of the real agony of creation in this tremendous piece of reconstruction was of course experienced by Morant . 
Professor Eric Eaglesham has now brought this out quite clearly . 
What can be said is that , after a number of gestures , some friendly , some ambiguous , towards the School Board in its hour of crisis , Sidney became confirmed in the belief which he must for some time have privately nourished that a monolithic education authority was appropriate for all areas having County Councils , and that London 's County Council , which had been omitted from Balfour 's measure as far too tricky a proposition to handle with the rest , ought to go into the Bill , as the sole governor of the schools within its area . 
In maintaining the latter view Sidney was part of an unsuccessful minority , hard as he seems to have tried to make it a successful majority ; and it was thus necessary for the whole process of wire-pulling and lobbying to be repeated when the problem of education in London came before Parliament for separate consideration in the following session . 
But perhaps it was from that preceding summer , when the general Bill was fought through many embittered weeks , that Sidney began to lose his assured touch in London county politics . 
Democratic feeling no longer supported him . 
He got no help from the Labour following of Ramsey MacDonald , always a little suspicious of higher education and of the Webbs as promoters of the self-regarding motives of London 's middle classes . 
Sidney himself was now distrustful of his old party the Progressives , and quite out of sympathy with the angry radical dissenters who would gladly have upset the education apple-cart to cheat the Anglicans and Romans of access to the rates . 
Having lost the chairmanship of the Technical Education Board , Sidney failed to get re-elected . 
It is reasonable to suppose that at this point Beatrice 's views , opposing what she called " pure materialism " as a national philosophy to be inculcated by school masters , had begun vigorously to assert themselves . 
Certainly they both wished to prevent the animosities and frictions hitherto encouraged by the dual system from becoming more severe or from wrecking the future of secondary education ; and so she for religious reasons and he because he believed in fairness and hated the bigotry of secularists , and because he thought efficiency would be served by having Roman Catholic and Anglican schools within the fold of public education rather than outside it , favoured the maintenance of voluntary schools out of local taxation . 
Yet the Webbs had their triumph , and incidentally Sidney lost even more of his radical support , with the shaping of the London Education Act of 1903 , with which the Unionist House of Commons completed the task of reconstruction . 
This measure reached its revised and final form only after the party leaders had terrified nearly every vested interest in London by the threat to create a new authority in the shape of a large { 6ad hoc body of nominated members on the pattern of the Metropolitan Water Board , at the same time offering much power and influence in school provision to the recently created metropolitan boroughs . 
The situation in the spring of 1903 has such a startling topicality in relation to the current proposals of the Royal Commission on Greater London that it is difficult to comment on one without expressing views on the other . 
The Webbs in any case knew what they wanted , and , although the whole thing was perhaps less of a one-man battle than is hinted at in Beatrice 's diaries , Sidney got his way for London ; and this was a county authority — an authority formally charged with responsibility for all educational activity on the public vote within its boundaries , save the University of course . 
There was not the least bit of ad hoccery here . 
It was a triumph for the Webb principle , as currently promulgated at the beginning of the century , of a consolidated all-purpose local responsibility vested in the County ; although it was decidedly against the general trend followed in the management of London 's water , road transport , harbour facilities and so on , which all slipped out of the control of municipal socialism . 
Perhaps because they operated a peripheral weapon , they thought more in order to justify its being and expansion . 
But they , too , were just as guilty as their superiors of over-estimating their weapon 's effectiveness and dreaming of its potential . 
On the other hand , the same people were apt to divert power from their own programme by boasting . 
The claims of airshipmen , it appears , helped create the vast anti-Zeppelin forces which were maintained in England in the First World War . 
It did not take a very astute man to realize that what could be done to the enemy if we had the equipment might well be done to us when he had it , particularly if invulnerability , which the German airships possessed at first , was claimed for the delivery system . 
Between them the enthusiasts and the reactionaries created a vast feeling of insecurity , and faced with this the responsible authorities generally erred towards the safe side . 
Any new weapon will have its small band of disciples . 
But if it is to be used effectively , more personnel must be recruited . 
Volunteers may be hard to come by owing to the lure of actual combat and the uncertainty of the future with a new-fangled device . 
Thus the expanded staff is apt to be short on experienced career men and long on Hostilities Only or draftee recruits . 
This places the weapon at a disadvantage in the battle of Whitehall where it may have difficulty breaking the thin red tape , and in peacetime it will be out of favour , but in a commanding position as far as wartime development is concerned for it may well acquire decidedly more brains than the normal unit . 
The undisciplined will be quite prepared to test regulations and equipment and by empirical means come to new conclusions in both technology and technique , as the Naval Air Service did with not only air equipment , but also with armoured cars and tanks . 
This is particularly important where an entirely new element is being investigated . 
Airships presented many unknowns to be solved and these ranged from metallurgical questions to matters of aerodynamics . 
The new weapon also presents all decision-makers with the problem of the evaluation of intelligence from both the enemy 's and one 's own work . 
In this respect , too , there arises the question as to what is the acceptable percentage of failure ? 
In the case of airships , should all the money have been put into one Mayfly ? 
While the answer in 1908-9 was probably yes , in 1924 it should have been no . 
In almost any programme , the construction of but one prototype is bound to lead to delay , confusion , and losses if there is a disaster . 
And the likelihood of such is by no means eliminated by the present advances in technology . 
Yet the combination of psychological and politico-economic forces in Britain still persists in an approach which may well be called into question where real economics are concerned . 
It is highly unscientific to place too many innovations in any one test vehicle , if for no other reason than it attenuates the whole testing period . 
Ideally , merely one change at a time should be tried until proven , and this was well demonstrated in R101 . 
Moreover , every new weapon needs at least three prototypes : one for operational research , one for technical modifications , and one for experimental use as a testbed for the next-generation ideas . 
Thus the building of only one prototype provides policy-makers with the rather appalling fact that they may have to accept a 100 per cent failure rate , and yet still have to justify continuing expenditure on such work in order not to be placed in a disadvantageous position in an international race . 
The loss of R38 , amongst other factors , immediately suspended work on more advanced types as well as discouraging commercial incentive . 
The obverse of this coin is the desire to standardize too soon , for duplication there must be if a weapon is to be handled by average troops and ordinary commanders . 
This was the difficulty of 1916 in the British rigid airship programme : the designers were allowed to seek after perfection to the detriment of operational uniformity , while the Royal Flying Corps had allowed similarity to preclude competitive progress . 
The ministerial head of a service department is always in a difficult position in peacetime . 
In Britain , for instance , the Treasury rules , so only a weapon with either the Prime Minister 's or the Chancellor of the Exchequer 's approval or diffidence can get sufficient funds . 
After a major conflict the Treasury is most apt to insist on the payment of past debts and the consumption of available equipment before authorizing any new expenditures . 
This it certainly did in the years immediately after the Treaty of Versailles . 
Peace is a dastardly affair where new weapons are concerned . 
There is an immediate erosion of personnel . 
Operations rapidly taper off and even constructional work will be suspended while politics and economics once more take the field to bid for the voters ' favour . 
The immediate hope is for some crisis , such as the suspicion that the Germans might not accept the Treaty of 1919 , or that the whole concern can be turned over to commercial profit . 
But the latter can be successful only if the entrepreneurs are allowed to obtain for a reasonable sum what would otherwise be scrapped and have facilities and official support to exploit it . 
Moreover , they must feel financially secure and not suspect that the State aims to take over once a service is established . 
The government may well face the choice as it did in 1919 of scrapping the whole business or of subsidizing a commercial operation . 
This creates a situation in which the weapons advocates may be able to divide and conquer . 
However , there are two difficulties — civilian acumen may be lacking , and the whole may be too peripheral and too much of a gamble for either of the other parties . 
As personnel and material deteriorate , immediate action is essential and this must be topped with a prestigial success which will create political pressure . 
This makes the odds high , and , in the case of airships , it led to R34 's trans-Atlantic flight and to R101 's death . 
How did all this affect the airship programme ? 
Mayfly was initiated in a period of concern with Germany 's intentions and collapsed at the end of a severe political crisis in Britain . 
Airship work was revived when another defence scare came along ; then cancelled when it was thought that the war would have cleared the air by late 1915 . 
The whole programme was revivified during the wide-open war economy and collapsed in the peacetime retrenchment . 
It then became caught up in the conflicting streams of the save-the-Empire movement and the Labour Party 's desire to run a successful national transport system . 
The collapse of the economy and the de2nouement of R101 caused airships to be abandoned for economic reasons , which were rapidly reinforced by technological arguments in favour of the aeroplane . 
Who Made Airship Policy ? 
The original impetus appears to have come from the Germans through the naval and military attache2s to Fisher and the Prime Minister . 
Asquith by his decision in July , 1908 placed the First Sea Lord in a position to implement plans already sketched out by Bacon and other technically astute officers . 
Bacon guided the early design stages of Mayfly until relieved by Sueter , and the first airship programme then proceeded under its own steam and with the blessing of the Committee of Imperial Defence until the disaster of September , 1911 . 
Churchill as the new First Lord with A. K. Wilson as his First Sea Lord then decided against any further work . 
The second programme came into being again because of the Germans and through the joint agency of Sueter and Seely , Secretary for War , who chaired the Committee of Imperial Defence sub-committee on aeronautics . 
Thus in mid-1912 a further reappraisal , at least in part , influenced by a change in heart at the Admiralty , came into being with Asquith , as head of the Committee of Imperial Defence , accepting in 1913 the need for another rigid airship . 
And once again Churchill in early 1915 became the one who decided that the whole thing should be abandoned and gave the order to cancel No. 9 , and presumably also earlier , No. 14 and No. 15 . 
And so it went on . 
After the war , the transfer of lighter-than-air from the Admiralty to the Air Ministry again put Churchill into a policy-making role in regard to airships over which he had exercised some influence as Minister of Munitions from 1917 to 1919 . 
As Secretary of State for Air he had to reconcile his fondness for maintaining the Empire with his desire for economy and political success . 
Airships fitted into both patterns . 
At the same time , Churchill was also Secretary of War and gave much of his time to the Army . 
The Under-Secretary of State for Air , Seely , was pro-airships as he had been as the pre-war Secretary for War , while Sir Frederick Sykes as Chief of the Air Staff and then as Controller-General of Civil Aviation was also a supporter . 
Sir Hugh Trenchard , who succeeded Sykes , appears to have favoured airships in their place , and if prestige , the Estimates , and the R.A.F. could allow for them . 
As Seely resigned and the other Under-Secretaries were not much interested , as long as Churchill remained the Air Minister , he and Trenchard made policy . 
But policy was also made at lower levels . 
In much the same class as Rickover , Whittle , and Dornberger , Sueter guided constructional and design concepts until he was posted . 
In the early years of the R.A.F. the Director of Research and the Air Member for Supply and Research had their says . 
Maitland as Superintendent of Airships appears to have been left on the fringes as was Masterman after he transferred from the Navy to the R.A.F. It must be recalled , however , that the Director of Research on one occasion made policy when he plumped for cutting R38 's trials to but fifty hours with subsequent unfortunate results . 
In the case of the Imperial Scheme , policy was made by a wide variety of people . 
A. H. Ashbolt and Cmdr. Burney provided the primary pressure . 
Trenchard was interested because he saw a way of acquiring military strength for a relatively minor expenditure on the Estimates while at the same time mollifying the Admiralty , then in the process of being denied a naval air arm and the destruction of the R.A.F. Sir Samuel Hoare was openly in favour and this was in keeping with his character as a publicity-conscious Air Minister . 
But in the case of the Conservative Burney Scheme there was one of those rare instances of the monarch helping make policy by taking a personal interest in a particular development . 
Into this picture then was catapulted Lord Thomson , an obvious enthusiast , who told the Air Staff to " screw up " the Conservative scheme . 
He and his Under-Secretary , a Bradford alderman and pacifist named Leach , knew nothing about airships and little about international commercial organizations . 
In the realm of civil air intelligence their natural advisor was the enthusiastic Sir Sefton Brancker , the Director of the Department of Civil Aviation at the Air Ministry . 
But Brancker was not exceptionally well-qualified to give advice on this subject . 
Moreover , the Secretary and his Under-Secretary called largely upon the serving members of the Air Council for their opinions , then made a scheme and submitted it to the Cabinet without allowing those very advisers time to consider it . 
Thus the latter were forced to the unusual step of drawing up a memorandum for the Cabinet for their own protection . 
Nor was the experienced Chief of the Air Staff adequately consulted . 
The Cabinet then proceeded to accept a programme which had not been approved by the Air Council . 
Yet in this case , while the Aeronautical Research Committee did not have the access to the Cabinet that it had had in 1909 , it did have considerable influence . 
It was the findings of the special technical committee on the loss of R38 which heavily influenced the Thomsonian decision to make this an experimental programme rather than an operational one . 
Some of the criticism of political expenditure has been directed as much against the goods and services purchased as against the amounts involved . 
Many leading members of the Labour Party dislike , distrust , and sometimes fail to understand , the world of public relations . 
In the words of Mr. Gaitskell , there are many in the party who " feel insulted and humiliated that their desires and wants are being dictated to them regardless of how real they are , or how genuine are the advertisers ' claims . 
They feel the whole thing is somehow false . " 
Alice Bacon , chairman of the NEC 's publicity and political education sub-committee , has denounced the Conservative Party 's public relations efforts for having " introduced something which is alien to our British democracy " . 
The Conservatives are charged with selling political ideas as if they were detergents . 
Distaste and disgust are strong emotions , but negative ones . 
The Labour Party has been singularly lacking in suggestions about what might be done to prevent the Conservatives from " subverting " or " Americanizing " the British electorate by public relations techniques . 
A small minority of Labour Party members would probably support a drastic curtailment of advertising by government action , and accept the implications of this for the press as well as for politics . 
Regulation of advertising which did not control it virtually outright would not seriously affect political expenditure . 
If a law could be drafted to prevent politically relevant advertising , one could also be drafted to prevent the expenditure in the first place . 
Parties , if not all their associates , could be prohibited from purchasing advertising space in newspapers and on the hoardings . 
If instead the Conservatives put more money into colour comics like " Form " , the level of debate would hardly have been raised . 
Much spending to which objections are made — for instance , the Colin Hurry poll , Aims of Industry press releases , the Economic League 's factory gate speakers — does not take the form of purchasing space ; only £445,000 of the £1,435,000 credited to business groups in the Nuffield study was spent on buying advertising space . 
Efforts to control the content rather than the volume of advertising are foredoomed to failure . 
It would be virtually impossible to discriminate in a statute between political advertising which does or does not lower the tone of debate . 
A promise to increase pensions appears as altruism to some ; to others it seems rank bribery . 
An Advertising Council might be created along the lines of the Press Council , to scrutinize advertising and censure offenders ; given the model suggested , little could be expected from such a body . 
It would be as difficult for a quasi-judicial tribunal to pass upon the content of political advertisements , rejecting those that were " unsuitable " , as for the Speaker of the House of Commons to do similarly in parliamentary debates . 
It might not be particularly difficult to attack the advertiser 's practice of using market research methods to study the wants of the electorate . 
A law could prohibit pollsters from asking questions on political topics . 
But this would not affect the substantive problem , which arises from the fear that some politicians frame or revise policies simply to win more votes , without regard to the national welfare . 
3 
All the proposed alterations discussed so far have been restrictive ones , intended to remedy deficiencies in the Representation of the People Act by reducing the amount of money spent on electioneering in the long run . 
But the Act might also be altered in such a way as to increase the scope for political expenditure . 
The foregoing analysis indicates that restrictive amendments to the present Act are not likely to remedy the alleged evils . 
The American experience of fifty years of attempted regulation would confirm this judgment . 
V. O. Key reports : " 
Legislation purports to require publicity of campaign finance , to limit the amounts spent , to prohibit certain types of contributions to campaigns , and to limit the size of contributions . 
In general , the laws do not in fact limit expenditures , substantially affect the size of contributions , or assure full publicity . 
" If means could be found to level up the resources of Labour and the Liberals , much of the bitterness might be removed from present discussion of election laws , and the practical consequences of major shortcomings of those laws would be greatly reduced . 
One remedy lies within the hands of the Labour and Liberal parties — it is to collect higher dues from members , a far easier task than greatly expanding present membership . 
In the words of Morgan Phillips , " Labour Party income is still geared to a different and far less expensive political era . " 
As long as five-sixths of the party 's members contribute three farthings a month ( 9d. a year ) to Transport House , Labour leaders can hardly plead that their relative financial weakness is solely the fault of the Conservatives . 
If dues for trade union affiliated members were raised to 1s. a year , Transport House would have an additional £70,000 to spend annually . 
If trade union members paid the party 2s. a year , as Phillips has suggested , the income of Transport House would be doubled . 
Since the Labour Party proclaims a desire to narrow income differentials , it might consider the membership scheme of the German Social Democratic Party ; it is a sliding scale , with contributions graded according to income . 
Nearly 600,000 German socialists gave the party more than £1 apiece on average ( £720,000 ) in 1957 ; dues for those in the highest income bracket were set at £50 a year . 
The Liberal Party is appealing for mass-membership contributions . 
The appeal leaflet , This is Your Party , estimates minimum annual needs at £172,000 . 
Another method of increasing party revenue would be to have the state make statutory contributions to the parties . 
At present the law penalizes the candidates who secure less than one-eighth of the vote at parliamentary elections . 
The law could equally give cash bonuses to the candidates who save their deposits . 
Grants are made to candidates in some foreign countries . 
The actual amount given might be determined in one of several ways . 
It could be equal to the sum of money spent in each constituency , or equal to the legally permitted maxima . 
Alternatively , it might be a lump sum of £500 or £1,000 . 
The grant could be paid after each election or annually . 
( A guarantee of campaign expenses would not only save parties this sum , but would also free them from the need to keep a sizeable cash reserve against the possibility of having to fight two elections in quick succession . ) 
A grant paid on the basis of sums spent by candidates in campaigning in 1959 would have brought the Conservatives £475,000 , Labour £435,000 , and the Liberals approximately £90,000 . 
It would be prudent to make such grants to candidates , in order to avoid the difficulty of defining a party , and the possibility of placing the Treasury in a position of having to arbitrate between two factions both claiming one grant . 
The sums of money involved would be small by Exchequer standards , but considerable in political terms ; the poorest party , the Liberals , would be aided most in proportion , the richest one , relatively least . 
The Labour Party 's dependence upon trade unions for finance could thereby be appreciably reduced . 
Another way of remedying deficiencies , which would also lead to greater expenditure , would be to abolish the present restrictions on spending by candidates . 
The Economist suggested this in a post-election editorial of 10 October 1959 , as a means of preventing the law from being brought into disrepute . 
Liberals , who depend more upon personal appeal and constituency efforts than do others , might gain most from such a step . 
4 
Most advocates of stricter accounting of political expenditure assume that money buys votes ; some charge that it buys votes in sufficient quantities to win elections . 
This assertion is truest when it is most platitudinous : a party can not operate without money . 
To go further , and say that a party such as the Liberals gains few votes because it has little money is to mistake cause and effect . 
It would be more nearly true to say that a party with relatively few voters , such as the Liberals , has difficulty in raising money . 
As the rise of the Labour Party shows , the necessary minimum is not great , nor is it impossible to secure if the party has strong support in the electorate . 
Many British discussions of political expenditure seem to assume a simple input-output model of electioneering : X thousand pounds will produce X or X/2 or X/4 or 2X or 4X votes . 
Y inches of advertising space will produce Y/2 or 2Y units of political influence . 
( How much of a reduction factor is needed for the 100,000,000 or so leaflets distributed by the Economic League between elections has never been specified . ) 
People unaccustomed to dealing with large sums of money might think it incredible that hundreds of thousands of pounds might be spent to no real effect . 
Socialists are further handicapped in viewing the problem if they believe that capitalists are not only wicked but also devilishly clever . 
The determinants of voting behaviour and election results are so infinitely complex that we can rarely separate out any single factor and assign to it a specific amount of influence . 
Since the introduction of the secret ballot , it has been impossible to establish a straightforward cause and effect relationship between expenditure and voting . 
We can only examine what we know about elections and about how money is spent , then make judgments based upon selective empirical data and logical analysis . 
Elections are determined by three interrelated factors — the material and social environment , individual values , and party activities . 
The influence of an individual party upon a given election result is a limited one ; therefore , the value of party spending is likewise limited . 
There is a ceiling ( and quite possibly a diminishing margin of utility ) for political expenditure . 
The Gallup Poll 's graph of the party standings in its monthly polls since 1945 suggests that the single most important influence upon voting behaviour is the economic state of the nation . 
This is little affected by the few hundred thousand pounds that the parties spend . 
Long-term environmental changes , important in setting the limits within which parties may manoeuvre , are also outside the control of party treasurers . 
This explains why the richest party does not always win elections in Britain or America . 
The successes of the Labour Party at the polls , particularly in the 1920's , are good evidence of this . 
Money can not purchase a large political following , although it can purchase attention . 
Lloyd George 's fund could underwrite constituency expenses , but it could not ensure the delivery of safe seats . 
In America the Democratic Party achieved five successive victories from 1932 against wealthier opponents . 
Only the most simple-minded materialist would reject Key 's statement : " Money is not the sole currency of politics ; Roosevelt held counters in the game that outweighed money . " 
There is , of course , a distinction between buying votes and buying political favours . 
Some Labour criticism of political spending by business firms has fastened upon the allegation that these firms are buying preferential treatment from Conservative governments , as well as seeking to influence all voters to oppose nationalization . 
It has similarly been charged that Labour 's failure to press nationalization of insurance was due to its financial links with the Co-operatives , and that its industrial policy , or the absence thereof , is dictated by the unions ' power over Labour 's purse . 
To note financial links between interested groups and parties is not to prove that government favours are for sale ; it only shows that there are some questions of public policy on which a party government can not be disinterested . 
Only if the Exchequer were made the sole source of party funds , which no one suggests , could parties be made absolutely independent financially of such pressure groups . 
Whether , as in the case of the Labour Party , the economic interest creates the political organization , or whether the party attracts the interests , is beside the point . 
Much of the money that the parties raise is spent on party headquarters and constituency organization ; the value of both of these is often overrated by those who are closest to them . 
Apart from South Africa , which does at least have the excuse that its coal is exceptionally cheap , Britain and Soviet Russia now have the dubious distinction of using the most fuel per unit of national product of all countries in the world . 
If you have to run a country on the basis of Marxist economics and the labour theory of value , you must expect something like this . 
No doubt , according to official Marxist doctrine , the more coal you use the more valuable the products you turn out , because more labour is incorporated in them ; although even in Soviet Russia common sense sometimes breaks in . 
Our policy , since the industries connected with fuel were nationalised , has not been avowedly Marxist as in Soviet Russia , but has been , perhaps unwittingly , based on many of the same ideas : fuel industries are " basic industries " , fuel ought therefore to be cheap , and the more that is consumed the better . 
This is the sort of muddled thinking which has already cost the country enormous sums . 
Until the advent of cheap oil in the last three years , the produce of the nationalised coal , electricity and gas industries ought to have been sold at much higher prices , on the one hand in order to bring some revenue to the Treasury , and on the other hand to compel industrialists and consumers to economise as they do in other countries . 
Bernard Shaw was a great dramatist ; but nobody now would suggest that his views on economics should be taken seriously . 
Many years ago he explained that the principal reason for nationalising the coal mines was that , as things were then , mines produced coal at a great variety of different costs , and that the primary duty of a national administration would be to average them out . 
Bernard Shaw 's ideas , however , had great influence in the Labour Party , and one almost suspects that some of them still linger on in the administration of our nationalised industries . 
Otherwise it is hard to explain their refusal to allow regional differences in prices , or their long hesitation before closing down uneconomic pits . 
It is true that there have been some economies in fuel consumption in Britain during recent years . 
But they have been slow and reluctant compared with the movements in other countries . 
The United States , up to the 1920s , used fuel lavishly , mainly because it was so cheap . 
But consumption per unit of national product is now lower than ours , even though fuel is still comparatively cheap in the United States . 
The detailed industry-by-industry comparison of trends in this country and Germany , reproduced in Table 4 , presents a really alarming picture . 
An industry by industry comparison of fuel consumed per unit of product in U.K. and Canadian industry , shown in Table 5 , is also very revealing . 
In order to effect most of these economies in fuel consumption , costly investments are not required . 
We have some figures given in an official document , and similar figures were estimated by the late Professor Sir Francis Simon . 
A ton of coal per year for many years into the future could be saved by investing no more than £7 in economisers and other forms of heat recovery , £12 or £13 in new kilns and furnaces and in mechanical stokers , £17 in replacing and modifying boilers , or £25 in insulating buildings . 
With coal at anything like its present price , every one of these investments is extremely well worth while . 
Our fuel consumption has now begun to fall , but it has a great deal further to go , judging by the experience of other countries . 
The National Coal Board for many years was unable to meet all the demands upon it , and had to import coal at high cost , which it then re-sold at a much lower price . 
Nevertheless , the Board seemed to like this situation , and in the programme of " Investing in Coal " which they published in 1956 they envisaged its indefinite continuance . 
The consumption of fuel , expressed as coal equivalents , had reached 254 million tons in 1956 . 
The figure subsequently fell , and rose only to 264 million tons in 1960 ; but the National Coal Board expected it to rise to 281 million tons by 1960 and 335 million by 1970 . 
To show how steadfastly a Conservative Government supports the administrators of nationalised industries we may quote a statement made by Lord Mills , the Minister of Fuel and Power , as late as 1958 , in which , while admitting that consumption had fallen to 250 million tons of coal equivalent for the current year , he still estimated that it would rise again to 300 million by 1965 . 
As coal became more difficult to sell , the Government seems to have become more determined to defend the coal industry , quietly blocking imports of cheap oil and of liquefied natural gas ( for which the transport technique has recently been discovered ) . 
It seems all too clear that much of our " investing in coal " has been wasted ; and we can now see some of the reasons why . 
( d ) Electricity 
Regarding electricity generation , which has taken a substantial share of the country 's capital during the last decade , we do not see obvious signs of waste as we do in coal . 
At the same time , there has not been any real reply to the case made by Dr. I. M. D. Little in his book The Price of Fuel that electricity has been sold unduly cheaply to household and commercial consumers , to encourage its use for space heating , which could be more economically done by gas . 
The supposed purpose of nationalisation was to bring about a rational co-ordination between industries , but this certainly does not seem to have been done in electricity and gas ( any more than between road and rail transport ) . 
The administrators of the nationalised electricity undertaking seem to have got their ideas from old-fashioned electrical engineers whose main purpose in life was to drive gas out of business . 
The Government has even permitted the nationalised electricity and gas industries to spend public funds , beyond the amounts reasonably required to make useful new equipment and processes known to the public , in advertising against each other . 
Dr. Little 's criticisms particularly applied to the fact that the scale of charges for household electricity gives consumers no incentive to economise during the peak hours , when electricity is most costly to the supplying authority , because expensive reserve capacity has to be kept in being to meet peak loads . 
Experience in other countries has shown that there are practicable devices for adjusting meters in order to charge more for peak hour use . 
Our nationalised electricity industry has stubbornly and irrationally refused to adopt them . 
The building of nuclear power stations has been criticized : though this form of investment is , I think , defensible on economic grounds , up to the point where the base or minimum load on the electricity system ( probably at 4 a.m. on a summer morning ) , constituting perhaps one-sixth of total capacity , is all supplied by them . 
It does not serve much purpose to work out a series of comparative costs of thermal and nuclear stations , under various assumptions , in pence per unit . 
The right approach is by an analysis of " opportunity costs " . 
A nuclear station of 300,000 kw capacity , expected to last for twenty years , costs £42 million , plus £8.8 million for its initial fuel charge . 
Such a station obviates the need for a thermal station of similar capacity — additional capacity is going to be needed , even if not at the rate at which we are building at present . 
The capital cost of the thermal station would be £15 million , with a life of twenty-seven years ; so we can " credit " the nuclear station with saving 20/27 x 15 = £11.1 million capital , and regard its net capital cost as £39.7 million . 
Running costs other than fuel , which are virtually independent of output , will be £0.5 million per year for a nuclear and £0.33 million for a thermal station . 
If the nuclear station works at 80 per cent load factor , which seems a reasonably cautious estimate , it will produce 2.1 billion kwh per year at a fuel cost of 0.149d.kwh , as against 0.420d.kwh for a thermal station . 
After allowing for running costs the net saving will be £2.23 million per year , or 5.6 per cent on the net capital cost of £39.7 million . 
This , however , still only represents costs as seen by the electrical engineer . 
When we take the costs of the National Coal Board into account also , we find a very much greater saving . 
As soon as total output of coal began to go down , during the last few years , the output of coal per manshift worked , which had been stationary for a number of years , leaped upwards . 
This was brought about only to a limited extent by closing pits : mainly , it appears , by the closing of uneconomic seams within mines . 
The movement of the figures of output per manshift appears to indicate that marginal coal may cost as much as £4 per ton more than average coal . 
If we take this saving into account , as we are fully entitled to do , we obtain an additional return of 8 1/2 per cent ( or less in proportion if the above figure of £4 is too high ) on our investment in nuclear power . 
By all means invest in nuclear power — but close down more coal mines . 
( e ) Roads 
At a special conference called by the Institute of Civil Engineers recently , a case was made for very large expenditure on both rural and urban roads . 
The economic return on such investments , in the form of faster-moving and less congested traffic , can be fairly precisely calculated , and fully justifies them , probably even to the extent of the £3,000 million which , it was suggested , should ultimately be spent on our road system . 
But here again , this expenditure should render redundant a considerable part of the railway system , which should be dismantled . 
The expensive "modernization programme " for the railways was prepared on quite unjustified assumptions about the amount of traffic which they could attract . 
Demand for transport , measured in ton-miles , has been increasing more slowly than national product , and its future rate of increase is expected to be not much over 1 per cent per year . 
Road transport already carries over three-quarters of the ton-mileage of all traffic other than minerals and at its present rate of expansion will easily provide for this increase , and go on cutting into what remains of the railway traffic too . 
There can now be no doubt , and no denying , that hundreds of million of pounds have , since the end of the war , been wasted on misdirected " investment " in the nationalised coal , electricity and railway industries . 
Because of this waste we have not been able to modernise the road system , cut taxes , or do the other desirable things that could have been done . 
There has been plenty of " investment " , but how much effective growth ? 
Net capital investment from 1955 to 1959 inclusive was £8,949 million , which means an addition to the capital stock of 19 per cent . 
But the increase in the real net national product from 1955 to 1959-60 was only 9 per cent . 
Have we been putting our money on the wrong horses ? 6 . 
THE INTERNATIONAL INVESTMENT " LEAGUE " 
The final section of this booklet might be described , in a certain sense , as an anticlimax . 
After Dr. Aukrust 's careful analysis of the Norwegian figures , and the extensive figures for other countries quoted above , it is going to be very difficult for anyone seriously to contend that increased investment is a sure way of increasing the rate of economic growth . 
However , there are many people , in responsible positions , who do not reason in this way . 
They reason in a simpler manner altogether . 
The procedure is to construct what is sometimes called a " League Table " , ranking countries according to the percentage of their gross national product which they devote to investment ; and then to set out to show that their position in this table is related to their rate of economic growth . 
Between those quarters transfer payments rose by an annual rate of $1.9 billion , against which must be set an increase in personal social insurance contributions of $0.5 billion ; Federal personal tax payments fell by $3.4 billion , while state and local tax payments rose by $0.3 billion . 
The fall in Federal personal tax payments and the rise in transfer payments were more than enough to offset the fall in personal income before tax and transfer , disposable income rising by $1.0 billion . 
Although the level of personal income before tax and transfer in the second quarter of 1954 was the lowest reached in the recession , disposable income was higher than the pre-recession peak , as was consumption . 
Although small changes from quarter to quarter as shown in the national income accounts must be treated with caution because of the " statistical discrepancy " , there is every reason to regard as correct the view held at the time in official circles that disposable income and consumption expenditure for goods as well as services was being well maintained despite the recession . 
As long as this was so the attempt to reduce inventories would succeed and before long inventory liquidation would have to come to a halt , with a consequent increase in total demand and production . 
The danger was that the fall in incomes caused by the reductions in output made in order to reduce inventories might lead to such a drop in consumers ' demand that the attempt to liquidate inventories would fail , leading to another round of cuts in output . 
The cut in incomes resulting from the fall in defence expenditure could intensify such a spiral . 
But in the early months of 1954 there was no sign of such a development . 
Retail sales of non-durable goods rose steadily , the total in each month except March being above that for the corresponding month in 1953 , and in April equalled the previous high point ( July 1953 ) . 
Sales of consumers ' durable goods were below the 1953 levels throughout 1954 , but in February and succeeding months were well above the low point of December 1953 and January 1954 . 
The movements of disposable income and retail sales indicated that the fall in production and in incomes derived from it was not causing a deflationary spiral , so that it was likely that the combination of reduced output and stable sales would run down inventories fairly quickly . 
It was reasonable to reach this conclusion in March or April 1954 . 
The above conclusion indicated that the consumption sector of the economy would be able to get by with the tax reduction already enacted , with the reduction in excise tax rates just to be on the safe side . 
The Administration 's approach was cautious ; in March and April 1954 definite evidence that the trough of the recession had been reached was not yet available and there were no grounds for believing that recovery had begun ; the risk of a deflationary spiral still existed . 
The Administration decided to take the risk , which indeed did not appear a large one , in order to avoid risking the inflation that might develop once recovery was well under way if the tax reduction could not be reversed quickly . 
While it was quite legitimate to argue that the risk of inflation should have been accepted and tax rates reduced , it can not be justifiably asserted that the issue was whether any attention at all should be paid to consumption ; talk about " a massive transfusion of purchasing power " implied that the consumption sector of the economy was in a much worse state of ill-health than it really was . 
The main tax bill of 1954 , that to enact a new Internal Revenue Code , was a measure of revision and reform . 
Indeed , the slow , deliberate progress that it had made since its inception in 1952 suggests that its coinciding with a recession was fortuitous , though had there been inflation serious enough to make any tax reduction undesirable it could presumably have been held over for a year or so . 
The majority of the Ways and Means Committee stated in their report on the bill : 
" This bill is a long overdue reform measure which is vitally necessary regardless of momentary economic conditions and should not be confused with other measures which may be , or might become , appropriate in the light of a particular short run situation .... " 
There was no reason why a tax reduction should not have been added to the reforms if the economic situation rendered this desirable . 
The most contentious provisions were the dividend credit and the more liberal depreciation allowances . 
The latter provided that the taxpayer might use the " sum of years digits " method of computing depreciation , or declining balance at double rate ( i.e. if the asset had a life for tax purposes of 10 years the annual allowance would be 20 per cent of the value not yet written off ) . 
The new formulae for computing depreciation allowances were to apply only to depreciable assets acquired after the Act had come into force , and thus were evidently intended as a device for encouraging investment rather than as an improvement in the equity of the tax system . 
The Administration proposed that the first $50 of personal income from dividends should be exempt from tax in 1954 and the first $100 in subsequent years , and that the taxpayer should be allowed to deduct from his tax liability 5 per cent of his income from dividends in the first year after the Act had come into force , 10 per cent in the second year , and 15 per cent in the third and subsequent years . 
The bill reported by the Ways and Means Committee ( H.R.8300 ) followed the Administration 's recommendations except that the credit of dividends against tax liability was limited to 10 per cent . 
The dividend credit had no relevance to the immediate economic situation ; it was supported on grounds of equity , as a means of providing relief from the " double taxation " of dividends . 
The minority report of the Ways and Means Committee denounced the dividend credit as an indefensible discrimination in favour of unearned income and as embodying the " trickle down " approach to tax reduction . 
The changes in the depreciation allowances were criticized on the ground that the fuller use of capacity that would result from an increase in consumption demand would be a more reliable inducement to investment , for since much existing capacity was not being fully used tax relief directed specifically to investment would not have much effect . 
The proposal for an increase in the individual exemption from income tax had almost unanimous support from the Democrats , including Representative Rayburn , House Minority Leader , and Senator George , the senior Democratic member of the Finance Committee , which made it " official " Democratic policy if anything could . 
There were also signs of Republican support . 
The Administration was sufficiently concerned for the President to make a special broadcast on the subject on 15 March , two days before the bill was due to be debated in the House of Representatives . 
After stressing the need to encourage investors to buy " lathes , looms , and great generators " the President expressed hostility to the proposed increase in the individual exemption on the ground that it would exempt a large number of taxpayers from tax liability altogether : 
" When the time comes to cut income taxes still more , let's cut them . 
But I do not believe that the way to do it is to excuse millions of taxpayers from paying any income tax at all ... every real American is proud to carry his share of any burden .... 
I simply do not believe for one second that anyone privileged to live in this country wants someone else to pay his fair and just share of the cost of his Government " . 
The debate on the bill in the House on 17 and 18 March 1954 took the form outlined above , with sundry Democratic assertions that since their opponents had decided to something as reckless as to reduce taxation in face of a deficit , it might as well be a more equitable tax reduction . 
The motion to recommit provided that the dividend credit and the depreciation provisions should be deleted and an increase in the individual exemption to $700 inserted . 
It was rejected by 210 to 204 , eight Republicans voting in favour and seven Democrats against . 
Not all of those voting in favour of the motion were voting in favour of a reduction of the income tax ; if the motion to recommit had been carried it would probably have been the end of the bill for the Session unless the economic situation were to deteriorate . 
Among those whose votes appeared to be influenced by this consideration were the Democrats from Virginia and Representative Cannon . 
There are signs that the President 's efforts were effective in whipping-in some of the Republican stragglers ; one of these , Representative Ayres , said that he had thus changed his mind . 
When the Senate Finance Committee opened hearings on the bill on 7 April 1954 Secretary Humphrey held firmly to the position that the measures already taken , plus the stimulation that the depreciation provisions of the bill would give , were adequate to deal with the recession , and that a further tax reduction would be inflationary . 
The representatives of NAM and the U.S. Chamber of Commerce supported the Administration 's position , but the Chamber 's representative recommended that personal income tax should be reduced by 5 per cent of liability and that expenditures should be cut sufficiently to make the tax reduction possible without further unbalancing the budget . 
The trade unions gave vigorous support to the increase in the individual exemption from income tax . 
Mr. Reuther said that there was " nothing wrong in the American economy that an increase in the purchasing power in the hands of the American people will not cure " . 
There was also the usual pleading for special relief and grinding of axes ; the General Counsel to the National Institute of Diaper Services , Inc. , asked that the cost of " antiseptic diaper service " be made a tax deductible expense . 
After the end of the hearings the Finance Committee devoted five weeks to its consideration of the bill , and proposed numerous amendments , none of economic significance in their effect on the revenue . 
Introducing the bill in the Senate of 28 June 1954 Senator Millikin declared that the bill would go part of the way towards restoring " normal economic incentives " , which was essential since the stimulus given to the economy by abnormal military expenditure was fast disappearing . 
He emphasized the by then apparent fact that the decline had come to an end , arguing that as a result further tax reduction was not necessary to bring about recovery . 
Senator George agreed that the recession had not got as bad as had at one time seemed likely ; he therefore proposed an amendment to increase the individual exemption from $600 to $700 , instead of to $800 as he had suggested earlier . 
Although his proposal would increase the deficit in the immediate future , he maintained that " There will be a greater deficit if we do not sustain the principles of a sound and expanding economy " and that it was more important to balance the " home budget " than to balance the budget of the Federal government . 
Douglas argued powerfully that the main economic problem at the moment was not lack of productive capacity but lack of effective consumer demand , and that no tax concessions to investment would achieve results if there was no market for the output from the increased capacity . 
The reasoning which underlay the bill was therefore fallacious ; it would add to private savings , but would do nothing to add to investment , which was being held back by lack of markets . 
Millikin moved an amendment to provide for a reduction of tax of $20 in tax liability for each taxpayer , a slightly less costly substitute for George 's proposal ; it was ill received by George and his supporters and was rejected by 49 votes to 46 , the vote being on party lines except that Langer voted with the Democrats . 
George 's amendment to increase the individual exemption was rejected by 49 to 46 , the margin of defeat being supplied by the four Democrats voting against it , Byrd , Robertson , Johnson of Colorado , and Holland . 
As they introduced longer lags in the price variable , the contribution of their demand coefficient steadily increased . 
From a technical point of view , using the method of least squares estimation , we find the principal factor at work to be that the introduction of a lag in the price variable systematically reduces its coefficient , while the other factors remain relatively stable . 
This effect is increased in the formulation of ( 4.1 ) where a moving average of price changes is taken . 
In all cases , the overall correlation remains virtually unchanged . 
Empirically , we have been unable to determine a unique lag between wage and price changes , and we have therefore had to rest content with the lag of six months built into the model from { 6a priori reasoning . 
We are disposed to conclude from our estimates that demand has been an important factor at the bargaining table . 
At the level of aggregation at which we are working , it is the general state of the demand for labour that is relevant . 
It has been pointed out by H. A. Turner that in 1952-53 recorded unemployment in the cotton industry was as high as 30 per cent . 
of the industry 's manpower , whilst the " unions not only presented to the employers a demand for a general wage increase but persisted to the point of partial success " . 
The point here is that the unions ' hand was strengthened by the existence of alternative employment . 
The kind of effect that we are considering is that of the influence of general unemployment . 
A 200,000 increase in the level of unemployment will doubtless have a greater effect on the change in wage rates if it is spread over all industries equally , rather than concentrated in one industry alone . 
The situation in the cotton industry can then hardly be cited as evidence against the influence of demand . 
The political variable , Ft , represents the influence of cost-inflation . 
It is sometimes argued that the trade union leader 's job is to obtain higher wages for his members , and it matters little how he does this . 
He may rationalize his demand for higher money wages in terms of the cost of living , the level of profits or increases in productivity . 
In the absence of such factors he may push for increases in money wages on principle , the strength of the push depending in part on the extent to which the government of the day can create an atmosphere of restraint . 
In the model , the coefficient of Ft indicates that in periods when the Conservative government has been in power , unions have been pushing harder to the extent of some three index points per year . 
This is a statistically firm coefficient which may be taken as evidence of the increased importance of autonomous trade union pressure over the second half of our sample period . 
It is extremely difficult on the basis of the evidence , in the form of our estimates , to maintain that over the whole sample period changes in the wage rate index have been " cost " rather than "demand " induced . 
This result can be rationalized by arguing that to some extent the strength of the " cost-push " at the bargaining table is governed by the demand for labour . 
The two complement each other . 
Without the existence of " excess demand " for labour , the " cost-push " might not go very far ; without the " cost-push " in a situation of " excess demand " , workers might be unable to exploit their favourable position . 
To this extent , changes in wage rates are dependent on both " cost-push " and the level of " excess demand " . 
Several writers have drawn attention to changes in the spread between wage earnings and wage rates , as a criterion to distinguish demand from cost inflation . 
The limited information estimate of equation ( 4.2 ) attributes greater significance to hours worked than to productivity , though both can be considered significant . 
The residual terms in this computation were , however , highly autocorrelated . 
The estimate from transformed data has no significant serial correlation in the residuals but gives a different estimate for the relative importance of productivity and hours worked in accounting for the spread . 
The hours worked variable dominates the relation and , if anything , our estimates in ( 4.2 ) are over-generous in attributing fluctuations in the spread to fluctuations in productivity . 
Our results are not inconsistent with the hypothesis that the spread is largely influenced by the level of demand . 
If this is correct , fluctuations in the spread could be regarded as an indicator of changes in the level of demand . 
Hours worked constitute a very sensitive indicator of the level of demand , although absolute changes in the hours worked index are small . 
In one sense hours worked contribute to the spread in a purely accounting manner as do , other things being equal , increases in output per man-hour for piece-workers . 
We are unable , however , to separate out the relative importance of these two influences . 
No doubt , overtime , bonus payments , premium rates , and changes in the length of the " official " working week , have all been important . 
On the demand side , it is often argued that a high level of demand has led to payments above the " official " rates to bid labour away from some firms into others . 
Our results are consistent with either hypothesis alone or a combination of both . 
It is interesting to compare our results with those obtained by the Swedish economists , Bent Hansen and Go " sta Rehn , in their study of the Swedish labour market . 
They start from the assumption that wage rates are fixed institutionally and that the influence of economic forces is reflected in the spread between earnings and wage rates , which they describe as the " wage drift " . 
In our model we have put forward the hypothesis that changes in wage rates are influenced by changes in the cost of living , by the demand for labour , and by the political climate . 
The procedure followed by Hansen and Rehn was to take a sample of annual data , 1947-54 , for eight main groupings within Swedish manufacturing industry . 
Briefly , their findings suggested that the main influence determining the " wage drift " in Sweden over these years has been "excess demand " . 
They tested the further influence of " excess profits " and the hypothesis that increases in productivity have contributed substantially to the " wage drift " . 
Neither was found to be significant . 
The relations estimated were between the rates of change of the " wage drift " , the level of " excess profit " , the level of " excess demand " and the rate of change in productivity . 
It may be pointed out that in our model productivity makes a significant contribution to the explanation of the spread between earnings and wage rates , when all variables are expressed as levels , but ceases to be a significant factor in our least squares computation in which variables are subjected to a first-difference transformation . 
It would appear , therefore , that our findings are not inconsistent with those of Hansen and Rehn . 
However , it must be re-emphasized that we have included hours worked in our computation , which are an indicator of the direct influence of demand on the spread , but also of other influences , and that our earnings variable is of average weekly earnings and not of hourly earnings . 
Hansen and Rehn , on the other hand , construct an index of " excess demand " for labour , in some cases by taking the difference between unfilled vacancies and numbers unemployed . 
Where numbers unemployed were not available for a particular industry , vacancies alone were used . 
It is not clear that the growth of the spread between earnings and wage rates in the UK over the period of our sample can be plausibly explained in " cost " terms . 
If it is argued that such a gap is automatically opened by the rise in piece-workers ' earnings as productivity increases , or by changes in the amount of overtime worked , such changes may themselves be traced back to the existence of a high level of demand . 
Equation ( 4.3 ) illustrates the close relation between hours worked and the level of industrial production , which itself reflects the level of demand . 
Passing through this chain of causation , it would be plausible to expect a high empirical correlation between changes in the " wage drift " and the level of " excess demand " for goods and services . 
Under the assumptions implicit in the model , this relationship merely constitutes a derived relation rather than a basic structural equation . 
To estimate the determination of the " wage drift " in this form would involve obscuring the underlying chain of relationship . 
It is sometimes held that the changes in the " wage drift " are not governed by the level of " excess demand " , since this would imply some bidding up of payments to workers over the " official rates " . 
It is then contended that just as manufacturers have not bid up prices directly in response to "excess demand " , so they have not bid up wage payments . 
The " mark-up " equation ( 4.4 ) suggests that earnings have been roughly twice as important at the margin as import prices in determining the general level of consumer prices over the sample period . 
The coefficient of the import price index represents the influence of " cost-push " to the UK economy . 
The level of earnings , on the other hand , may represent both the influence of " cost-push " and that of demand , for it is through earnings that demand affects the general consumer price level in our system . 
The Implications of the Model 
Our particular model of the inflationary process brings out points that have been raised by different writers and attempts to follow through some interrelated patterns of behaviour in the sphere of wage and price determination . 
The model illustrates the influence of both cost and demand elements . 
It is not unique , as judged by its agreement with observed data , and it contains flaws ; nevertheless it appears to be reasonable , and the difficulties that it encounters are inherent in the nature of our basic economic information . 
Our statistical analysis covers the post-war period as a whole . 
As such , it gives a set of average relationships which do not rule out dispersion . 
In the Korean war period , for example , the rise in import prices would appear to have made a much greater contribution to the rise in the general consumer price level than earnings , although , on average over the period as a whole , earnings appear to have been the more important factor . 
This fact limits the usefulness of the model in enabling us to comment on the debate on the character of inflation over such a short period as say 1956-57 . 
Our results seem to show that for the period of the sample as a whole it is not possible to assert categorically that we have had either demand or cost inflation . 
The model attributes significance to both cost and demand elements . 
Even Professor Robbins , a firm protagonist of the importance of the influence of demand over the period , is prepared to concede that for the latter half of 1957 and the first half of 1958 , the rise in final prices may have been largely "cost-induced " , as an overshoot from the period of " excess demand " . 
Consider , however , the period 1956-57 when price and wage changes were substantial and over which much controversy has raged . 
In 1955 and 1956 unemployment had fallen considerably from the relatively high level of 1952 . 
If we accept our equation ( 4.1 ) as a basic structural relation , then we are virtually committed to accepting the view that the level of "excess demand " for labour had a significant effect on wage rate changes in that period . 
It may however be argued that ( 4.1 ) places overmuch weight on the influence of average unemployment . 
In the base year our average of registered unemployment , in numbers , was around 350,000 . 
If the price level were stationary for sufficiently long so that the influence of that variable in ( 4.1 ) were to become zero , then average unemployment in terms of numbers registered unemployed would have to reach only 500,000 before the four-quarter change in the wage rate index would become negative ( assuming **f ) . 
Many would , however , find this conclusion implausible . 
They would no doubt argue that ( 4.1 ) can hardly be considered reversible . 
Wage rates go up but they do not come down . 
More moderate exponents may grant the sincerity of those who make the claim , but suggest that notions of justice differ so widely that a situation which seems to justify parity in the eyes of one man will justify a differential in the eyes of another . 
The public services , however , are committed to a different view . 
Since the Priestley Commission , the government and the civil service trade unions have been in agreement that the wages and salaries of civil servants should be settled by " fair comparison with current remuneration of outside staffs employed on broadly comparable work , taking account of differences in other conditions of service " , and the Civil Service Pay Research Unit has been established to provide the information on which these comparisons should be made . 
The Pilkington Commission , the Guillebaud Committee and the Willink Commission have since extended " fair comparisons " of one sort or another to the medical and dental professions , to the railwaymen , and to the police . 
It is , of course , possible to argue that this use of " fair comparisons " in the public service is only market forces at one remove . 
In a service financed out of taxation the normal processes of the market are not available to determine wages . 
Consequently wages in the public service should be settled by comparison with rates in outside occupations where market forces apply . 
On this view the fair wage means the market rate . 
This view probably lay behind the original formulation of the Fair Wages Resolution of the House of Commons in 1891 . 
Fair wages were those " generally accepted as current " . 
Trade unionists , however , agitated for many years for a change which was finally accepted in the revision of 1909 . 
Fair wages were then defined as " those commonly recognized by employers and trade societies " . 
This suggests that the fair wage is the wage settled by collective agreement — the " acceptable wage " . 
I do not think either of these definitions can be accepted as satisfactory . 
The first difficulty is that every detailed study of wages in Britain reveals startling variations and inconsistencies for the payment for what is apparently the same job even within a single town or district . 
Thus the market , or collective bargaining , or both , lead to a whole range of rates , any one of which could be fair . 
If there are grounds for arguing that the public servant should , on grounds of justice , be paid the average of this range of rates , then this average must be the fair wage not only for the civil servant , but also for the workers in comparable outside occupations . 
Those of them who are getting less than the average have , on grounds of equity , a case for an increase to bring them up to that figure . 
A second difficulty is that we sometimes wish to say that a market rate , or even a rate settled by collective bargaining , is unfair . 
The wages paid to coal-miners and agricultural workers in the 'thirties , for instance , would perhaps have been generally regarded as unfair , but necessary because of the depressed markets for coal exports and for agricultural products . 
The fact that the wages of coal-miners were settled by collective agreement did not , I suggest , make them appear fair in the eyes of the public . 
I would also suggest that it is a common view in modern Britain that wages paid in the manufacture of motor vehicles are unfairly high compared with the wages of other workers , although they are settled by collective bargaining . 
Many of those who hold this view , however , might be reluctant to voice it in public . 
There are therefore grounds for supposing that there is some other way of determining fairness in addition to the " higgling of the market " , or the process of collective bargaining . 
The four inquiries which I have mentioned seem to accept this supposition and to suggest that the British public holds to certain common standards whereby it can compare one job with another and decide whether the remuneration is fair or not . 
The interim report of the Willink Commission , for example , argues that the pay of the police should be " based on conditions recognized by the police themselves and by the public as fair and reasonable " . 
Treasury evidence to the Priestley Commission argued that : "... if a civil servant can be seen to be getting , as near as may be , what citizens of similar attainments are getting for doing similar work in the country at large , that is a situation which will surely be commended as fair by the civil servant himself , by his outside analogue , and by the taxpayer who foots the bill ... " 
The main difference between the two reports is that the Priestley Commission thought that fairness demanded the same rate of pay as for the " outside analogue " , whereas the Willink Commission recommended considerably higher rates for the police than for the outside occupations with which they compared them . 
Thus both these reports hold not only that it is possible to say that workers — or at least some grades of workers — are fairly paid , but also that there would be general agreement from all sections of society on what would constitute fair payment . 
No evidence is given in support , although it would clearly be possible to devise empirical tests to discover whether there are generally accepted standards of fairness . 
The view is presented as self-evident , or at least as not worth arguing . 
The questions I wish to pursue , therefore , are : can we accept the methods of these four inquiries as satisfactory and dependable procedures for establishing the " just " wage ; and , if we can , how wide is the scope of their application ? 
First , however , it is necessary to set out some information about each of them . 
The job of the Civil Service Pay Research Unit is fact-finding . 
It assists in establishing job comparability by describing "the similarity or difference in the duties of the grades with which comparison is being made " ; and it discovers " the pay and conditions of service that attach to jobs regarded as comparable " . 
Armed with this information the two sides of the appropriate Whitley Council can negotiate what wage or salary is required by " fair comparison " , or , if they fail to agree , refer the decision to arbitration . 
The Guillebaud Committee 's terms of reference were wider than this . 
The Committee was instructed " to conduct an investigation into the relativity of pay " of railway workers with other workers , and to "establish the degree of job comparability " as well as to discover the rates of pay and other emoluments of the other workers . 
The Committee was also empowered to offer " general observations and conclusions " along with " the ascertained facts " . 
The terms of reference of the Pilkington Commission were wider still . 
They were asked to consider how the remuneration of doctors and dentists compared with that of other professions , and what , in the light of this comparison , their remuneration should be . 
Finally the Willink Commission has been given no instructions to make comparisons . 
They have been asked to consider : " the broad principles which should govern the remuneration of the constable , having regard to the nature and extent of police duties and responsibilities and the need to attract and retain an adequate number of recruits with the proper qualifications " , and their interim report rejects the principle of " fair comparison " as inapplicable to the police service . 
But it goes on to argue that the pay of the constable should be settled by means of a formula which yields almost 70 per cent more than the wage rates in certain selected skilled occupations . 
This process must be based on a comparison of some kind . 
The criteria which justify the same remuneration are , however , simpler than those which justify differences in remuneration , and also logically prior to them ; for how could comparisons which reveal differences between jobs be used to justify differences in pay unless comparisons which did not reveal those differences justified the same pay ? 
We start therefore with the principle of the rate for the job , the principle that the same job should carry the same rate of pay . 
The Willink Commission have , in fact , annexed this phrase to cover another principle , which they call their " third principle " . 
They do not state what the principle is , but they say that " it relies for its operation very largely on a judgement of the constable 's value to the community " . 
But as I understand it , the phrase has always described the old trade union principle that a fitter must not take less than the fitter 's rate , nor a compositor than the compositor 's rate , as it stands in the district in which he happens to be working . 
I can see no reason for using it in this novel and imprecise sense . 
The difficulty is to know when two jobs are the same , or rather , since two jobs are never exactly the same , to know which differences can be regarded as negligible for the purpose of settling payment . 
The ingenuity of man can create reasons for additional payments out of everything and out of almost nothing — out of slight differences in materials , in tools and machinery , or in the product ; out of differences in the heat , dirt or noise of working conditions ; out of responsibility for men , materials , machinery , or money ; and so on . 
Some reason can always be found for paying X more than Y , and probably also for paying Y more than X. 
Before we write the problem off as insoluble , however , we must remember that men have repeatedly cut their way through it over the centuries , and do so constantly today . 
The fitter 's rate , or the compositor 's rate , is only meaningful because there is agreement about what is the proper work of a fitter and of a compositor , either by rule or by custom . 
Every grading structure , in public and in private employment , decides that certain differences in work warrant differences in pay , and also that the great majority do not . 
The process whereby the National Coal Board reduced something like six thousand daywage job titles to 367 titles , and then grouped these titles into thirteen different wage grades , is but one outstanding example of a common process . 
Such examples show that , in the settlement of salaries and wages , men are willing to neglect many differences between jobs , and also to recognize others as important . 
They do not , of course , prove that there would be general agreement on what should count and what should not . 
We can , however , find some evidence on this point . 
We know , for instance , that many thousands of problems about jobs and about gradings are amicably settled each year . 
Strikes over demarcation disputes or arbitration awards on grading questions only serve to emphasize the wide area of undisputed territory behind them . 
It is hardly possible that this could be so without widespread agreement on which differences count and which do not . 
The experience of the Guillebaud Committee was that " our team of investigators , coming from widely-varied backgrounds and with different industrial experience , agreed closely among themselves , and their opinions corresponded , in most instances , with those of our Secretaries and ourselves . 
There were no disagreements which could not be settled by discussion " . 
Whether differences count or not is at least largely a matter of social convention . 
Only empirical tests could discover whether there are generally accepted conventions , but , until such tests are carried out , I submit that these are grounds for supposing that there are some conventions which are fairly widely accepted . 
The Priestley Commission included amongst their criteria of fairness " the educational or other qualifications required " . 
In fact , the Civil Service Pay Research Unit seems to have concentrated more on work than on qualifications . 
For the Pilkington and Willink Commissions , on the other hand , qualifications seem to take first place . 
The Pilkington Commission was instructed to consider " the proper current levels of remuneration " of doctors and dentists in the light of a comparison with the remuneration of other professions . 
The professions on which they based their inquiry were : accountants , actuaries , barristers , solicitors , architects , surveyors , engineers and university teachers , together with a category entitled " graduates in industry " . 
Most of these studies are partial , dealing with particular aspects of world trade . 
There is only one that I know of which tries to use the statistical information to formulate a model of world economic development and trade . 
This Professor Lewis did in 1952 , based on statistics for 1870-1950 , in terms of six world variables : world industrial production , world food production , world trade in manufactures , world trade in primary products , the price of primary products and the price of manufactures . 
The model , although attractively simple , fails to fit developments since 1950 partly because it makes one important assumption not borne out by events — the assumption that the ratio between world trade in primary products ( food and raw materials ) and manufactures would remain unchanged . 
In fact , one of the new features of the development of world trade since 1950 has been the rapid relative growth of world trade in manufactures and a corresponding relative fall in world trade in primary products . 
This relative fall is particularly marked if oil is excluded . 
The causes of this change have aroused great controversy , controversy which illustrates how difficult it is to interpret significantly this mass of statistical information . 
There is on the one side the argument , put forward strongly by the late Professor Nurkse , that the relative decline in world trade in primary products is mainly due to a fall in demand by industrial countries : a fall due to agricultural protection , a change in the structure of industrial production towards products using less raw materials and the substitution of synthetics for natural products . 
Others , including Professor Cairncross , who spoke on this theme here a few months ago , have argued that one of the main factors inducing industrial countries to use less primary products was a shortage of supply , and that this shortage of supply was , to a substantial degree , the result of the economic policy followed by many primary producing countries . 
The analysis by GATT in successive reports on " International Trade " since 1956 has tended to confirm this conclusion . 
GATT classified the non-industrial primary producing countries into two groups : ( 1 ) the semi-industrialised countries where industrialisation has already made substantial progress ( countries such as Argentina , India and Australia ) , and ( 2 ) the remaining non-industrial countries ; and then showed that the bulk of the relative fall in trade came in the first and not in the second group of countries . 
This seemed to lead conclusively to the view that reduced supply had at least been a very important contributory element in the relative reduction in world trade in primary products . 
But since then Mr. A. Maizels of the National Institute has attempted to show that the results obtained by the GATT analysis are largely fortuitous and do not point to the conclusion which is drawn from them by the authors of the GATT reports . 
Mr. Maizels shows that if exports of primary products from semi-industrialised countries are compared with world demand for the same commodities ( which he measures by world trade ) over the period 1937-38 to 1955 , then in most cases the semi-industrialised countries have maintained their share of the world total . 
From this he concludes that the relative fall in the trade of the semi-industrialised countries is due mainly to its commodity composition , and the fall in world demand for these commodities ; thus confirming the demand deficiency , rather than the supply deficiency , view . 
There is , however , one weakness in Mr. Maizel 's main calculations . 
In the case of some commodities a substantial part of the total of world trade is accounted for by the trade of the semi-industrialised countries . 
It is hardly surprising that in these cases exports from the semi-industrialised countries on average show much the same movement in volume as world trade as a whole . 
Take wool as an example . 
This appears as an important export for four semi-industrialised countries — Argentina , Australia , New Zealand and the Union of South Africa . 
But the exports of these four countries between them account for the bulk of world export trade in wool . 
It is hardly surprising therefore that the export volume of wool from these countries , on average , approximates to the world total , some above and some below . 
The nearness of the world total and the figures for the four semi-industrialised countries can not be taken in this particular case to demonstrate the validity of the demand deficiency view . 
The same point applies to coffee , which appears as an important export of three semi-industrialised countries , Brazil , Colombia and Mexico , which between them account for a substantial part of world trade in coffee . 
Indeed , one inevitably gets into difficulty if one has to use , as so often happens in analyses of world trade , the same figures as representing both world supply and world demand ; and when one begins to look at the position of individual semi-industrialised countries , Argentina for example , there seems strong evidence that there has been a reduction in the supply of primary products for export , and a substantial case for arguing that Argentinian economic and commercial policy has been an important element in this reduction . 
I would expect to find differences in the relative importance of changes in demand and supply from country to country , and suspect that any generalisation which attempts to settle this controversy in terms of general figures for world trade is likely to be too sweeping in ignoring the peculiar and divergent experience of individual countries . 
The other major feature of the statistics of world trade that has commanded great attention in recent years , is the rapid growth and changing character of world trade in manufactures . 
In the 1930 's and during the war most of those who attempted to look ahead to future developments in world trade in manufactures were inclined to take rather a gloomy view . 
The traditional trade , especially in cotton textiles , was disappearing rapidly as domestic industries were being built up in the newly-developing industrial countries . 
And the opportunities for increased trade between the advanced industrial countries seemed likely to become restricted rather than wider as the character of their industrial development became more and more similar . 
In fact , world trade in manufactures has increased more rapidly than world industrial production compared with 1938 , the rise in European trade in manufactures being most remarkable and unexpected . 
Now that we have a mass of regular statistical information , on a standard international classification , about this trade , we can examine its pattern and structure in great detail . 
Familiarity with this statistical detail can no doubt give us a comfortable feeling that we know what is going on in international trade , which lines and markets are expanding or contracting . 
And we can pay particular care , as the Board of Trade does each quarter in the tables in the Board of Trade Journal , to look at the fortunes of United Kingdom trade in this international competition . 
But I doubt very much myself whether the accumulation of statistics of this kind and the grubbing about among them for significant statistical trends by itself gives us much understanding of what is going on and the forces which are making for change . 
We need much more understanding and analysis of the forces that are behind the statistics . 
It may be , however , that the changes are the result of such a complex interaction of forces and that our analytical tools are so primitive that we can not yet hope to acquire this deeper understanding and will have to confine ourselves , for the time being at least , to the search for statistical trends which we hope will endure for some time . 
One of the main problems in understanding the significance of the shifting pattern of the world trade in manufactures is to be able to distinguish between changes in the fundamental forces in operation , and the time period which it takes for trade to adjust itself to those forces . 
Take , for example , one of the major changes in British foreign trade over the last 50 years — the almost complete disappearance of the United Kingdom as a net exporter of cotton textiles . 
Looking back now it could be argued that the fundamental forces which led to this change were already in operation in the years immediately after the first world war — the acquisition by Japan , India and other countries of the necessary technical and economic experience to enable them to develop efficient cotton textile industries of their own , and the consequential loss by Lancashire of the special comparative advantage that she had had in this field of manufacture for over a century . 
But although the fundamental forces had already changed by 1920 , it took many years for the full consequences to work themselves out . 
And because the process of adjustment took so long and was so slow , it was a long time before the change in the underlying situation was recognised . 
Throughout the 1920 's and 1930 's it was still a widely held view that , given the appropriate re-organisation of the industry , Lancashire could regain her pre-1914 world trading position . 
It is obviously not easy to recognise powerful new economic forces affecting world trade when they first emerge . 
It is easier to treat the structure and pattern of world trade as relatively stable and unchanging until change makes itself clearly evident in the statistics . 
I have discussed very briefly only one or two examples of the way in which statistical information about world trade is used in an attempt to understand the main forces making for change . 
But these I think are quite typical and , unfortunately , do not lead to the clear conclusion that this new approach is leading to great enlightenment . 
It is , I take it , hardly necessary for me to sum up my view that we are still far from having , either in theory or in statistical analysis , techniques which enable us to explain satisfactorily the main features of international trade . 
Many of you will no doubt think that I take too gloomy and sceptical a view . 
But in this field of economics , as in many others , however complex our theoretical and statistical models may be , I am impressed , perhaps over-impressed , by their relative crudity and simplicity compared with the intricacy and complexity of the real world . 
A Simple Model of Employment , Money and Prices in a Growing Economy By A. W. PHILLIPS 1 . 
INTRODUCTION 
The purpose of this article is to develop a simple aggregative model which may be used to study both the problem of reducing short-period fluctuations of an economy and the problem of attaining longer-term objectives relating to employment , the price level and growth . 
To do this the Keynesian model of employment , interest and money is extended in a number of ways . 
The concept of " normal capacity output " is introduced , with the hypothesis that normal capacity output increases continuously as a result of investment in improving productive resources . 
Actual output is then expressed as a proportion of normal capacity output . 
The rate of change of the price level is assumed to depend on the ratio of actual output to normal capacity output and on the rate of change of productivity . 
The rate of interest is assumed to depend on the quantity of money , actual output and the price level . 
Investment demand is made a function of the ratio of actual output to normal capacity output , the expected rate of growth and the rate of interest . 
By defining some variables in the model to be either logarithms or ratios of the usual economic variables , assuming continuously distributed time lags in the behaviour relations and making certain linear approximations , which should be satisfactory for moderate fluctuations in output and employment , the model can be written as a system of linear differential equations . 
The steady state solutions give the paths of the variables in conditions of steady or " equilibrium " growth and in particular show the long-run relations between the rate of change of the quantity of money , the ratio of actual to normal capacity output , the rate of change of the price level and the rate of growth of normal capacity output . 
The transient solutions , which show deviations from , or short-period fluctuations about , the " growth equilibrium " paths , are used to investigate the stability of the system and the effect of a stabilisation policy . 
1880 may be quite a good watershed for other reasons . 
The Public Health Act of 1875 had enabled local authorities to pass bye-laws regulating the structure of walls and foundations of new buildings on health grounds and not merely on grounds of stability and fire prevention . 
In the late 1870s the Local Government Board published a series of model bye-laws for the guidance of local authorities in these matters . 
A recent estimate suggests that almost a quarter of the dwellings occupied today , some 3 2/3 million , were built before 1880 . 
To demolish them by 1980 would require a rate of demolition of nearly 200 thousand a year . 
Thereafter , assuming no shortening in the average life , the need for demolition would fall to about 100 thousand a year , since houses were being built at roughly this rate in the twenty-five years before the First World War . 
There is , admittedly , no overriding reason for picking 100 years as the natural term of life for a house , rather than , say , eighty years ; nor is there any special reason why the backlog should be cleared in twenty years , rather than in ten or thirty . 
But , given the likely increase in stock required in this period , it should be well within the capacity of the house building industry to deal with a replacement programme of this kind by 1980 . 
This aim is not , perhaps , an ambitious one ; even if it were achieved , the housing stock in England and Wales might still be one of the oldest in western countries , apart from France . 
To carry out the programme in , say , ten years would mean forcing up the annual rate of house building to something near 500 thousand a year , with a subsequent severe drop . 
3 . 
POLICY 
The main housing need , therefore , between now and 1980 is likely to be for the replacement of old houses , not for additions to stock . 
At the moment , the pattern of house building is the reverse . 
Only about 60-70 thousand houses are being demolished each year ; so , of the 260-270 thousand houses being built in England and Wales , just on 200 thousand are adding to the stock . 
This pattern can hardly continue for long ; it certainly can not go on up to 1980 . 
The stock of houses is rising by some 200 thousand a year ; the number of households needing separate dwellings over the next twenty years is likely to increase by an average of around 100 thousand a year . 
Vacancies are therefore likely to increase by some 100 thousand a year — this is only a little less than the total number of unfurnished vacancies in 1951 ( 140 thousand ) . 
Clearly there is a limit to the proportion of houses which will be allowed to remain vacant . 
Owners of vacant houses will reduce prices or rents in order to sell or get tenants , and the falling price of older houses must eventually depress the prices that are offered for new houses . 
This will cut into building profits , and so slow down new house building by private developers . 
How big the vacancy proportion has to be before this begins to happen is difficult to say : American experience suggests that the critical vacancy level might be about 5 per cent or a little more . 
With the present pattern of house building this vacancy level could be reached in about five years ' time . 
Imperfections in the housing market — the fact that the proportions of old houses and vacancies may be high in the North while demand for additional new houses is heavier in the South — might insulate new buildings for a while from the depressing effects of high vacancies . 
But if the present pattern of building continues , some time between now and 1970 the critical level of vacancies will certainly be reached . 
Taking the "maximum " estimate of household formation instead of the " medium " one ( page 22 ) and consequently assuming an increase of 125 thousand households a year instead of 100 thousand , the present rate of additions to stock would still bring about a 5 per cent vacancy rate within less than a decade . 
The question therefore is whether resources will be channelled from additions to replacement . 
But it is not easy for the private developer to undertake the demolition and replacement of old houses . 
He has to acquire groups of old dwellings , because of the high cost of individual demolition and because old houses are often so densely packed that perhaps three or four have to be demolished for every new one built . 
The developer may therefore have to negotiate with a large number of owners : ownership of old property is becoming even more fragmented as landlords sell houses on which rent control has been lifted . 
There is also the problem of rehousing the old tenants . 
Finally , when the developer does build , the houses will be much more expensive than houses built on virgin land because of the cost of demolition . 
He may doubt whether clients wealthy enough to buy relatively expensive houses will in fact be tempted back from the suburbs to predominantly working class neighbourhoods . 
If , notwithstanding these difficulties , when old houses are demolished , the new houses ( whether built on the same site or elsewhere ) are built for those who can afford to buy them , the housing subsidy bill would certainly be kept down . 
This policy would imply that the blocks of old houses in the inner rings of cities , now occupied by the relatively poor , should be rebuilt with houses for the relatively wealthy . 
For it is at most the top third of households in the income scale who are likely to be able to afford to buy a new house out of income in the next twenty years — though rather more than this would be able to pay the economic rent , if the cost of building was amortised over 60 years ( page 27 and table 4 ) . 
Those who previously lived in the centre would move to better but still old houses in outer districts . 
There would be an ordered improvement in standards for households in all income groups , each household moving to a house a little better than the one it previously lived in . 
Housing standards in general would be improved by a process of percolation . 
But this policy would require a great deal of mobility , and this is a further difficulty . 
Obstacles to mobility 
Mobility is high when the household is growing but this rapidly tails off as the parents reach middle age . 
By the time the children are leaving home , the parents are attached to the district by jobs and friends and often by the improvements made to the house and garden . 
When — as usually happens — the husband dies first , the widow often stays on her own . 
This is why a four-roomed dwelling — was , in 1951 , the most common size of dwelling for a one-person household . 
There are other obstacles to mobility . 
For the owner-occupier , the fees for selling a £3,000 house and buying and surveying another at the same price can easily amount to £160 , excluding removal expenses . 
Even on a £1,000 house fees may well come to £80 or so . 
It is cheaper for those renting houses to move : here the main obstacle in the next few years will be that tenants of rent-controlled dwellings will be reluctant to leave them . 
Finally , the number of people who can become owner-occupiers is limited : it is difficult to get a mortgage on an old house , and only a small proportion of the population can afford , out of income , to repay the mortgage on a new one ( page 27 ) . 
The problem will grow as the supply of privately-rented houses dwindles . 
Old houses are lived in mainly by people who can not afford to buy and who need to be able to rent ; unless , therefore , the replacements of the old houses are also built to let , there is likely to be a serious shortage of rented accommodation which will further hinder mobility . 
Economic rent and home ownership 
On the other hand , if it is the tenants of the pre-1880 houses who are to be rehoused in the new houses , it is only the local authorities who can undertake this operation ; for this housing would have to be subsidised substantially . 
The people who live in these old houses can not — either now or in 1980 — afford the economic rent of a new house , particularly since the cost of demolition will make the new houses more expensive than most . 
New houses are expensive to buy out of income , partly because , although the life of a house is at least sixty years , the cost usually has to be repaid to a building society over about twenty years . 
For a £2,500 three-bedroomed house , this makes the total annual cost ( at an interest rate of 6 per cent ) £284 ( table 4 ) . 
Spreading the cost over sixty years brings down the annual sum required to £214 ; this figure can be considered as the economic rent ( including rates and maintenance ) of a typical local authority new house , since most local authorities assume a sixty-year life . 
Virtually no private developers are building ordinary houses for renting . 
Any who did , after forty years of rent control , would probably wish to get their capital back in , say , ten to twenty years ; and the economic rent on this basis would be higher than the local authority figures and indeed than the cost of buying . 
The most that a household can normally be expected to pay for housing is probably about a quarter of its income , and most people pay far less . 
The building societies seem to take 25 per cent as the maximum . 
" A very common rule is that all regular outgoings on account of house ownership shall not exceed 25 per cent of an applicant 's basic income ( excluding overtime , bonuses and spare-time earnings ) . 
Both sums are normally considered without taking account of tax . " 
Even taking this maximum figure of 25 per cent , two-thirds of households still can not afford to pay the economic rent of a new house , and something like 90 per cent can not afford to buy one out of income ( table 4 and chart 2 ) . 
This is purchase out of income only : rather more than 10 per cent of households have a significant amount of capital — for instance , over a third of households now own , or are in the process of paying for , a house of some kind . 
Consequently rather more than 10 per cent can afford to buy a new house if they use part of their capital . 
It would , of course , help to extend the range of possible owner-occupation if mortgages could be given for a period nearer to that of the life of a house . 
This would bring the proportion of households who could buy nearer to the proportion who can afford to rent . 
But , even so , it is clear that most of the people who are now living in pre-1880 houses would be unable to buy or pay the economic rent for a new house ; for they are , by and large , in the bottom half of income-receivers and are unlikely to have any substantial assets . 
How is the position likely to change within the next twenty years ? 
Real incomes might nearly double in that time . 
But new house prices are likely to continue to rise faster than other prices , since productivity in house building increases more slowly than in most other industries . 
For instance , comparing 1960 with 1938 , the cost of a local authority house ( excluding land ) rose appreciably faster than the average household income . 
Longer term comparisons are possible for some other European countries : in those for which information is available — the Netherlands , France and Ireland — house building costs rose faster than wages from 1914 to 1956 . 
On the other hand , there is considerable scope for productivity rises . 
In a study of traditional houses completed in 1949-1951 the labour costs of the least efficient firms were almost three times as great as those of the most efficient ones . 
Some improvement may come from the better-managed firms ousting some of the less efficient but the fact that so old an industry is still composed of so many small firms , varying so widely in efficiency , argues that the forces of competition are not strong . 
A notice to quit may name the exact day for the termination of the tenancy , or it may be expressed generally ; for example , by such words as " at the expiration of the year of your tenancy , which will expire next after the end of one half year from the service of this notice " ( Addis v. Burrows , [ 1948 ] 1 K.B . 
444 ) . 
But if the notice is such as to leave doubt in the mind of the tenant as to when the tenancy will come to an end , the notice is bad . 
Similar rules to those stated above apply in the case of weekly , monthly and other periodic tenancies . 
The period of notice necessary to determine such a tenancy is a period not less than the length of the tenancy ; thus in the case of a weekly tenancy at least one week 's notice is necessary , to expire at the end of a period of the tenancy . 
A statutory exception to this rule exists in the case of premises let as a dwelling ; section 16 of the Rent Act , 1957 , provides that no notice to quit in respect of such premises shall be valid unless given not less than four weeks before the date on which it is to take effect . 
CHAPTER EIGHT Stamping and Registration of Leases 1 . 
— STAMPING 
The Stamp Act , 1891 , which regulates the payment of stamp duties on instruments , imposes duties upon leases and agreements for leases . 
The relevant sections of the Act will be found in Appendix 2 ( post at p. 85 ) . 
An agreement for a lease is chargeable with the same duty as the actual lease and must be stamped accordingly ( section 75 ( 1 ) of the Act ) . 
If a lease is subsequently executed which conforms with an agreement for a lease which has been stamped , it is chargeable with duty of sixpence only ( section 75(2) ) , but the agreement must be produced at the time of the stamping of the lease and the lease will then be stamped with a duty paid denoting stamp under section 11 . 
The amount of duty payable is set out in the First Schedule to the Stamp Act , 1891 ( the relevant parts of which will be found in Appendix 2 , post at p. 89 ) , taken together with section 34(1) of the Finance Act , 1958 ( see Appendix 2 , post at p. 169 ) . 
Although an agreement for a lease must be stamped , a distinction is drawn between an agreement for a lease and a mere proposal for a lease ; the latter does not require a stamp . 
As a general rule all stamps are required to be impressed ( section 2 of the Stamp Act , 1891 ) , but section 78 provides that in certain cases the stamp may be an adhesive stamp ; but where an adhesive stamp is used it must be cancelled by the person who first executes the instrument . 
An adhesive stamp may be used in the following instances : — 
( a ) in the lease of a dwelling-house , or part of a dwelling-house , for a term not exceeding a year at a rent not exceeding forty pounds { 6per annum ; 
( b ) in the lease of any furnished dwelling-house or apartments for any indefinite term less than a year . 
The duplicate or counterpart of any such instrument may also be stamped with an adhesive stamp . 
The First Schedule to the Act also provides for the payment of stamp duty on duplicates and counterparts of leases . 
They are liable to the same duty as the original lease if the duty on the original lease does not exceed five shillings ; in all other cases they must be stamped with a five-shilling stamp . 
Section 15(2) of the Act requires leases to be stamped within thirty days of execution , and if this is not done the lessee is liable to a fine of ten pounds and a further penalty equivalent to the stamp duty unless there is a reasonable excuse for the delay in stamping the lease and the Commissioners of Inland Revenue mitigate or remit the penalty . 
This penalty only applies in the case of leases executed after the 16th May , 1888 . 
The effect of failure to stamp a lease or other document is not to invalidate the document ; but the document is not admissible as evidence unless and until it is properly stamped and any penalty is paid . 
2. — REGISTRATION 
In any area in which compulsory registration of title has been introduced the provisions of section 123 of the Land Registration Act , 1925 , apply . 
By this section the title of a tenant on the grant of a lease for a term of not less than forty years , or on the assignment of a lease having not less than forty years to run , must be registered at the Land Registry . 
The lessee or assignee must apply for registration ; and if he fails to do so , he will be deprived of a legal estate . 
At the present time compulsory registration has been introduced in the following areas : — London , Eastbourne , Hastings , Middlesex , Croydon , Surrey , the City of Oxford , Oldham , Kent , the City of Leicester , and the City of Canterbury . 
A tenant of land not situated in a compulsory registration area may register his title at his own option at any time if he holds a term of which more than twenty-one years remain unexpired ; section 8 of the Land Registration Act , 1925 . 
Registration of titles in such areas is not , however , compulsory . 
Registration of titles in the three ridings of Yorkshire is governed by the Yorkshire Registries Act , 1884 . 
Registration under this Act is not compulsory , and section 28 of the Act provides that leases of property in Yorkshire may be registered unless the lease is for a term not exceeding twenty-one years and is accompanied by actual possession from the making of the lease . 
Failure to register a registrable lease does not invalidate the lease ; but registration constitutes notice of it to all persons . 
Section 31 of the Act establishes three deeds registries , which are situated at Northallerton for the North Riding , at Beverley for the East Riding , and at Wakefield for the West Riding . 
Section 125 of the Land Registration Act , 1925 , provides for the transfer to the Land Registry of any of the business of the Yorkshire deeds registries in the event of an order for compulsory registration under the Land Registration Act , 1925 , being made in respect of any part of Yorkshire . 
At the present time no such order has been made . 
APPENDIX ONE Precedent of a Lease 
THIS LEASE made the ... day of ... 
BETWEEN [ lessor ] of etc. ( hereinafter called the landlord which expression where the context so admits shall include the reversioner for the time being immediately expectant on the term hereby created ) of the one part and [ lessee ] of etc. ( hereinafter called the tenant which expression where the context so admits shall include his successors in title ) of the other part 
WITNESSETH as follows : 
1 . 
The landlord demises unto the tenant the premises described in the first part of the schedule hereto ( hereinafter called the demised premises ) with the exceptions and reservations specified in the second part of the said schedule TO HOLD unto the tenant from the ... day of ... for the term of ... years 
YIELDING AND PAYING therefor the net yearly rent of £ ... clear of all deductions except landlord 's property tax and [ other agreed deductions ] by equal quarterly instalments commencing on the ... day of ... and thenceforward on the usual quarter days . 
2 . 
The tenant covenants with the landlord as follows : 
( 1 ) To pay the reserved rents on the days and in the manner aforesaid . 
( 2 ) To pay all existing and future rates taxes duties assessments and outgoings payable by law in respect of the demised premises either by the owner or the occupier thereof . 
( 3 ) To keep the demised premises including the drains and sanitary and water apparatus and all fixtures and additions thereto in tenantable repair and condition throughout the term and to yield up the same in such repair and condition at the determination of the tenancy . 
( 4 ) To keep the demised premises insured at all times against loss or damage by fire in the joint names of the landlord and tenant in some insurance office or with underwriters to be named by the landlord in the sum of £ ... at least and to make all payments necessary for the above purposes within seven days after the same shall respectively become due and to produce to the landlord or his agent on demand the several policies of such insurances and the receipt for each such payment and to cause all moneys received by virtue of any such insurance to be forthwith laid out in rebuilding and reinstating the demised premises and to make up any deficiency out of his own moneys PROVIDED ALWAYS that if the tenant shall at any time fail to keep the demised premises insured as aforesaid the landlord may do all things necessary to effect or maintain such insurance and any moneys expended by him for that purpose shall be repayable by the tenant on demand and may be recovered by action forthwith . 
( 5 ) Not to use the demised premises otherwise than as a private dwelling-house . 
( 6 ) Not to assign or underlet or part with the possession of the demised premises or any part thereof without the written consent of the landlord . 
( 7 ) To permit the landlord and his agent with or without workmen to enter upon and view the condition of the demised premises at all reasonable times during the said term and forthwith to execute all repairs and works required to be done by written notice given by the landlord . 
3 . 
The landlord hereby covenants with the tenant as follows : 
( 1 ) That the tenant paying the rent hereby reserved and performing the several covenants herein on his part contained shall peaceably hold and enjoy the demised premises during the said term without any interruption by the landlord or any person rightfully claiming under or in trust for him . 
( 2 ) That the landlord will on the written request of the tenant made ... months before the expiration of the term hereby created and if there shall not at the time of such request be any existing breach or non-observance of any of the covenants on the part of the tenant hereinbefore contained at the expense of the tenant grant to him a lease of the demised premises for a further term of ... years from the expiration of the said term at the same rent and containing the like covenants and provisos as are herein contained with the exception of the present covenant for renewal the tenant on the execution of such renewed lease to execute a counterpart thereof . 
( 3 ) That if the tenant within ... years from the commencement of the term hereby created shall give to the landlord ... months ' notice in writing that he desires to purchase the reversion in fee simple in the demised premises the landlord upon the expiration of such notice and on payment of the sum of £ ... and of all arrears of rent up to the expiration of the notice and of interest on the said sum of £ ... at the rate of £ ... per cent . 
{ 6per annum from the expiration of the notice until payment thereof shall convey the demised premises to the tenant in fee simple from incumbrances . 
4 . 
PROVIDED ALWAYS and it is hereby agreed as follows : 
( 1 ) If the rents hereby reserved or any part thereof shall be unpaid for twenty-one days after becoming payable ( whether formally demanded or not ) or if any covenant on the tenant 's part herein contained shall not be performed it shall be lawful for the landlord at any time thereafter to re-enter upon the demised premises or any part thereof in the name of the whole and thereupon this demise shall absolutely determine but without prejudice to the right of action of the landlord in respect of any breach of the tenant 's covenants herein contained . 
( 2 ) If either party shall desire to determine the present demise at the expiration of the first ... years of the said term and shall give to the other party ... months ' previous notice in writing of such his desire then immediately on the expiration of such ... years the present demise and everything herein contained shall cease and be void but without prejudice to the remedies of either party against the other in respect of any antecedent claim or breach of covenant . 
In cases where there is no relevant statutory rule , and the rule has to be drawn from cases , and not from a statute , the absence of an unalterable verbal formulation of the rule reduces the importance of the conventions of language , and makes it less natural to talk of "interpretation " , though sometimes the courts do behave just as they do with a statute , when , for some reason or another , a common law rule has achieved a settled formulation . 
But this is rather exceptional . 
The consequence is that problems of applicability which arise in the courts about Common Law rules can not be solved by interpretation — that is by a process of reasoning which attaches particular importance to linguistic considerations — for there is no text to interpret . 
Solved they have to be , however , but by other types of reasoning . 
So it is that usually arguments as to whether an earlier case should be followed or distinguished do not rest primarily upon linguistic grounds ; they rest rather upon the use of analogy , and upon the discovery of factual similarity and difference between cases . 
But just as difficulties of interpretation , which seem to be difficulties about words , are really difficulties about the applicability of rules to facts , so also are many difficulties involved in the use of precedent . 
Thus even if there is a measure of agreement about the ratio of an earlier case , an agreement , that is , as to what rule can be extracted from it , there may still be difficulty in the second task which confronts a court in using precedents — the task of deciding whether the rule does or does not fit the case before the court . 
Neither being bound by statute , nor being bound by cases , absolves a court from this second task ; indeed it is only when a person or a court is to some degree or other bound by a rule that the second task becomes necessary at all . 
Distinguishing cases , which consists in giving reasons why a rule in a case ought not to be followed or applied in a later case , is often conceived to be an indication that courts are not " really " bound ; in truth , earlier cases are distinguished , and have to be distinguished , just because they are binding , so that they ought to be followed unless a reason can be given for not following them ; in much the same way courts have to interpret statutes just because statutes are binding . 
The comparison between parliamentary and judicial legislation leads on to a second point . 
When we ask in what way Parliament exercised its power to formulate a rule of the legal system , it is the existence of a text which enables an answer to be given without initial difficulty , except in rare and anomalous circumstances , and the lack of such a text which lies at the root of many of the difficulties when the same question is asked in relation to the judicial power of legislation . 
There is a natural temptation to seek for some technique for determining the { ratio decidendi of a case which will repair the initial absence of a formal text : some formula such as "read a Queen 's Printer 's copy " , which works well enough for Parliament . 
There is a temptation to feel that there ought to be some formula , if only we could find it ; after all the whole doctrine of precedent depends upon the conception of the { ratio decidendi , and it seems somehow absurd to accept the doctrine of precedent if we have to admit that we are not able to say what is the { ratio decidendi of a particular case . 
The difficulty may perhaps be solved if it is realized that there are really two problems involved in the use of cases . 
The first is the problem of defining the { ratio decidendi , that is to say defining what is meant by " the ratio of a case " . 
A satisfactory definition will indicate what a lawyer is to look for in his case . 
The second is the problem of determining the { ratio decidendi . 
This is the problem of how to look , and not the problem of what to look for . 
It would indeed be odd if it was not possible to formulate a satisfactory definition of the expression " { ratio decidendi of a case " ; indeed , failure here would indicate that it was high time to abandon the conception . 
It is quite another matter to suppose that there ought to be one technique or one set of rules , or one formula , which will serve as a general solution for the problem of determining what precisely is the ratio of a particular case . 
There may indeed by as many ways of finding the ratio of a case as there are ways of finding a lost cat ; certainly the ratio of some cases seems as elusive . 
DEFINING THE { RATIO DECIDENDI OF A CASE 
In defining the { ratio decidendi of a case , then , we must seek for a definition which will serve as an answer to the question " What am I to look for ? " 
For purely legal purposes we may take it for granted that we should look in cases for a rule or rules of some kind or other . 
Furthermore the term { ratio decidendi is normally used to refer to some binding rule ( or rules ) which is to be found in decided cases — some rule which a later court ( appropriately placed in the hierarchy ) can not generally question . 
Bearing all this in mind , a possible defining technique is to elucidate the judicial power to make binding rules , and to tell our questioner to seek for a rule ( or rules ) made within the ambit of this power — such a rule ( or rules ) will constitute the ratio of the case . 
This method of definition will have an obvious advantage , for it will be closely related to the purpose for which the conception of the { ratio decidendi has been developed . 
For the conception only serves to point the distinction between the rule-making of judges which is { 6intra vires a power to make binding rules , and the rule-making of judges which is { 6ultra vires this power . 
Furthermore the method suggested closely resembles the normal defining technique adopted to isolate the product of other law-making activities — for example , Acts of Parliament . 
And finally it leads to a very orthodox and unstartling result , for it is not in the least a novel technique . 
What then are the bounds upon the power of rule-making which is vested in judges ? 
The most important limitation is to be found in the principle which denies them the power to make binding rules except when those rules are relevant to the determination of actual litigation before the court in which they are empowered to sit . 
Historically this limitation dates from the seventeenth century , when it became recognized that a court ought not to give official opinions upon hypothetical problems — a convention which has become refined and elaborated since then . 
As this convention came to be accepted an obvious corollary develops ; there must be some principle which has the effect of reducing the importance of enunciations of the law which have in fact been delivered by judges — either accidentally or deliberately — upon hypothetical issues . 
Thus the conception of { 6obiter dicta grows up ; { 6obiter dicta are in some sense { 6ultra vires enunciations of law . 
The distinction between such dicta and the elusive { ratio decidendi is in essence a distinction between relevance and irrelevance , and much of the difficulty in elucidating the conception of the { ratio decidendi arises from attempts to give a precise meaning to relevance in this context . 
Without some criterion of relevance the judicial power of rule-making seems to have no limit , and in a country wedded to the conception of the rule of law there is naturally a desire to state with precision where the limit lies . 
Limitations upon a rule-making power may be formal or substantial ; they may restrict the way in which rules are made , and they may restrict what rules are made . 
The power vested in the judges is subject to both kinds of limitation , but the concept of the { ratio decidendi seems to embody only a formal limitation . 
This is that only a rule ( or rules ) acted upon in court can rank as a binding rule . 
Once this primary condition is satisfied the rule will so rank , unless one of the various exceptions to the doctrine of precedent apply — for example the { per incuriam rule . 
The rule becomes binding , subject to exceptions . 
The fact that the rule has been acted upon is the hallmark of relevance , and this may no doubt be expressed in a variety of different ways ; thus we talk of " the rule applied " , " the reason for the decision " , " the grounds upon which the decision rested " , " the basis of the decision " , and there is no particular advantage in adopting one of these formulations rather than another , for they are but variations upon a single theme . 
All state the primary formal limitation upon the judicial power , or , to put it another way , all state the manner and form in which the judicial power is exercised . 
They thus serve as definitions of the source of law under discussion — the { rationes decidendi of cases — in much the same way as similar " manner and form " statements of the parliamentary power serve to define what a statute is . 
But , however we define the { ratio decidendi of a case , we encounter difficulties in applying our definition which are much greater than those which accompany parliamentary law-making . 
The rule-making procedure of Parliament operates on a text — a definite and settled verbal formulation of a rule or body of rules — and it is to the rules so drafted that legal validity is attached . 
With case law it is different ; we do not require the courts to draft the rules upon which they act . 
Even where a judge does take some peculiar care to formulate a rule accurately and precisely , we do not usually treat such a formulation in the same way as a section in a statute , for the prerogative of judges is not to confer binding force upon a rule by formulating it and submitting the formulated rule to some procedure , but rather to decide cases by acting upon rules , without settling for the future the verbal form of the rule on the basis of a single application of it . 
The minimum required before a judge may be said to act upon a legal rule is that 
( a ) He should have a rule in mind when he decides to act . 
This does not mean that he should have in mind a precise formulation of a rule ; a person may act upon a rule without thinking out a draft of the rule . 
( b ) He should decide that the rule is applicable — that is to say he should decide that some fact or set of facts should be subsumed under the rule , and this will involve a task of classification . 
( c ) He should deliberately so conduct himself that his conduct conforms to the conduct prescribed by the rule . 
In everyday life this acting upon a rule may be quite a casual process ; in the judicial process the convention is that the judge should "show his working " , and this produces a reflective " acting upon a rule " not so often met with outside the law and other special fields . 
And with this reflective " acting upon rules " which is characteristic of the judicial process goes the custom which the courts have adopted of justifying the action taken by an opinion delivered openly in court , which opinion provides the best possible evidence of the rule upon which the court did act . 
It will be noted that to say that a person acted upon a rule is not to assert anything about the psychological motivation of his action . 
Recognition of this has wide implications in legal theory . 
Furthermore , in general , a person may act upon a rule notwithstanding the fact that he may himself be the originator of the rule , as will sometimes be the case in judicial decisions . 
TRUSTEE INVESTMENTS ACT , 1961 
THIS Act received the Royal Assent on August 3 , 1961 , and came into force on the same day . 
Trustees can invest their trust funds only in investments authorised either by the express terms of their trust instrument or by statute . 
Before this new Act the investments authorised by statute did not include any " equities " and were a limited range prescribed , in England by the Trustee Act , 1925 , and in Scotland by the Trusts ( Scotland ) Act , 1921 , with subsequent statutory extensions . 
Generally speaking , the statutory Trustee List was restricted to stocks issued by the British Government and by the governments of Commonwealth countries and the colonies , stocks guaranteed by the British Government , stocks and mortgages issued by British local authorities , and mortgages of land in Great Britain . 
Most of the investments in the List earn interest at a fixed rate and , with certain notable exceptions , are eventually repayable at par . 
In recent years there have been serious disadvantages in the old List . 
The immediately realisable market values of investments eventually repayable at par have fluctuated widely , with the variations in the prevailing rates of interest ; and , in the case of the " undated " stocks in the List , market values have declined very seriously . 
Eventual repayment of invested capital at its nominal par value takes no account of inflation and the decline in the value of money , and represents , in real values , a capital loss . 
In the case of a trust fund established twenty or more years ago , with investments limited to the statutory List , the annual trust income may be nominally the same today as when the trust began , although of course the income will buy far less than when the trust began . 
A life tenant depending for his income and standard of living on such a trust would be much worse off today than twenty years ago ; and the real value of the trust capital may be disastrously less than when the trust began . 
This sort of case history is , unhappily , not unusual . 
The statutory Trustee List has always had two objects : first , the protection of trustees ; secondly , the protection of the beneficiaries , by ensuring both the preservation of trust capital and a steady yield of income . 
The first object has always been successfully achieved . 
Trustees who invested within the range permitted by the statutory List were reasonably safe from legal attack by disgruntled beneficiaries . 
But , for more than twenty years before the passing of the new Act , the second object had not been achieved at all . 
The statutory List ( which was always somewhat out of date ) provided no " hedge " against inflation and no protection against the continuous fall in the value of the £ . 
Experience of investment within the range provided by the statutory List offered a sad contrast with the profitable experience of other people able to invest in equities . 
For years most lawyers have advised settlors and testators to confer on their trustees much wider investment powers than those permitted by the statutory List . 
In the House of Lords debate on the Second Reading of the Trustee Investments Bill a peer who is a solicitor of great experience said : " In the course of some forty years of practice I have made it a point always to advise that settlors and testators should leave the widest possible discretion to their trustees ; that the powers contained in the Trustee Act were far too limited . " 
Naturally enough , the demand for reform of the List has grown and has commanded some powerful supporters . 
In 1952 the Report of the ( Nathan ) Committee on the Law and Practice relating to Charitable Trusts advocated reform . 
In 1955 a White Paper on Government Policy on Charitable Trusts in England and Wales referred to the Government 's intention to propose a general reform of the statutory List . 
Charities were already able to obtain from the court a general extension of investment powers ; and , particularly after a decision in 1955 drew professional attention to this , a number of the larger charities obtained wide powers of investment in the ordinary and other shares of the larger companies . 
In 1958 the Variation of Trusts Act permitted applications to the court for ( { 6inter alia ) extended powers of investment ; and applications under that Act were soon very widely used for the purpose of obtaining power to invest in equities . 
But applications to the court cost money , and the power conferred by the 1958 Act was no substitute for general reform of the statutory List . 
On May 13 , 1959 , a statement in the House of Lords promised early legislation ; and in December 1959 a White Paper was published setting out the Government 's proposals . 
These proposals , with some minor changes , were embodied in the Bill introduced into the House of Lords in November 1960 . 
The period of almost a year between the publication of the White Paper and the introduction of the Bill was intended to provide time for interested persons and bodies to consider , and make representations about , the Government 's proposals . 
This was a good idea , and the time was not wasted ; but the period might have been more useful if the White Paper had included a draft of the intended Bill . 
This Bill , when published , turned out to be quite complicated ; and it soon received anxious scrutiny from professional bodies , including the Law Society , whose simplifying amendments were debated at length when the House of Commons was considering the Bill in committee . 
The Act replaces the former statutory Trustee List . 
The new List , set out in the First Schedule to the Act , is divided into three parts . 
Parts 1 and 2 list the " narrower-range " investments . 
Part 3 lists the " wider-range " investments . 
The narrower-range comprises mainly fixed-interest investments , and includes the whole of the former statutory List with some changes and additions . 
These additions include fixed-interest securities issued in the U.K. by the International Bank for Reconstruction and Development ; the debentures ( not being convertible debentures ) of United Kingdom companies that comply with certain conditions ; and deposits in the ordinary and special investment departments of trustee savings banks . 
Commonwealth government stocks are included in the narrower-range without the governments concerned having to comply with the conditions laid down in the Colonial Stock Acts . 
The difference between Part 1 and Part 2 of the narrower-range is that trustees may invest in Part 1 without first obtaining advice , whereas they may not make an investment in Part 2 of the narrower-range without obtaining and considering proper advice as to the suitability of the investment . 
Part 1 is very simple . 
It includes Defence Bonds , National Savings Certificates and Ulster Savings Certificates ; and deposits in the Post Office Savings Bank , in the ordinary departments of a trustee savings bank and in savings banks certified under section 9 ( 3 ) of the Finance Act , 1956 . 
Deposits with designated building societies are in Part 2 of the narrower-range ; and it is puzzling that trustees should not be allowed to make such deposits without obtaining expert , written advice . 
The greatest interest , however , attaches to the new wider-range . 
This includes the shares , stock and convertible debentures of United Kingdom companies that comply with certain conditions ; the shares of designated building societies ; and units of authorised unit trusts ( i.e. , authorised by order of the Board of Trade under the Prevention of Fraud ( Investments ) Act , 1958 , or by the Ministry of Commerce under the Prevention of Fraud ( Investments ) Act ( Northern Ireland ) , 1940 ) . 
The " equities " ( i.e. , ordinary shares and stock ) and other securities of U.K. companies are included in the wider-range only if the particular company has a total issued and paid-up share capital of at least £1 million and has paid dividends on all its issued shares in each of the five years preceding the year in which the investment is made . 
As with Part 2 of the narrower-range , investments must not be made in the wider-range unless the trustees obtain and consider written expert advice about the particular investments . 
Further , trustees are not to make or retain investments in the wider-range unless their trust fund has been divided into two parts . 
This once-for-all division of the trust fund is the most important ( and controversial ) feature of the new statutory scheme for permitting wider-range investments . 
The division must be into two equal parts ; but there is power for the Treasury , by statutory instrument , to order that division shall be into unequal parts ( provided that such an order shall not authorise a division in which the narrower-range part is less than one-quarter of the fund at the time of division ) . 
The division , once made , is permanent . 
Thereafter , funds belonging to the narrower-range part must be invested in narrower-range investments , while funds belonging to the wider-range part may be invested in wider-range or narrower-range investments . 
It is not essential for the whole of the wider-range part to be invested immediately in wider-range investments . 
The discretion to invest in the wider-range is available only in respect of the wider-range part . 
If property is transferred from one part of the divided fund to the other , there must be a " compensating transfer " in the opposite direction . 
Where any property accrues to a trust fund that has been divided , and the accruing property is not otherwise obviously attributable to some particular part of the fund , the accruing property must be divided so that each part of the fund is increased in value by the same amount . 
Where capital is taken out of the trust fund ( as , for example , in the exercise of the statutory power of advancement ) , the trustees are not required to take it equally from the two parts of the divided fund : the Act does not fetter their discretion as to the choice of property to be taken out . 
The new statutory powers of investment are additional to any special powers , e.g. , those conferred expressly by the will or settlement . 
Any property ( not including statutory narrower-range investments , but including statutory wider-range investments ) which trustees are authorised to hold pursuant to such special powers , must be carried to a separate " special-range " part of the fund . 
The effect may be that a single fund will be divided into three parts : the special-range part , the wider-range part and the narrower-range part . 
Division of the fund into two parts and the subsequent maintenance of that division will require very careful administration and records ; and even greater care will be needed where the division is into three parts . 
Will ordinary private trustees be able to do the necessary administration and keep satisfactory records ? 
In the case of the larger trust funds , where the expense of obtaining constant professional assistance is not regarded as extravagant , the additional work will present no problem . 
But , with a relatively small trust fund , the trouble and expense may perhaps be too great , and the trustees may therefore decide that they can not operate the statutory scheme for investment in the wider-range . 
The fear of undue complexity in the administration of relatively small trust funds led the Law Society to advocate a scheme permitting investment in the wider-range without a once-for-all division of the fund ; but the advocacy was unsuccessful ; the complexity remains ; and time will show to what extent , in practice , trustees of small trust funds take advantage of the new power to invest in the wider-range . 
The other provisions of the Act do not call for extended comment . 
Section 6 ( 1 ) is of interest in that it attempts a statutory definition of a trustee 's duty in choosing investments . 
He must have regard — 
"( a ) to the need for diversification of investments of the trust in so far as is appropriate to the circumstances of the trust ; 
( b ) to the suitability to the trust of investments of the description of investment proposed and of the investment proposed as an investment of that description . " 
The new powers apply to persons and bodies , not being trustees , who have trustee investment powers . 
Section 9 ( 1 ) amends section 10 ( 3 ) of the Trustee Act , 1925 to remove a defect ( disclosed in Re Walker 's Settlement ) which has occasionally caused trouble where trustees hold shares in a company that is the subject of a " take-over " bid . 
Granted , however , that events at A after E1 and before E2 are in an empirically undetermined order with respect to event EB at B , must we accept Robb 's contention that Einstein was mistaken in allowing A to assign a theoretical epoch to EB ? 
In other words , if we reject the classical doctrine of time which stipulates that there must be a unique event at A which is absolutely simultaneous with EB , does it follow that Einstein ought not to have ascribed a definite conventional system of time-relations ( earlier than , simultaneous with , and later than ) between EB and all events at A ? 
The function of convention in the construction of theories is descriptive simplicity , and it must be admitted that Einstein 's Special Theory of Relativity is simpler than Robb 's alternative . 
But that is not all . 
As we have seen , Einstein 's conventional rule by which A assigns a theoretical epoch to EB is not a " mere " convention in the sense of being wholly arbitrary . 
For , although it is a convention in so far as it is freely chosen and not imposed upon us , it can be isolated uniquely from other admissible rules by means of the axioms stated above . 
With all due respect to Robb , the essential question is not the conceptual legitimacy of Einstein 's convention but its practical scope , that is , the range of physical contexts to which it can be most usefully applied . 
4 The Correlation of Time-Perspectives 
So far we have considered only a single observer A. Unlike Frank and Rothe , Whitehead and others who sought to deduce the existence of a finite universal velocity from more primitive postulates , we have not found it necessary to consider the correlation of the space and time coordinates assigned to a distant event by different observers . 
Although this presented no special difficulty for the classical Newtonian physicist who believed in an absolute world-wide simultaneity and an absolute physical space governed by the laws of Euclidean geometry , as soon as these assumptions were abandoned the problem had to be re-examined . 
It is now generally recognized that the most satisfactory method of solution is to consider first the correlation of two observers ' clocks by means of the same experiment in light-signalling as we introduced above ( pp. 186-7 ) . 
There we considered the assignment by A of times to events occurring at B. As we have seen , Einstein 's solution was based on his postulate that the velocity of light according to A is a universal constant , independent of position and direction of propagation . 
We must now consider the correlation of this theoretical time assigned by A to an event at B with the empirical epoch t7 which would actually be recorded on a clock placed at B. To make the problem precise we postulate that B is now an observer " similar " to A. In particular , this implies that B carries a clock " similar " to the one carried by A. For example , if A carries a particular type of atomic or molecular clock , we assume that B carries another clock of identical construction . 
With the aid of this clock , B can partake in A 's light-signalling experiment , the signals being instantaneously reflected back to either observer on arrival at the other , as indicated in Figure 7 . 
In the Special Theory of Relativity it is assumed that A and B are associated with inertial frames of reference . 
Consequently , they are either at relative rest or in uniform relative motion . 
The Principle of Relativity on which the theory is based was formulated by Poincare2 in a lecture at Saint Louis , U.S.A. in September 1904 . 
According to his statement , " the laws of physical phenomena must be the same for a " fixed " observer as for an observer who has a uniform motion of translation relative to him : so that we have not , and can not possibly have , any means of discerning whether we are , or are not , carried along in such a motion " . 
Shortly afterwards , and independently , the principle was enunciated in a much more explicit form by Einstein : " the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good " . 
This principle presupposes that the observers associated with such frames of reference employ similar measuring instruments , for example clocks , and adopt the same metrical rules and definitions . 
Therefore , if A assigns a universal value c to the speed of light , then B must do the same . 
It is customary when considering the correlation of the clocks and time-perspectives of A and B in Einstein 's Special Theory to concentrate on the case in which they are in uniform relative motion . 
Instead , in view of its importance for establishing one of the main results in the following chapter , I shall begin by considering the case in which they are at relative rest . 
If A and B have similarly graduated clocks , then , apart from the possible adjustment of an additive constant depending on the choice of zero-time on each clock , the principle of relativity can be reduced , as far as kinematics is concerned , to the following : 
Axiom 10 . 
Principle of kinematic symmetry : t2 is the same function of t7 as t7 is of t1 . 
Hence , there must be functional relations of the form **f . 
Consequently , the function th , which we will call the signal function correlating A and B , must be such that **f . 
But , since B is at a fixed distance from A and the light-signals travel with constant speed , it follows that ( t2-t1 ) must be a constant . 
Hence , th must be such that **f , 
for all values of t1 and some constant a . 
If we drop the suffix , an obvious solution of this functional equation is given by **f . 
More generally , by operating on each side of ( 23 ) with th we deduce that **f , 
whence it immediately follows that must be of the form **f , 
where is of period 2a . 
To reduce this to the particular form **f , we must consider other similar stationary observers . 
Thus , if A , B , and C are collinear , with B lying between A and C , and f is the signal function correlating B and C , then A and C will be related by the signal function ps given by **f . 
Consequently , th and f must be commutative functions . 
Since C is at a fixed distance from B , f must satisfy a functional equation of the form **f , 
where b is some constant . 
It is then easily proved that **f , 
and so we deduce that A and C are at a fixed distance apart equal to the sum of the respective distances of A and B and of B and C. By operating on both sides of ( 24 ) with the function th and appealing to the commutative property of th and f , we deduce that **f , 
whence it follows that **f , 
where must admit both 2a and 2b as periods . 
If A , B , and C are any three members of a continuum of relatively stationary observers , then 2a and 2b will , in general , be incommensurable . 
Consequently , by a well-known theorem the only continuous form for the function is a constant , and so from equation ( 23 ) it follows that **f . 
With this solution for , equations ( 21 ) give **f . 
By comparison with equation ( 19 ) , we deduce that t7 = t , that is , the time recorded on B's clock when any event occurs at B is the same as the time theoretically assigned to that event by A on the basis of the uniform velocity of light . 
Therefore , all relatively stationary observers assign the same time to any given event , and this time agrees with that actually recorded on the clock kept by the observer at the point where the event occurs . 
In this conventional sense , there is world-wide simultaneity of events , and therefore universal time , for all relatively stationary observers . 
The above analysis was based on the " kinematic symmetry " of relatively stationary observers with similarly graduated clocks who assign the same constant value to the speed of light-signals passing between them in free space . 
In his Special Theory of Relativity , Einstein showed how the same principle of kinematic symmetry in light-signalling experiments could be extended to observers in uniform relative motion , although the consequences are not entirely the same as for relatively stationary observers . 
In particular , there is no longer world-wide simultaneity , and hence no universal common time , for the aggregate of uniformly moving observers . 
Consequently , although the theory is based on the hypothesis that the general laws governing physical formulae are of the same form for an observer associated with any inertial frame in uniform relative motion as for an observer associated with any inertial frame at relative rest , there are important differences regarding the epochs assigned to particular events . 
To see this most simply , we again consider light-signalling from A to B and from B to A , as in Figure 7 , but this time we stipulate that the two observers concerned move away from coincidence with each other at a particular epoch with uniform velocity in a radial direction . 
We also postulate that the two similar clocks were synchronized to read time zero at the original instant of coincidence . 
As before , we consider a signal emitted by A at time t1 , recorded on A's clock . 
We suppose that this signal is instantaneously reflected on arrival at B at time t7 , according to B's clock , returning to A at time t2 , according to A. From the principle of kinematic symmetry it follows that , if **f , then **f . 
Therefore , **f . 
But **f , 
where r is the distance of B from A , according to A , at the instant of reflection , and t is the epoch theoretically assigned by A to this event . 
Since B is moving away radially from coincidence with A at time zero , it follows that **f , 
where V is the relative speed of B. Hence , **f , 
where **f . 
Consequently , on comparing ( 25 ) and ( 26 ) we see that the function ps must be such that for all values of the variable t **f . 
By operating on each side of this equation with ps , we deduce that **f , 
whence **f , 
the prime symbol denoting the derivative . 
The only solution of equation ( 28 ) which is continuous as **f ( positively ) is , where k is a constant . 
Since t7=0 when t1=0 , it follows that . 
Comparison with ( 27 ) yields k2= { 15a2 . 
In order to obtain the unique solution k=a , and hence **f , 
where a is positive , we must invoke a further axiom : 
Axiom 11 . 
The order of reception of light-signals by B , according to B , corresponds to the order of emission of these signals by A , according to A. 
We have seen that , according to A , there is at any point at a given ( theoretically assigned ) epoch a unique value for the speed of light in free space . 
It follows that the order , according to A , of arrival of light-signals at B must be the same as the order of their emission from A. For , if a signal emitted by A at some epoch were to arrive at B , according to A , before an earlier signal emitted from A , then , assuming continuity , there would be some event occurring in between A and B at which the second signal would overtake the first and pass it . 
At such an event there would be , according to A , two values for the speed of light in free space . 
Axiom 11 can therefore be regarded as asserting that the theoretically assigned time-order of events at B , according to A , agrees with the time-order of these events as actually experienced by B. In this sense , we can speak of the time-order of these events according to A being in the same sense as the time-order of the same events according to B. By the principle of relativity , A and B are interchangeable in Axiom 11 . 
Since t2= { 15at7 , t7= { 15at1 , and **f , where t is the time theoretically assigned by A to the arrival ( and reflection ) of the signal at B , it follows that **f . 
Hence , we deduce that , although A and B agree on the time-order of events at B , they will assign different measures to the time-interval between any two instants at B. Then only at the stage of the build-up on a screen does the object enter into the mind of a perceiver as perception . 
If we accept the analogy of the television apparatus then here is mediation of the most absolute sort . 
Is it possible to reconcile this mediation with the sense of utter transparency which accompanies the act of "seeing , " upon which Professors A. J. Ayer and Gilbert Ryle , and Mr. R. J. Hirst and Mr. M. Lean have placed such necessary emphasis ? 
Or in more general terms can we reconcile the body as instrumentality with the world as immediacy ? 
The problems which have so far proved so insoluble for perception are even more central to the discussion of the ro5le of feeling in man 's experience of himself and the world . 
For here again in a theory of prehension there would seem to be yet another scientific schema interposed between man and the world he directly experiences through perception , and , it could be argued , with less justification or profit . 
The questions come thick and fast . 
If there is a universal but unconscious " feeling " in what sense is it " knowledge ? " 
If it is not " knowledge " to the organism , what is its ro5le ? 
Does unconscious feeling rise in some symbolic form into consciousness or as an emotional pressure like instinct ? 
How is an unconscious feeling to be reconciled with a conscious sensory experience of the sort we describe as a " feeling ? " 
As for example , " I feel good " or " I have a stomach-ache ? " 
Though I can only do so as a layman , it is going to be necessary to look at some of the scientific findings . 
But we can easily be dazzled by science into imagining that we know more about our bodies than we do know in direct experience . 
The body-schema science has built up for us is apt to obscure the enigmatic experiential relation a man has to his own body . 
Common sense suggests that we should look at the body as given in private experience before we decide what it is like in terms of public science . 
3 : THE SELF 'S KNOWLEDGE OF THE BODY 
On the threshold of every man 's awareness is his intimate sense of being , or being identified with , a body . 
He is this body . 
He exists this body , as M. Jean-Paul Sartre would say . 
He can not conceive existence without it . 
If he stops to reflect on it , he is conscious on the threshold of perception of its enjoyable warmth and beyond its warmth , obscurely felt , its energy , its nature of seeming to be coiled like a spring ready to do his bidding . 
It is difficult to analyse this situation except in Cartesian terms , much as one would like to avoid them , for man both is his body and conceives his body as his instrument in the world . 
In a discussion of animal behaviour Professor Michael Polanyi remarks that " There is a purposive tension from which no fully awake animal is free . 
It consists in a readiness to perceive and to act , or more generally speaking , to make sense of its situation , both intellectually and practically . " 
Man 's existential encounter with himself could be described in these terms . 
He knows himself as a " purposive tension " seeking " control of itself and of its surroundings . " 
Dr. Erich Kahler speaks of man 's bodily consciousness in a more general but still illuminating way : 
" When I try to delve into my innermost feelings , my initial feeling of self , I find that at the bottom there is not just a feeling of sheer existence , or of sheer thinking , the Cartesian cogito . 
There is , immediately and simultaneously , something more . 
There is implicit in my feeling of existence a feeling of organic existence , or organicity , of wholeness . 
Distorted , stunted as it may be by the wear and tear of modern life the original form is still traceable as it was present in the bud of youth : a ball of radiating strength and capacity ; all-sidedness , all-potentiality ; coherence , correspondence , co-operation of all my organs and faculties . 
A young healthy human being feels the unity of body and mind " ( or rather , one might say , since this is already metaphysical , he can not conceive their disunity ) " the one present in the other , and the mind governing the body in a still nai " ve , unconscious , spontaneous manner ; neither intellect nor brute force is autonomously prevalent . 
Such elemental feeling of organic existence shines forth in the beautiful , masterly , fully animated bodies of "primitive " people ... in whom the whole body is face and has the playful , controlled expression of a face . " 
Man 's consciousness of his almost hidden organic energy is more difficult to reach than the sense of warm bodily being , for when we reflect on the body it becomes passive and relaxes , but for the most important part of our waking lives we are " keyed up " to activity , without taking thought about it . 
When we are stretched in attention , ready to act , as a runner waiting for the starter 's pistol , we are in the worst possible position for reflection . 
But the state of action , or of being coiled for action , probably fills more of our waking lives than the relaxed and reflective situation , even with such notably recumbent figures as philosophers . 
In the active state , the separation of the will from the bodily activity is so impossible to conceive that we are barely conscious of using the will to perform actions . 
The whole body becomes pervaded with will , is will . 
This identity of body , self and will has important consequences for the theory I am developing . 
What other modes of the body-self 's generalized awareness are there ? 
I think we must add the sense of a locus of our perceptions and ideas . 
We have a spatial presence , and we have an inner space which this presence guards . 
We have the sensation of thought going on inside us , as it were in the head , though grief and heartache are genuinely elsewhere . 
The sense of location is not a sharp one . 
" In " us , we say , and less vaguely , " in our heads , " but never as " in " an organ open to any perceptual inspection like a hand or a finger-nail . 
Erich Kahler speaks of man not as a spot of sheer being thrown into existence in the existentialist sense , nor as a function of thinking , but as "an inner space , a latent arena , an area of self . " 
For him this self-identity also involves " the silent presence of a person 's whole background and surroundings ... the total potentiality of his experiences ever ready to be called into function , in short the immeasurable avenues of his memory and of his interiorized world . " 
The perceiving , thinking , worrying , planning processes of the self are " us " as much as the body is " us . " 
And though they can not be apprehended like the body , they belong to it . 
As David Hume pointed out , we can not turn round and catch our minds or selves : the mere act of trying to seize upon personal identity as if it were another " thing " we could handle , defeats us , for it is in the nature of personal identity always to be doing and seizing and never to be seized . 
Here lies the guarantee of its inalienability . 
Though it was not part of David Hume 's argument the fact that there is an inviolable element in man and other organisms may be important for more than knowledge . 
Whitehead emphasized that we see with the eye . 
No purpose would have been served by creating the eye to see the eye . 
The organs of sense function in the world , and in relation to the self , in a transparent way . 
As far as the eye is concerned I mean this literally . 
If one turns one 's attention from what one sees to that by which one sees , one is conscious of a pool or area of pure transparency in the region of the eye-sockets , an emptiness into which the world pours without hindrance . 
The eye itself is withdrawn from the dimensions of sight into pure nothingness . 
Of the senses , only touch brings presence to the body . 
This bodily absence , or to put it in the teasing way the existentialists might adopt , presence-in-absence , points to the need for a new metaphysic of the body . 
That which is most near to us and necessary to us in existence is almost without a philosophy except where its perceptual machinery is concerned . 
The first bodily circumstance to be understood is how little knowledge of the body is given to us in nature . 
To understand this we have to escape from the all too common assumption that the body-schema we learn from text-books is given to us as part of natural equipment . 
Even a mirror is not given to man in nature , except perhaps in a sheet of water , and we can conceive of a prehistoric man going through the whole of his life without ever seeing his body brightly mirrored before him . 
And how little even the mirror would tell him ! 
What we see , or see in a mirror , or infer from the bodies of others , is the external sack , or skin , containing the external organs and covering the muscles which shape the torso and the limbs , but masking the internal organs completely , and helping to hold them in position against a rigid skeleton , that grotesque caricature of a living man which comes to light for the primitive only when a man is some time dead . 
Detailed knowledge , especially about the interior , we secure only from surgical and physiological research , just in the same way as our knowledge of the functioning of our senses is the product of research . 
In a pleasing and thoughtful essay on the aesthetics of the body , Mr. John Brophy speaks of the skin as mental frontier seldom crossed except by those whose studies compel it . 
Even they in their initial training have to overcome a profound repugnance when called upon to cross that human boundary . 
" It seems to be the natural order that the skin should conceal all the internal workings of the body , and , when this convention is overthrown , whoever views the exposure feels a violent protest in both mind and body . 
This protest is doubtless closely associated with the realization of pain , which no merely intellectual observation of anaesthetic affects can compensate . 
It is also heightened by sense impressions from the opened-up body which differ noticeably from those given out by a body enclosed in an intact skin : the internal organs are often exceedingly brilliant in colour , and some of them emit odours and heat . 
Moreover , even if the revelation is made by skilful surgery , the tissues are likely to be continuously bathed in blood . 
When wounds or injuries are inflicted the exposure will also be untidy , and the suffering of the torn body , unmitigated by anaesthetics , will be expressed in writhings , shouts or moans , unless shock brings about unconsciousness or death . 
By all this the observer 's senses are outraged . " 
Mr. John Brophy 's comments are much to the point , yet not all the story . 
The intense psychological shock which is the immediate consequence of another 's injured body has really to be explained on more than aesthetic grounds . 
There are aesthetic grounds for shock , but no one is shocked by animal carcases dripping blood in the butcher 's shop or by the mighty blows of his cleaver through the quivering flesh of the joints exposed for sale . 
Indeed the young wife who might faint at the sight of blood from a cut finger will become expert in handling and judging ( to say nothing of cooking ) the flesh of dead animals . 
Clearly the aesthetic protest is not the whole one if such experiences can be even pleasurably borne . 
We have to relate shock over bodily injury to what has been said of the transparency of the sense organs . 
Consciousness of them would block consciousness through them . 
Intense consciousness of the body interferes with the instrumentality of the body in the world . 
Only when the young tennis player forgets his racket and forgets to be proud of it can he really hit with it . 
This principle , which , it should be noted , requires no " objective " demonstration , marks Schiller 's advance to an independent position in aesthetic theory . 
As he argues , whereas important elements of the experience of beauty had been severally declared and championed in recent time , the specific quality of beauty had been fragmented and lost in the process . 
In its most obvious aspect Schiller 's problem is again one of mediation , now on the grand scale , between the advocates of sensualist and intellectualist aesthetics , between the type of Burke and the type of Baumgarten . 
Schiller applauds in the former the rejection of conceptual form from the fabric of beauty , and in the latter the reference of beauty , in some sense , to the organization of the higher faculties . 
Schiller has somehow to vindicate in exact theory his conviction that the beautiful is objective , self-contained , { " selig in ihm selbst " — and that it is also , paradoxically , a reflex of freedom in the percipient . 
Of these two essential attributes , it is the sense of independence , of self-containedness , of "objectivity " in the beautiful which is of greater moment in Schiller 's feeling , about which he is evidently more excited . 
It is the aspect in which Schiller brings to bear an aesthetic sensitivity in contrast with Kant 's ingenious aesthetics , and in which , therefore , his more positive individual contribution lies . 
It is the empirical part of the argument which Schiller is impatient to reach from the very beginning of this correspondence . 
Yet , before he will allow himself to communicate the essence of his own experience of beauty he insists on examining the conditions which make that experience theoretically possible . 
And , in this area , he vies with Kant in stressing the subjective limits of experience . 
In the letter of the 18th of February Schiller endorses the major principle of the theoretical philosophy : { " Die Natur steht unter dem Verstandesgesetz . " 
In the later part of the correspondence his main argument rests on assumptions which conflict with this principle . 
To the degree , however , that Schiller emancipates nature from reason , to the degree that he " breaks through the Kantian dogma " , as Baumecker asserts with approval , he does so without adequate systematic justification . 
The special kind of " objectivity " upon which Schiller hopes to rest his theory is quite capricious by the standards of exact thought from which the argument sets out . 
The position is that , whereas this claim of " objectivity " is of extreme interest as evidence of Schiller 's aesthetic consciousness and of his efforts to bring it to terms with his theoretical reflections , he does not in fact substantiate the claim in its more far-reaching implications . 
Besides , it is not in this area that the main advance is made . 
So that , although this whole series of letters is formally directed towards the establishment of an "objective " principle of beauty , it is not any direct and brilliant challenge to Kant on this issue which we have to applaud . 
The valuable and the major part of the theory is subjective in essentials . 
It has to do firstly , and more particularly , with the conditions in the mind of the percipient which permit the transference of the idea of freedom to the object " in appearance " , and secondly , and more generally , with the whole concept of aesthetic form as an abstract based upon forms of other orders , preparing a far more sensitive redisposition of the theoretical , moral and aesthetic faculties . 
These trends , and not the special claim of " objectivity " , belong to the general evolution of Schiller 's aesthetic philosophy , regarded as a body of doctrine having final coherence and universal validity . 
If , on the other hand , the " Kallias " Letters are examined as evidence of the interplay of rational and irrational motives , and of contrasting forms of vision and language , in Schiller , then a quite different valuation of the " objective " principle becomes appropriate . 
For this principle , to which Schiller subordinates the whole argument in a formal way , may then be seen as the extreme of the tendency to rationalize elements which belong properly to the aesthetic mode of vision . 
It covers and attempts to legitimate the extrusion of the idea of the anima , of the " Person " , { " die Natur — das Wesen des Dinges " , from its proper location in unreflective poetic conviction into the alien province of systematic aesthetic philosophy . 
It appears as an irrational impulse to authorize and to dignify the products of artistic intuition . 
Further , it is precisely this , presumably unconscious , attempt at maximum assimilation to each other of the disparate functions of aesthetic imagination and aesthetic philosophy that perplexes criticism of the " Kallias " Letters . 
The nai " ve perception of beautiful forms as animated by a personal will , whose expression they are , is explained by Schiller with subtlety and detachment in the earlier letters . 
Yet in the later , " empirical " part of the argument the perspective changes , analogies become facts , aesthetic configurations become " things " , having their private essences . 
And this wholly contrasting , aesthetically valid and systematically untenable vision is adapted and assimilated to the abstract terminology of the strictly logical framework . 
Conceptual myths are generated in the vacuum between philosophical and poetic language . 
There is a grade of " objectivity " in Kantian usage which may be more closely defined as ( the assumption of ) a universal subjective necessity in regard to any mental disposition or content . 
Kant develops this sense of the term , for example , in the final section of the { " Analytik des Scho " nen " : { " Die Notwendigkeit der allgemeinen Beistimmung , die in einem Geschmacksurteile gedacht wird , ist eine subjektive Notwendigkeit , die unter der Voraussetzung eines Gemeinsinnes als objektiv vorgestellt wird . " 
But Schiller is from the outset dissatisfied with this attenuated " objectivity " , which is the maximum that Kant will allow to aesthetic experience . 
Schiller 's ambition is to show that a concept of beauty is deducible from { 6a priori principles directly , yet he must admit at an early stage that he is compelled to turn partly to " the testimony of experience " : In this initial usage " objective " has more the sense of " theoretically cogent " ; it points beyond Kant 's pronouncement : { " Die Allgemeinheit des Wohlgefallens wird in einem Geschmacksurteile nur als subjektive vorgestellt " , and challenges Kant in the assertion : { " Unter einem Prinzip des Geschmacks wu " rde man einen Grundsatz verstehen , unter dessen Bedingung man den Begriff eines Gegenstandes subsumieren , und alsdann durch einen Schluss herausbringen ko " nnte , dass er scho " n sei . 
Das ist aber schlechterdings unmo " glich . " 
Schiller does not meet directly Kant 's main argument for this view , which is , in essence , that the aesthetic judgement rests on a subjective pleasure , which can not itself be the product of a deduction . 
Indeed , there is already evidence that it is not in this teasing issue of the " objective " principle , in the sense developed above , that Schiller 's vital concern lies , but rather in the vindication of beauty as a function of the human totality . 
Schiller is dissatisfied with Kant 's manner of excluding rational form entirely from the province of beauty . 
He concedes the necessity of a sharp distinction between perfection , logically apprehended , and the beautiful , but considers that Kant 's solution is misguided and impoverishes the idea of beauty : It is here that Schiller 's more valid challenge lies , from the beginning of his { " Auseinandersetzung mit Kant " . 
Here , that is , in aesthetic theory proper . 
In ethical theory Schiller 's defence of natural feeling against Kantian rigorism is a closely related impulse . 
Significantly , as Schiller now approaches the vital core of his idea , his mode of expression changes . 
He speaks , for the first time , of that critical insight into the structural relations of the theoretical and aesthetic faculties which is to affect his doctrine so profoundly . 
Although distinct from it in kind , beauty is dependent on a technical structure for its realization : { " Denn eben darin zeigt sich die Scho " nheit in ihrem ho " chsten Glanze , wenn sie die logische Natur ihres Objektes u " berwindet ; und wie kann sie u " berwinden , wo kein Widerstand ist ? " 
At a critical point Schiller passes into metaphor and personification , although at this stage he provides also an equivalent statement in abstract terms : { " — Die Vollkommenheit ist die Form eines Stoffes , die Scho " nheit , hingegen , ist die Form dieser Vollkommenheit : die sich also gegen die Scho " nheit wie der Stoff zu der Form verha " lt . " 
The appearance of the personal analogy may thus be thought of as a sort of rhetorical stress , but there is already some resemblance to the later invasion of the abstract area by notions of irrational origin . 
The idea of the " conquest " of a " resistance " , for example , is not quite commensurate with the abstract statement . 
There is a certain irony in the next letter to Ko " rner ( 8th Feb. ) , for Schiller reproaches him for tendencies which he is himself to exhibit , although more subtly : Or the passage may be read as a self-admonition , in the light of the remark which follows : { " U " brigens rede ich hier mehr als Kantianer , denn es ist am Ende mo " glich , dass auch meine Theorie von diesem Vorwurfe nicht ganz frei bleibt . " 
For Schiller must sense that there is a rather precarious distinction between Ko " rner 's resort to the concept of unity in the manifold and his own indirect but undeniable import of concepts of reason , which similarly threatens collision with the accepted Kantian pronouncement : { " Das Scho " ne gefa " llt ohne Begriff . " 
By insisting on his " objective " principle and at the same time allowing himself only such departure from the Kantian philosophy as he may hold compatible with the main dicta of that philosophy , Schiller prescribes for himself a very difficult task , which could only be accomplished , if at all , by the intricate verbal adjustments which in fact he makes in the course of the exposition . 
For , firstly , as emerges between the lines of his letter of the 8th of February , if the attempt is made to " establish objectively a concept of beauty and to legitimate it completely { 6a priori from the nature of reason " , then elaborate precautions will be needed so as not to offend against that precept that " the beautiful pleases without concept " . 
Indeed , for this initial dilemma the only direct resolution would seem to require psychological schemes not then available . 
If , for example , the second limiting proposition were modified to read : " the beautiful pleases without the conscious intrusion of concept " , then Schiller 's whole argument would be facilitated in the direction which it takes in any case . 
The besetting difficulty of the Kantian type of thinking , which Schiller inherits , is the extensive use of analytical schemata which transform mental faculties into virtual entities , which tend to appear as segregated elements standing in an external relationship to each other , and constrained , in the extreme case , into a misleading geometrical symmetry . 
This tendency is reinforced by the personifying drive in Schiller himself , and runs counter to that important systematic idea which is emerging , that conceptual activity is somehow implicit or submerged in aesthetic experience , without however belonging to the fabric of that experience as it appears in consciousness . 
Since Schiller feels strongly that ( practical ) reason and beauty have some profound kinship , he is impelled to assert this by the most authoritative means known to him , that is , by the deduction { 6a priori , by a demonstration that , in given circumstances , the experience of beauty is a logically predictable consequence of our psychic constitution . 
But he realizes by both systematic thought and immediate experience that concepts are no part of the experience of beauty : And so , apparently , a hiatus is opened , such that it must seem there is no way of penetrating to the sense of beauty by the alien apparatus of concepts . 
In what follows Schiller feels his way towards an aesthetic psychology , whose advantage over Kant 's doctrine is that it gives a fuller account of the latitude of the aesthetic vision , which may abstract from the forms of the practical and theoretical faculties , and so derive its own proper symbolical forms . 
Kant 's aesthetic judgement is but one limitation of the general idea of judgement , which in turn is assigned to an intermediate and subordinate position between the faculties of reason . 
In Schiller the aesthetic judgement becomes primary in both an emotional and formal sense . 
It is expanded to include the " forms " of the rational world , on its own terms . 
It becomes the focus of totality , concord and freedom . 
As in the attempt to construe the difference between mere bodily movements and actions in terms of acts of volition , so here in the case of wanting when this is identified with some Humean cause of doing , we are faced with a manifest contradiction . 
Construed as an internal impression which is thought to function as a cause that issues in some item of so-called overt behaviour ( whether this be some bodily movement or an action is of no matter for our present purposes ) , the impression must be describable without reference to any event or object distinct from it . 
It must be possible to characterize that internal impression without invoking any reference to the so-called object of the desire , no less than the action that consists either in getting or in trying to get that object . 
But as a desire , no account is intelligible that does not refer us to the thing desired . 
The supposition , then , that desiring or wanting is a Humean cause , some sort of internal tension or uneasiness , involves the following contradiction : As Humean cause or internal impression , it must be describable without reference to anything else — object desired , the action of getting or the action of trying to get the thing desired ; but as desire this is impossible . 
Any description of the desire involves a logically necessary connection with the thing desired . 
No internal impression could possibly have this logical property . 
Hence , a desire can not possibly be an internal impression . 
This contradiction comes close to the surface in a number of familiar accounts of wanting . 
Wanting is usually identified with some internal mental event — a felt tension or uneasiness . 
But as internal event , whether mental or physiological , there is no intrinsic feature of that event that reveals its connection with anything else ; yet as desire the very characterization of the desire involves a reference to the thing desired . 
Hence Hobbes ' interesting remark about the intimate relation between names applied to desires and the objects of desire . 
Shall we then say with G. F. Stout that " desire and aversion , endeavour to and endeavour from , are modes of attention " ? 
Certainly if there is endeavour to x , there must be attention to x . 
But if we think of a desire as an internal event that causes or produces an endeavour to the thing in question , then it is self-contradictory to say that the desire is both cause and the attention involved in the endeavour which this cause produces , just as much so as it is for Prichard to say in the case of so-called acts of volition that such acts are causes and also involve the idea of that which they produce . 
Alternatively , if the desire just is the endeavour , it is difficult to see how there could be desire without endeavour , i.e. without trying to get the thing desired . 
But putting this aside , we shall have to say that this endeavour , mental or physiological , involves the idea of that towards which the endeavour is directed — endeavour being necessarily endeavour to something , just as a desire is necessarily a desire for something . 
And this implies that the endeavour can not possibly be a causal factor in the proceedings that issue in the getting of what is desired , since if it were , it would be possible to describe it without referring in any way to anything else in or out of the proceedings , including the thing in question towards which the endeavour is directed . 
Hobbes and his present-day followers who speak of the endeavours of the body or of physiological drives are similarly involved in contradiction . 
Physiological occurrences are blind ; as such they can be described without reference to anything else including the thing wanted , or the objective of the endeavour . 
As drives , endeavours or desires , no such logical divorce is possible . 
The whole modern picture from Hobbes on down , of wanting or desiring as interior events that operate in some sort of causal mechanism of the mind or body , is in fact a disastrous muddle . 
So far I have been concerned with this logical feature of a desire , namely , that a desire , whatever else it may be , is a desire for something . 
But there are other important features of the concept of desiring or wanting which this modern picture simply can not accommodate and which therefore spell disaster for this view of the matter . 
It will be remembered that I began this discussion by considering the truism that because one wants or desires one does ; in other words , that we explain conduct by reference to , among other things , what agents want or desire . 
But if desiring is some sort of interior event that functions as a causal condition , no such explanation is possible . 
Desiring , on this modern view , is some sort of causal factor , an itch , twitch , internal impression , tension or physiological occurrence ; but as such , supposing that these are causal factors , it can give rise only to other occurrences . 
An action , however , is no mere matter of bodily happening . 
Grant then that wanting or desiring explains the bodily movements that take place when a person does anything , e.g. raises his arm in order to signal ; as internal occurrence what it explains , at best , is the bodily movement that occurs when the person raises his arm , not the action he performs which we describe as " raising his arm " or , further , as " signalling " . 
A gap then appears in the alleged explanation , between bodily occurrence and action performed , and what is purported to be an explanation of conduct turns out to be nothing of the kind . 
But like many another gap that appears in philosophy ( here readers will be reminded of the familiar gap with which moral philosophers are plagued between the " is " and the "ought " , between matters of fact and matters of morality , between description and evaluation ) , this one is a product of our own confusion . 
Specifically , it is the failure to recognize the logical relation between the concept of wanting or desiring and that of action , including the logical scaffolding that gives the latter term its import or use in our language . 
Earlier I contended that by no logical alchemy is it possible to make good the claim that an action is a bodily movement plus some other concurrent factor . 
Suppose , for argument 's sake , we take as concurrent factor , wanting or desiring . 
Then the latter can be understood independently of the concept of the action . 
If we explain A in terms of B and C , our explanation , if it is to avoid circularity , presupposes that C can be understood without invoking A. So if the action of raising the arm can be understood as the bodily movement incurred in raising the arm together with a desire , one can understand the desire without invoking the idea of this action . 
This implies that the desire can not possibly be the desire to raise one 's arm , since it would be circular to define the action of raising one 's arm as a bodily movement together with the desire to raise one 's arm . 
But is it possible , in general , to define action as bodily movement or happening plus desire ? 
Only if we can understand what a desire is without invoking the concept of an action . 
Is this possible ? 
Only if in our account of the action of raising one 's arm , we do not invoke any desire to do , e.g. the desire to notify others that one is about to make a turn . 
Or , if we do this , only if we go on to explain a desire to do in terms of a desire together with some feature of the desire which does not involve a reference to doing at all — in which case the desire to do would then be " reduced " to some sort of occurrence called " a desire " having a feature that could be described without reference to any doing at all . 
Now what sort of thing called a " desire " could this possibly be ? 
Here is one suggestion : the desire is a desire for something , e.g. the food that one will get if such-and-such things take place . 
Let us then see if it is possible to " explain " the desire to do in terms of a desire for something . 
In our example , this then is the situation : One is hungry ; food is around the corner , so one notifies others that one is about to make a turn in order to get food ; one desires to notify others that one is about to make a turn and one desires to do what is needed in order to get the food ; but to say that one desires to do these things can be explained or elucidated simply and solely in terms of the presence of a certain occurrence called the desire for food . 
On this suggestion , the notion of desiring to do is elucidated in terms of the logically prior notion of a desire for something . 
Here I shall not dwell further upon the now obvious and fatal objection to the identification of the desire for something with some internal occurrence , an objection that is decisive in refuting the contention that an action consists of the dual occurrence of bodily movement and internal event . 
What I want to examine now is the contention that desires for something are somehow logically more primitive or basic than desires to do , and hence that it is possible to understand the notion of a desire without invoking the concept of an action . 
There are two questions here : first , is it possible to want or to have a desire for something without wanting to do , and secondly , is it possible that one may have what one wants but not want to do anything with it ? 
Consider the first question . 
If I want food but do nothing to get it , that surely is intelligible . 
I may be unable to get it when , for example , I am tied and gagged . 
Or , I may do nothing to get it because I am fasting — doctor 's orders , you know . 
Or , I may want this food before me but since it disagrees with me I do nothing to get it . 
But can I want this food , but not want to do anything to get it ? 
This much is possible : the food is on display in a shop , I have no money , and the only way I can get it is by stealing . 
Now I do not want to steal — least of all do I want to get it by stealing — let it be that I want to refrain from doing anything that is stealing . 
Does it follow that I do not want to get the food ? 
Certainly not , since if this did follow it would be logically impossible for anyone to be tempted . 
The man who is tempted wants to get something despite the fact that by getting it he will be doing the wrong thing ; his trouble is that he finds some difficulty in refraining from getting what he wants to get , not that he does not want to get what he wants . 
If he did not want to get what he wants , it would be impossible for him to be tempted . 
Nor is it necessary to hold that if a man wants to get food , where getting it would be stealing , that he must be tempted to steal . 
" Temptation " is a strong term . 
The man who is tempted feels the urge to do something to which he has an aversion and must resist it ; but a man may want to get something but remain steadfastly in control of his desire and feel no temptation . 
Now one way of establishing complete self-control is by losing the desire for the thing in question — this in fact is how the man who wants to lose the urge for smoking succeeds . 
But one may , as in the case of our example of the man who wants food , continue to want it and yet remain free from temptation . 
If , indeed , we are inclined to deny that if a man wants the food , he must want to get it , this is because of the failure to recognize that , in the particular circumstances , the person would be doing not one thing — getting the food — but at least two things : not only would he be getting the food , but in doing this he would also be stealing . 
The solution to the dilemma lay in the successful application of coke to the smelting of iron ore ( coal had long been used in the further working of the pig ) . 
In Belgium this was first done in 1823 at Seraing . 
Almost simultaneously another British invention of great importance made its first appearance . 
This occurred in 1821 when Michael Orban built the first Belgian puddling furnace at Grivegne2e . 
Puddled iron and steel were vital to the new engineering industries . 
The new techniques spread rapidly . 
By the middle thirties there were more than twenty coke-fired blast furnaces in operation . 
Their success was made easier by the fact that the Belgian coalfields , especially those of Hainaut , were already producing much more than other Continental fields , and had a long history of economic importance behind them . 
The outcrop areas had been in use for many centuries . 
In the coal industry , like the iron , technological change was rapid in the early years of the century . 
Perhaps the most important single advance was the harnessing of the steam-engine to raise coal from the pit bottom to the surface . 
This took place first at Bois-du-Luc in Hainaut in 1807 : four years later Michel Orban brought the system to Lie3ge province when he installed the new winding gear at his Plomterie colliery ( in both areas steam drainage of water from the mines , initially with Newcomen engines , had long been a commonplace ) . 
The ventilation of pits was improved . 
Their safety was enhanced by developments such as the introduction of the Davy safety-lamp ( again a result of Orban 's initiative at Plomterie ) in 1817 . 
Joseph Chaudron with his { cuvelage en fer found a better way of strengthening mining shafts with a revetment of iron . 
The production of coal grew rapidly . 
By the decade 1831-40 it was averaging 2,917,000 tons { 6per annum ; in the following decade the annual output was 4,815,000 tons . 
A small group of able and determined men was rapidly transforming the economy of the country — the Orbans , the Bauwens , the Hudsons , the Lelie3vres ; but above all the Cockerill dynasty , whose history , as an epitome of Belgian industrial growth during the first half of the century is worth sketching . 
Continental industrial advance in the early decades of the nineteenth century was largely a matter of absorbing the lessons afforded by the British example . 
Frequently it was an Englishman who taught the lesson . 
It is ironical that the Englishman whose family was to do more than any other to give Belgium the lead for many decades should have been found out of work in the country which was ultimately to advance further and faster along the road to industrial achievement than any other Continental state . 
William Cockerill , the founder of the line , was discovered by a member of the Verviers firm of Simonis et Biolley in Hamburg in 1798 . 
Within two years he was producing textile machinery . 
In 1802 his two sons , James and John , built their own textile machinery factory in Lie3ge . 
It was immensely successful , and a decade later in 1812 was producing spinning and carding machines at a rate of several hundreds a year . 
The Cockerill interests expanded rapidly . 
An important stage was reached in 1817 when their Seraing iron-works was built : an old episcopal palace was converted into a machine shop for the construction of steam-engines . 
In 1823 James retired from the firm , making over his share to his remarkable brother . 
This was a significant year for John in another direction also since it was then that he disproved the belief , general at the time , that Belgian coal would not coke satisfactorily . 
He supervised the installation of the first coke-fed blast furnace in Belgium at Seraing . 
This plant was capable of a daily output as high as ten tons , or more than most charcoal furnaces could manage in a week . 
By 1829 the Lie3ge district was producing over 7,000 tons of pig-iron a year , chiefly at Seraing . 
In 1835 the first continental-built railway locomotive was constructed there . 
Two years later Cockerill 's enthusiasm for technical excellence led him to introduce the hot-blast system into his Seraing plant , at a time when Neilson 's invention was less than a decade old , and still little used in Britain outside Scotland . 
In 1840 shortly before the death of John Cockerill , his Seraing works alone employed 2,000 men and were reckoned the largest in Europe ( eight years later Krupp , the colossus of the future , employed only 70 men ) . 
This man , described by Schnabel as the first " truly princely businessman since the days of the Fugger " , travelled constantly to foster his interests , which extended over most of western Europe north of the Alps . 
His range of interest , knowledge and energy were invaluable to the Belgian metal , engineering and textile industries . 
The new developments of coalfield industry had revolutionized the scale of production of certain industries and lowered unit costs of production ; but it is easily possible to exaggerate the degree to which the country outside the coalfields had come under the sway of the new coal age . 
Older methods of production were not entirely replaced even in those industries which were most changed by the new conditions . 
This was true , for example , even of the iron industry . 
In 1838 sixty-six out of the eighty-nine blast furnaces in the country were still charcoal fed . 
It was not until the middle fifties that the Semois iron industry in the Belgian Ardennes , which was entirely dependent on charcoal , fell into decline , although its annual capacity , which never much exceeded 10,000 tons , had for many years been far outdistanced by Seraing . 
The implications of the new age were to be seen in Belgium not only in the positive achievements of the age — the great growth in coalfield industry and the exciting possibilities of the new and developing railways ; but equally strikingly in a negative sense . 
In the 1840s the largest of the traditional industries of Belgium , the linen industry of Flanders , was in crisis , a fatal one as it proved , because the Flemish spinsters could not compete with the machine-made thread of the English mills . 
Since there were estimated to be 280,000 spinsters in the linen industry in 1840 ( often , of course , only partly dependent on their spinning for a livelihood ) the negative side was as keenly felt and widely recognized as the positive side represented by the work of the Cockerills and their rivals . 
There was a whip to goad as well as a carrot to entice . 
The new pattern of industrial life which was spreading to the Continent from England affected Belgium a little earlier than other countries . 
Within the Austrasian field it was two Belgian areas , Hainaut and Lie3ge , which were first to use the two key advances of the new age extensively . 
The coke-fired blast furnace and the steam-engine were commonplaces there when they were still rare in Nord and almost unknown in the Ruhr . 
It was natural , therefore , that Belgian men and Belgian money should have taken the lead within the field even in French and German areas . 
Capital , technical expertise and entrepreneurs proved quite footloose within the field in its formative years , seeking employment always where the expectation of profit was greatest . 
Since it is important to the theme of the other chapters of this first part of the book to show that in such matters national boundaries were seldom of great consequence in the early years , it is worthwhile considering the extent of Belgian participation in the development of areas of the Austrasian field outside Belgium before considering Nord , Aachen and the Ruhr separately . 
The Belgian Influence in the Nord 
Between Nord and Hainaut there had long been close ties . 
The Mons portion of the Hainaut coalfield had been occupied by France during the War of the Spanish Succession from 1701 to 1709 , and during this short time French capital gained a foothold in the coal industry of the area which proved long lasting . 
The industry of Nord became heavily dependent upon coal drawn from this source during the eighteenth century , and remained so to a lesser and declining extent into the nineteenth . 
It was recognition of the danger of this dependence combined with the high duties on Belgian coal which prompted a persistent search for a French source of coal in Nord itself ( when this search culminated in a great success at Anzin in 1734 , the vicomte de Desandrouin , whose tenacity under disappointment led to the discovery , imported 200 Belgian miners and their families from Charleroi to help to bring the new pits into production ) . 
In spite of the development of local production , Nord 's dependence on Belgian coal remained considerable , and was a source of weakness and distress in troubled times . 
Towards the end of the century in the Revolutionary Wars an Austrian threat to cut off supplies of coal to Nord caused consternation among the local manufacturers . 
They feared to see " their commerce and manufactures completely destroyed by competition and the interruption in the supply of Austrian coal " . 
Nord was as dependent upon Belgium for pig-iron for her metal industries as she was for coal , even before the obsolescence of charcoal smelting . 
The { pays de Lie3ge supplied the great bulk of the needs of the Maubeuge and Valenciennes areas , the two chief groups of metal-using communes in the department . 
There were only two blast furnaces in Nord at the time of the Revolution , at Hayon and Fourmies : and it was said that these were preserved from unsuccessful competition only by the tariff on Belgian iron . 
At the turn of the century , therefore , French dependence physically upon Belgian materials was very marked in the heavy industries ; but Belgian men and money were of little importance , and she had no clear-cut technological lead . 
The new century brought no immediate change . 
Indeed the second period of French occupation of Belgian soil served only to accentuate the existing pattern . 
In 1814 the completion of the Mons-Conde2 canal increased the ease with which Mons coal might be sent to Nord ( ten years later the opening of the Saint-Quentin canal allowed the passage of Mons coal by a cheap water route all the way to the Paris market ) . 
As the years passed , however , Belgium did more than supply coal and raw pig for the iron industry : Belgian firms took a leading part in the establishment of modern works in Nord . 
In 1849 the largest metal works in Nord was the Belgian S. A. { Hauts-fourneaux , forges et laminoirs de Hautmont , near Maubeuge . 
It had been built in 1842 , and employed more than 400 workers . 
It was only one of several Belgian metal firms which became established in the Maubeuge area in the forties and fifties to gain access to the French market , or even , as in the case of Victor Dupont at Sous-le-Bois to avoid labour difficulties at home . 
Maubeuge lay less than thirty miles up the valley of the Sambre from Charleroi , one of the two largest centres of the Belgian iron industry . 
Its metal industries were an extension across the national frontier of the industries of Charleroi : its economic life was orientated to Charleroi . 
The penetration of Belgian industry and entrepreneurs is therefore very understandable . 
Belgian influence extended further , however . 
There was at least one Belgian metal venture in the Valenciennes metal region — the rolling mills at Blanc-Misseron : and Belgian influence in Nord 's most important industry , textiles , was important . 
Belgian capital and personnel were seldom directly concerned in the industry ; but Belgian textile machinery found a ready market in Nord . 
Once again Cockerill was the great stimulus . 
Mahaim , after describing the early days of the Cockerill plant in Lie3ge , added , " Then , with an astonishing rapidity in view of the slowness of communications , the clothing centres of northern France took part in the re-equipment . 
Once Cockerill was established at Lie3ge , his cliente3le appeared in France . " 
While Belgian influence in Nord was considerable , it was less marked here than in the parts of the Austrasian field which lay to the east . 
Although Belgian coal and coke was indispensable to Nord ; Belgian firms in the van in the metal industry ; and Belgian technological leadership often apparent , even in textiles , French capital and industry could show reason for a claim to near equality . 
In Italy , too , the part played by some of the provocative post-war striking , openly aimed at factory-expropriation , in bringing adherents and factory- and landowner-subscriptions to the Fascists , is often ignored so that the story only seems to begin with the otherwise inexplicable lorry-forays against Red centres , already in 1921 rising to anarchic heights . 
Of course , the Italian governing classes were to pay dearly for the mingled cynicism and cowardice with which they finally allowed the apparatus of State to pass into the hands of the leaders and organizers of the huge bands of street-fighters at whose illegalities they had winked so long . 
The whole world was , in fact , destined to pay for , before long , there were to be growing apprehensions among the " advanced " as to whether Mussolini 's success would not attract power-hungry imitators in every land . 
In Germany , for example , the ambitions of Adolf Hitler were certainly stimulated , and in that suffering country there had already been such threatening displays from the frustrated Right as the Kapp putsch of 1920 , the Erzberger murder of 1921 , and the Rathenau murder of 1922 . 
The attempted Nazi seizure of Bavaria , when it came in November 1923 , enlisted Ludendorff 's support . 
And it was not insignificant that the Daily Mail should publish , in 1923 , its own version of Italian Fascismo 's history and that the Labour Publishing Company should issue a very different account . 
As September 1923 had seen a Spanish Army coup sweep aside the politicians and institute , without any obvious sign of public displeasure , the authoritarian re2gime of Primo de Rivera , the I.L.P. 's urge to issue Matteotti 's The Fascisti Exposed , during 1924 , becomes more explicable . 
Yet Matteotti 's murder in June 1924 , a worse and more widely-resented scandal than any he exposed when alive , failed ultimately to weaken the Fascist grip on Italy and may in the long run have served to strengthen it . 
Certainly , a third Dictatorship appeared when General Pangalos seized control in Greece during the summer of 1925 . 
All this , as it turned out , was not yet the primary danger to the " advanced " and to their social democracy . 
Pangalos 's dictatorship , after all , was short lived , and Primo , in Spain , never built up and doubtless despised , the Mussolini demagogy , complete with fighting street-rowdies . 
In fact , despite some ominous undertones even in Britain and France , not to mention Mussolini 's increasing grip of Italy , it might be assumed that democratic prospects were on the mend between 1925 and the great " economic blizzard " which began towards the end of 1929 . 
It was when German unemployment began rising again catastrophically in 1930 that Hitler , whose denunciation of Jews , Versailles , and traitors , sold to Moscow or the Entente , had become part of the German political scene , scented his first chances of establishing an altogether more formidable dictatorship than Mussolini 's . 
And the street-fighter apparatus which some German capitalists , fearful of Communism and Moscow , helped him to perfect , began to assume , in the S.A. and the S.S. , forms destined to leave the Italian models far behind . 
Already by the summer of 1932 , a possible Storm Troopers ' transfer from the harrying of Communists and Jews in the streets to operations on the Polish and Czech frontiers was being taken seriously at the German War Department . 
By 1932 , of course , English theorists of the Left had been speculating for some time on how a British Dictatorship threat might come to be used against them and , in point of fact , several times during the 1920s Winston Churchill had been cast for the part of the British Mussolini . 
But there were mockers among them who claimed that the British ruling classes would never have to meditate the risks of calling in Fascism if the Labour Movement allowed itself to be run out of power as tamely as had been the case in 1924 and 1931 . 
These mockers of " gradualism " were in favour of assuming in advance that yet another "conspiracy " would be attempted against any third Labour Government , even if possessed of a Majority , and that such a Government was therefore entitled to arm itself with drastic emergency Powers usable against all manner of " capitalist sabotage " . 
It was a most dangerous line of advocacy , almost certain to lead not merely to Fascism but to bloodshed and the complete antagonization of still important Radical forces , yet for a time it became the policy of the Socialist League led by Stafford Cripps . 
There had been Radicals who had prophesied that Labour would itself breed British Fascism 's would-be leader , and they had been able , as justification , to point to Mussolini 's violent Socialist past and to Hitler 's description of what he stood for as National Socialism . 
And , of course , it provided an additional reason for Radicals to refuse absorption into the Labour movement to find its most discontented wing , after 1931 , forming Mosley 's New Party or entering Cripps 's Socialist League or , finally , like John Strachey , preaching a break-away into Leninite Communism . 
As Mosley might well have become a " Man of Destiny " if Hitler 's success against Britain had been greater than it was , some remarks on his strange political career between 1918 and 1930 are justifiable . 
The heir to a baronetcy and considerable wealth , he had , after some service in France , entered the " Coupon Parliament " at the age of twenty-two and married Lord Curzon 's daughter in 1920 . 
But , before long , the urge to make a mark had led him on to activities on the Irish Question which his brother-Conservatives found unpardonable , and after four years as Conservative M.P . 
for Harrow between 1918 and 1922 , he had to overcome party resistance to retain his seat in the Bonar Law Parliament as an Independent Conservative . 
By the time of the first Labour Ministry in 1924 , he was lending Labour " Independent " support for some time before he announced his conversion . 
Thereafter he fought his way back into the House for Smethwick as a Socialist , was admitted to the friendship and confidence of MacDonald and accompanied him on a continental tour in the autumn of 1928 . 
When he entered MacDonald 's second Government as Chancellor of the Duchy of Lancaster with a place on Mr. Thomas 's Committee for combating Unemployment , there were already those who predicted that he would succeed to the party Leadership . 
Possibly his ultimate chances were made no worse by the fact that he resigned in May 1930 when , despite growing unemployment , he found virtually all his suggestions , summarized in the once-notorious " Mosley Memorandum " , treated as inadmissible . 
Mosley 's long and pertinacious struggle during many ensuing months to convert the Leadership or force its hand , with Back-Bench aid , had some remarkable features — particularly during the Llandudno Conference of October 1930 and at the extraordinary meeting of the Parliamentary Labour Party held on January 27 , 1931 . 
It was , to some extent , because he came so near to dividing the Party dangerously between " Mosleyites " and the rest that the Leadership succeeded in defeating him and never more effectively than when urging , privately , that Mosley was merely a rich young man whose ambition was over-reaching itself . 
Mosley persisted , until March 1931 , with the effort to create an Action Group within the party but , under the frown of official disapproval , its numbers sank from forty to twenty . 
When the final break came , only six Members in all were available as the foundation of a New Party and the six included Mosley himself and his wife , Lady Cynthia . 
The election of October 1931 , moreover , came in circumstances peculiarly unfavourable to the New Party which polled badly and lost all Parliamentary representation . 
Though a great deal is still fundamentally unexplained in the story of the New Party 's evolution towards an Anti-Semitic Fascism , it is not impossible to find some guidance by checking the twenty-four constituencies before whom New Party candidates placed themselves . 
Stepney and Whitechapel were two of those constituencies destined , before long , to supply a steady stream of Blackshirt recruits and to become the nucleus of metropolitan Fascism , and both those areas had , for a couple of generations , heard much complaint of Jewish immigrants , Jewish employers , Jewish business methods , Jewish landlords , and much else . 
It only needed reports of what the Nazis were doing , especially after Hitler became Chancellor , for Blackshirt contingents to become available not merely in the East End , but in Islington , Hackney , Stoke Newington , and many other quarters of London where there were prosperous Jewish businesses and yet much native unemployment and distress . 
Of course , the very name Blackshirt , and the uniform , is an indication that it was Mussolini , rather than Hitler , who was being originally imitated . 
And though some of Mosley 's Action associates like Oliver Baldwin and John Strachey were shocked into a complete break with him when they first discovered him sanctioning , in his party 's rooms and meeting-places , exercises in physical force , there was a possible defence in the plea , that after he had left the Labour Party , Mosley 's own meetings were broken up by dangerous mobs , and that in Birmingham and Glasgow police protection had to be secured . 
It has , of course , been the fashion of Communists and Fascists to demand complete freedom of speech and assembly for themselves until they are prepared to destroy it and all the other democratic " liberties " by force . 
And the Radical tradition of tolerance for the extremest views is so strong in Britain that matters have normally reached a dangerous stage before any widespread assent can be obtained for " coercion " . 
And if " Reds " were still , in 1934 and 1935 , being allowed to experiment unceasingly with organizing " Unemployed Marches and Demonstrations " that might become something more , the case for exceptional vigilance and severity against the Blackshirts was correspondingly weaker . 
Yet by 1934 a British Fascist movement of some potential strength was certainly being reared , already capable of attracting support from those who feared "Red " plans and activities and wanted Britain rescued , besides , from the depths , as they considered it , of the ignoble pacifism to which Radicalism and Socialism had brought the country . 
The most formidable patron the Blackshirts acquired , for a time , was the great newspaper magnate , Lord Rothermere , though he finally shrank , under the stimulus of an enormous roar of " progressive " indignation , from the odium of swallowing virulent Anti-Semitism with his Anti-Bolshevism . 
As Rothermere put it himself : " 
I refused to give more than ordinary publicity to Sir Oswald Mosley 's Blackshirt movement the moment I discovered it had an anti-Jewish bias . 
I supported it at first with the idea of promoting a right wing appanage of the Conservative Party , which should form a counterblast to left wing activities . 
Mosley 's correct procedure was to develop a Youth movement inspired by anti-Bolshevist ideals , instead of basing himself on Continental models which , obviously , would not appeal to our British mentality or temperament . " 
Yet if he withdrew special patronage from Mosley 's Blackshirts , Rothermere had an obvious admiration for the services he considered Hitler and Mussolini to have rendered their countries as well as a readiness to lead a great Air-Rearmament Campaign which constituted him one of the hopes in Britain of those who wanted the country to be at once too strong and too friendly for the Dictators to dream of attacking . 
It was , perhaps , as well therefore for the general cause of " progress " in Britain that all parties in Parliament decided that they had had enough of provocative Fascist tactics in the East End after some notorious affrays in October 1936 faced a dismayed nation with the prospect of a repetition in Britain of full Nazi-style street hostilities . 
And Sir John Simon 's Public Order Bill , to ban the wearing of uniforms in connection with political objects and the maintenance by private persons of associations of military or quasi-military character , was , if specially welcome to Radicals and Socialists , hardly opposed during its rapid progress through Parliament in November and December 1936 . 
Fascism , however , if deprived of one of its most dangerous and provocative means of display , remained a possible peril to " progressives " till the Fascist Dictators were defeated and destroyed . 
Yet for years the destruction that finally overtook the Fascist Dictators seemed most unlikely and the chances to be the other way as the notorious case of the Spanish " progressives " seemed to show between 1936 and 1939 . 
He yielded . 
On 25th January he issued two strongly worded Cabinet Orders . 
The first reiterated the command that Bismarck was to be kept informed of the course of military operations , and directed Moltke to take such effective steps to do so that Bismarck would have no further cause for complaint ; while the second expressly ordered that in any correspondence with members of the French Government or Delegation which might have any political significance , and in the drafting of any replies , the Ministry of Foreign Affairs was always to be consulted . 
The royal decision was unequivocal and settled the matter . 
The reply which Moltke at first projected was virtually a letter of resignation . 
The royal order , he said , was " ungna " dig " , un-Gracious . 
His communications with Trochu , he maintained , had been strictly military . 
All he had withheld from Bismarck was information and plans which would be of value to the Chancellor only if he as well as Moltke were advising the King about operations ; and rather than have the war conducted by such a dual authority Moltke declared himself ready " to leave the relevant operations and the responsibility for them to the Federal Chancellor alone . 
I await " , he concluded grimly , " Your Imperial Majesty 's most gracious decision on the matter . " 
The letter which he actually sent , however , was considerably milder . 
In it he merely defended his conduct with dignity , complained at Bismarck 's repeated and unjustified accusations , asked for a clear ruling about his relationship with the Chancellor , and requested the Emperor 's protection against any further attacks . 
The Imperial secretaries drafted an anodyne reply , but it was not sent . 
There was no need . 
On 28th January an armistice was signed with the Government of National Defence . 
For the preservation of peaceful relations within Royal Headquarters it had come not a moment too soon . 
Bismarck 's de2marche of 18th January took effect almost immediately . 
Two days later , on the evening of 20th January , Trochu sent his request for an armistice to bury the dead after Buzenval . 
The Kaiser at once referred the request , not to Moltke , but to Bismarck ; and Bismarck grimly refused it . 
The brusqueness of the refusal , the failure to take advantage of what was generally sensed in Versailles to be the beginning of the end , seems so out of keeping with Bismarck 's desire to renew peace negotiations that the explanation must surely be sought in Bismarck 's attitude to the earlier exchanges between Moltke and Trochu . 
In this new overture he may have seen another move in the negotiations which he believed the soldiers to be conducting behind his back , and it is not surprising that he should have taken advantage of his new established dominance to end them . 
In any case he was convinced that after the failure of the Buzenval sortie capitulation could not be long delayed , and then the peace-proposals of the Imperial party could be seriously considered . 
Cle2ment Duvernois was expected at any moment . 
But Duvernois did not come : the stubbornness of the emigre2 group in Brussels threw his whole time-table out of joint , and before he was ready to talk to Bismarck Jules Favre had reached Versailles . 
Favre arrived at German Headquarters late in the evening of 23rd January . 
His journey followed a day of stormy debate while the Government in Paris discussed whether he should negotiate for an armistice for the fortress of Paris only or for the whole of France . 
The question was left open : he was instructed only to discover what terms were available , without betraying the desperate state of the city 's supplies . 
Favre himself hoped to secure , as a minimum , that there should be facilities given for the free election of a National Assembly to decide the question of war or peace ; that there should be no entry of Prussian troops into Paris and no imprisonment in Germany of the garrison , and that civil war should not be provoked by an attempt to disarm the { Garde Nationale . 
Failing these conditions , he was prepared to threaten a renewal of the fighting and ultimately a total surrender which would compel the Germans to accept complete responsibility for the civil administration of Paris . 
Bismarck was able to bluff much more effectively than Favre . 
As at Ferrie3res , he was able to state truthfully that he was in negotiation with the Empress , who alone represented lawful authority , for the summoning of the only legal representative body in France , the { Corps Le2gislatif . 
Favre 's project of a freely elected Assembly he declared to be no longer realisable : under the dictatorial republicanism of Gambetta elections would not be free . 
He was prepared however to talk in general terms about conditions for Paris . 
He agreed that the garrison should not be sent as prisoners to Germany , where their presence would only be an embarrassment ; he considered that although opinion in the Army and in Germany would insist on a triumphal entry into the city , the scope of this might be strictly limited ; and while refusing to waive the disarmament of the { Garde Nationale , he suggested that the most politically reliable battalions alone should be allowed to keep their arms . 
The contrast between these terms and the draconian conditions demanded by Moltke speaks for itself . 
By the end of the first evening 's discussion it was evident that the chances of agreement were good . 
Bismarck said nothing to the curious bystanders as he left the room in which he had been closeted alone with Favre , but he whistled a hunting call of unmistakable meaning : the chase was over . 
Next day , 24th January , both negotiators came into the open . 
Cle2ment Duvernois had still not arrived , and Bismarck consented to abandon his negotiations with the Empress if he could reach agreement with the Government of National Defence . 
In return Favre agreed to sign an armistice covering the whole of France , and to ensure that no resistance by the Delegation would be allowed to stand in the way of its implementation . 
Only the question of the armament of the { Garde Nationale remained unsettled , and on this Bismarck , faced by Favre 's convincing assurance that it would be physically impossible to disarm them without a civil war , was eventually to yield . 
For the rest , the Government in Paris with some reason accepted Bismarck 's terms as " inespe2re2es " . 
Thanks to the Chancellor 's diplomatic moderation , the honour of the city and the troops who had defended it would remain intact . 
On 25th January Favre was therefore authorised to sign an armistice for three weeks , to enable a National Assembly to meet at Bordeaux and finally resolve the question of war or peace . 
So far Bismarck had carried on the negotiations single-handed . 
Now the military had unavoidably to be called in to settle the details of the armistice . 
It was unfortunate that this stage in the negotiations coincided exactly with the crisis of the quarrel between the civil and military authorities ; and Bismarck rubbed salt into the wounds of his defeated rivals by insisting that the agreement with the French should take the form , not of a Capitulation , which would signify surrender , but of a Convention , which indicated only a negotiated settlement between equals . 
Moltke began attending conferences on 26th January , the day after his rebuff by the Emperor . 
The French negotiators noted , without fully appreciating the cause , the unpleasant contrast between his grim , unsmiling dourness and the easy affability of Bismarck , and Bismarck openly stigmatised Moltke 's attitude as mean , pettifogging and unrealistic . 
But the French had trouble enough with their own military representatives . 
Trochu 's oath never to capitulate made it impossible for him to undertake the responsibility of negotiating surrender , and Ducrot had never been forgiven by the German Emperor for his apparent breach of parole after Sedan . 
Favre therefore found to accompany him a certain General Beaufort d'Hautpoul , who proved quite incapable of carrying on negotiations . 
The French attributed his peculiar condition to honourable mortification ; the Germans , less charitably , said he was drunk . 
He was succeeded after one embarrassing day by General de Valdan , Vinoy 's Chief of Staff , by whom , on 28th January , the armistice was signed . 
The armistice was to take effect in Paris immediately — indeed on Bismarck 's suggestion the bombardment and counter-bombardment had ceased two days earlier — and was to come into action elsewhere in France in three days ' time . 
It was to last until 19th February , during which time full facilities would be given for an Assembly to be freely elected and to meet at Bordeaux , where it would debate whether the war should continue and on what terms peace should be made . 
Meanwhile Paris was to pay a war-indemnity of two hundred million francs . 
It was to yield up its perimeter forts and dismount the guns from its walls , but the ground between the forts and the city would be considered neutral , and no German troops would enter Paris . 
The Germans would provide full facilities for the rapid re-provisioning of the city . 
12,000 men of the Paris garrison would retain their arms , an essential minimum to preserve order , as Favre insisted . 
The rest were to surrender their arms and remain in Paris until the end of the armistice ; when , if peace had not yet been made , they were to be taken over by the Germans as prisoners-of-war . 
The terms for the rest of the country were less satisfactory to the French . 
It was agreed that a military demarcation line should be drawn , from which both armies should withdraw ten kilometres ; but Favre and his military advisers depended entirely on the Germans for information about the position of the existing front line , and Moltke was in no mood to interpret doubtful cases to his opponents ' advantage . 
The agreed line was to involve at several points the withdrawal of French troops from positions which they had quite securely held . 
Moreover about the operations still in progress in the Jura both Favre and Bismarck were equally ill-informed . 
Favre knew only that the fortress of Belfort was still intact and that Bourbaki 's relieving force still held the field . 
To enforce an armistice in this area might be to spoil the chance of a military victory which would considerably strengthen the French hand when it came to negotiating the final peace . 
Moltke , though he had received little news from the swiftly moving Manteuffel , was sufficiently confident of the outcome to allow Favre to nurse his illusions ; so by common agreement military operations were allowed to continue in the department of Jura , Co5te d'Or , and Doubs . 
When Favre telegraphed the news of the armistice to Gambetta on the evening of 28th January he made the astonishing and notorious mistake of failing to inform him of this omission . 
How this error contributed to the final agonies of the Army of the East we have already seen . 
Moltke admitted the validity of the political considerations which had led Bismarck to conclude the Convention with the Government of National Defence , but he made no secret of his dissatisfaction with the moderation of its terms . 
In this he spoke for the Army , but not for the Army alone . 
His views were widely echoed throughout Germany . 
On the French side it was the civilians , Gambetta and the politicians of the Paris Clubs , who wished to prolong the war after all but a tiny minority of their military advisers had urged the conclusion of peace . 
The relaxing of the tension which was brought about by even a temporary suspension of hostilities undermined the strength of the extremists on both sides . 
The parties of { guerre a3 outrance dwindled to impotent if vociferous cliques at Bordeaux and Versailles , able to embarrass the peace-makers but not to thwart them . 
That this was so in the French ranks was due to the openly expressed determination of the French people , through their elected representatives , to have peace at any cost . 
But Bismarck , in dealing with his own military party , did not enjoy a comparable advantage . 
Instead public opinion in Germany as overwhelmingly supported a peace of extermination as did that in the Allied nations in 1918 . 
If the opposition to Bismarck at Versailles which had been at its height on the eve of the armistice abated rapidly once the armistice was signed , it was not because the military party was accepting defeat with a good grace . 
Secondly , even if the bitter struggle for the hegemony of the peninsula was punctuated by spells of mutual tolerance , these respites did not last long . 
The years when the three rival cults were celebrated on an equal footing at Toledo had no more permanent result than had the fleeting Christian-Muslim rapprochement achieved in Sicily under the rule of Frederick 2 , { Stupor Mundi , in the same period . 
In the fifteenth century , at any rate , the average Iberian Christian — like any other European — never referred to the Muslim and the Jewish faiths without adding some injurious epithet . 
Hatred and intolerance , not sympathy and understanding , for alien creeds and races was the general rule . 
" Moors " ( i.e. Muslims ) , Jews , and Gentiles were alike regarded as being doomed to hell fire in the next world . 
It inevitably followed that they were not likely to be treated with much consideration by Christians in this one . 
The intolerance was not , of course , only on one side . 
The Christian crusade had its counterpart in the Muslim jihad , or holy war against the unbeliever . 
The orthodox Muslim regarded with horror all those who would "give associates to God " ; and this was just what the Christians did with their Trinity , their Virgin Mary , and ( to some extent ) with their saints . 
Medieval Europe was a harsh and rugged school , and the softer graces of civilization were not more widely cultivated in Portugal than they were elsewhere . 
A turbulent and treacherous nobility and gentry ; an ignorant and lax clergy ; doltish , if hard-working , peasants and fishermen ; and a town rabble of artisans and day-labourers , like the Lisbon mob described by Ec6a de Queiroz five centuries later , " fanatical , filthy , and ferocious " — these constituted the social classes from which the pioneer discoverers and colonizers were drawn . 
Anyone who doubts this need only read the graphic pages of Ferna4o Lopes , " the best chronicler of any age or nation , " as Robert Southey described him . 
The first stage of the overseas expansion of Europe can be regarded as beginning with the capture of Ceuta by the Portuguese in 1415 and culminating in the circumnavigation of the globe by the Spanish ship Victoria in 1519-22 . 
The Portuguese and Spaniards had their precursors in the conquest of the Atlantic Ocean , but the efforts of these adventurers had not changed the course of world history . 
Vikings had voyaged to North America in the early Middle Ages , but the last of their isolated settlements on Greenland had succumbed to the rigours of the weather and the attacks of the Eskimo before the end of the fifteenth century . 
Italian and Catalan galleys from the Mediterranean had boldly ventured into the Atlantic on voyages of discovery in the late thirteenth and early fourteenth centuries ; but what they sought is uncertain , and what they found is equally obscure , though they may well have sighted Madeira and some of the Azores . 
Why did the Iberians succeed where their Mediterranean predecessors had failed ? and why did Portugal take the lead when the Biscayan seamen were as good as any in Europe ? 
Historians are still far from agreed on the precise answers to these questions , but the main impulses behind what is known as the " Age of Discovery " evidently came from a mixture of religious , economic , strategic and political factors . 
These were by no means always mixed in the same proportions ; and motives inspired by Mammon were often inextricably blended with things pertaining to Caesar and to God . 
At the risk of oversimplification , it may , perhaps , be said that the four main motives that inspired the Portuguese were , in chronological but overlapping order , ( 1 ) crusading zeal , ( 2 ) desire for Guinea gold , ( 3 ) the quest for Prester John , and ( 4 ) the search for spices . 
An important contributory factor was that , during the whole of the fifteenth century , Portugal was a united kingdom which experienced only one brief episode of civil strife . 
The consolidation of the power of the Portuguese Crown during this period forms a marked contrast with the confused situation obtaining in the rest of Europe . 
France was distracted by the closing stages of the Hundred Years War — 1415 was the date of the battle of Agincourt as well as of the capture of Ceuta — and by rivalry with Burgundy ; England by the struggle with France and the wars of the Roses ; and Spain and Italy by dynastic and other internal problems . 
The seizure of Ceuta in 1415 and , more important , its retention , were probably inspired mainly by crusading ardour to deal a blow at the Infidel , and by the desire of the half-English princes of Portugal to be dubbed knights on the field of battle in a spectacular manner . 
Economic and strategic motives may also have played a part , since Ceuta was both a thriving commercial centre and a bridgehead for an invasion across the straits of Gibraltar . 
It has been suggested that the fertile corn-growing regions in the hinterland also formed an attraction for the Portuguese , whose own country was even then normally deficient in cereals . 
Ceuta was one of the terminal ports for the Trans-Sahara gold-trade , though how far the Portuguese knew this before their capture of the city is uncertain . 
But the occupation of Ceuta undoubtedly enabled them to obtain some information about the Negro lands of the Upper Niger and Senegal river regions , where the gold came from . 
They soon began to see that they might , perhaps , establish contact with those lands by sea , and so divert the gold-trade from the " caravans of the Old Sahara " and the Muslim middlemen of Barbary . 
They had the more incentive to do this since Western Europe in general , and Portugal in particular , were then suffering a serious shortage of precious metals . 
This was partly due to the drain of silver and gold to the East , to pay for spices and other Oriental exports , and partly to the insufficient production of the Central European mines . 
The crusading impulse and search for gold were soon reinforced by the quest for Prester John . 
This mythical potentate was vaguely located in the " Indies " — an elastic and shifting term that often embraced Ethiopia and East Africa , as well as what little was known of Asia . 
The passage of time , romantic travellers ' tales — of which Marco Polo 's supply the classic example — and wishful thinking , all combined to build up the late medieval belief that Prester John was a mighty , if probably schismatical Christian priest-king . 
His domains were believed to lie somewhere in the rear of the Islamic powers that occupied a wide belt of territory from Morocco to the Black Sea , thus cutting off Christendom from direct contact with the peoples of Asia and the isolated Coptic Christian kingdom of Abyssinia . 
From 1402 onwards , occasional Abyssinian monks and envoys reached Europe , and at least one of them got as far as Lisbon in 1452 ; but the Portuguese , like most other people , still seem to have had only a hazy idea of what or where his country was . 
The mixed motivation behind the Portuguese overseas expansion was explicitly recognized in the Papal Bull { Romanus Pontifex ( January 8th , 1455 ) , which categorically commended the crusading inspiration of the Infante Dom Henrique and his desire to reach the mysterious Christian potentate(s) of the Indies by circumnavigating Africa . 
This Bull also recognized the commercial motive inherent in Portuguese expansion by granting the King of Portugal and his successors the monopoly of the trade with the inhabitants of the newly discovered regions , subject to the proviso that the sale of war material to the enemies of the Faith was forbidden . 
Finally , it may be mentioned that as the Portuguese pushed their exploratory voyages down the west coast of Africa , they added the acquisition of Negro slaves to that of Guinea gold , and the search for spices to the quest for Prester John . 
The spices , however , only appear as a major motive after the death of Prince Henry in 1460 , by which time the West African slave-trade was an established fact . 
The Portuguese voyages of discovery and trade down the west coast of Africa did not really get going until Cape Bojador ( or , more probably , Cape Juby , which was then apparently known by the former name ) was rounded in 1434 , after many futile efforts . 
The voyages then continued systematically , and a great spurt of progress was made during the eight-year regency ( 1440-48 ) of Dom Pedro , elder brother of the better publicized Dom Henrique , belatedly and somewhat inappropriately named "the Navigator . " 
Prior to his assumption of the Regency , Dom Pedro had been violently critical of the policy of holding Ceuta , and had shown no particular interest in the voyages of discovery patronized by his brother . 
But once in power , as so often happens , Dom Pedro adopted wholeheartedly some of the policies that he had previously criticized , or to which he had been indifferent . 
All talk of abandoning Ceuta in exchange for the freedom of his youngest brother , Dom Fernando ( who had been held as a prisoner by the Moors since a disastrous attack on Tangier in 1437 ) , was dropped , and Dom Pedro actively backed the voyages of discovery and the colonization of the Atlantic islands . 
Nevertheless , Dom Henrique 's share in these twin enterprises was the more important in the long run . 
The voyages themselves , and the colonization of Madeira and the Azores , which began soon after their discovery — or re-discovery — in 1419-27 were largely financed from the revenues of the military Order of Christ , of which Dom Henrique was the administrator and governor ( but not the Grand Master as is often stated ) from 1420 until his death forty years later . 
Some of the leading Lisbon merchants also had a hand in financing and organizing these voyages . 
From 1470 to 1475 they were leased on the basis of a monopoly contract to a certain Ferna4o Gomes , under whose administration a large stretch of the Guinea coast was opened up to Portuguese enterprise and trade . 
It is still uncertain how much was directly due to government initiative and to resources supplied by the Crown or by the Order of Christ , and how much was due to private enterprise , or to both the Crown and the merchant-adventurers acting in conjunction . 
But it can be said without undue simplification that right from the beginning , the planning , organization , and financing of these voyages owed a great deal to intelligent government initiative and support , as personified in the activities of Dom Henrique , Dom Pedro , and , above all , of King Dom Joa4o 2 in the final stages ( 1481-95 ) . 
In other words , as C. R. Beazley pointed out over sixty years ago , Prince Henry 's achievement was that he " altered the conditions of maritime exploration by giving permanence , organization , and governmental support to a movement which had up to this time proved disappointing for lack of those very means . " 
It was this steady government support that gave the Portuguese the edge over their Spanish neighbours and rivals , who for long contested the papal awards that granted a monopoly of the West African coastal trade to the former . 
But save during the years 1475-1480 , when the Spanish adventurers made determined but unsuccessful attempts to secure the lion 's share of the Guinea trade for themselves , the Spaniards did not receive the same consistent and energetic support from their rulers as did the Portuguese from theirs . 
Moreover , for much of the fifteenth century , Spain 's cereal and financial problems were less acute than were those of Portugal , and therefore the Spaniards had not the same economic incentives to seek new lands to conquer or to exploit . 
Finally , the existence of the Moorish kingdom of Granada on Andalusian soil , the prior commitments of the Crown of Aragon in the Mediterranean , and the need to strengthen the Crown of Castile against unruly vassals at home , provided powerful distractions that were not present to the same extent in Portugal . 
The actual voyages down the barren and featureless Saharan coast presented no exceptional difficulties to experienced seamen , other than the legendary but none the less real terrors of the unknown . 
These latter included the common , though not universal , belief that the torrid zone was too hot to support life , and that the { Mar Tenebroso , or " Sea of Darkness " south of Cape Nun , was too shallow and too dangerous for navigation . 
Lytton 's telegram announcing his intentions reached the India Office on 9 September : Cranbrook was not at this time in London : he was at Braemore in the north of Scotland . 
He received his copy of the telegram on the 12th . 
Meanwhile Horace Walpole , his private secretary , a permanent civil servant , who was suspicious of Lytton 's policies , had read Lytton 's telegram , noticed that it proposed to send the mission off from Peshawar in less than a week , and decided that the telegram ought to be answered . 
He , therefore , at the same time as he sent Cranbrook his copy of the telegram , sent also a copy to Beaconsfield at Hughenden and one to Salisbury at the Foreign Office . 
The effect on both of them , and on Cranbrook when he read it , was immediate . 
To all of them it seemed that the proposal to insist on the expulsion of the Russian mission before the beginning of Anglo-Afghan negotiations would be " an affront which a great power could not endure " . 
It would intensify Russian activity in Afghanistan ; it would bring the Russian government into direct conflict with the government of India ; it would endanger peace in Europe and it must , therefore , before it was attempted , be considered very fully by the Cabinet . 
The Cabinet , however , could not meet . 
Its members were scattered over the country houses of England and Scotland . 
It was clear , from Lytton 's telegram , that he did not know of the diplomatic protest to St. Petersburg and did not intend to wait for a Russian answer . 
The impression made by the telegram , as Horace Walpole found when he visited Salisbury on the morning of the 11th , was the thought that " Lord Lytton [ was ] going a little too fast and plunging us into an Afghan war " . 
The effects of such a war would be felt not only in Europe , but also in the constituencies . 
Less than a week later the prime minister was noticing "symptoms ... by no means confined to one party " of a " strong and rising feeling respecting this Afghan business " . 
" So long " , he told Salisbury , " as the country thought they had obtained " Peace with honor " , the conduct of H.M. Government was popular , but if the country finds there is no peace , they will be apt also to conclude there is no honour " . 
And his conclusion was not that Lytton should make the pace but that Salisbury himself , in Cranbrook 's absence , should make sure that Lytton was properly informed of the views of a Government that would need to act " with decision and firmness " . 
It is , as we have seen , by no means clear that the decision to send the diplomatic protest to Russia on 19 August had been accompanied by a decision to delay Chamberlain 's mission until a reply had arrived from St. Petersburg . 
So long as it was imagined that Lytton knew his limitations , Salisbury seems to have attached little importance to the protest . 
But as soon as it seemed that Lytton might be steering towards war , it comes forward from the back of Salisbury 's mind as an occasion , or excuse , for delaying Lytton 's action in India : and as a move in the parliamentary game which would , when the time comes , show that the British government had done its best to avoid war and accomplish by peaceful diplomacy what Afghan or Russian obstinacy had made impossible . 
Beaconsfield , as soon as he saw the telegram of 8 September and had talked to Salisbury , wrote tartly to Cranbrook regretting that Lytton seemed not to know of the protest . 
Salisbury , on the 11th , after correspondence with Beaconsfield , telegraphed Horace Walpole to ask Cranbrook urgently for authority to stop Lytton sending the mission until the Russian reply had arrived . 
Cranbrook , meanwhile , feeling the same way in Scotland , had sent a telegram to Walpole forbidding the departure of the mission until further orders . 
On the 14th , two days before Chamberlain was supposed to start , this message was in Lytton 's hands . 
When Lytton received the telegram , however , he was in no mood to delay . 
The events he had set on foot in August could not now be controlled . 
Chamberlain was already in Peshawar ; Cavagnari had committed himself in the Khyber : the native ambassador had left for Kabul and the wide publicity Lytton had given to the mission through his private press officer in India , made it difficult to give the slightest sign of turning back . 
His information about the state of opinion in England came mainly through Burne in the India Office . 
Burne had been Lytton 's private secretary in India until he returned to England with a sick wife in the spring of 1878 . 
When his wife died and he returned to work at the India Office , he spent much time and money providing Lytton with telegraphic reports of the state of feeling in England and of conditions in the India Office . 
By the middle of August he had spent , out of Lytton 's pocket , £197 on private telegrams . 
Burne was not altogether a reliable guide . 
From his telegrams Lytton gathered , what was only half true , that there was much support for him in Afghan matters . 
He learnt from Burne 's letters , also , what he thought he knew himself , that Cranbrook was too much under Salisbury 's thumb , was lazy , well-meaning , and " timid " . 
Nor did he believe , or imagine anyone else seriously to believe , that the protest to St. Petersburg would achieve any result . 
Finally , perhaps most important of all , he knew that Cranbrook was not in London when the restraining telegrams were sent and he saw in them the influence , not altogether friendly and certainly not at all sensible , of Lord Salisbury . 
These things encouraged him to disobey . 
On the 13th , together with the telegram in which he was first told about the protest to St. Petersburg , Lytton also received one to say that Cranbrook would not send detailed approval and modification of Chamberlain 's instructions until the Russian reply arrived in London . 
On the 17th , Lytton heard that an abstract of this reply had been received from Plunkett , the { 6charge2 d'affaires in St. Petersburg : he heard also that it was not satisfactory . 
But he was given no authority to send the mission off and no authority had arrived on the morning of the 21st . 
On the 16th he had , in accordance with Cranbrook 's telegram of the 13th , postponed Chamberlain 's departure from Peshawar for five days . 
On the 20th , he ordered Chamberlain to move forward to Jamrud : on the 21st , these five days having passed , he told him to enter Afghanistan . 
In sending Chamberlain forward in this way , Lytton did not wish to provoke war . 
He had written a friendly , though overbearing , letter to Sher Ali on the 14th asking again for his cooperation . 
He did not suppose that Sher Ali would refuse to admit the mission ; and he hoped that Chamberlain would , within a week , be established in Kabul . 
His purpose in forcing the pace was therefore not so much to commit the cabinet to a policy of which it did not approve , as to achieve , by rapid action on the spot , a success which he supposed the Cabinet to desire but which , because it was hampered by all the stupidities of " democratic " England , and wrestling in the clutches of " that deformed and abortive offspring of perennial political fornication , the present British constitution " , it could not easily authorize or agree upon . 
At the same time , the publicity with which the mission was sent to Jamrud , gave to its conduct an appearance of deliberate finality which was no accident . 
Chamberlain had not wanted to go forward to Jamrud to ask for entry into Afghanistan . 
He , a great frontier officer with the great frontier officer 's personal prestige , did not want to risk a snubbing at the Afghan frontier which would affect that prestige whatever might be done afterwards to avenge it . 
He would have preferred to find out from Peshawar whether his mission would be admitted ; and , if it were refused , to take whatever action might be necessary from there . 
But for Lytton this was not enough . 
This was a spectacular moment . 
This was Sher Ali 's last chance . 
A great public affront , one of India 's greatest frontier officers , waiting on the Afghan border and turned away by the commander of an outlying Afghan post — this , if Sher Ali were really hostile , must certainly convince the Cabinet , and might even impress the Opposition . 
Chamberlain was chosen because he was , of active Indian frontier statesmen , the greatest pupil of Lord Lawrence . 
Lawrence , the greatest name amongst Lytton 's critics , had attacked Lytton 's frontier policy with mounting hostility ever since he arrived in India . 
If a lawrentian of Chamberlain 's importance were snubbed by the Afghans , Lawrence would have an important weapon removed from his critical armoury . 
So Lytton in India , like Beaconsfield and Salisbury in London , continued his political posturings . 
Chamberlain moved from Peshawar to Jamrud on 20 September . 
On the following morning he sent Cavagnari and Colonel Jenkins , the commander of the mission 's escort , together with a small section of the escort , on to Ali Musjid to ask for admission to Afghanistan . 
They were halted by Afghan troops a mile from the fort and forbidden to come closer . 
Faiz Mohamed , the commander of the garrison ( whom Cavagnari knew well ) , asked Cavagnari to give him time to refer the request to Kabul . 
Cavagnari refused . 
He said that unless Faiz Mohamed specifically forbade the mission to advance , it would advance on the following morning . 
Faiz Mohamed replied that he would attack the mission if it attempted to pass Ali Musjid . 
Cavagnari and Jenkins thereupon returned to Jamrud and reported their failure to Chamberlain . 
Chamberlain reported the failure to Lytton : and Lytton , from Simla , ordered Chamberlain to return to Peshawar . 
So ended , he thought , the " first round of the rubber " . 
He could now prepare to coerce Sher Ali . 
With the repulse of the mission , Lytton 's actions on the frontier became clear and vigorous : Sher Ali had shown himself to be hostile : of that in Lytton 's mind there could be no doubt . 
He must be upset : his treachery demanded his downfall . 
To that end all the forces of the government of India must be turned . 
The problem , in this respect , was a problem in political warfare , how may one best upset an inconvenient neighbour ? 
Also , how may one with the smallest expenditure of energy establish a new re2gime in Kabul ? 
Lytton was not a soldier ; he was a diplomat who had spent the better part of his professional life in comparatively junior positions in civilized capitals . 
He had an almost vicious contempt for military " bumpkins " when they could not understand that large political objects may often best be accomplished by employing a small military force . 
If he could arrange the deposition of Sher Ali without fighting a battle , could see an anglophile emir settled on the throne and could make a treaty with him , then it would be the merest professional obstinacy , an aspect of the " K.C.B. mania " , to collect a large force on the Indian frontier . 
Having manufactured the situation , Lytton would manage with the smallest force possible . 
After 23 September , therefore , he pushed forward his preparations , stationed troops in the cantonments of Thal , Sukkur and Peshawar and watched for the flight and departure of the emir . 
He prepared , in the last week of September , to issue a proclamation calling on the Afghan people to rise against the enemy of the Indian government : but was restrained because the Cabinet regarded this as tantamount to a declaration of war . 
He felt that he should send a force to the assistance of the Khyber tribesmen who helped to escort Chamberlain 's mission . 
The Cabinet made it clear that he must not advance beyond Ali Musjid because that too would seem to imply war . 
But he did not , at any time during September or October , cease to hope that Sher Ali might fall spontaneously by the mere expression of Lytton 's disfavour . 
From Kabul , however , there was no sign of weakness : the emir remained firm and unpoisoned ; and he replied unhelpfully and ( it seemed to Lytton 's orientalists ) insolently to Lytton 's letter of 14 September . 
The fact that he is not in possession of the details probably explains why his confidence in technique is so unbounded . 
There is even more of the mystic than of the intellectual in the young Vale2ry . 
No wonder that at this stage he more or less gives up the writing of poetry . 
Literature is { " l'art de se jouer de l'a5me des autres " ; by his own definition , poetry is not now for him the attempt to give expression to something in himself ( however deliberately or consciously ) ; the poet gets to know his material ( language , poetry ) , the nature of the public ( human psychology in relation to art ) , and then , like da Vinci , having discovered the { " relations ... entre des choses do nt nous e2chappe la loi de continuite2 " , he can , at will , produce whatever effects he desires to produce in the reader . 
There is only one thing missing in this ideal scheme : a desire on the part of the poet to produce any effect at all . 
What would be the point ? 
{ " Le ge2nie est facile . " 
{ " Facil cosa e farsi universale . " 
The young Vale2ry has more important things to do : he wants to follow up his programme of knowledge and self-knowledge ( among other things , to fathom art and psychology , the complete knowledge of which is presumed in the da Vinci and the Monsieur Teste created by him ) . 
The art of poetry as defined by Vale2ry is no longer of any interest from the creative point of view . 
It demands a { " certain sacrifice de l'intellect " , chiefly because he would , if he went on composing poetry , be simply giving to any public for which he wrote what he knows would affect it , playing a rather inferior game which , in theory , he knows he could not lose . 
The implicit reasoning is somewhat circular . 
If he were a da Vinci or a Monsieur Teste , he would not trouble himself with poetic composition . 
So he abandons it . 
But he is not yet , in fact , a da Vinci or a Monsieur Teste , so he will devote all his time and energy to becoming a universal mind . 
Such , in outline , and with only a little simplification , is the theory of the young Vale2ry concerning inspiration and technique . 
It is clear that he has not yet formulated clear distinctions between " total inspiration " and the forms we have called " intermittent " , " intuitive " , " exalted " and " personal " ; but he rejects them by implication . 
" Attributed inspiration " would presumably , it is true , have been accepted by him . 
But the other five forms he would have rejected : his theory allows them to be completely dispensed with . 
But is his theory convincing ? 
Let us consider the first of the two conceptions of creation implicit in the { Technique litte2raire article , according to which the poet has something in himself , impression , dream or thought , which he must communicate by controlled technique . 
Whilst surely nearer the truth than the other , the theory that works backwards , even this conception seems mechanistic , too simple and unsatisfactory . 
Vale2ry does not examine how impression , dream or thought originate . 
There is no mention of any possible dynamism behind them , no mention of the fact that the initial impetus may be accompanied by emotion or excitement which are commonly envisaged as attributes of inspiration . 
It may be conceded that poetry is certainly the communication of something , and that accordingly it is sound to claim that the poet is concerned with an audience , so that the more knowledge he has of this audience and of the nature of his art , the better . 
But it is surely not simply a question , in poetic creation , of the poet 's having something clearly formed in his mind , even something so vague as a dream , and then transferring it to a reader by the technique of language . 
The truth surely is ( and the mature Vale2ry certainly subscribed to this view ) that the poet is concerned with clarifying and making enjoyably articulate for himself and the reader something within him which does not exist as poetry until the poem is composed . 
Given the nature of language and poetic creation , the poet is , to a certain extent , discovering what he has to say , or rather , what he can say , as he composes the poem . 
The poem is a kind of compromise between what the poet wanted to say initially ( and this phrase " what the poet wanted to say " is perhaps too rational and explicit to describe what for many poets is vague and more anticipation than exact intention at this stage ) , what he finds to say , and all the new things to express which occur to him as he actually composes the poem . 
All these aspects of poetic creation will indeed be admirably brought out by the mature Vale2ry . 
Louis MacNeice writes of that " dialect of purification " whereby a poem is produced , " 
a poem which is neither the experience nor the memory , nor an abstract dance of words , but a new life composite of all three . " 
In this respect , then , poetry can be considered as a kind of knowledge , of self-knowledge particularly , only to be found during the struggle to compose . 
Vale2ry in his youth does not show much awareness of these aspects of poetic creation and of this kind of self-knowledge . 
He is obsessed with the notion of art as communication , and therefore with the fact that , though the poet may be able to make the reader react as he wishes by his all-conquering technique , he is nevertheless , because he indulges in poetic composition , a slave to the reader and to language : 
We are thus led on to the second theory of poetry revealed with some uncertainty in the { Technique litte2raire article and unequivocally expounded towards the end of the { Introduction a3 la me2thode de Le2onard de Vinci , the theory according to which the poet works backwards from the reader . 
This stands condemned on two counts . 
Firstly , it is a partial view of poetic creation , neglecting the personal contribution which the poet can , must , make ( i.e. " personal inspiration " ; and this is not to mention the importance of " intermittent " , " intuitive " and " exalted inspiration " ) . 
Vale2ry is at least consistent : having defined the work of art as { " une machine destine2e a3 exciter et a3 combiner les formations individuelles de ces esprits " ( the public ) , he rejects such an activity as beneath him , as time-wasting when he has more important things to do . 
His initial definition of art is faulty , incomplete . 
Secondly , it stands condemned by the very inadequacy of its presentation . 
Not only is art ill defined , but no details are given of the nature of human psychology on which the success of the triumphant technique is supposed to depend . 
The fact is that , at this stage of his career , he has no adequate theory of language and no adequate conception of poetic creation such as he will have in later years . 
Few would question the value of technique , but how many would subscribe to the exaggerated thesis put forward by Vale2ry in his youth ? 
Nothing is more significant than the detached humour with which Vale2ry , in 1919 , in the { Note et Digression which he wrote for his { Introduction a3 la me2thode de Le2onard de Vinci , looks back , not without sympathy despite the detachment , at the ideas and difficulties which he had had in 1894 , about the time of composition of the Introduction . 
He excuses himself , so to speak , but does not really explain enough for our purposes . 
We are still left wondering why he should have had this absolute faith in the powers of technique and why therefore he believed , if only for a short time , that poetry can be composed without any trace of inspiration . 
The influence of Poe and Mallarme2 , and the part it played in Vale2ry 's abandonment of poetry and the development of his programme of knowledge and self-knowledge , has been clearly indicated by Vale2ry himself and often discussed by his critics . 
Less attention has been paid to an influence probably no less potent : that of contemporary scientific thought . 
The last three decades of the nineteenth century were an age in which , as the rift between philosophy and science widened , it was becoming evident that there was more than one reality , depending on the viewpoint of the observer . 
The scientist was cautious of claiming to interpret or explain phenomena : on the one hand , there was reality with its multiple facets , on the other , the man who sought to understand this reality . 
His understanding was necessarily subjective , but hope lay in his attempt to capture the manifold aspects of this reality . 
In fact , reality as such had no meaning : it is we who supply the meaning . 
The upshot of these tendencies of enlightened positivism was that the scientist avoided any metaphysical claims for his discoveries ( similarly , Vale2ry had rejected philosophy , metaphysics , any form of "absolute " in the normal sense ) : he sought a limited goal , continuity , by establishing relationships between phenomena . 
Henri Poincare2 probably played a decisive ro5le in causing Vale2ry to shift his attention " from "objects in themselves " to the " relationships existing between objects " , in which alone is any meaning to be found . " 
Thanks to his purely personal preoccupations ( his cult of consciousness , together with his reaction against love and poetry , { " les choses vagues " generally ) , thanks to the influence of Mallarme2 's formalism , Vale2ry was already by the early 1890s well along the road of " relations " as opposed to " objects in themselves " . 
Marked similarities of attitude can be discovered between the views of Poincare2 and Vale2ry on intellectual creation , both poetic and scientific . 
Vale2ry writes in 1919 : " 
{ Toutes choses se substituent , — ne serait-ce pas la de2finition des choses ? " 
and , in 1944 , looking back to his youth : 
The young Vale2ry is interested in the { " esprit universel " , da Vinci or Napoleon , whose supreme secret " 
{ est et ne peut e5tre que dans les relations qu'ils trouve3rent , — qu'ils furent force2s de trouver , — entre des choses do nt nous e2chappe la loi de continuite2 . " 
Vale2ry is drawn by the rigour and the universality of mathematics and of positivistic science generally towards the end of the nineteenth century . 
His da Vinci of the Introduction , his Monsieur Teste , are animated by a central belief in the continu ; his attitude before 1900 , and even long after that date , like that of Poincare2 , rests on the postulate that we can not yet explain all the relations between all phenomena , but that we shall be able to do so eventually . 
The da Vinci of the Introduction believes that our inability to see everything minutely and clearly is due merely to the infirmity of our senses ; such was Clerk Maxwell 's point of view , as exemplified by his imaginary demon who could perform various fantastic tasks beyond the powers of ordinary men . 
The function of the universal mind is to transform discontinu into continu , and there is a tacit assumption that if this process can be continued , all the elements which do not fit in with what we already know , all the discontinu , past , present or future , will be transformed into continu . 
Maxwell 's demon is essentially the same monster as Vale2ry 's da Vinci — a projection to the infinite of their positivistic belief in rapports and the possibility of explaining the relationships between everything . 
Maxwell 's demon and Vale2ry 's da Vinci ( or Teste ) are what Poincare2 , Maxwell and Vale2ry wanted to be , hoped to be — the universal mind . 
This Maxwell-Poincare2-Vale2ry relationship becomes all the more understandable if we remember that Poincare2 , naturally , was well acquainted with the work of Maxwell , and Vale2ry acquainted with the work of both Poincare2 and Maxwell . 
So we see how Vale2ry came to transfer his interests and hopes from poetic creation to this positivistic ideal of universal knowledge . 
With a youthful enthusiasm and impatience which he later acknowledged in the { Note et Digression of 1919 , he fathoms , as he thinks , " { le proble3me litte2raire " in the way we have seen , and more or less abandons poetic composition : Poe and Mallarme2 had , in a sense , led him in the same direction as Poincare2 . 
He is strong in his belief that there is { une sorte de contraste entre l'exercice de la litte2rature et la poursuite d'une certaine rigueur et d'une entie3re since2rite2 de la pense2e . " 
This is also where we get the stage-villain 's hiss of " Die he or Justice must " . 
God is much at his worst here , in his first appearance ; but he needs to be , to make the offer of the Son produce a dramatic change . 
I do not know what to make of his expressing the Calvinist doctrine that the elect are chosen by his will alone , which Milton had appeared to reject ( 185 ) ; it has a peculiar impact here , when God has not yet even secured the Fall of Adam and Eve . 
One might argue that he was in no mood to make jokes ; and besides , the effect here is not a sardonic mockery of Satan , which can be felt in the military joke readily enough , but a mysterious and deeply rooted sense of glory . 
A simple explanation may be put forward ; Milton felt that this was such a tricky bit to put over his audience , because the inherent contradictions were coming so very near the surface , that he needed with a secret delight to call on the whole of his power . 
This is almost what Shelley took to be his frame of mind ; and it is hard to accept , with the { De Doctrina before us , without talking about Milton 's Unconsciousness . 
But we may be sure that there is a mediating factor ; if he had been challenged about the passage , he would have said that he was following the Old Testament scrupulously , and allowing God to mock his foes . 
This has often been said about the jokes of Milton 's God , or at least about the one which ca n't be ignored because it is explained as a joke ( 5.720 ) ; and one can make a rough check from the Concordance at the end of a Bible . 
The only important case is from Psalm 2 ; here again we meet the ancient document in which the King of Zion is adopted as the Son of God : " 
{ 1Why do the heathen rage ... ? 
The kings of the earth set themselves , and the rulers take counsel together , against the Lord , and against his anointed ..... 
He that sitteth in the heavens shall laugh ; the Lord shall have them in derision . " 
This is echoed in Psalms 37.13 and 59.8 , and perhaps in Proverbs 1.26 , where Wisdom and not God mocks the worldly rather than a powerful aggressor ; but after trying to look under all the relevant words I do not find that the Concordance ever ascribes the sentiment to the Prophets . 
It was thus an ancient tradition but one treated with reserve , as Milton would understand . 
Naturally his intention in putting so much weight on it has been found especially hard to grasp . 
The views of M. Morand about the divine characters have been neglected and seem to me illuminating . 
In the same year as { De Comus A Satan he published a pamphlet in English , The Effects of his Political Life on John Milton , concerned to show that a certain worldly-mindedness entered Milton 's later poetry as a result of his rather sordid experience of government , politics , and propaganda . 
What chiefly stands out in this lively work , I think , is an accusation that Milton himself had smuggled into a later edition of { Eikon Basilike the prayer , derived from Sidney 's Arcadia , for which he then so resoundingly denounced King Charles in { Eikonoclastes ; we are given a shocking picture of an English expert getting the evidence of a Dutch researcher ignored by gentlemanly bluff . 
Mr Robert Graves used the main story in Wife to Mr Milton , but I had not realized that the evidence for it was so strong ; indeed , Mr Graves often seems too disgusted by Milton to be convincing — disagreeable in many ways he may have been , but surely not a physical coward . 
I do n't feel that the action is too bad for Milton ; he would think the divine purpose behind the Civil War justified propaganda tricks , and need not have thought this a particularly bad one . 
The King was dead , and the purpose of the cheat was merely to prevent the people from thinking him a martyr . 
He had n't written any of the book really , and Milton suspected that at the time , so it was only a matter of answering one cheat with another . 
Milton must in any case have been insincere in pretending to be shocked at the use of a prayer by Sidney , given in the story as that of a pagan , but so Christian in feeling as to be out of period ( it assumes that God may be sending us evil as a test or tonic for our characters , which even if to be found in Aeschylus or Marcus Aurelius is not standard for Arcadia ) . 
Milton might comfort himself with the reflection that he was n't even damaging the man 's character in the eyes of fit judges , only making use of a popular superstition — as Shelley expected on another occasion . 
However , M. Morand finds that this kind of activity brought about a Fallen condition , as one might say , in the mind of the poet , and such is what { De Comus A Satan examines throughout the later poetry . 
There is an assumption here that to do Government propaganda can only have a bad effect upon a poet 's mind , and I feel able to speak on the point as I was employed at such work myself in the Second World War , indeed once had the honour of being named in rebuttal by Fritzsche himself and called a curly-headed Jew . 
I was n't in on any of the splendid tricks , such as Milton is accused of , but the cooked-up argufying I have experienced . 
To work at it forces you to imagine all the time what the enemy will reply ; you are trying to get him into a corner . 
Such a training can not narrow a man 's understanding of other people 's opinions , though it may well narrow his own opinions . 
I should say that Milton 's experience of propaganda is what makes his later poetry so very dramatic ; that is , though he is a furious partisan , he can always imagine with all its force exactly what the reply of the opponent would be . 
As to his integrity , he was such an inconvenient propagandist that the Government deserve credit for having the nerve to appoint and retain him . 
He had already published the Divorce Pamphlets before he got the job ; well now , if you are setting out to be severe and revolutionary on the basis of literal acceptance of the Old Testament , the most embarrassing thing you can be confronted with is detailed evidence about the sexual habits of the patriarchs ; it is the one point where the plain man feels he can laugh . 
Milton always remained liable to defend his side by an argument which would strike his employers as damaging ; his style of attack is savagely whole-hearted , but his depth of historical knowledge and imaginative sympathy keep having unexpected effects . 
He was not at all likely to feel that he had forfeited his independence of mind by such work . 
M. Morand therefore strikes me as rather innocent in assuming that he was corrupted by it , but I warmly agree that it made his mind very political . 
Professor Wilson Knight has also remarked that Milton wrote a political allegory under the appearance of a religious poem , though he did not draw such drastic consequences from the epigram . 
On the Morand view , God is simply a dynastic ruler like those Milton had had to deal with ; Cromwell had wanted his son to inherit , no less than Charles . 
M. Morand does not seem to realize it , but the effect is to make Milton 's God much better . 
His intrigues and lies to bolster his power are now comparatively unselfish , being only meant to transfer it unimpaired to his Son , and above all he feels no malignity towards his victims . 
His method of impressing the loyalist angels will doom almost all mankind to misery , but he takes no pleasure in that ; it simply does not bother him . 
The hypocrisy which the jovial old ruffian feels to be required of him in public has not poisoned his own mind , as we realize when he permits himself his leering jokes . 
This does , I should say , correspond to the impression usually made by the poem on a person not brought up as a Christian , such as my Chinese and Japanese students . 
The next step is to regard the debate in Heaven , where the Son , but no angel , offers to die for man , as a political trick rigged up to impress the surviving angels ; the Son is free to remark ( 3.245 ) that he knows the Father wo n't let him stay dead , so that the incantationary repetition of the word death comes to seem blatantly artificial . 
( We find in the { De Doctrina Chapter 12 that Milton includes " under the head of death , in Scripture , all evils whatsoever " ... ) . 
Nobody is surprised at the absence of volunteers among the good angels , whereas Satan , during the parallel scene in Hell ( 2.470 ) , has to close the debate hurriedly for fear a less competent rebel put himself forward . 
Otherwise the two scenes are deliberately made alike , and the reason is simply that both are political : " 
{ Ce qui frappe , c'est le parallelisme des moyens employe2es , conseils , discours . 
Me5me souci de garder pour soi tout gloire. " ( p. 145 ) 
On reaching Paradise Regained , M. Morand is interested to learn how the Son grew up . 
In Paradise Lost he often seems half ashamed of the autocratic behaviour of his Father , because his role is to induce the subject angels to endure it ; but when he is alone on the earth-visit which has been arranged for him we find he has merely the cold calculating pride which we would expect from his training . 
However , we already find this trait , decides M. Morand , at the early public moment when he offers his Sacrifice ; he is unable to avoid presenting himself as solely interested in his own career ( p. 169 ) . 
As the Creation for which he was the instrument has already happened , he might at least speak as if he could tell a man apart from a cow , but he says that his Father 's grace visits " all his creatures " ( 3.230 ) . 
Satan , on the parallel occasion , was at least genuinely concerned to get the job done , whoever did it ; and M. Morand decides that the ringing repetition of ME in the speech of sacrifice of the Son is a little too grotesque , however perfectly in character . 
Milton " 
{ n'eu5t pas pense2 a3 ce que peut contenir de ridicule ce martellement du moi . 
De personnages extra-terrestres , le moins e2loigne2 de la modestie est encore Satan . 
" ( p. 171 ) 
This is at least a splendid reply to the argument that pride is the basic fault of all the characters who fall . 
The Morand line of argument can be taken an extra step , to argue that the Son too is being cheated by the Father ; and this excites a suspicion that there is something inadequate about it . 
He says nothing of the means of his death , and speaks as if he is going to remain on earth till the Last Day : 
Our chief impression here , surely , is not that he is too little interested in mankind but that he does not know what is going to happen , except for a triumph at which he can rejoice . 
If the Jews had not chosen to kill him , he would presumably have remained on earth till the Last Day , making history less bad than the poem describes it as being ; and what they will choose can be foreknown by the Father only . 
The Son expects to find no frown upon the face of God on Judgement Day , the { Dies Irae itself , so we can hardly doubt that he expects things to turn out better than they do . 
His prophecy appears to be a continuous narrative : " not long lie ... rise victorious ... then ... then " , as if he will lead the blessed to Heaven very soon after the Resurrection . 
Among human speakers " lastly die " is a natural way to express pathos , though a tautology ; but a meaning which would make it a correct description of the career of the Son is hard to invent . 
The wife , in this story , was dead and buried and yet her husband found her " { in magno feminarum cetu de nocte " and snatched her away and brought her back home to human life once more . 
Whether this old Breton tale had already been contaminated with the classical legend of Orpheus and Eurydice we can not say , but the strange oscillation between contrary concepts is characteristic of Orfeo as well . 
The motive for abduction in fairy tales is usually love , as , for example , in Guingamor , Lanval and Graelent ; but Heurodis was not snatched away for love ; the fairy king had his own queen ; besides , to have introduced the love motive in this fashion would have cut across the theme of marital love and loyalty upon which the tale of Orpheus and Eurydice hinges . 
If the king of Fairy is not to be entirely identified with the king of the Dead , what reason can be offered for his behaviour ? 
It is at this point , when Orfeo saw his wife lying under the { 1ympe tre in the castle courtyard , that the interlacing of the classical and Celtic stories appears at its most intricate . 
Heurodis was abducted in the " { 124e comessing of May " . 
In a vague , imperceptible way , the fairy king , who was also the god of an underworld , since Orfeo had to go " { 1In at a roche " to reach him , seems here to have taken on some of the attributes of Dis , who stole Proserpina away as she was gathering spring flowers in the meadow ; and Heurodis also seems to take the place of Proserpina , for Eurydice was not abducted , but killed by the poisonous fangs of a snake . 
In classical legend , Dis or Pluto was the king of the underworld and the dead ; but , according to Caesar , the Celts also had a god of the underworld similar to Dis , from whom all the Gauls claimed to be descended : "{ Galli se omnes ab Dite patre prognatos praedicant " , and in later fairy lore he or the classical Dis or both became identified with the king of Fairy , if Chaucer is to be believed : " Pluto that is the kyng of fairye " ( Merchant 's Tale , 983 ) . 
Again , in the classical legend , the two attributes of Dis fell together ; he was not only the power of winter in seasonal myth , he was also the god of Hades , the ruler in the kingdom of the Dead . 
In Celtic legend also , there existed a seasonal myth similar to that of Dis and Proserpina ; it took the form of an abduction story , closely resembling the abduction of Heurodis in some of the details to which the classical versions offer no similarity . 
Traces of this myth are to be found in Culhwch and Olwen and the { Vita Gildae , said to have been written by Caradoc of Llancarvon : " 
( a ) Creiddylad daughter of Lludd Silver-hand ( the maiden of most majesty that was ever in the Island of Britain and its three adjacent islands ) . 
And for her Gwythyr son of Greidawl and Gwyn son of Nudd fight for ever each May-calends till the day of doom ... 
Creiddylad daughter of Lludd Silver-hand went with Gwythyr son of Greidawl ; and before he had slept with her there came Gwyn son of Nudd and carried her off by force . 
Gwythyr son of Greidawl gathered a host and he came to fight with Gwyn son of Nudd . 
And Gwyn prevailed ... 
Arthur heard tell of this and he came into the North and summoned to him Gwyn son of Nudd and set free his noblemen from his prison and peace was made between Gwyn son of Nudd and Gwythyr son of Greidawl . 
This is the peace that was made : the maiden should remain in her father 's house unmolested by either side , and there should be battle between Gwyn and Gwythyr each May-calends for ever and ever , from that day till doomsday ; and the one of them that should be victor on doomsday , let him have the maiden . " 
The details worth noting in relation to Orfeo are : the abduction had reference to the May-calends or " { 124e comessing of May " in ( a ) and there is an implication of seasonal cycle in " { per unius anni circulum " in ( b ) ; the husband was a king and the stolen wife a queen in ( b ) ; the ravisher was also a king in both ( a ) and ( b ) , but whereas in Culhwch and Olwen he was undoubtedly the king of the underworld , Gwyn ap Nudd , king of Annwn , Melvas was made king of the " summer region " or Somerset , since it was to his castle in Glastonbury that he carried the queen . 
Possibly the roles of Arthur and Melvas have been exchanged , for Gwythyr ap Greidawl seems to be equated with the sun or summer , if the elements in his name are any guide , Gwythyr , Victor and Greid- , Old Irish ? 22greid , to scorch . 
Melvas ought to be the equivalent of Gwyn ap Nudd . 
However , as the version in the { Vita Gildae was obviously altered to boost Glastonbury abbey and Gildas , these differences may be bits of local colour . 
Finally , in both ( a ) and ( b ) , an attempt was made to recapture the woman with the help of armed knights , and in ( b ) Guinevere was restored to her husband just as Heurodis was given back to Orfeo . 
Why Orfeo was a " king " might now appear to be more reasonable ; and the fact that he was successful in bringing his wife safely out of Fairyland becomes something more than a mere romantic and neo-fairy ending to an old , tragic story . 
Yet , to understand Orfeo completely , we must turn again to the classical tale of Orpheus and Eurydice , for it is this alone which can explain why Heurodis was abducted for no apparent reason . 
Eurydice , like the dead mother in the Breton tale , { Filii Mortue , was the beloved wife who died ; Heurodis , her nominal counterpart , was at the same time semi-Proserpina , semi-Creiddylad-Guinevere , and was abducted ; the reason for her abduction is omitted because , as Eurydice , she should have died , and , as Proserpina-Creiddylad-Guinevere , she should have been stolen for love ; either reason is incompatible with the theme of Orfeo . 
When Orfeo arrived in the fairy underworld , he saw his queen , not in the palace among the ladies with whom he had met her in the forest , but in the outer courtyard , among a collection of sick , mad , crippled and headless people , who were lying there exactly as they had been on earth when they had been snatched away in their noontide sleep . 
In the forest she had been " alive " ; she had recognized him and had wept ; yet , when he followed the fairy company and came to find her in Fairyland , she is pictured as being in her first condition , not as she was the day she was abducted , for then she was not asleep , but as she was when the fairy king first appeared to her — asleep under the { 1ympe tre . 
The poet says that all the people who were lying there , and that includes Heurodis , " { 124ou26t dede and nare nou26t " . 
Even when full allowance has been made for the marvellous things which could happen in Fairyland , it is difficult to believe that a person without a head was not " dead " in the first instance . 
And are we to understand that these headless , armless , burnt and choked people , to say nothing of the mothers in childbed , also " arose " as Heurodis evidently did , and took part in the dancing and hunting in the forest ? 
Analysis of this kind emphasizes the slight inconsistencies in the narrative and serves to show up the seams in the joining of the Celtic and classical tales . 
At the same time , we can scour Georgics , 4 and Metamorphoses , 10 in vain for any hint or detail which might help to throw light on this odd picture . 
The bodiless phantoms that came in their thousands from the depths of Erebus at the sound of Orpheus 's lyre ( Georgics , 4 , 475-7 ) and the bloodless spirits who wept at the strain ( Metamorphoses , 10 , 41 ) can not honestly be considered as in any way comparable to the folk " { 1liggeand wi24in 24e wal " , for Orfeo had not yet entered the king 's palace nor had he touched the strings of his harp nor did these people outside come in later on to listen to him . 
If it be remembered that not only the legend of Orpheus , but the whole of Virgil 's work was widely known in the Middle Ages , a clue may be found in another Virgilian description of the classical underworld , the one in Aeneid , Bk. 6 . 
Aeneas , when he prayed to be allowed to visit his father 's shade in Hades , made use of the story of Orpheus and Eurydice to strengthen his petition ; if Orpheus could call up his wife 's shade in Erebus , could not he , Aeneas , also a descendant of the gods , make the same journey ? 
He was allowed to do so and when he reached the entrance to Hades he is pictured as approaching it across the vestibulum or forecourt , with the limen and fores , the main door , at the far side ; that is , Virgil has imagined the entrance to Hades in contemporary terms , those of the Roman house , just as the poet of Orfeo has visualized the entrance to the fairy underworld in terms of a medieval castle : 
What Aeneas saw in the forecourt of Orcus was very similar to that which Orfeo saw in the courtyard of the fairy king 's castle ; all kinds of horrors had "made their beds " there , but where Virgil has enumerated abstractions and the customary grisly inhabitants of Tartarus , the author of Orfeo has presented a picture of examples , an oddly assorted gathering of people , most of whom would have been found , in the Middle Ages , in Purgatory , because they had died suddenly and unshriven — the burnt , the drowned , women who had died mad in labour , soldiers killed in battle and those who , like Hamlet 's father , had been taken , " grossly , full of bread " and had died choking . 
None of them has a right to a home in Fairyland , at least , not according to the ancient tradition concerning that place ; all who go there are either stolen or lured from earth on account of their beauty or desirability . 
That Heurodis should be there is intelligible , but the rest seem to belong to the Christian otherworld of punishment , which , in the Middle Ages , owed many of its features to the pagan conception of Tartarus ; both were places in which the wicked or the unassoiled found themselves after death and every traveller who had the temerity to visit them , were he an Orpheus , an Aeneas or a Knight Owen had his sight seared with visions of human agony . 
Orpheus descended into Hades , Orfeo tunnelled into Fairyland ; the two stories which are so successfully merged in other parts of Orfeo are just here a little divergent , or perhaps it is that the classical element is for the moment uppermost and has , in its detail , been partly overlaid with contemporary notions . 
In any case , the similarity between the settings is very close . 
Another interesting point of comparison lies in the linking of sleep with the idea of Death 's kingdom . 
Virgil has used the word sopor , which has an intensive force , implying a torpor akin to the sleep of death , " { consanguineus Leti Sopor " . 
Sleep , in classical legend , was associated with Hades . 
According to Hesiod ( Theogony , 1 , 211 ff . ) , 
Erebus and Night were the children of Chaos ; and Night , the mother of Doom , Fate and Death , also gave birth to Sleep and the tribe of Dreams and " painful Woe " . 
Cicero echoes this in his { De Natura Deorum , 3 , 17 : " Amor Dolus Metus ... 
Mors Tenebrae Miseria ... 
Somnia quos omnes Erebo et Nocte natos ferunt " . 
In Orfeo the same idea is present , for , in the fairy otherworld , which is also an underworld , the miseries , exemplified by the folk "{ 1liggeand wi24in 24e wal " , are definitely related to sleep : " { 1ri24t as 24ai slepe her vndertides " . 
Next , there is the tree , the great Elm of Dreams . 
No true parallel to it has yet been found in classical legend . 
For Hardy , then , Correggio is the artist of yearning , as , indeed , he himself tells us in A Pair of Blue Eyes in the passage describing the appearance of Elfride Swancourt , where he extends his method and sees his heroine through the eyes of three painters , Raphael , Rubens , and Correggio , in turn : " 
Elfride had as her own the thoughtfulness which appears in the Madonna della Sedia , without its rapture : the warmth and spirit of the type of woman 's feature most common to the beauties — mortal and immortal — of Rubens , without their insistent fleshiness . 
The characteristic expression of the female faces of Correggio — that of the yearning human thoughts that lie too deep for tears — was hers sometimes , but seldom under ordinary conditions . " 
This is the most elaborate of all Hardy 's experiments in what might be called pictorial definition . 
It will be observed that in all the examples that I have given he seizes upon some quality that is peculiarly characteristic of the artist in question , so that the reader at once receives an impression of a general facial type before being invited to consider its particular manifestation . 
With quite subsidiary characters , however , a mere impression is sufficient , and no qualifications are added : thus the woman who opens the lodge gate at Endelstow , in A Pair of Blue Eyes , is simply described as having " a double chin and thick neck , like the Queen Anne portrait by Dahl " — and although the incident has no importance in the story there is point in the choice of a painter who seems to have had no qualms about stressing the plainness and stodginess of his sitters . 
Even the nationality of the artist alluded to contributes to our impression of the character whom Hardy is presenting . 
If Cytherea Graye could have been painted by Greuze , or Lucetta Templeman by Titian , Liddy Smallbury , Bathsheba 's servant in Far From the Madding Crowd , suggests rather the healthy , well-scrubbed girls of Dutch art : " 
The beauty her features might have lacked in form was amply made up for by perfection of hue , which at this winter-time was the softened ruddiness on a surface of high rotundity that we meet with in a Terburg or a Gerard Douw ; " 
while Sue Bridehead , with her dark beauty , conjures up in Jude 's mind a recollection of "the girls he had seen in engravings from paintings of the Spanish School " . 
An effective use of this device of pictorial allusion to suggest the attitude of a character at a particular moment is to be found in the glimpse of Mr. Penny at work at his trade , in Under the Greenwood Tree . 
Mr. Penny is a shoemaker , and his house looks out on to the main road , " Mr. Penny himself being invariably seen working inside like a framed portrait of a shoemaker by some modern Moroni " . 
Although this is not a reference to an actual picture by Moroni ( and no painting of a shoemaker by Moroni exists ) , the effect is still precise , for we know what such a picture by a nineteenth-century Moroni would look like . 
Moroni , we know , specialized in single portraits in which he emphasized his sitter 's trade or calling , as in the " Portrait of a Tailor " in the National Gallery , which was probably the picture by which Hardy knew him best ; and it was clearly Moroni 's practice of putting a frame , as it were , around a single figure , and of isolating him in the context of his daily work , that Hardy found interesting . 
Many of the artists who fascinated Hardy were not particularly fashionable in his own day ; and names of some of them would have been known to a mere handful of his readers . 
A curious example of his tastes is provided by his two allusions , first in The Return of the Native , and then in Tess of the D'Urbervilles , to Sallaert and Van Alsloot , artists in whom only recently much interest has been taken , and then mainly by specialists . 
Both worked in Brussels in the early years of the seventeenth century , devoting themselves chiefly to a class of processional scene crowded with tiny figures . 
Among the best known of these are the two pictures by Van Alsloot in the Victoria and Albert Museum representing the annual procession in Brussels known as the Ommeganck , which was held under the patronage of the church of Notre Dame de Sablon , a church founded by the Guild of Crossbowmen . 
The object of the procession was to commemorate the translation to this church , from Antwerp , of a miraculous image of the Virgin , and it was preceded by the ceremony of the Shooting of the Popinjay ( a wooden representation of a parrot fixed to the top of a steeple ) . 
Van Alsloot 's pictures record the Ommeganck of 1615 , when the Infanta Isabella , the consort of the Archduke Albert , had succeeded in shooting the popinjay at the first attempt . 
The Ommeganck was an extremely colourful affair , dominated as it was by the triumphal cars carrying elaborate enactments of tableaux of such scenes as the Nativity and St. George 's fight with the Dragon . 
And dotted all over Van Alsloot 's representations of it are the quaint little figures that seem above all else to have caught Hardy 's fancy . 
Hardy first alludes to them in The Return of the Native : " 
What was the great world to Mrs. Yeobright ? 
A multitude whose tendencies could be perceived , though not its essences . 
Communities were seen by her as from a distance ; she saw them as we see the throngs which cover the canvases of Sallaert , Van Alsloot , and others of that school — vast masses of beings , jostling , zigzagging , and processioning in definite directions , but whose features are indistinguishable by the very comprehensiveness of the view . " 
In Tess of the D'Urbervilles , published thirteen years later , it is a large herd of cows that brings these processional pictures before Hardy 's eyes : " 
The green lea was speckled as thickly with them as a canvas by Van Alsloot or Sallaert with burghers . 
The ripe hue of the red and dun kine absorbed the evening sunlight , which the white-coated animals returned to the eye in rays almost as dazzling . " 
It may be added that this passage has a further interest , for it suggests that Hardy was aware of the colour-theories of men like Rood and Chevreul , which were to have some influence on Impressionism . 
We may compare a similar but much earlier observation upon the nature of colour in Far From the Madding Crowd ( published in 1873 ) : " We learn that it is not the rays which bodies absorb , but those which they reject , that give them the colours they are known by . " 
If Hardy could scarcely have assumed in the generality of his readers any knowledge of Sallaert or Van Alsloot , he could presumably have counted upon a much wider familiarity with the white horses which almost invariably appear in the landscapes of Wouwermans , always a popular artist in England , and which are alluded to in the scene in The Woodlanders where Grace Melbury watches her husband , Fitzpiers , who is being unfaithful to her , riding away on a white horse named Darling to his assignation with Mrs. Charmond : " 
He kept along the edge of this high , uninclosed country , and the sky behind him being deep violet he could still see white Darling in relief upon it — a mere speck now — a Wouwermans eccentricity reduced to microscopic dimensions . 
Upon this high ground he gradually disappeared . " 
Equally effective is the description , in the same novel , of a freshly pressed tablecloth — " reticulated with folds as in Flemish Last Suppers " — or of the clear outlines of figures thrown into relief by the light of a bonfire , in The Return of the Native : " 
The brilliant lights and sooty shades which struggled upon the skin and clothes of the persons standing round caused their lineaments and general contours to be drawn with Dureresque vigour and dash . " 
And , if poets and novelists have strained themselves to say something original about the moon , only Hardy could have likened it , as he does in Tess , to " the outworn gold-leaf halo of some worm-eaten Tuscan saint " . 
As Hardy develops as a writer it is interesting to observe the growing maturation of this device of pictorial allusion , which in his hands becomes a unique skill . 
In the later novels he is able to employ it in ways that go far beyond a purely descriptive intention . 
Towards the end of Tess , he wishes to suggest the psychological change which has been brought about in Angel Clare by his wife 's confession , and he puts it thus : " 
The picture of life had changed for him . 
Before this time he had known it but speculatively ; now he thought he knew it as a practical man ; though perhaps he did not , even yet . 
Nevertheless humanity stood before him no longer in the pensive sweetness of Italian art , but in the staring and ghastly attitudes of a Wiertz Museum , and with the leer of a study by Van Beers . " 
Although the Poe-like horrifics of Wiertz are still remembered and have won a small place in the history of Romanticism , Van Beers , who seems to have deliberately invited comparison with him , has now been completely forgotten . 
In Hardy 's day , however , he enjoyed something of a { 6succe3s de scandale with periodic exhibitions in Bond Street . 
One of these , held in November 1886 , was condemned by a critic writing in The Magazine of Art as appealing " to a class of sensations which have but little to do with those which art ... should aim at evoking " . 
Even " as a purveyor of horrors " the artist was unsuccessful , for he entirely lacked "the vastness of conception , the measure of sincerity which gave to the art — if we must so designate it — of a Wiertz , resulting , as it did , from the real hallucinations of a diseased brain , a certain interest and a { 6raison d'e5tre " . 
Towards the end of Tess , Clare returns at length from his wanderings , and we are given a striking picture of the outward change in him which has accompanied the inner : " 
You could see the skeleton behind the man , and almost the ghost behind the skeleton . 
He matched Crivelli 's dead Christus . 
His sunken eye-pits were of morbid hue , and the light in his eyes had waned . 
The angular hollows and lines of his aged ancestors had succeeded to their reign in his face twenty years before their time . " 
The painting to which Hardy refers is in the National Gallery . 
Here Hardy 's imagination is stimulated to enlarge upon the allusion and to paint a word-picture of great power . 
Crivelli was one of his favourite painters , and it is easy to see why the severity of Crivelli 's types — the farthest remove , as they are , from the pretty — particularly appealed to him . 
As Hardy masters this technique he employs it more and more for dramatic effect . 
Tess again provides a fine example , in that melancholy scene at the end of the book when Angel Clare and 'Liza-Lu walk slowly up to the summit of the West Hill above Wintoncester to watch for the prison flag that will tell them that Tess 's execution has been carried out : " They moved on hand in hand , and never spoke a word , the drooping of their heads being that of Giotto 's "Two Apostles " . " 
The picture to which Hardy here refers is a fragment of a fresco purchased for the National Gallery in 1856 . 
It comes from a large decoration in the Carmine in Florence which was at that time believed to be by Giotto but which has since been reattributed to Spinello Aretino . 
The two heads originally formed part of a " Burial of St. John the Baptist " . 
Even more touching , perhaps , is the long , beautiful description , earlier in the same novel , of the labours of Tess and Marion in the fields , where again the image of two bowed heads is evoked by a simple and telling pictorial allusion : " The pensive character which the curtained hood lent to their bent heads would have reminded the observer of some early Italian conception of the two Marys . " 
While the technical quality of the tapestry is high , the style is rather coarse and there is an element of doubt as to its origin in the imperial workshops . 
The second object which may refer to an imperial triumph is the ivory casket now in the Cathedral Treasury at Troyes . 
On the sides the casket is remarkable for hunting scenes of considerable power and for phoenixes in the Chinese style ( Fig. 125 ) ; on the lid two mounted emperors placed symmetrically on either side of a town are offered a city-crown by a woman emerging from the gate followed by townsfolk ( Fig. 126 ) . 
It has been suggested that this last scene is related to the Triumph of Basil 2 but , although undoubtedly portraying a victorious emperor , judging from the other scenes on the casket , it seems not to be connected with any particular event . 
A date , however , in the eleventh century is possible . 
More textiles may be assigned to the reign of Basil 2 . 
Several fragments of silk woven in compound twill with representations of large stylized lions at Berlin , Du " sseldorf , Krefeld and Cologne ( Fig. 127 ) bear inscriptions referring to the Emperors Constantine 8 and Basil 2 , the sovereigns who love Christ . 
Constantine 8 , younger brother of Basil 2 , idle and pleasure-loving like his father Romanus 2 , ruled jointly with the Bulgaroctonos between 976 and 1025 . 
Earlier versions of this type of silk , however , were known at one time . 
In the Cathedral at Auxerre under Bishop St. Gaudry ( 918-933 ) were two fragments of a Lion silk bearing the inscription " in the reign of Leo , the sovereign who loves Christ " , which must refer to the Emperor Leo 6 ( 886-912 ) . 
At Siegburg another great Lion silk , now destroyed , bore an inscription referring to Romanus 1 Lecapenus and his son Christopher , whose joint reign lasted from 921 to 923 . 
A number of reduced , coarser versions of these Lion silks have survived but without inscriptions and in this case it is tempting to make a distinction between work done in the imperial factory and work done in the city . 
The magnificent Elephant silk ( Fig. 128 ) , introduced into the tomb of Charlemagne at Aachen by the Emperor Otto 3 during the " recognition " of the year 1000 , must also date from the early part of the reign of Basil 2 and Constantine 8 , although the Greek inscription refers only to the fact that it was made " under Michael , kitonite and eidikos , and Peter , archon of the Zeuxippos " . 
In addition , two Eagle silks may claim to have come from the imperial workshops under these emperors . 
The Chasuble of St. Albuin ( 975-1006 ) in the Cathedral Treasury at Brixen is made up from a silk compound twill woven with a pattern of large stylized eagles in dark green on a rose-purple ground with large dark green rosettes in the intervening spaces — eyes , beaks , claws , and the ring in the beak are yellow ( Fig. 129 ) . 
The Shroud of St. Germain in the Church of Saint-Euse3be at Auxerre bears an identical pattern but in colours of dark blue , dark blue-green , and yellow , and the quality is finer than the Brixen silk . 
Unfortunately neither of these superb silks bears an inscription . 
With the possible exception of the last two silks , which differ considerably from Islamic Eagle silks that have survived , it may be said that Byzantine silk production of this time was heavily indebted to Persian and Abbasid models . 
The Elephant silk is clearly based on a Buwaiyid model for its subject matter and particularly for the stylized tree and its foliage behind the elephant , though the border of the medallion contains more specifically Byzantine ornament . 
It may be that the introduction of the inscriptions referring to the emperors and used as part of the design is an adoption of Islamic tiraz protocol . 
Later in the century , when a series of particularly subtle silks , known for convenience as " incised twills " because the pattern in a silk of one colour appears to be engraved , are known in several sequences , the problem of deciding which were made in the Byzantine world and which were made under Islam , or by Islamic craftsmen in the Byzantine Empire , becomes acute . 
Some bear fine Kufic inscriptions with the name of an Amir of Diyarbakr in northern Syria dating about 1025 , others bear polite wishes in Kufic , some have no inscriptions at all , and there is one remarkable silk , with the portrait of a Byzantine emperor , found in the tomb of St. Ulrich of Augsburg ( d. 955 ) , which seems to be without question of Greek manufacture . 
The textiles found in the tomb of Pope Clement 2 ( d. 1047 ) at Bamberg , of which one is closely related to a silk from the tomb of King Edward the Confessor ( d. 1066 ) , present similar problems . 
There can be no doubt , however , that the imperial Byzantine silks have a power and a dignity , a feeling for design and texture , seldom rivalled in the history of textiles . 
There is little wonder that Bishop Liutprand of Cremona was tempted on his return from his unsatisfactory mission to the Emperor Nicephorus Phocas to smuggle imperial silks through the Byzantine customs . 
The mosaic panel in the South Gallery of Agia Sophia at Constantinople with the portraits of the Emperor Constantine 9 Monomachos and the Empress Zoe standing on either side of the seated Christ presents certain problems ( Fig. 130 ) . 
It continues the tradition of ex-voto mosaic panels representing the Augusti bearing gifts familiar in San Vitale at Ravenna in the sixth century and panels of a less exalted nature in the Church of St. Demetrius at Salonika in the seventh century . 
But in this panel all three heads and the inscriptions are substitutions . 
It is probable that the original mosaic was executed between 1028 and 1034 and it represented the Empress Zoe ( 1028-1050 ) , daughter of Constantine 8 , and her first husband Romanus 3 Argyrus ( 1028-1034 ) . 
There is no documentary evidence , incidentally , that the Empress Zoe was interested in patronizing large-scale works of art though she had a fancy for expensive trinkets and chemical experiments , but Romanus 3 instigated repairs to Agia Sophia and to the Church of St. Mary at Blachernae . 
His name would seem to fit the space allowed for the inscription better than that of Michael his successor and , since he was unpopular , it was more likely to be excised than that of Michael 4 the Paphlagonian ( 1034-1041 ) , who was well liked and the uncle of Michael 5 Kalaphates ( 1041-1042 ) . 
Zoe , who was not fitted by temperament to govern , according to Michael Psellus , retained the affection of the people in spite of her eccentricities . 
She had lived in retirement during the later years of Michael 4 's rule and had been persuaded to adopt his nephew as Emperor . 
Michael 5 , however , induced the Senate to banish Zoe as a nun to the island of Prinkipo . 
It was presumably at this time that the mosaic panel was defaced . 
Michael 5 's triumph was brief . 
The people were not prepared to see a daughter born to the purple of the Macedonian house treated with such contumely and they rioted . 
The Empress was brought back from exile . 
She and her sister Theodora , who had long been a nun in the convent of the Petrion by the Phanar , were reinstated in the purple . 
Michael 5 was persuaded to leave the altar in the Church of St. John of Studius where he had taken refuge , and was blinded in a street of the city . 
The two sisters , who had little love for one another , ruled for a few months as co-Empresses and coins were struck with their images ( Fig. 131 ) but later in the year of 1042 Zoe at an advanced age took another husband , Constantine Monomachos ( 1042-1055 ) , and Theodora was kept in the background of affairs . 
About this time the imperial portraits were restored . 
It is still far from clear , however , why it was necessary to restore the head of Christ . 
As opposed to the figures of Constantine and Justinian on the tympanum of Basil 2 ( Fig. 123 ) , which are seen in depth and modelled with some solidity , the bodies of the Augusti are little more than lay figures of imperial power . 
In contrast with the Virgin in the south vestibule the drapery of Christ has become considerably more mannered with its cross-currents of folds and the face shows a marked difference of approach , more sketchy and schematic . 
But in view of the different styles current in Constantinople it would be rash to press these contrasts too far . 
The figures of Constantine and Justinian were probably copied from earlier imperial portraits , which would give them the definition that the Macedonian Augusti lack . 
The portrayal of the reigning Augusti behind a flat curtain of patterned dress and regalia establishes a convention of official portraiture which continued to the end . 
The heads in official portraiture , on the other hand , are presented in terms which presuppose recognition . 
While the restored heads in the Zoe panel have become considerably more conceptualized than all three heads in the tympanum of Basil 2 — the accentuation of the cheek-bones by circular devices , the broadening of the planes of the face — the Empress and her consort are rendered as plausible historic statements . 
Constantine 9 , brought back from exile in Mytilene to marry an aged Empress preoccupied with religion and making scents , flaunted a beautiful Caucasian mistress at public ceremonies , but for all his love of entertainment , he was by no means unaware of the responsibilities of his position . 
He built the church and convent of St. George of the Manganes and founded the Nea Moni on Chios after the miraculous discovery of an icon by shepherds on Mount Privation . 
It is probable that mosaicists were sent from the capital to decorate the church on Chios . 
Fragments of their work have survived including a Virgin Orans in the apse , a few angels and saints , and fourteen scenes ranging from the Annunciation to the Pentecost . 
But the sombre , forceful style of these mosaics has unfortunately no counterpart in the capital and contrasts strangely with the slightly inconclusive images of imperial power in Agia Sophia . 
The style at the Nea Moni does not resemble the work done at Osios Loukas in Phocis about the middle of the eleventh century , which seems to be the work of a provincial school , nor the uneven quality of the work done in Agia Sophia at Kiev about 1045 with the help of mosaicists sent from Constantinople . 
The style , moreover , contrasts with that of the mosaics executed in the narthex of the Church of the Dormition at Nicaea , now destroyed , under the patronage of the patrician Nicephorus after the earthquake of 1065 . 
This decoration consisted of a double cross against a ground of stars within a roundel in the centre of the vault surrounded by medallions containing the busts of Christ Pantocrator , St. John the Baptist , St. Joachim and St. Anne ; in the lunette over the door there was a bust of the Virgin Orans ; in the four corners of the vault there were the four Evangelists . 
The meaning of this iconographical programme is far from clear and the absence of comparable programmes in the capital handicaps speculation . 
Stylistically the forms are rather broad and heavy ; the face of the Virgin Orans in the lunette over the door seems to be a development of the Virgin and Child over the door in the south vestibule of Agia Sophia but the work , as far as one may judge from the the photographs , seems coarser . 
In the portrayal of the Evangelists the bodies tend to disintegrate under the pattern of folds ; in St. Matthew , for example , the relationship of the upper part of the body to the lower is uneasy and the right thigh seems unwarrantably stressed — this figure executed during the reign of Constantine 10 Dukas ( 1059-1067 ) looks forward to late Comnene art ; St. Luke , on the other hand , depends almost directly from the works executed in the palace scriptoria ; in all four figures , the tendency of the drapery to create its own pattern counter to the form it covers echoes one of the main features of middle Byzantine style . 
RITUAL ART by CECIL ROTH 
A CHARACTERISTIC recommendation of the Talmud justifies and proves the antiquity of the ritual art of the Jewish synagogue and home . 
Rabbis make this comment about the Biblical verse " This is my God , and I will glorify [ lit. " adorn " ] him " ( Exodus , 15 , 2 ) : " Adorn thyself before Him in the performance of the commandments . 
Make before him a goodly succah , and goodly lulab , and a goodly shophar , and goodly fringes for your garments , and a goodly { Sepher Torah ... and bind it up with goodly wrappings . " 
Elsewhere , we learn of the adornments hung in the succah , and of the gold fillets used to bind up the lulab , and more than once of the wrappings for the sacred books . 
But there is no evidence that at this time any of these appurtenances had any uniformity or were expressly made for a specific purpose . 
With the exception of a few eight-burnered clay lamps presumably intended for use on the feast of Hanukkah , there is barely any evidence of specifically-made Jewish ritual adornments , other than those of the Temple , until the close of the first millenium . 
It must have been about this period that their manufacture began , for not long after we read of such objects as commonplace . 
Thus in an inventory of the property of the Palestinian Synagogue in Fostat ( Cairo ) , drawn up in 1186-87 , we find scheduled " Two Torah-crowns made out of silver , and three pairs of finials ( rimmonim ) made of silver , and twenty-two Torah-covers made of silk , some of them brocaded with gold , " and so on . 
Presumably , domestic ritual objects began to be made at much the same time . 
The name of Rabbi Meir of Rothenburg , the great German Jewish ritual art as we know it now had begun to frequently in connection with our literary evidences , and it may be assumed that by his day Jewish ritual art as we know it now had begun to assume its form . 
Little or nothing of this date , however , has been preserved to the present time , our evidence being indirect . 
The primary reason for this was presumably the vicissitudes of Jewish life . 
Synagogues everywhere were sacked , burned , and pillaged ; communities were driven into exile , expressly forbidden to take with them anything made of precious material : synagogues could sell their sacred treasures in order to ransom prisoners or succor refugees . 
As a result of all these and similar recurrent crises , as well as normal wear and the natural tendency ( from the antiquary 's point of view disastrous ) to replace the old by the new , Jewish ritual art of the medieval period has disappeared almost entirely . 
Hardly more than a handful of specimens anterior to the sixteenth century are now traceable . 
This generalization , to be sure , may perhaps need qualification in due course . 
If careful and expert inspection could be made of the property of ancient and even modern synagogues , especially in the East , with the same care as has been devoted to the study of ancient manuscripts , it is not improbable that some memorable ritual objects of great antiquity might even now be discovered . 
However that may be , the fact remains that the objects of Jewish ritual art which are now extant are virtually all of the post-medieval period . 
After a trickle of the sixteenth century , there is a great mass of material of the seventeenth and eighteenth , some of it very fine . 
Perhaps an unduly large proportion is German in origin , reflecting the religious enthusiasm , economic well-being and good taste of the new groupings in those countries , especially the newly-arisen class of Court Jews . 
It may be remarked that here domestic religious adornments figure in great abundance side by side with those intended for the synagogue . 
The taste and charm of some of the objects then manufactured in Poland and Eastern Europe belies the general impression of the economic misery and unaesthetic outlook of the Jewish communities in this area . 
On the whole , these objects reflect the tastes and fashions of the countries and periods in which they were manufactured . 
To be sure , in some cases the craftsmen were Jews . 
Gold and silver-smithery was one of the characteristic Jewish occupations in most countries . 
It is believed that from early times until the modern era , Jews in the Eastern countries were responsible for the manufacture of most of these objects . 
But in Western Europe , with the growing tendency to exclude the Jews from handicrafts after the period of the Crusades , this was different . 
Moreover , in remote communities where a Jewish craftsman might not be available , it was necessary to have recourse to the local silversmiths . 
However that may be , it is certain that much Jewish ritual metal-work is of non-Jewish manufacture ; in England , Germany and Holland it often bears the mark of the Gentile manufacturers , sometimes well-known masters of their craft — e.g. the prolific Matthews Wolff ( Augusburg , c. 1700 ) , Jeremiah Zobel ( Frankfurt am Main , c. 1700 ) , and John Ruslen , Frederick Kandler , Hester Bateman and William Grundy ( London , 18th century ) . 
We know of at least two medieval contracts for the manufacture of silver ornaments for the Torah , made between Gentile craftsmen and the leaders of the local Jewish communities — one from Arles ( 1439 ) , the other from Avignon ( 1477 ) . 
In the former instance , silversmith Robin Tissard undertook that the commission was to be executed in a room placed at his disposal in the house of one of the local Jews , and that no work should be done on Sabbaths or Jewish holy days . 
On the other hand , besides the vast amount of anonymous work of this type which falls into this category , a good deal was carried out by ascertainable Jewish craftsmen of some reputation . 
We know , for example , of the London silversmith Abraham d'Oliviera ( d. 1750 ) , who has been mentioned elsewhere in this work in connection with his work as an artist-engraver , who designed and executed a good deal of ritual silver in London in the first half of the eighteenth century ; and his younger contemporary Myer Myers ( 1723-94 ) , first President of the Silversmith 's Guild of New York , who carried out some distinguished work for synagogues ( as well as churches ) in America . 
Certain decorative features became very common in , and almost characteristic of , the Jewish ritual art of the post-medieval period . 
In St. Peter 's in Rome there is a spirally fluted bronze column , the { colonna santa , late Classical in origin ; it is legendary said to have been brought from the Temple in Jerusalem , where Jesus leaned against it while disputing with the rabbis . 
From the Renaissance period , two twisted columns , apparently copied from the { colonna santa , and inevitably identified with Jakhin and Boaz of Kings 7 , 21 , began to figure as a typical feature on the engraved title-pages of Hebrew books ( see fig. 175 ) . 
It was from there that this feature was copied on various objects of European Jewish ritual art until the end of the eighteenth century . 
Other symbols which are commonly found include the lion , representing the Lion of the Tribe of Judah ( Genesis 49 , 9 ) which , as we have seen , was one of the most common symbols found in Jewish art from classical antiquity . 
This illustrated also the Rabbinic dictum ( Ethics of the Fathers , 5 , 23 ) that a man should be bold as a lion , light as an eagle and fleet as a deer to fulfill the will of his Father in Heaven . 
The eagle and deer also figure , though less commonly ( fig. 138 ) . 
The two Tablets of Stone bearing the Ten Commandments , in the shape which had become conventional in the Middle Ages ( among the Christians perhaps earlier than among the Jews ) is found very frequently ( fig. 139 ) . 
Sometimes , too , we see other ancient Temple furniture , such as the altar and table of shew-bread , perpetuating the tradition already found in medieval manuscripts . 
A gift presented by a Cohen would often bear a representation of the hands joined in the priestly benediction , of a Levite that of the ewer and basin used by members of that tribe in laving the priest 's hands . 
In Italy ( and later in the ex-Marrano communities ) other family badges and armorial bearings were not unusual . 
The whole would be commonly surmounted by a crown , symbolizing the traditional Crown of the Law : sometimes by a triple crown , in reference to the Rabbinic dictum ( Ethics of the Fathers , 4 , 17 ) that there are three crowns — that of the Torah , of Monarchy , and of Priesthood " and that of a Good Name surpasses them all . " 
2 
THE RITUAL art of the synagogue naturally centered on the Scroll of the Pentateuch or { Sepher Torah , used in the Biblical readings , and wound upon two staves . 
It is impossible to determine when the practice arose of covering this by an ornament of precious metal . 
Probably , however , it was relatively late . 
The Talmud ( Baba Bathra 14a ) speaks of the Pentateuch deposited by Moses in the Tabernacle as being on silver rollers , but this legendary model does not seem to have been imitated , and in representations in synagogue interiors and on Holy Scrolls in various media ( gold glasses , etc. ) in the classical period there is no trace of anything in the way of ornament . 
The account of the sack of the Synagogue of Minorca in 438 speaks of the synagogical ornaments and silver , without giving any further details . 
The same is true of the sacred appurtenances which Pope Gregory the Great ordered to be restored to the Synagogue of Palermo in 599 . 
In Oriental communities , the Scroll of the Law was enclosed entirely in a case ( tik ) , which was placed upright on the reading desk and opened out for reading the prescribed portion . 
This was the general practice in Iraq and the neighboring countries as early as the 10th century , and has remained to our own day . 
These cases were usually of wood , frequently with inscriptions applied in metal , but were occasionally of silver , finely worked and engraved , and sometimes of gold . 
In the former metal , a few fine examples are extant ; none , however , which are anterior to the seventeenth century ( fig. 140 ) . 
Though the tik was commonly used only in Eastern communities , cases were made for the scrolls sometimes also in Western countries , especially for well-to-do householders , who wished to have portable Torah-scrolls on their travels . 
An exquisite pair of such cases in silver , with polygonal sections opening on hinges and spirally fluted handles and finials , was executed in 1766-7 by a Gentile master craftsman for " Dr. " Samuel de Falk , the so-called { Baal Shem of London . 
The practice of placing crowns of precious metal on the { Sepher Torah — at least on such special occasions as the feast of the Rejoicing of the Law — seems also to have been established in Iraq as early as the tenth century ( { Shaare Semahot , p. 117 ) . 
The Fostat contract of 1186-7 lists among other objects " Two { Sepher-Crowns made out of silver . " 
This form of ornament was naturally suggested by the Rabbinic dictum cited above which refers to the dignity of learning as " the Crown of the Law " — a phrase inscribed innumerable times on such objects and others connected with the synagogue ritual . 
These objects , which became known generally as atarah , were at the outset especially associated with Southern Europe . 
Aaron of Lunel tells in his { Sepher haManhig how in 1203 he persuaded some community which he visited , in Southern France or Spain , to make a silver crown ( atarah ) for the { Sepher Torah instead of decorating it with miscellaneous female adornments . 
The contract already referred to of March 12 , 1439 between the Avignonese silversmith Robin Tissard and the baylons of the Jewish community of Arles was for manufacture , for a total sum of fifty florins , of an atarah for the " scroll of the Jews , " hexagonal in shape , superimposed on a copper drum with which Tissard was to be provided . 
There were to be six towers — one at each corner — the top crenellated like a fortress , and the surface to be engraved in imitation of masonry . 
Chains and columns decorated with lions ' heads were also to be part of the design . 
Referring to this very impressive example of expressionist painting , Ensor himself stated that "{ Je me suis joyeusement confine2 dans le milieu solitaire ou3 tro5ne le masque , tout de violence , de lumie3re et d'e2clat . 
Le masque me dit : fraicheur de ton , expression suraigue " , de2cor somptueux , grands gestes inattendus , mouvements de2sordonne2s . " 
Following the Belgian school , we come to the French Nabis with fine examples of the intimiste work of Vuillard and , in particular , of Bonnard whose { Nu a3 Contre-Jour , painted in 1908 , and lent by the { Muse2es Royaux des Beaux-Arts de Belgique , Bruxelles , is possessed of every single quality of drawing , painting and composition that any , and every , artist seeks to achieve . 
This exhibition of " { Les Sources du 20e3me Sie3cle " has been so well planned and displayed that one is continually startled and excited by the contrasting schools and groups of artists that confront one as one moves on from room to room . 
After the reposed and subdued work of the Nabis we suddenly come face to face with the agitated , violent chromatic paintings of the Fauves and the cynical , cruel expressionism of Rouault whose large strident water-colour on paper of { M. et Mme. Poulot ( collection of M. Philippe Leclercq , Hem ) reproduced here , is one of his greatest works . 
Next come the German Expressionists and the paintings of Nolde and of Munch , in particular , have been carefully selected to indicate the important role that this School played in the formation of 20th-century art . 
L'Angoisse , by Munch ( which is reproduced here , and lent by the { Collections Municipales des Beaux-Arts , Oslo ) is , to say the least , agonizing in its able form of expression . 
And then we come to the British section which is very revealing ( for the French public , anyway ) in that the accent is much more on arts and crafts than on painting and sculpture . 
The artist-architect who stands out most prominently is Charles F. Annesley Voysey , member of the Art Workers Guild and nominated , in 1936 , Royal Designer for industry . 
Principal among the number of exhibits lent to the Museum of Modern Art by the Victoria and Albert Museum , is an enchanting tapestry , designed by Voysey and which was executed , in 1899 , by Alexander Morton and Co ; and a series of delightful wall-paper designs by Arthur Heygate Macmurdo , who was a close friend of William Morris and of Ruskin . 
From the elegant designs of these British artists we are shown the fantastic French " { style metro " furniture of the turn of the century . 
A complete dining-room suite has been transported from the { Muse2e de l'E2cole de Nancy and installed in a separate room in the exhibition at the Museum of Modern Art . 
This ensemble , executed in 1903 , has to be seen to be believed . 
This likewise applies to the ghastly style of the " { Lit Papillon " , also lent from the Museum in Nancy . 
But it was not only in France that the craftsmen produced furniture and fittings of extraordinary and extravagant design . 
During the reign of Queen Victoria , sensational " works of art " were fabricated such as the startling dining-room table centre-piece , executed by Alfred Gilbert and his assistants , to commemorate the jubilee of Queen Victoria , in 1887 , and which Her Majesty the Queen has graciously lent to the present exhibition in Paris . 
Again , by way of contrast , the exhibition continues with the work of the Cubists and important painting-collages by Braque and Picasso . 
Le2ger , too , is exhibited to marked advantage with his cubist composition , { La Noce , painted in 1910 , and owned by the Museum of Modern Art in Paris . 
Guillaume Apollinaire , speaking of this canvas , said " { Les gens de la Noce se dissimulent l'un derrie3re l'autre . 
Encore un petit effort pour se de2barrasser de la perspective , du truc mise2rable , de la perspective , de cette quatrie3me dimension a3 rebours , la perspective , de ce moyen de tout rapetisser ine2vitablement . " 
And then we come to the grandfather of the { Peintres de Dimanche , { Le Douanier Rousseau . 
His { Charmeuse de Serpents ( from the Louvre ) is surely one of the greatest , and most natural , of primitive paintings . 
{ Der Blaue Reiter group of avant-garde artists is admirably represented with important paintings by Kandinsky , among which the dramatic and powerful composition entitled { Avec l'Arc Noir , painted in 1912 , and lent by the widow of the artist ; by Jawlensky , whose { Portait de Jeune Fille ( from the Kunstmuseum , Dusseldorf ) is a superb example of his work ; and by Franz Marc whose well-known composition of { Les Trois Chevaux Rouges ( lent by M. Paul Geier , Rome ) typifies his search after the " spiritualization of nature " . 
Nearby are hung a few small water-colours and drawings by Klee . 
This is the only artist in this very important and instructive exhibition whose work I find poorly represented . 
The originality , the fascination of his very individual art certainly merited more than this . 
Futurism , the short-lived beginning of the century revolutionary movement , founded by Marinetti who spoke of " a roaring motor-car , which runs like a machine-gun and is more beautiful than the Winged Victory of Samothrace ... " is mainly represented by Boccioni with a disturbing quasi-religious composition entitled Matie3re ( lent by M. Gianni Mattioli , Milan ) . 
The origin of pure modern abstract painting is fully exemplified in the work of Mondrian . 
In the present exhibition I was intrigued by his { L'Arbre Rouge ( from the Gemeente Museum , La Haye ) for I always remember Mondrian telling me , in his own studio in Paris , that he was more interested in painting a lamp-post than a tree ! 
" { Les sources du 20e3me Sie3cle " exhibition concludes with some fine examples of the work of Modigliani , de Chirico , and Chagall . 
Kokoschka , I am pleased to say , is very well represented with several portraits and landscapes which reveal the true talent of this artist who , I feel , is still not sufficiently known and appreciated . 
There is much I would have liked to say about many other interesting exhibitions now taking place in Paris . 
But I find I have sacrificed my allotted space to this outstanding exhibition at the Museum of Modern Art . 
Thus I am obliged to leave reviews of the exhibition of sculpture by Lilla Kunvari ( at the Galeries Raymond Duncan ) ; of enamels , by Andre2 Marchand ( at the Galerie David & Garnier ) ; of painting by De Gallard ( at the newly opened Galerie Herve2 ) ; and of the annual E2cole de Paris show ( at the Galerie Charpentier ) until the next issue . 
NEW ART GALLERIES continue to spring up in Paris all over the place . 
Since six months ago , when I calculated that there were more than two hundred and fifty of them , I reckon that the figure is now not far off the three hundred mark . 
As this is one of the busiest seasons of the year for exhibitions , I am receiving daily so many invitations for private views that I have to decide which shows are not worth seeing . 
The other day , one of the small Left Bank galleries sent me an invitation for a new exhibition and stamped on the envelope was " { Les tableux sont le meilleur placement au monde " ( " paintings are the best investment in the world " ) , which is proof enough of the very profitable business now being done by the Paris dealers during the present boom . 
After reviewing the remarkable exhibition at the Museum of Modern Art , of " { Sources du 20e3me Sie3cle " , in last month 's Paris Commentary , there was not space enough left for me to refer to Lilla Kunvari 's sculpture , at the Galeries Raymond Duncan ; and Michel de Gallard 's paintings at the new Herve2 gallery . 
I have followed the progress of this talented young artist 's work since I called on him , shortly after the war , in his tiny , drab " studio " in the squalid La Ruche building way over in the 15th arrondissement . 
De Gallard managed to escape from La Ruche a few years ago and he now lives outside Paris where he leads a retired and happy life painting realistic scenes of the countryside and of the peasants working in the fields . 
His drawing has gained in strength and his palette is becoming more varied while he seeks to bring more light into his well balanced compositions . 
His impressive { Cathedrale de Sens , which was reproduced in last month 's Studio , testified to these qualities . 
Lilla Kunvari is an able Hungarian sculptor who was educated in France and who studied art in the Paris academies . 
Her drawings have the delicate force of Rodin while her small terra-cotta busts and figures ( like that of L'Orateur : see my last Paris Commentary ) recall the grotesque heads so cleverly caricatured and modelled by Daumier . 
For all that , Lilla Kunvari 's art has an appealing individuality . 
One of the most thrilling exhibitions I have seen for a long time at the very active Galerie de France is that of recent paintings by Tamayo who is considered one of the greatest living Mexican artists and whose work is well known and admired in America , but less known in France , and even less in the U.K. 
Tamayo was born in Oaxaca , in 1899 . 
He took to painting when very young and , at sixteen years of age , studied at the { Academie des Beaux-Arts de San Carlos . 
He left the Academy three years later and devoted himself to a study of the Impressionists and the Cubists . 
He held his first one-man exhibition when twenty-two years old at a time when he was attempting to combine in his compositions both the pre-Columbian tradition and the modern expressionism that he had learnt from his study of the School of Paris . 
In 1929 , he was nominated Professor at the { E2cole des Beaux-Arts in Mexico City . 
Four years later he executed the first of a series of outsize mural decorations for the { E2cole Nationale de Musique , Mexico City . 
In 1943 , Tamayo moved to New York where he held his first one-man show there at the Pierre Matisse Gallery . 
Since the war , he has travelled widely throughout Europe and has exhibited at all the big international shows while executing frescoes here and there . 
I saw and spoke to him in Paris during his exhibition at the Galerie de France and he told me he had to hasten back to Mexico City where he had to start work on a gigantic mural for the { Muse2e de l'Histoire which will measure about 100 metres by 15 metres ! 
He reckoned that this will take him at least a full year 's hard work to complete . 
Tamayo is , indeed , a prodigious worker . 
The twenty-five canvases on view at the Galerie de France represented only a part of what he had produced in 1960 . 
His particular form of expression is difficult to describe on account of its striking originality ; but what is apparent is the strange and unusual combination of Mexican folklore art and a quasi-abstract European form of painting , as can be judged from his { Homme au Mur , reproduced here . 
At the same time there exists a fantasy , especially in his smaller canvases , which reminds one of the intriguing and charming esprit of Paul Klee . 
A certain cubist expressionism is to be found in his compositions wherein the arithmetical balance is based on the laws of The Golden Section . 
And there is a haunting , evasive , subtle quality about his colour orchestration of harmonies of pastel hues . 
The texture , too , of his paintings is of a very individual and striking quality . 
Tamayo himself told me of the secrets of this : he mixes his paint with powdered marble . 
An exhibition which was not widely advertised but which was , in my opinion , of equal importance and significance to that of Tamayo — though quite different in aspect — was the show held at the re-opened Galerie Jeanne Bucher , in the Rue de Seine , of recent paintings by Vieira da Silva , whose work I have always greatly admired . 
I hope to be able to write about her at some length in a forthcoming series of articles in THE STUDIO on leading abstract , and near-abstract , artists of the School of Paris , so I shall praise her work here in short terms . 
Like those of Tamayo , Vieira da Silva 's paintings are very individual and original and this in itself is a rare enough quality these days . 
A GROUP OF ENGLISH AND IMPORTED MEDIEVAL POTTERY FROM LESNES ABBEY , KENT ; AND THE TRADE IN EARLY HISPANO-MORESQUE POTTERY TO ENGLAND By G. C. DUNNING , F.S.A . 
THE group of medieval pottery described in this paper was found at Lesnes Abbey in June 1959 , when the smaller of two stone-lined pits added against the west end of the Reredorter was cleared . 
The pit measured 8 ft. by 5 ft. internally , and was about 10 ft. deep . 
The greater part of the filling , about 7 ft. in depth , consisted of chalk and stone rubble , fragments of sandy mortar , a few pieces of worked stone , and broken roofing tiles . 
Below this filling was a layer of dark soil , about 2 ft. in depth , at the bottom of the pit . 
All the pottery was found in the layer of dark soil ; there is thus no doubt that it is contemporary , and was absolutely sealed by several feet of building debris . 
I am indebted to the officers of the Historic Buildings Section of the London County Council for these details , and for permission to examine the pottery and prepare this report for publication . 
The pottery belongs to six vessels , of which four are almost complete and must have been thrown away whole . 
It is divided into the following classes : 
1 . 
Two green-glazed jugs of types frequently found in the City of London , and probably made in east Surrey . 
2 . 
An unglazed jug , probably made at Limpsfield , Surrey . 
3 . 
A jug of polychrome ware decorated with birds and shields , and part of a glazed pitcher . 
Both were made in western France in the region of Saintes . 
4 . 
A large cover of Hispano-Moresque lustreware , imported from Malaga . 
The group is outstanding for several reasons . 
In a single find pottery made in the locality is associated with imports from two different countries on the Continent . 
The three English jugs are of different types , and it is valuable to have them together in a group . 
The polychrome jug is a type long recognized as imported to England , and brought here by the wine trade of Gascony . 
The cover of Spanish lustreware is new to British medieval archaeology , and increases the range of imported pottery known to have reached England in the course of sea-trade . 
The date of the group is closely determined by the polychrome jug . 
Pottery of this class was made in western France and exported to England during a very short period . 
The available evidence , cited below ( p. 5 ) , points to the period c. 1280-1300 for the date of the group of pottery from Lesnes Abbey . 
1 . 
GREEN-GLAZED JUGS ( pl. 1a and figs. 1 , 2 ) 
Fig. 1 . 
Baluster jug , 16 1/4 in. high , made of light grey sandy ware , mostly covered outside by a buff slip , and glazed streaky light green on the neck and body to below the bulge . 
The profile shows a continuous curve , the only demarcation between neck and body being a ridge at two-thirds of the height . 
The handle is plain and circular in section . 
The edge of the base is slightly moulded , and the middle of the base sags slightly below the level of the edge . 
This is a typical example of the standard type of baluster jug frequently found in the City of London . 
The slender form , absence of decoration , and unstable base suggest that the type was not primarily intended for use at the table , but rather for drawing water out of a well . 
That pottery jugs were used for this purpose is shown by the accumulation of over fifty jugs , many intact , in the filling of a medieval well excavated by Mr. S. S. Frere between St. George 's Street and Burgate , Canterbury , in 1952 . 
Fig. 2 . 
Ovoid jug , 12 1/4 in. high , made of light grey sandy ware with light reddish buff surface , covered by yellow slip . 
Mottled green glaze covers the neck and body to below the bulge . 
The neck is cylindrical , separated from the bulbous body by a ridge , and the base is retracted above the foot-ring on which the jug stands steadily . 
The rim has an outward slope , with a groove and moulding below , and is pinched to form a small lip . 
At the middle of the neck is a broad rounded cordon between a ridge and a narrow flat cordon . 
The handle is plain and circular in section . 
The ovoid jug with retracted foot is also a type common in London , and sometimes profusely decorated . 
The contemporaneity of these two jugs is confirmed by the finding of fragments of both types in medieval buildings in Joyden 's Wood , near Bexley , where the occupation is limited to the period c. 1280-1320 . 
The kilns where they were made have not yet been located , but probably they were to the south of London , in east Surrey . 
One site was at Earlswood , where potters ' refuse and wasters have been known for a long time . 
2 . 
UNGLAZED JUG ( fig. 3 ) 
Large part of neck , body , and base of a small jug , about 6.1 in. high , made of grey sandy ware with dark grey surface , unglazed . 
The body is bulging , with wide sagging base . 
The upper part of the body is marked by fine horizontal grooves and wheel-marks . 
The neck contracts upwards , and the rim was everted . 
The lower part of the handle is preserved separately ; it is roughly circular in section , and deeply stab-marked down the back . 
Unglazed jugs of grey ware , rather archaic in character , are known from a number of sites in north-west Kent . 
The major site is Eynsford Castle , where excavations by the Ministry of Works have produced many jugs of this type in deposits of the end of the thirteenth century . 
Other sites are at Joyden 's Wood near Bexley , and at Bexley . 
Pottery of this character was made in east Surrey , where at least one kiln-site is known . 
Recently Mr. Brian Hope-Taylor excavated a kiln and potter 's workshop at Vicars Haw , Limpsfield , which produced a mass of jugs , cooking-pots , and bowls with the characteristics given above . 
3 . 
POTTERY FROM WESTERN FRANCE Polychrome jug ( pl. 1b and fig. 4 ) 
Several fragments of a nearly complete jug , skilfully restored at the Institute of Archaeology , London . 
The jug , 10.3 in. high , is made of thin whitish ware with a thin colourless glaze on the outside surface . 
It is of slender pear-shape with retracted foot . 
The decoration in free-style is of a bird and a shield on each side , and a third shield beneath the spout . 
The figures are outlined in dark brown ; the birds are coloured green and the shields are orange-yellow , with three bars instead of the more usual two . 
One bird and two shields are nearly complete , but the rest of the decoration is fragmentary . 
The bird and shield design is one of the leading patterns on polychrome ware . 
Examples , more or less complete , are known in England and Wales from London , Stonar , Felixstowe , Cardiff , and Llantwit Major . 
The shape of the jug also occurs several times on jugs from London , Ipswich , Writtle , Canterbury , Old Sarum , Glastonbury Abbey , and Whichford Castle . 
Since the initial discussion and inventory of polychrome ware in Archaeologia in 1933 , a considerable number of new finds has been made in Britain . 
The total number of sites now stands at twenty-five in England , six in Wales , still one in Scotland , and Ireland ( as predicted in the original paper ) can now show three sites . 
These additions alone call for a re-evaluation of the material , but even more significant is the new evidence in France . 
The kilns of an intense medieval pottery industry have been discovered at La Chappelle-des-Pots , a village to the east of Saintes in Charente Maritime . 
The manufacture here of polychrome ware and the other types of pottery also exported from France to England is now an established fact . 
It is now possible , therefore , to discuss more fully the trade in polychrome ware from its centre of production in France , and to give a more balanced evaluation of its distribution in the British Isles . 
For the present purpose it must suffice to summarize the evidence for the date of polychrome ware . 
This is based on finds made at five castles , either built by Edward 1 , occupied by the English for a limited period , or where the deposits are related to building periods of the structure . 
The castles and the limiting dates are as follows : 
The gist of this evidence is that at the longest range polychrome ware dates between 1270 and 1325 . 
In fact the range can be narrowed down to between 1280 and 1300 , since most of the initial and terminal dates overlap . 
Although pottery of other types made in the same part of western France has been found in Britain in contexts both earlier and later than the above dates , there is no evidence otherwise that polychrome ware had a longer range in date . 
The evidence as a whole suggests that polychrome ware was not only imported but indeed made during a very short period , and that it was produced in the lifetime of one or at most two generations of potters . 
Glazed pitcher ( fig. 5 ) 
The base and lower half of a pitcher is also identified as an import from western France . 
It is made of thin , hard yellow ware with fine red grit . 
The surface is smooth and yellow-buff , with patches of green glaze above the bulge . 
The base is markedly raised at the middle . 
The pot belongs to a group well represented at Saintes by barrel-shaped and ovoid pitchers and jugs . 
These have a large bridge-spout and a single strap-handle , as on the polychrome jugs , and the base is usually hollowed underneath . 
On some of the jugs the decoration consists of slip lines in brown or red forming a chevron or trellis pattern limited to the upper part of the body , as was evidently the case on the Lesnes Abbey pot . 
The ware of the pots at Saintes is sometimes equal in quality to that of the polychromes , and sometimes more gritty . 
It is probable , therefore , that these vessels , of which fragments were found at the kiln-sites at La Chappelle-des-Pots , were also made elsewhere in the vicinity of Saintes . 
A pitcher decorated with a trellis in red slip , in the { Muse2e Municipal at Saintes , has been used to complete the drawing of the Lesnes Abbey pot . 
4 . 
SPANISH LUSTREWARE ( pl. 11 and fig. 6 ) 
Two fragments of thick whitish ware , glazed and decorated on both surfaces . 
The outside is mostly covered by zones of pale amber lustre , comprising broad and narrow solid bands , sloping panels , chevrons , and large scrolls . 
Between the lustre are two narrow bands painted in cobalt-blue ( hatched in the drawing ) . 
The smaller fragment has two concentric mouldings on the outside above the inner blue band ; the inner moulding is more prominent than the outer . 
On the inside surface the lustre is fainter , and shows the same range of motifs as on the outside , also a narrow band of guilloche ; no blue bands are present on the inside . 
The pieces belong to the same vessel , a large cover or lid , 15 3/4 in. in diameter at the rim . 
At the inner edge of the upper piece the profile turns sharply upwards for a knob for lifting , as restored in the drawing . 
The Lesnes Abbey cover is identified as Hispano-Moresque ware made at Malaga in Andalusia by comparison with numerous fragments , in the Victoria and Albert Museum , found at Fostat near Cairo . 
The origin of this lustre-painted pottery is demonstrated by a foot-ring from Fostat , inscribed with the Arabic word Malaga . 
Such marks are seldom found on this class of pottery , and may indicate that they were limited to vessels destined for exportation . 
A close parallel for the shape and decoration of the Lesnes Abbey cover is provided by a large piece of a cover from Fostat ( pl. 3a ) . 
This is also decorated on both sides by bands of pale amber lustre , and near the top are mouldings precisely like those on the Lesnes Abbey cover . 
The shape of these covers is given by a complete cover for a pedestalled bowl , both painted with arabesque patterns in lustre and in blue , also in the Victoria and Albert Museum ( pl. 3b ) . 
All this , the great corpus of Russian song , remains almost unknown — or known by its least fine and subtle examples . 
And not only Russian song ; Poland has produced at least two remarkable song-writers , Moniuszko in the last century and Szymanowski in the present one , of whom Szymanowski is known only in German translations and Moniuszko not at all , for his songs have never been translated into English and the wretched French selection is a hundred years old . 
Instrumental music , of course , penetrates the curtain with no difficulty , with the result that we think of Russian and Polish music as mainly instrumental . 
This is a false picture . 
It is less false , I think , of Czech music . 
The Czechs ( among whom I include the Moravians and Slovaks and Ruthenians , beside the Czechs proper ) are an intensely musical people but , whether because they nearly lost their language as a culture-language under the Habsburg monarchy ( so that even Smetana had to learn it as a foreigner ) or from deficiencies in the language itself ( e.g. in vowel-sounds ) , for some reason their vocal literature is less rich than their instrumental . 
The language-curtain obstructs much more than the free passage of Slavonic vocal music . 
It obstructs our knowledge of a great deal of music that would present no difficulty at all if we could only hear it : the older instrumental music of the Czechs and Poles , and their Latin church music . 
For — and here I come at last to the very heart of my subject — the Czechs and Poles have always shared the culture of Western Europe , including its music , whereas the Russians began to do so only in the second half of the eighteenth century . 
Not only were the Russians Christianised from Byzantium , either directly or through Bulgarian missionaries , and left with a different alphabet , a different liturgy and a different liturgical language , for two centuries in the later Middle Ages they suffered under the " Tatar yoke " and the Princes of Moscow were mere tributaries to Mongol khans . 
On the other hand , whatever the penetration of Central Europe by the old Slavonic liturgy , whatever the nature of the conflict there between Eastern and Western churches ( and on this there are many important points on which the experts still disagree ) , whatever the political vicissitudes of the Western Slav states , they were never detached in this way from the influences of Western Christendom ; the Roman alphabet conquered the Cyrillic and in the church Latin conquered Old Slavonic . 
Polish and Czech chapter and monastery libraries at Gniezno and Vys10ebrod possess Gregorian missals from the eleventh or early twelfth century , and although these no doubt came from the West — the Gniezno missal has St. Gall-type neumes — manuscripts of Polish and Czech origins were compiled before long . 
The Prague Troparium of 1235 is only the earliest of a number of Czech and Moravian musical codices of the thirteenth and fourteenth centuries and the Poles claim the composition of a plainsong antiphon which can hardly be later than the twelfth century : " { Magna vox , laude sonora " in honour of St. Adalbert , who played such an important part in the Christianisation ( or Romanisation ) of both Poles and Czechs . 
And there is a significant parallelism in the appearance of the earliest religious songs with Czech or Polish words ; both the Polish " Bogurodzica " ( Hymn to the Mother of God ) and the Czech " { Hospodine , pomiluj ny " ( " Lord have mercy on us " , a vernacular Kyrie ) are more or less centos of plainsong motives . 
Moreover the earliest preserved sources for both date from the same period ; the oldest known manuscript of the " Bogurodzica " dates from about 1407 , that of " { Hospodine , pomiluj " from just ten years earlier , though the words are found without the music as early as c. 1380 . 
I have no intention of inflicting on you a potted history of Western Slavonic music , beginning with the Middle Ages . 
I wish , by these facts , only to drive home two points : the essential oneness of this musical culture with that of Europe generally — and the differences . 
The Western Slavs shared in the common stock but often drew from it elements which they put to their own special uses . 
Standing on the outer edge of Western culture , they developed all the fascinating peculiarities one expects to find in peripheral cultures . 
One finds similar things in the music of Portugal and at some periods of history in our own . 
Peripheral cultures naturally tend to be " backward " ; even in a country the size of England , provincial architecture has often been half-a-century or more behind the style fashionable in London ; as we all know , even Germany was very late in developing polyphony . 
But there are wonderful compensations in the variety , in the range of dialects ( as it were ) . 
Sometimes political or other non-musical factors play a part ; the Hussite wars of the fifteenth century gave a tremendous stimulus to vernacular Czech song just as the two centuries and more of Habsburg domination after the Battle of the White Mountain overlaid and even seemed to extinguish the peculiarly Czech elements in the music of Bohemia . 
But the Slavs were quite capable of developing special musical characteristics without the help of extra-musical circumstances . 
Even in the field of notation , Czech neumes evolved with certain differences . 
In the thirteenth century the Czechs were still using non-diastematic neumes ; in the fourteenth they progressed to the stave — and their neumes began to assume peculiar rhomboid forms . 
But let me remind you again how much more different things were in Russia , where liturgical melody had developed — and developed quite a long way on its own lines — from Byzantine chant but was stuck fast in a primitive notation which is still unreadable up to the late fifteenth century , although comparative study with Byzantine notation is now showing how it may be deciphered . 
As for the five-line stave , it reached the Ukraine only in the seventeenth century and Russia proper in the eighteenth . 
Genuine polyphony was impossible though a very primitive form of three-part polyphony — in the so-called troestrochnoe style , noted in three rows of neumes — begins to appear about the middle of the sixteenth century : the liturgical { 6cantus firmus in the middle part is supported at first in unison or octaves by upper and lower voices which branch out from it and close in again to the unison in the manner of the podgoloski of Russian polyphonic folk-music . 
It is not until the mid-seventeenth century that one begins to find four-part polyphony , with the { 6cantus firmus in the tenor and the added parts in note-against-note style producing common chords in root position . 
At this period , when Russian liturgical polyphony was in its earliest infancy and Russian secular music reached no higher level than the songs and dance music of the skomorokhi ( buffoons ) , Poland and Bohemia were enjoying what modern Polish and Czech historians claim as a "golden age of polyphony " . 
It may at first strike us as no more than a pale reflection of the golden age that was being enjoyed at the same time by all Europe , but that is not the whole truth . 
A great deal of this music deserves not only intensive study but performance . 
Two difficulties confront the Western student of this music . 
One I have already mentioned : the language curtain . 
It does not conceal so much of the music itself , for a great deal of it is Latin church music , but it makes it difficult for most of us to get at the information about it , the existing stylistic research , and so on . 
Czech and Polish musicology have fairly long traditions and very high standards , as indeed has Soviet musicology , and the amount of study devoted to the Western Slav polyphonists — to say nothing of the instrumental composers of the seventeenth and eighteenth centuries , and early Czech and Polish romantic piano music — is enormous . 
It exists in print , in books and monographs and learned periodicals , but it might be in Etruscan or Cretan Linear B for all that most of us can make of it and it would be well worth the while of some of the young musicologists now studying Russian to make Polish or Czech their second Slav language . 
The second difficulty is that of actual scores . 
It has at times seemed as if Western Slav musicologists were more interested in studying their old masters than in getting their texts published . 
Josef Syrzyn2ski made an excellent start in 1885 with his Polish Monumenta but succeeded in bringing out only four volumes ; the later Polish series , { Wydawnictwo dawnej muzyki polskiej , edited by Chybin2ski and begun in the 1930s , has produced nearly forty numbers but many of them are very slim , containing only a single work or a selection of short pieces . 
( The editorial prefaces were from the first provided with a French translation and the post-war numbers are translated into English , French , German and Russian . ) 
The somewhat similar Czech series , { Musica Antiqua Bohemica , has been devoted almost entirely to instrumental music of the late eighteenth and early nineteenth centuries ; it is only in the last few years that the Czechs have begun to publish the work of their classic polyphonists — with trilingual re2sume2s of the prefaces , but not of the critical apparatus . 
A third difficulty is the paucity of surviving material . 
Poland and the Czechoslovak lands have provided innumerable battlefields during the last four centuries ; the Thirty Years War and the two World Wars were only the worst of a series , and the total destruction of music , both manuscript and printed , must have been enormous . 
( Incidentally , these countries began to print music quite early ; a Czech-printed Catholic Kanciona2l appeared in 1529 and a Polish music-publisher , L11azarz Andrysowic , was active at Cracow from 1553 onward ) . 
One reads of a Polish master such as Wacl11aw z Szamotul — or Szamotulczyk , as he is often called — who was obviously a very considerable figure in the middle of the sixteenth century ; two of his psalm-motets were published by Montanus and Neuber at Nuremberg in 1554 and in 1564 in collections of works by the leading French and Netherland masters , and what survives of his music justifies the high esteem in which he was held . 
Yet one finds so little that does survive : these two motets , another preserved only in organ tablature , some songs with Polish words — a very small proportion of what he is known to have written . 
His eight-part Mass for the wedding of King Sigismund Augustus is lost ; his Office settings are lost ; of his Lamentationes , printed at Cracow by Andrysowic , only the tenor part has been preserved . 
Another , rather later composer Tomasz Szadek — a member first of the king 's private chapel and later of the royal chapel of the Rorantists at Cracow , the two chief centres of the Polish "golden age " — survives in only two works , other than fragments , and of those two Masses one lacks the Agnus . 
Technically these works are more or less in the " late Netherland " style . 
What distinguishes them and gives them special interest is the infusion of Polish melodic elements , here a phrase from a Polish devotional song , there a pseudo-plainsong found only in Polish sources . 
Marcin Leopolita , composer and organist to the king in the early 1560s , composed a five-part { Missa paschalis or { Missa de resurrectione , the earliest complete setting of the Ordinary by a Polish composer that has come down to us , which is based on four Easter songs current in Poland and Germany . 
The Polish " golden age " was finally submerged by a flood of Italian musicians brought in by Sigismund 3 . 
There had of course been foreign musicians at the Polish court before ; Heinrich Finck was a chorister in the royal chapel in his youth and returned there for fourteen years , perhaps as director , from 1492 to 1506 . 
And there had been Italian musical influence . 
But Sigismund 3 was a fanatic for the Counter-Reformation and for everything Italian ; he moved his court from Cracow to Warsaw , enticed Marenzio to go there ( but failed to keep him ) , invited Giovanni Gabrieli ( also in vain ) and appointed a whole series of Italians as directors of his chapel , including Asprilio Pacelli , an ancestor of the late Pope ( Pius 12 ) , and Giovanni Francesco Anerio . 
On differentiation , each reverts to the other : **f 
and **f 
The hyperbolic tangent , , is **f and , starting at zero , never exceeds unity , however large t may become . 
The remaining three hyperbolic functions , sech , cosech and coth , are the reciprocals of the above three ratios respectively . 
Fig. 1.4 shows the whole family of curves . 
Tables of the hyperbolic functions are available , but are not so readily available as those of the circular functions . 
A device by which the more extensive circular function tables may be used in conjunction with a subsidiary table ( the Gudermannian ) is described in Appendix 2 . 
The general case , where the time constants of the two exponential terms are not the same , may be expressed as the product of another exponential and a hyperbolic function . 
Thus : **f 
If a is positive , this expression will always diverge . 
If a is negative ( with b positive ) , the final value will always be zero , and this is the more usual in practice . 
Fig. 1.5(a) shows the result of the sum of two negative exponentials , and Fig. 1.5(b) the difference . 
The second is seen to start at zero , reach a maximum , and then decay . 
As Sallust remarked : { Omnia orta occidunt et aucta secuntur , or " Everything rises but to fall and increases but to decay " . 
The time at which the maximum is reached is easily found to be **f 
and there is a point of inflexion where **f 
This type of curve is encountered , for example , in radioactive cases where a substance A decays into another substance B , which , in turn decays into a stable end-product C. The curve shows how the amount of the second substance varies with time . 
Intuitive estimation of transients 
A demonstration will now be given of how the transient current resulting from switching operations may be obtained in simple cases , without resort to mathematics ( or very little ) . 
The following plausible assumptions are made : 
1 . 
That an uncharged capacitor behaves as a short circuit at the instant of applying a steady p.d. ; and after a long time , when fully charged , acts as a disconnexion or infinite impedance . 
2 . 
That a pure ( resistanceless ) inductance behaves in the opposite way ; offering apparently infinite impedance at the instant of application of the direct voltage , and short circuit after a long time — that is , when the current is steady . 
3 . 
That , in the interim period , the current changes according to a simple exponential law ; the time constant of which is either RC or L/R , where R , L or C may be simple or compound . 
4 . 
That there can be no discontinuous jumps in either the voltage across a capacitor or the current in an inductor . 
The magnetic space constant { 15m0 ( otherwise the permeability of free space ) has dimensions henrymetre , and the electric space constant , or permittivity of free space , { 15e0 , faradmetre . 
The square root of the reciprocal of the product of these two , therefore , has the dimensions of velocity and this is the velocity of electro-magnetic waves , c , equal to 299792 km/ sec , according to the latest evidence . 
It follows that has dimensions of time , and dimensions of resistance . 
In fact , is the well-known expression for the characteristic impedance of a loss-free transmission line . 
From this it is seen that L/R and CR both have dimensions of time , and this time is the time constant . 
Any time constants we may encounter in the study of transients must be in the form of a certain inductance divided by a certain resistance , or a capacitance multiplied by a resistance , or else the square root of the product of an inductance and a capacitance . 
No other combinations are possible . 
Let a simple series LR circuit be suddenly connected to a constant voltage source V , at time t = 0 . 
The initial current will be zero and after the transient has subsided will be V/R . 
At first sight , this is not a decaying exponential ; it decays upwards , so to speak . 
It may be easier to consider the voltage across the ( pure ) inductance L. The initial voltage across this part of the circuit is equal to V , and the final value will be zero . 
Using the assumptions made above , the voltage across L in the transient period will be **f 
and , because there are only two circuit elements , T is obviously equal to L/R . 
The voltage VR across the resistive part of the circuit when added to VL must always give V , hence **f 
and the current in R ( and also L , of course ) is **f 
the well-known result of a problem which is often given to beginners as an exercise in solving differential equations of the first order . 
By similar reasoning , the current through a CR series circuit is found to be **f 
The voltage across the resistor is **f and that across the capacitor is , therefore , **f , and so the charge in the capacitor at time t is **f 
Theoretically , the current never does reach its final value ; the " final value " may be said to be attained when it falls short of the theoretical final value by an amount too small to be detected by the measuring instrument in use , or , in decay , when it has reached the r.m.s. value of the noise level . 
For practical purposes , and as a rough guide , the current will have reached within one per cent of the final value in a time five times the length of the time constant ( see p. 2 ) . 
This is roughly seven times as long as the half-life of radioactivity . 
One can not help feeling that , subconsciously or not , people who think in terms of half-life have the idea that all activity will have ceased in about twice that time . 
Three-element circuits 
It may well be argued at this point that the above type of reasoning is all very well for simple two-element circuits , but would fail if carried further . 
Let us consider , therefore , the circuit of Fig. 1.6 in which the capacitor C has a leakage resistance R2 . 
The initial current on making the switch ( t = 0 ) is V/R1 , and the final current will be **f . 
This fixes the limits between which the current must vary exponentially . 
The time constant of this exponential must be the product of a capacitance and a resistance . 
The capacitance is obviously C , but what are we to take as the resistance ? 
The answer is , that resistance which effectively appears across the terminals of C when the switch is closed ; this is clearly R1 and R2 in parallel , the voltage source having no internal resistance . 
So the time-constant is **f 
and we can now sketch the currenttime curve as in Fig. 1.7 . 
The exponential part is **f 
and to this must be added **f ; after a little manipulation the current can be written **f 
The final capacitor voltage **f will be **f , and its variation with time is **f 
The case of two capacitors and one resistor is amenable to similar treatment , though not quite so easily ( see Fig. 1.8 ) . 
Here there is a little awkwardness due to the fact that the initial rush of current is very high ; theoretically infinite but lasting for zero time ( see under " Delta Function " in the next chapter ) . 
We shall side-step the current question and work , instead , in terms of voltage or quantity of charge , neither of which becomes infinite . 
When the switch is made , the capacitors immediately charge up to **f and **f volts respectively , and the quantity of charge on the plates of each is **f coulombs . 
Because of the presence of the resistance , C1 will discharge exponentially , with T = while C2 , following its initial charge at time t = 0 , will acquire further charge until its p.d . 
reaches the source voltage , V , and it holds C2V coulombs . 
Hence : charge in C1 **f 
and charge in C2 **f 
The current taken from the supply , which is the same as that in C2 may be found by differentiating **f with respect to time and is **f 
plus , of course , the initial pulse of current . 
See p. 43 , equation ( 2.8 ) . 
Circuits comprising R , C and L are , in general , beyond this simple intuitive treatment , though there are exceptions . 
One of these is shown in Fig. 1.9 where a constant voltage source , V , is applied to two elementary circuits , LR1 and CR2 respectively . 
We shall suppose that the two time constants are the same ; L/R1 = CR2 or R1R2 = L/C . 
The initial current i0 will be V/R2 and the final current , **f will be V/R1 . 
Thus , during the transient period , the current will be switched over from the capacitive side to the inductive side at a rate governed by the common time constant . 
Alternatively , we can make use of results already obtained on p. 9 and write down the supply current immediately as **f 
In the special case where R1 = R2 = R , the term containing the exponential vanishes , so there is no transient and the current taken from the supply is constant and equal to V/R . 
In other words , the network is distortionless and free from phase shift for all frequencies ; provided always that R = . 
Analogies 
In the elementary teaching of electricity use is often made of analogies with mechanical systems . 
Electricity seems to be more difficult to understand than mechanics for most people , because the mind can readily picture mechanical processes , but electrical phenomena require the effort of abstract thought . 
As the understanding develops , the debt can be repaid , often with much interest , as problems in mechanical engineering are referred to their electrical counterparts for solution ; an example of this is in the theory of vibrations , both free and forced . 
The analogue of electro-motive force , E , is force , F , or mechano-motive force as it has been called : that which moves mechanical systems or particles , the unit being the newton ; though it is only fair to say that this unit is making but slow progress into mechanical circles . 
The magnetic circuit analogue , magneto-motive force , is not so good since , although we speak of flux , there is nothing which actually flows . 
In angular motion the equivalent is torque , Tq , measured in newton . 
metre or jouleradian . 
Electric current has its analogue in velocity — linear , v , or angular , o , and consequently quantity of charge , the time-integral of current , corresponds to linear displacement x , or angular displacement th . 
Mass ( kilogram ) or moment of inertia ( kilogram . 
metre2 ) is analogous to inductance . 
It is noteworthy that while there has never been any confusion in the mind of the electrician between electro-motive force and self-inductance , the tyro mechanician often finds difficulty in distinguishing force and mass , and tortures himself with " big pounds " and " little pounds " as well as "slugs " and " poundals " . 
The increased use of the newton might soften these difficulties . 
Electrical **f 
Mechanical **f 
Rotational **f 
( I being the moment of inertia ) . 
Figure 1.10 shows how current and angular and linear velocity increase with time in systems where the resistance or friction is zero . 
If the force is removed after a certain time , t1 , the current will go on flowing with circuit energy **f , or the wheel will continue to rotate with angular energy **f , or the particle will continue with constant velocity ( Newton 's law ) , and kinetic energy **f . 
If resistance is present , the current ( or velocity ) does not increase indefinitely but reaches a limit , as we have already seen ( p. 9 ) . 
The initial slope is the same as for the resistanceless case and the final value is given by the resistance divided into the electro-motive force , or the mechanical resistance divided into the mechano-motive force and so on . 
Alternatively , the electrical resistance in ohms ( or volt . 
ampere-1 or henry . 
second-1 ) is given by E/I where I is the final value of current : and similarly , mechanical resistance is **f , where vT is the final or terminal velocity ; and rotational resistance is Tq/ { 15oT . 
It follows that the unit of mechanical resistance is newton . 
metre-1 . 
second , or kilogram . 
second-1 , and of rotational resistance is newton . 
metre . 
second , or kilogram . 
metre2 . 
second-1 . 
The terms mechanical ohm and rotational ohm are used by Olson , but these seem rather far-fetched , particularly as they are referred to c.g.s. and not practical units . 
2 General Properties of Ferrites 2.1 FERRITE STRUCTURE 
APART from ferromagnetic metals , a number of chemical compounds ( e.g. ferrites , garnets , plumbites and perovskites ) exhibit ferromagnetic properties . 
Of these compounds ferrites have to date proved to be the most important from the standpoint of microwave applications . 
As the majority of ferrites crystallise with a cubic structure , similar to the mineral spinel , ( magnesium aluminate **f , the term ferromagnetic spinel is sometimes used to describe those ferrites which exhibit magnetic properties . 
The general chemical formula of a ferrite is **f where M represents a metallic cation . 
It is found that a spinel crystal structure is only formed if the ionic radius of the cation M is less than about 1 A15 . 
If it is greater than 1 A15 then the electrostatic Coulomb forces are insufficient to ensure the stability of the crystal . 
For example Ca++ ( ionic radius 1.06 A15 ) does not form spinel crystals , while Mn++ ( ionic radius 0.91 A15 ) does . 
The cation M is generally divalent , but other valencies are possible if the number of anions is doubled , e.g. lithium ferrite **f . 
The ions forming ferrites of practical importance are Ni++ , Mn++ , Fe++ , Co++ , Cu++ , Zn++ , Cd++ , Li+ , Mg++ . 
The spinel unit cell ( see Fig. 2.1 ) consists of a close packed cubic array of 32 oxygen anions , between which there are 96 spaces or interstices , 24 of which are filled with a cation , the remaining 72 being empty . 
The sites occupied by the cations are of two kinds known as tetrahedral or A sites and octahedral or B sites . 
The A sites of which eight are occupied , are surrounded by four oxygen anions and the B sites of which sixteen are occupied , are surrounded by six oxygen anions . 
When the chemical formula is written , the ions in the B sites are often enclosed in brackets to indicate their position , e.g. Fe(NiFe)O4 for nickel ferrite . 
It might seem at first sight that the most likely arrangement of the cations would be with M++ ions on the A sites and Fe2+++ ions on the B sites but in practice three types of spinel can be distinguished . 
( 1 ) Normal spinels in which M++ ions occupy the A sites and Fe2+++ the B sites . 
( 2 ) Inverse spinels in which M++ ions occupy the B sites together with half the Fe+++ ions , the other half being on the A sites . 
( 3 ) Random spinels in which both M++ ions and Fe+++ ions occur on the A and B sites . 
The preference of certain ions for A or B sites is of importance , as it is found that in general normal ferrite spinels are paramagnetic while inverse spinels are ferromagnetic . 
Many ions show no strong preference for a particular site , this being especially true for those ions with a noble gas configuration such as Li+ , Mg++ , Al+++ and also those with a half-filled 3d electron shell e.g. Fe+++Mn++ . 
Where there is no strong site preference the most stable cation distribution can be calculated from a static model of charged spheres . 
Of the remaining ions in ferrites which are of microwave interest Zn++ , has a preference for A sites while only Ni+++ and Cr+++ have a strong preference for B sites . 
When two or more cations are present , the distribution of ions with weak site preference may be affected by the presence of an ion with a strong site preference . 
Most ferrite spinels can form solid solutions with each other in any proportion . 
This arises since there is a greater probability of a solid solution when two ferrite spinels are reacted together , than there is of the formation of separate crystals of the two spinels . 
A well-known example of a solid solution is nickel zinc ferrite , **f , where a can take any value between 0 and 1 . 
Unless great care is taken in the manufacture , the final ferrite formed is not exactly that corresponding to the proportions of raw materials used . 
This is because most ferrites can take up oxides into solution without forming a second phase and thus give rise to non-stoichiometric ferrite . 
In particular the ability of most ferrites to take up Fe2O3 in solution is important . 
In the preparation of ferrites the component oxides are reacted at high temperatures . 
During this sintering process there is a tendency for most ferrites to give off oxygen , as the equilibrium pressure in this reaction is often greater than one atmosphere and increases rapidly with temperature . 
This gives rise to an oxygen deficiency in the final product and to the formation of ferrous ions . 
The presence of ferrous ions in microwave ferrites is undesirable however , since it causes increased dielectric and magnetic loss as is discussed in this chapter and Chapter 4 . 
For this reason , compounds are often made iron deficient , great care being taken to avoid loss of oxygen during sintering. 2.2 . 
PREPARATION OF FERRITES 
Ferrites are prepared by a ceramic technique which involves sintering the component oxides at temperatures between 1000° and 1450°C . 
The stages in the preparation of ferrites are listed below : — 
Raw materials 
16 
Decomposition to oxide 
16 
Milling 
16 
Presintering ( partial reaction ) 
16 
Remilling 
16 
Pressing and Extruding to shape 
16 
Final sintering 
16 
Grinding to shape 
A number of raw materials can be used in the manufacture of ferrites ; these include oxides , carbonates , oxylates and nitrates . 
The last three compounds decompose to oxides on heat treatment , and are thus prepared { 6in situ at a temperature near to that at which solid state reactions commence . 
This process should favour the formation of good quality homogeneous materials . 
For example in the case of MgMn ferrites it has been reported that the use of nitrates gives rise to better microwave properties . 
An explanation is that the high decomposition temperature of the nitrates and the presence of nitrogen oxides help to prevent the formation of ferrous ions during the sintering process . 
The raw materials are first milled , usually in a steel ball mill , to give a homogeneous mixture of very fine particles . 
The process is generally carried out with the raw materials in a slurry of methylated spirit or any other liquid which is easily removed after milling . 
The evaporation of the methylated spirit is carried out rapidly to avoid any heavier particles separating out . 
The mixture of raw materials is then pre-fired at a temperature some 200°C below its final firing temperature . 
This process causes partial reaction of the constituents and helps to reduce shrinkage during final sintering . 
The presintered powder is then remilled . 
Two methods of moulding the powder into shape prior to the final sintering are commonly employed ; die pressing and extrusion . 
For die pressing a small quantity of binder is added to the powder so that when the sample has been pressed to shape , it can be handled relatively easily . 
To avoid the possibility of contamination of the sintered ferrite , distilled water has been used as a binder , although for certain shapes ( e.g. rods ) organic wax emulsions have been found more satisfactory . 
Gentle heating to remove the binder is necessary as violent volatilisation could cause the sample to crack . 
A moulding pressure of between 2 and 10 tonssq. in. ensures a uniform end product without the risk of forming laminates in the pressed sample . 
For satisfactory extrusion a higher percentage of binder is required than for moulding . 
A solution of wax in petroleum has been used as a binder for extrusion and by careful choice of extrusion orifice very dense samples may be produced . 
As high a density as 99% has been achieved under special conditions . 
Extruded samples , in general , however are not as dense or uniform as those produced by die-pressing . 
The principal use of extrusion techniques has been for the manufacture of long thin rods , a shape often required in microwave applications . 
Rods as long as 12in. x 0.04 in. diameter have been produced by this method . 
The properties of the final product depend critically on the sintering process and the closest control of sintering time , temperature and atmosphere is required . 
Generally , the sintering process is carried out at a temperature between 1000° and 1450°C for between 4 hours and 24 hours , depending on the ferrite . 
Ferrites containing lithium and cadmium are usually sintered at lower temperatures due to the volatility of LiO and CdO2 while those containing nickel , cobalt and magnesium are sintered at the highest temperatures . 
By sintering for a long time at high temperatures , a uniform final product with a minimum of air pores can be obtained . 
The near absence of pores is a requirement for certain microwave ferrites . 
This is discussed in greater detail in Chapter 3 . 
As already mentioned , however , the oxygen equilibrium pressure increases rapidly with increasing temperatures and this sets a limit on the maximum sintering temperature that can be used without reduction of ferric iron to ferrous iron . 
The porosity of a particular polycrystalline ferrite sample is usually quoted with reference to its X-ray or single-crystal density . 
The X-ray density is determined from measurements of the spinel lattice constant and Table 2.1 gives values for a number of commonly used ferrites , for which the lattice constants are known . 
The density of typical polycrystalline pressed samples is between 80% and 95% of X-ray density , though figures as high as 99% have been achieved . 
During sintering , shrinkage of the ferrite sample occurs . 
This may be controlled by careful preparation and by ensuring a uniform temperature over the sample , although the final shape may not have the tolerances required in practice . 
Sintered ferrites , being ceramic in nature , require special methods of shaping . 
Cutting can be carried out by use of a thin diamond slitting wheel or by use of an ultrasonic machine with a knife edge cutting head . 
An accurate finish can then be obtained by surface grinding with a carborundum wheel . 
The growth of single crystals of ferrite was originally of interest mainly to the physicist , as the crystals produced were too small for use in microwave applications . 
However , the development of non-linear devices employing small single-crystal samples has modified this situation , although they are still extensively used for the study of the fundamental properties of ferrites . 
Two principal methods have been used for the formation of single crystals ; the borax melt and the flame fusion process . 
In the borax melt process , the constituent oxides of the ferrite are dissolved in a flux of molten borax by heating the mixture to between 1300° and 1400°C and maintaining this temperature for several hours . 
The melt is then cooled at a few degrees per hour until crystals start to form , or alternatively the flux is evaporated at a constant rate . 
A disadvantage of the method is that the borax vapour evolved is very corrosive and destroys most refractory materials , which necessitates the use of special furnace equipment . 
Crystals of linear dimensions of about 1 cm can be obtained by this method . 
In the flame-fusion process constituent oxides are mixed in the correct proportions and sprinkled into an oxy-hydrogen flame . 
Crystals of reasonable length , e.g. 1-2 cm can then be grown on a refractory rod held in the flame . 
It is , however , very difficult to control the exact chemical composition of the crystal obtained by the flame-fusion process . 
2.3 MAGNETIC PROPERTIES OF FERRITES 
The purpose of the following section is to provide an elementary account of the magnetic properties of ferrites , together with enough background material to enable the reader to place the section in perspective . 
It is stressed that since the object is to equip the microwave user of ferrites with a knowledge of their magnetic properties , the finer details of the subject must be sought in the bibliography provided . 
Consideration will first be given to the origin of magnetism in electrons , atoms and ions , choosing as examples of the latter , elements which occur in ferrites . 
The mechanisms of para- , ferro- and ferri-magnetism will then be explained and reference made to the temperature behaviour of the saturation magnetisation of certain ferrites . 
In ferrites , one is principally concerned with the phenomenon of ferrimagnetism which will be treated in greater detail . 
5.5 . 
VARIATION OF MATERIAL STRENGTH 
Two alloys of widely different strengths from HE30-WP were selected in order to study the effect of material properties on strut behaviour . 
The alloys were NE6-M and HE15-WP , which have 0.1% proof stresses of approximately 10 tonsin2 and 28 tonsin2 respectively . 
The specimens were fabricated from 3 in. x 2 1/4 in. x 0.15 in. ( 76.2 x 57.15 x 3.81 mm ) A.D.A . 
unequal bulb angle section , and were of the same design as for the first series of A.D.A . 
specimens shown in Fig. 13 . 
As material failure might be expected to have the greatest influence on strut behaviour in the lower slenderness ratios , these specimens were made in a limited range of slenderness ratios only : 30 to 60 for the HE15-WP and 30-90 for the NE6-M . 
The overall picture of failure behaviour was similar to that for the previous sets of specimens — torsion-flexure . 
Failure of the higher strength material specimens was generally of an elastic buckling nature , with torsional and flexural deflections starting near the ultimate load and growing very rapidly to large magnitudes , when no further increase in load could be sustained . 
On unloading , there was almost complete recovery , showing that the buckling was largely elastic . 
An exception was one of the L/k = 40 specimens where the torsional deflection was increased so much that local collapse occurred in the lower third of the specimen . 
The lower strength specimens generally failed quite suddenly , with very little deflection visible beforehand . 
Failure was of the torsion-flexure form , with flexure more predominant than in the tests previously described , coupled in all cases below L/k = 50 with local failure of the outstanding bulbed edge of the individual angle member . 
There was scarcely any recovery on unloading , showing that the distortion had given rise to large areas of plasticity . 
The forms of specimens of the two materials after failure for slenderness ratios 30 , 40 and 50 are shown in Fig. 33 , where the large permanent set of the NE6-M specimens can be clearly seen , and compared with the almost complete recovery of the HE15-WP ones . 
The right-hand specimen of the middle pair is the exceptional case of local collapse in the HE15-WP series referred to above . 
Fig. 34 shows the L/k = 90 specimen in NE6-M after failure . 
The results of this series of tests are given in Table 16 and Fig. 35 shows the strengths of the two series of specimens compared with those for the HE30-WP . 
It will be noticed that the results for NE6-M are presented in two parts : this is because a second batch of material for these specimens had an appreciably higher strength than the first . 
5.6 . 
DETERMINATION OF MATERIAL PROPERTIES 
Tension specimens were taken from each different batch of section . 
In some cases machined round specimens of 0.282 in. ( 7.16 mm ) diameter were made from the corner of the section or from the bulbed edge , in others standard flat specimens were made from the longer leg of the section . 
Strains were measured with a 1 in. ( 25.4 mm ) gauge length Robertson optical extensometer on the round specimens , and with a Gerard extensometer on the flat ones . 
To make a satisfactory compression test , the length of the specimen should not exceed about 2 1/2 times its diameter ; therefore the length of compression specimens taken from small structural sections must be small . 
As the greatest diameter of specimen that could be obtained from the 3 in. x 2 1/4 in. ( 76.2 x 57.15 mm ) A.D.A . 
Section was about 3/8 in. ( 9.5 mm ) the length was limited to 1 in. ( 25.4 mm ) . 
A jig was made in which the specimen was clamped and both ends could be ground at one setting , so that they were finished accurately flat and parallel . 
Strains were measured by a pair of Martens extensometers having a gauge length of 0.6 in. ( 15.24 mm ) . 
The test was carried out in parallel platen apparatus to ensure , as far as possible , that compression took place without bending . 
The results are summarised in Table 17 . 
It will be noticed that where test pieces were taken from both the bulb and corner and from the flat part of the section , the material in the flat part of the section had an appreciably lower tensile proof strength . 
The Young 's moduli are generally of the order of 5% higher in compression than in tension . 
Observations of this nature have been recorded before with aluminium alloy but no satisfactory explanation seems to have been offered . 
6 . 
Analysis of Results 
The analysis of the results falls naturally into three categories : the comparison of values of failing stress predicted analytically with those obtained experimentally : a similar comparison of the results obtained from standard design methods ; and a study of the behaviour of double angle struts having different cross-sectional profiles. 6.1 . 
PREDICTION OF FAILURE 
The prediction of the elastic buckling load of members where there is interaction between the flexural and torsional modes has been fully dealt with by Timoshenko and many other authors . 
For members having one axis of symmetry , the critical load is given by the smallest root of the equation : **f 
where p1 , p2 , p3 , are respectively the critical stresses for flexural buckling about the principal axis x-x at right angles to the axis of symmetry , flexural buckling about the axis of symmetry a-a , and torsional buckling . 
The value of r is given by **f 
where a is the distance between the shear centre and the centroid , and kx and ka are the respective principal radii of gyration . 
The exact analysis of the buckling of built-up members such as those considered here is extremely complex , but provided the individual members are fastened together at a sufficient number of points it is justifiable , as a first approximation , to treat the members as being homogeneous . 
In the case of the struts used in this investigation the bending stiffnesses about the two principal axes are approximately equal ; therefore , as the member is effectively fixed-ended for buckling about the x-x axis , p1 will always be greatly in excess of the actual buckling stress , and may be disregarded . 
The stiffness for bending about the axis of symmetry is taken as the reduced value calculated in 4.1 . 
The value of the torsional stiffness used in calculating the torsional buckling load is obtained for the various slenderness ratios by multiplying by the appropriate factor b from Table 11 . 
The warping stiffness of the angle sections themselves , which is very low , has very little effect on the torsional buckling load and is neglected in the calculation . 
Thus the torsional buckling stress **f , 
where GJ is the free-ended torsional stiffness of the composite member , and Ip is the polar second moment of area of the cross-section about the shear centre . 
The values obtained for the buckling stresses are shown below in Table 18 . 
Fig. 36 shows these values graphically , curve ( 1 ) , and those for the HE30-WP struts ( 2 ) . 
The immediate observation is that the experimental failing stress curve lies well below the theoretical one , the discrepancy being most marked in the lower slenderness ratios . 
The most obvious explanation for this is the reduction of the effective stiffness due to inadequate rigidity of the fastenings , discussed in 4.1 . 
If the experimental results were re-plotted on a basis of slenderness ratios calculated from actual stiffness , then the curve would be moved to the right . 
Some confirmation of this explanation is given by the results for the few tests with the knife-edge along the x-x axis , in which the effects of the fastenings on flexural buckling might be expected to be much smaller , which lie much nearer to the theoretical curve . 
It is interesting to re-calculate the torsion-flexure buckling stress values when the flexural buckling stress is derived from that obtained by taking the measured bending stiffness , the torsional stiffness remaining as before . 
These values are plotted in curve ( 3 ) , Fig. 36 , which lies much closer to the experimental values of curve ( 2 ) than does the original theoretical torsion-flexure curve . 
On the other hand , it might be argued that compression should tend to reduce the effects of bolt clearances and that the discrepancy between the experimental and theoretical values might be due to plasticity of the material at the higher stresses . 
From the compression stress-strain curve of the HE30-WP material used , values of the tangent modulus may be deduced , and the Engesser plastic flexural buckling curve can be constructed , curve ( 4 ) , as a continuation of the Euler curve for the elastic range . 
This curve diverges rapidly from the Euler and elastic torsion-flexure curves as the slenderness ratio diminishes . 
The limit of proportionality of the HE30-WP was just below 8 tonsin2 ( 12.7 kgmm2 ) , and it might be expected that after the critical stress of this value , which occurs at about L/k = 70 , the true torsion-flexure buckling curve would begin to diverge from the elastic one . 
There is no direct method of constructing the plastic torsion-flexure buckling curve . 
However , by assuming that the critical load for the torsional mode does not change , which is reasonable if the shear modulus remains nearly constant , it is possible to devise a method of successive approximation . 
Taking for the flexural buckling stress , p2 , the value obtained for flexural plastic buckling , a new value can be obtained for the torsion-flexure buckling stress p . 
From the compression stress-strain curve the value of the tangent modulus Et at the stress p is obtained . 
Using this value of Et in the Engesser equation , **f , the buckling stress of a strut of the same slenderness ratio can be calculated . 
This value will generally be found to differ from the value chosen for p2 . 
Another value is now chosen for p2 , and the process repeated until a value is obtained , for the plastic torsion-flexure buckling stress , at which the value for the tangent modulus corresponds to plastic flexural buckling at the chosen value of p2 . 
The values obtained by this method are shown in Fig. 36 , curve ( 5 ) , where it will be seen that , except for slenderness ratios below 40 , the curve lies above the experimental one — between those obtained from the elastic torsion-flexure equation using modified flexural stiffness and the ordinary elastic torsion-flexure equation . 
It may be concluded that both plasticity and loss of expected stiffness contribute to the divergence of the experimental from the predicted values . 
Confirmation of this is obtained by examination of the results for HE15-WP and NE6-M materials ; the elastic limit of HE15-WP is about 23 tonsin2 so that , as the critical stress for elastic torsion-flexural buckling at L/k = 30 is 23.1 tonsin2 , it might be expected that plasticity would have scarcely any influence on failure in the range of slenderness ratios used in the tests . 
Fig. 37 shows that the experimental values are in reasonable agreement with the values obtained from the elastic torsion-flexure equation with modified flexural stiffness . 
The small discrepancy at the lower slenderness ratios could be attributed to an over-estimation of the torsional stiffness . 
The NE6-M alloy , with an elastic limit of between 4 and 5 tonsin2 , gives the opposite picture in that plasticity affects failure over the whole range of slenderness ratios considered . 
The plastic torsion-flexure curve , in Fig. 37 , lies well below the elastic values and a little above the experimental ones . 
This seems to indicate that , although plasticity is the dominating factor affecting failure , the reduced flexural stiffness contributes to the difference between experimental and predicted values , and the best prediction might be obtained from the plastic torsion-flexure approach using the reduced , experimental flexural stiffnesses . 
The results of this calculation for HE30-WP and NE6-M are shown in Fig. 38 , where it will be seen that good agreement is obtained except at the lowest slenderness ratio where the stiffnesses have probably been over estimated . 
6.2 . 
DESIGN METHODS 
As the mode of failure at all slenderness ratios up to 150 was torsion-flexure it is evident that direct design from the Perry-Robertson strut curve is unsatisfactory . 
Forms of compression instability , other than purely flexural , may be dealt with by the Equivalent Slenderness Ratio ( e.s.r. ) method . 
SUMMARY 
The authors discuss the testing of explosives with special reference to the ability of a test to indicate the presence of significant differences in ignition probability and also to the reliability of the test . 
It is suggested that tests requiring low ignition rates , and particularly no-ignition tests , are , as a class , poor discriminators . 
The ability to discriminate can be increased by increasing the number of ignitions accepted as the pass level . 
It is suggested that a test of 26 shots , in which 13 ignitions are permitted , represents a good compromise , in view of the need to keep the number of shots within reasonable limits . 
1 . 
INTRODUCTION 
About a hundred million shots a year are fired in British mines and usually about 6 ignitions are reported each year . 
It is clear that with a practical ignition rate of roughly 10-7 , a test no more severe than practical use required an impossibly high number of shots to give a reliable answer ; and therefore the test must be made so much more severe ( i.e. the ignition rate in the test must be made so much higher ) that an effective assessment of the safety of an explosive may be made with a practicable number of shots . 
In rigorous terms this thesis demands that the ignition rate be multiplied ten million times or so . 
The multiplying factor can be made up by 
( 1 ) Ensuring the presence of practical conditions which are dangerous but rare , e.g. the presence of considerable volumes of an explosive mixture of methaneair , the absence of stemming in the shothole , and so on . 
( 2 ) Modifying the test apparatus to increase the ignition rate , e.g. firing the shot in a steel cannon instead of the rock or coal in which it is fired in the mine . 
All of these devices are used in explosives testing ; but apart from some tentative results recorded in the literature ( Cybulski , 1959 ; Schultze-Rhonhof and others , 1959 ) no firm estimate can be made of the relative contributions they make to the multiplying factor . 
However it is probably wise to assume that the contribution of the second group is substantial rather than preponderant . 
This is fortunate rather than the reverse because scientifically any process that extrapolates a million times may be expected to require a lot of proving . 
British approval tests have been such that an explosive is failed if ignitions are obtained in any of the tests . 
This reliance on no-ignition tests has been an almost uniform feature of explosive testing throughout the world although the French system permits ignitions in one of the tests , and recently the United States Bureau of Mines has made a decided break with tradition in this regard ( United States Bureau of Mines , 1961 ) . 
For the past three years a detailed study of the testing procedure has been conducted at S.M.R.E. ; particular attention has been paid to the statistical problems raised by no-ignition tests . 
It has been concluded that the no-ignition test , as applied to explosives , gives too little information about the ignition probability of the material tested , and that this weakness can not be removed by any practicable increase in the number of shots fired . 
2 . 
RELIABILITY AND DISCRIMINATION 
A good test should meet , { 6inter alia , two requirements : 
( 1 ) It should be reliable , i.e. a repeat test of the same material should give the same result . 
( 2 ) It should have adequate discrimination , i.e. it should indicate the presence of significant differences . 
No measurement is exactly reproducible , since all are subject to random errors . 
In explosive testing random error appears as a variation in the number of ignitions obtained in repeated tests on identical material . 
However often a trial is repeated , one can never say how many ignitions will take place ; but , at the same time , the more often a trial is repeated , the more exactly can the probability of ignition by an individual shot be stated . 
Once this probability of ignition by an individual shot is known it becomes possible to calculate the probability of any particular number of ignitions in a given number of shots . 
Alternatively , it is possible to calculate the number of shots that must be fired to achieve a given probability of a particular number of ignitions . 
In this situation , complete reliability of acceptance or rejection is impossible ; one may assign only the probability with which material of specified characteristics shall be accepted or rejected . 
This probability can , by firing enough shots , be made to approach certainty as closely as is desired , although a situation is rapidly reached where an enormous number of shots must be fired to achieve a small improvement . 
It is also fundamental that the acceptance and rejection limits can not be equal although , again , by firing enough shots they may be made to approach each other as closely as is desired . 
The difference between the acceptance and rejection levels is analogous to discrimination . 
Whatever values of ignition probability are chosen as the rejection and acceptance limits and whatever level of probability be chosen for the rejection or acceptance at those limits , material with an ignition probability equal to the mean of the limits will be almost as likely to fail as it is to pass . 
This again is fundamental to all systems of assessment . 
It will be seen therefore that the concepts of reliability and discrimination as applied to testing are complex ones : overall , a system can be made reliable to a chosen extent at the limits of a chosen range . 
3 . 
EXAMINATION OF THE NO-IGNITION TEST 
In the last section it was pointed out that the reliability of rejection or acceptance is a matter of choice , and clearly opinions will differ as to the desirable level . 
However , it appeared reasonable to the present writers to require that the test should have a 0.95 probability of rejecting an explosive having an ignition probability at the chosen reject level . 
Correspondingly there should be a 0.95 probability of accepting an explosive at the acceptance level . 
Calculations were then made which permitted the plotting of Curve 1 in Fig. 1 . 
In this figure the true probability of ignition with a single shot is plotted against the number of shots of the explosive that must be fired to give a 0.95 probability of one or more ignitions . 
For example a " no-ignition " test of 28 shots will reject , 19 times out of 20 , an explosive with an ignition probability of 0.1 ( for the rest of this paper 19 times out of 20 will be called " reliable " rejection or acceptance . ) 
Curve 2 in Fig. 1 shows the number of shots for which the probability of one or more ignitions is 0.05 , i.e. there is a probability of 0.95 of acceptance . 
From these curves it will be seen that although a 28-shot sequence will reliably reject an explosive of ignition probability of 0.1 , it will not reliably accept explosives until the ignition probability has fallen to 0.0018 ; in other words , if a manufacturer submits an explosive that has a slightly lower ignition probability than 0.1 , he has a moderate chance of getting it through the test but if he submits another that is ten times better in this respect , he has a fair chance of having it rejected . 
Summarizing , if the probability is lower than 0.0018 or higher than 0.1 , the explosive will be reliably passed or failed , but if it has an intermediate value , the test will not give reliable results . 
The curves in Fig. 1 also show that the rejection level and the number of shots in the test may be varied over a wide range but without an appreciable change in the value of approximately 50 for the ratio of the acceptance to the pass level . 
It appears to be impossible to avoid poor discrimination with no-ignition tests . 
4 . 
TESTS PERMITTING IGNITIONS 
In the last section it was found that poor discrimination appeared to be a characteristic of no-ignition tests : the effect of permitting one ignition is shown in Fig. 2 and Fig. 3 shows the characteristics for 2-ignition tests . 
It will be noted that the gap between the rejection and the acceptance curves narrows , i.e. the discrimination is improved when the number of permitted ignitions is increased . 
The calculations on which Fig. 2 and 3 are based have been extended , and the results are summarized in Table 1 . 
The accuracy of discrimination steadily increases with the number of ignitions ( m ) accepted as the pass level . 
Confining attention for the time being to a reliable rejection level of pr equal to 0.1 , Table 1 shows that the ratio ( pr/pa ) does not fall to the neighbourhood of 2 until the number ( n ) of shots fired is nearly 200 and the acceptable number ( m ) of ignitions rises to 12 . 
The table does not extend beyond the point where ( pr/pa ) falls to the neighbourhood of two because this seemed a good compromise , as far as explosives are concerned , between the requirements of discrimination and the need to keep the number of shots within practicable limits ; in view of the variabilities inherent in the conditions of use , perhaps it should not be taken too seriously if the value of ( pr/pa ) for a given explosive fluctuates in the range of 2 to 1 . 
The following example may illustrate the operation of a test with a pass level of not more than 12 ignitions in 200 shots . 
This test has a reliable pr of 0.1 and a reliable pa ( acceptance level ) of approx 0.05 ; for reliable acceptance the manufacturers must work to an ignition probability per shot ( p ) of 0.05 . 
If the product deteriorates , and is then re-tested , there is a probability of 0.95 that the deterioration will be detected when the ignition probability has increased by a factor of 2.0 . 
To a considerable extent the sensitivity of existing explosives tests is adjustable at will , usually by adjusting the charge weight but also by changes in the test apparatus . 
What are the consequences of changing the sensitivity ? 
Table 1 gives the appropriate figures for rejection ignition probability of 0.5 and shows that equally good discrimination can be obtained but with far fewer shots . 
Table 1 indicates that an economical and discriminating test at a rejection level of pr = 0.5 is to fire 35 shots and permit 12 ignitions . 
The calculations have since been extended by Mr. G. Fogg of S.M.R.E. and it appears that at a rejection level of pr = 0.673 a discrimination ratio of 2 is obtained with a round ( n ) of 26 shots and a permitted number ( m ) of 13 ignitions. 5 . 
MATHEMATICAL BASIS 
The mathematical basis on which Figs 1 , 2 and 3 and Table 1 were calculated is simple and well-known ; see for example David , F.N. ( 1949 ) . 
The probability , P , of an explosive being accepted after a series of tests is a calculable function of the probability of ignition in a single test , p , and of the standards required in the series . 
For example , if our standard requirement is 0 ignitions in n trials , we have **f 
For sufficiently large p , P is small and the explosive is almost certain to fail the test . 
It is useful to consider the probability of ignition which will almost certainly cause a device to be failed . 
To do this , it is necessary to fix a corresponding value for P ; that is , to give a numerical expression to the phrase " almost always failed " . 
If we define " reliable rejection " by requiring P < 5%,we will obtain it whenever p > pr such that **f 
Similarly , for sufficiently small p , P approaches 1 and the explosive is almost certain to pass . 
So if we define " reliable acceptance " by requiring P 95% , we will obtain it whenever p <pa such that**f The range of possible p-values can thus be divided into three parts : 
Reliable rejection , P < 5%, pr < p < 1 Results not consistent , 5% < P < 95%, pa < p < pr Reliable acceptance , 95% < P, 0 < p < pa If we put these ranges side by side for different values of n , we obtain Fig. 1 , in which two curves of pr against n ( Curve 1 ) and of pa against n ( Curve 2 ) divide the area into three regions : consistent failures , results not consistent and consistent passes . 
Details can be seen in the photograph , Fig. 4 . 
During the early part of the tests the rotors were run at 1,800 r.p.m. , at which speed the radial acceleration was approximately 2,350 g , resulting in very high forces at the hub . 
The blades were provided with both flapping and drag hinges , the former being freely mounted on ball races and the latter having adjustable cork friction dampers . 
The blades were found to vary slightly in weight so provision was made for final balancing by means of small adjustable weights on screwed rods radiating from the hubs between the blades . 
These can be seen in the photograph , Fig. 4 . 
In order to avoid the possibility of resonance it was at first thought advisable to run the rotors with drag hinges locked . 
Eventually however fatigue cracks were noticed in the roots of two of the blades and it was suspected that the lack of freedom in the drag hinges was the possible cause . 
Later , after new blades had been fitted , it was thought better to run with drag hinges free and so reduce root stresses , experience having shown that the possibility of resonance was small . 
As a further precaution , to eliminate fatigue failure , the new blades of a modified design were run at a reduced top speed of 1200 r.p.m . 
This question of blade fatigue is more fully discussed in the Appendix . 
2.3 Equipment for measuring tracking of blades and flapping angle 
The front rotor carried a commutator with a single brass segment contacting four carbon brushes mounted on a ring attached to the front rotor spindle housing . 
Three of these brushes were approximately 120° apart and the fourth diametrically opposite to one of the three . 
The brush contacts were used to trigger off a stroboscope lamp illuminating the blades whilst rotating . 
The three contacts at approximately 120° spacings were set so that , with all three in circuit together , they were successively out of phase by about one chord length when the ends of the rotor blades were observed . 
By this method it could be seen if the blades were tracking correctly . 
The two diametrically opposed contacts were used to facilitate the observation of flapping angles . 
Each contact had a switch in circuit and the timing adjusted so that the stroboscope flashed when a particular blade was parallel to the longitudinal body axis either in a fore or aft direction . 
The height of the blade tips in each position was measured by means of a travelling periscope projecting vertically downwards into the tunnel . 
The difference in height of the blade tips in these two positions gave a measure of flapping angle . 
The periscope was of the type used on midget submarines . 
The stroboscope lamp was mounted on gimbals and the direction of the light , shining through a thick perspex window , could be adjusted by the observer to illuminate the particular blade tip under observation . 
It was estimated that the accuracy of the measurements was of the order of one tenth of a degree . 
A photograph of the head of the periscope is shown in Fig. 6 from which can be seen one of the two vertical slides behind which is the measuring scale . 
As the periscope weighed about 60 lb it had to be counterweighted and the wires carrying these weights , passing over pulleys , can be seen in the photograph . 
3 . 
Safety Precautions 
Due to the high value of centrifugal force on the rotors and the possibility of instability , resonance , or fatigue , it was thought expedient to protect the personnel by reinforcing the tunnel inside with sheet steel and outside with shutters . 
These shutters were of sandwich construction comprised of blocks of paper between 1/48 thick plywood , totalling about two inches in thickness . 
To minimise the possibility of stopping the rotors before the tunnel and thereby losing the stabilising effect of centrifugal force on the blades , an interlock was incorporated in the electrical circuits , with a time delay of about a quarter of a minute , to ensure that the rotors attained a reasonable speed before starting the tunnel and also that the tunnel speed had dropped sufficiently on shutting down . 
As the electrical supplies to the tunnel and rotors were separate there remained the danger arising from a failure of the current to the rotors but as that was thought to be very improbable , no attempt was made to cover that eventuality . 
4 . 
Method and Scope of Experiments 
The model was suspended from the main roof balance by two struts spaced 22 1/28 apart . 
These struts carried at their ends a spindle mounted on ball races , passing through and fixed to the helicopter body 29 1/28 from the nose . 
This spindle being freely mounted acted as a pitching axis . 
A further support was provided towards the rear of the body , using a pair of V-wires attached to an overhead split-beam balance , see Fig. 2 . 
These wires were adjustable by means of a windlass carried on the balance , so that the attitude of the model could be varied . 
The earlier tests were made at 1800 r.p.m. giving a tip speed of about 400 ftsec . 
Later the speed was reduced to 1200 r.p.m. and a tip speed of 267 ftsec . 
Lift , drag , and pitching moments were measured at wind speeds of 40 , 80 , 120 , 160 and 180 ftsec for the tests at a rotor speed of 1800 r.p.m. giving approximate values of tip-speed ratio , m , of 0.1 , 0.2 , 0.3 , 0.4 and 0.45 . 
When the rotor speed was reduced to 1200 r.p.m. the wind speeds used were 25 , 55 , 80 , 100 and 120 ftsec giving values of m = 0.094 , 0.206 , 0.300 , 0.374 and 0.449 respectively . 
Measurements were made for blade angles , th0 , of 4° , 8° and 12° . 
The angles were set by a worm and wheel at the blade roots using a surface table and scribing blocks to measure the difference in heights at leading and trailing edges . 
Flapping angles were also measured by the method described in para. 2.3 . 
Although it would have been desirable to make measurements at very low values of m , less than 0.1 , difficulty was experienced due to the flow induced by the rotors themselves , especially at the higher body angles . 
For example , without the tunnel motor running , a vane anemometer indicated a wind speed of about 15 ftsec at th0 = 8° and th = 20° . 
As the flow was unreliable these tests were abandoned . 
Table 1 gives a summary of all the tests on the various rotor combinations together with references to the tables giving the results . 
5 . 
Corrections 
The tunnel measurements were converted to the coefficients CT and Cm where CT is the coefficient of the force normal to the longitudinal axis of the helicopter and Cm is the pitching moment coefficient about the axis shown in Fig. 3 . 
A further correction was made for the forces and moments on the body and rig , etc. , by making the appropriate measurements with rotors removed and subtracting from the total . 
No account is therefore taken of forces due to the interference between rotors and body . 
As the final results were to be presented for constant values of tip speed ratio , m , and the wind speeds chosen did not give exact values and also as **f , where th is the body angle , the correction varied with attitude of the model and so all the results had first to be plotted against m and then the values for m = 0.1 , 0.2 , 0.3 , 0.4 and 0.45 taken from the curves . 
Corrections had also to be made to th due to tunnel interference and therefore the values corrected for m had then to be plotted against th and values read off at the chosen values of th viz. , 0° , 5° , 10° , 15° , 20° and 25° . 
For convenience th has been taken to be positive with the nose of the model downwards which is opposite to the normal convention . 
For the 97 x 77 wind tunnel the correction to body angle ( th ) has been taken to be **f 
where A is the total rotor disc area C is the cross-sectional area of the wind tunnel , CL is the overall lift coefficient based on total disc area . 
The correction is such that the effective inclination is less than the geometric inclination . 
It is felt that the above correction is not entirely satisfactory as it is based on fixed wing theory . 
It is hoped that at some future time a systematic series of experiments will be made to establish the order of wind tunnel corrections to be applied to helicopter model testing . 
The corrections to pitching moment due to flapping hinge offset are included in para. 6. 6 . 
Results 6.1 Effect of flapping hinge offset 
In addition to the corrections mentioned in para. 5 account had also to be taken of the effect of flapping hinge offset which , due to design difficulties , was of necessity rather large , about 6.275% . 
The effect of flapping hinge offset on the characteristics of a rotor is dealt with in a report by Meyer and Falabella and the analysis given in that report has been used to estimate the theoretical values of rotor thrust and flapping angles and also the effect on overall pitching moment . 
6.2 Thrust coefficient 
Assuming uniform distribution of induced velocity and neglecting blade tip losses the theoretical value of CT is given by equation ( 38 ) of Ref. 3. **f 
As there is no cyclic pitch B1 = 0 and the term involving a1 is small and may be neglected and therefore approximately **f 
For zero forward speed where m = 0 **f 
Also **f 
In order to determine " a " the slope of the lift curve of the blade section CT was required for zero wind speed . 
As the tunnel was of the return flow type it was difficult to obtain a true zero wind speed due to the flow induced by the rotors . 
This was cut down to a minimum by closing the tunnel with a screen , but even so there was a circulation of air in the neighbourhood of the model , particularly at the larger blade angles . 
It was assumed that at zero tunnel speed the induced circulation at th0 = 4° would be very small and the measured value of CT = 0.00142 was inserted in the equations ( 2 ) and ( 3 ) . 
This gave a value of a = 5.0 ( per rad ) which was subsequently used in equation ( 1a ) . 
A curve of static thrust coefficient using the above value of " a " is given in Fig. 7 . 
The theoretical values of CT using equation ( 1a ) for th0 = 4° , 8° and 12° are included in Figs. 9 , 13 and 19 . 
It is of interest to note that the effect of flapping hinge offset on CT is negligible , particularly at the lower values of m. 6.3 Division of thrust 
From a knowledge of the total thrust and the pitching moment about a defined axis the contribution of thrust due to each rotor has been calculated . 
It was assumed that the thrust of each rotor acted at the disc centre and normal to the body axis and also that the rotor drag force , parallel to the longitudinal axis , acted at the mean height of the two rotors . 
The pitching moments as measured in the experiments included a contribution due to the effect of the offset flapping hinges and therefore before the thrust due to each rotor could be calculated the pitching moments had to be corrected for offset . 
In the report by Meyer and Falabella an expression is given for pitching moment due to hinge offset ( My ) . 
This expression is **f 
where **f **f . 
Values of a0 , b1 , and a1 are obtained by solving three simultaneous equations ; these solutions are given in equations ( 27 ) , ( 28 ) and ( 29 ) in the report . 
As there is no cyclic pitch , i.e. , B1 = 0 in the case of the model , these solutions become **f 
The value of l is given by the expression **f 
and **f **f . 
Using the wind tunnel values of CT , in equation ( 9 ) My has been calculated for various cases and it was found that the terms involving a0 and b1 were quite small compared with the a1 term . 
Introduction . 
When considering the design of a jet-flapped aircraft from a stability and control aspect , it is necessary to have fairly accurate information concerning the downwash field behind the jet-flapped wing , particularly in those regions where it is practicable to locate the tailplane . 
The evaluation of the downwash at the tailplane is dependent upon a knowledge of the strength and position of the vorticity distributions which represent the wing and the jet . 
In his treatment of the flow past a wing with a jet-flap , of infinite span , Spence assumes that the incidence of the wing and the deflection of the jet are small , and hence the usual assumptions of thin aerofoil theory , in which the wing and jet are replaced by vortex sheets in the direction of the free stream , apply . 
The results so obtained for the vorticity distributions on the wing and jet are used in Part 1 to give the downwash at any position relative to the plane vortex sheet in the form **f , 
where e = downwash angle , t = jet deflection angle , and a = wing incidence . 
However , in the calculation of the downwash induced at a point ( P ) in the field , it is necessary to allow for its location relative to the actual wing and jet . 
To the order of accuracy consistent with the previous assumptions , this implies calculating the downwash at a point whose ordinate relative to the plane vortex sheets is equal to the distance of the tailplane from the jet ( as shown in Figs. 1a and 1b ) . 
The functions { 15de/dt and { 15de/da depend upon the jet momentum coefficient CJ , and on the relative position of the tailplane ; charts for these functions , and for the position of the jet , are given for various specific CJ values . 
The downwash has been evaluated for ranges of the tailplane position , wing incidence , jet deflection and jet momentum coefficient . 
For the unswept wing of finite span , with a full-span jet-flap , considered in Part 2 , Maskell has introduced the concept of an effective wing and jet flap of infinite span , in order to obtain the strength of the bound vorticity , elliptic spanwise loading being assumed . 
This solution may be used to give the contribution to the downwash from the bound vorticity , in a similar way to that described in Part 1 , but it does not account for the effect of the trailing vortices arising from the pressure gradients along the wing and jet spans . 
In the case of a wing without a jet-flap , it has been found that the downwash is very sensitive to the relative distance between the tailplane and the wake , and that the spanwise loading has more effect on the downwash than the chordwise loading , and so the wing and its wake are replaced by a lifting line and its trailing vortices , the latter being displaced in order to keep the tailplane at the correct height above the wake . 
The effect of the rolling-up of the wake has also been investigated for a wing without a jet-flap , and it is shown that rolling-up is not important for normal tailplane positions behind wings of large aspect ratio . 
The distance e behind the wing at which rolling-up may be assumed to be complete is given by **f for a wing without a jet-flap , where k7 depends upon the plan-form and spanwise loading of the wing . 
For the jet-flapped wing , the CL will be greater than for the normal wing , but k7 may now be a function of CJ , and will probably increase with increasing CJ ( since the bound vorticity on the jet will tend to resist rolling-up ) , so that e/c will not decrease so quickly with increasing CL and CJ , as might have been expected from first considerations . 
Thus , in order to evaluate the contribution to the downwash behind a jet-flapped wing from the trailing vorticity , it is assumed that the majority of the load is carried on the wing , so that the trailing vortices may be considered to arise from one chordwise position on the wing with no rolling-up taking place . 
The displacement of the jet and trailing vortices is accounted for by taking the position of the tailplane relative to the wake , and a chart is given for the downwash due to the trailing vorticity . 
Calculated values of the downwash are in good agreement with the few experimental results available , especially if the difference between the experimental and theoretical lift coefficients is taken into account . 
Theoretical results for the downwash on the centre-line are also given for a wing of aspect ratio 6.0 , showing variation with tailplane position , wing incidence , and jet parameters . 
PART 1 
1 . 
Vortex Representation of the Wing and Jet-Flap of Infinite Span . 
The wing and jet-flap of infinite span may be represented in two dimensions by vorticity distributed on the chordal plane of the wing and the median line of the jet ( assumed to be thin ) . 
The downwash relations have been solved by Spence , using the assumptions of thin-aerofoil theory , so that the aerofoil incidence and jet deflection are considered to be small . 
The vorticity distributions and the position of the jet are given in Fourier-series forms , with coefficients as functions of the jet momentum coefficient CJ . 
Let be the vorticity distribution on the aerofoil ( at incidence a to the mainstream ) and the vorticity distribution on the jet ( emerging at deflection t to the extended chord-line of the aerofoil ) , as shown in Fig. 1a . 
The x axis is taken parallel to the main stream , and the z axis vertically downwards , with the origin at the leading edge of the aerofoil . 
The chord of the aerofoil is taken to be unity , so that x and z are non-dimensional . 
Thus the vortex representation of the flow which is in accordance with the assumptions of thin aerofoil theory is as shown in Fig. 1b , with located on the x axis , between 0 and 1 , and also on the x axis , between 1 and 25 . 
Then the expressions for and , the jet displacement , as obtained from Ref. 1 , are : For **f **f . 
For **f **f . 
2 . 
The Downwash . 
The downwash induced by the vortex distributions at the point ( X , Z ) is given by **f 
to the first order in a and t ( see Fig. 1b ) . 
In order to apply the results calculated for the simplified configuration ( Fig. 1b ) to the actual configuration ( Fig. 1a ) , where the jet is displaced a distance below the x axis , it is assumed that the downwash calculated for the point in Fig. 1b is equal to the downwash at the point in Fig. 1a . 
A similar procedure is followed in Ref. 3 , where the displacement of the wake of a finite wing has to be considered . 
In general , the tailplane will be located a distance H above the jet , as indicated in Fig. 1a , so that to evaluate the downwash at the tailplane , i.e. , at the point in Fig. 1a , we must evaluate the downwash at the point ( X , - H ) in Fig. 1b . 
The position of the tailplane is usually given as the distance along and height above the extended chordline . 
If l is the distance of the aerodynamic centre of the tailplane behind the wing leading edge , measured along the extended wing chord-line , and h the height above the chord-line , when the chord is of length c , as shown in Fig. 1a , then the non-dimensional co-ordinates ( X , Z ) at which the downwash is to be evaluated are given by **f , 
where zJ may be obtained from Fig. 3 ( or equation ( 4 ) ) . 
For the numerical evaluation of the two integrals in equation ( 6 ) , it is necessary to change the variables of integration , in the first integral using equation ( 1 ) in order to avoid the infinite value of at the leading and trailing edges , and in the second integral using equation ( 3 ) to make the range of integration finite . 
Thus , if we write **f , 
then the downwash at the tailplane is given by **f , 
where **f and **f remain finite as x and th tend to zero , and as **f , **f . 
Equation ( 10 ) may be rewritten in the form **f , 
where { 15de/dt and { 15de/da are functions of Cj , X and Z. These have been evaluated for Cj = 0.5 , 1.0 , 2.0 and 4.0 , with **f and **f , the results being shown as charts in Figs. 4a to 4d . 
Thus the procedure for the evaluation of the downwash at a given tailplane position , h/c and l/c , and given a , CJ and t , is to calculate the functions in the following order : 
( 1 ) X from equation ( 8a ) 
( 2 ) zJ from Fig. 3 
( 3 ) Z from equation ( 8b ) 
( 4 ) { 15de/dt , { 15de/da from Figs. 4a to 4d 
( 5 ) e from equation ( 11 ) . 
Interpolation will be necessary for CJ values other than 0.5 , 1.0 , 2.0 and 4.0 , and it seems better to evaluate e for a range of CJ , and then to interpolate the final result , rather than to interpolate for zJ , { 15de/dt and { 15de/da separately . 
For large X , the downwash is given by **f , ( see Ref. 1 ) 
so that **f and **f . 
It may be noted that the value of **f for the downwash far behind the aerofoil is also obtained when the aerofoil is without a jet-flap . 
3 . 
Results . 
The results for the downwash behind an infinite wing and jet-flap are shown in Figs. 7 to 11 . 
It should be remembered that the theory is only strictly valid for small a and t , so that the use of the method to obtain the downwash for the larger values of a and t must wait to be justified or otherwise until experimental data are available . 
However , the results should indicate the trends in the variation of downwash with the various parameters . 
In Figs. 7 and 8 , the variation of the downwash with tailplane position is shown for two values of jet deflection angle , t , and two values of wing incidence , a , for CJ = 2.0 . 
Fig. 7 shows that on the extended chord-line , h/c = 0 , the downwash decreases quite sharply with increasing distance behind the wing , l/c , but when h = 2c , the downwash is practically constant in each case for **f . 
The results have been replotted in Fig. 8 to show the downwash field ( i.e. , contours of equal downwash ) , in the tailplane region . 
A comparison between the fields for the various t and a shows that the downwash is more sensitive to tailplane position for the higher t and a values , as might be expected . 
The results for the variation of e with CJ , t and a are given in Figs. 9 and 10 for a representative tailplane position , l/c = 3.5 , h/c = 1.5 , and also for a position on the extended chord-line , l/c = 3.5 , h/c = 0 . 
It will be noticed in Fig. 9a that e does not increase linearly with t for a given CJ value ( as might be implied by a glance at equation ( 11 ) ) due to the correction made to the downwash field for the displacement of the jet relative to the tailplane position . 
Fig. 9b indicates that { 15de/dCJ decreases with increasing CJ . 
The variation of downwash with wing incidence is more important for stability and control considerations and the results are shown in Figs. 10a to 10d for t = 30 and 60 deg , and for various CJ values . 
Ranges of values of **f are also indicated on the diagrams , and are seen to be the same for the two different t values over the same range of CJ for a given value of h/c . 
Since **f increases with CJ , it is not possible to assess a maximum , but for CJ = 4.0 , **f is well below 1.0 at the tailplane and on the extended chord-line , being 0.20 and 0.35 respectively . 
It also appears that { 15de/da increases as a increases , but this is only noticeable at the higher values of CJ , and for CJ = 4.0 , a = 20 deg , { 15de/da is still less than 0.4 at the extended chord-line position . 
Effect of Cross Draughts on the Exhaust Air Volume required for Hot Knock-out 
The obstruction offered by the side of a mould does not shield the depressed velocity zone above the mould from disturbance by the horizontal motion of cross draughts . 
Consequently , cross draughts can enhance the rate of diffusion of rising thermal currents and blow them sideways into exhaust air streams at a point nearer to the grid , where the exhaust air velocities are higher . 
It follows that the performance of down-draught systems can be improved by the influence of cross draughts only if the thermal currents are blown into exhaust air streams moving at higher velocities than the cross draughts , so that the resultant direction of all dust-bearing air streams is towards the grid . 
If the grid is unduly blocked on the down-wind side of the cross draughts , the thermal currents will be blown into a zone of reduced exhaust air velocities , and control of the dust-bearing air streams can be impaired , particularly if the speed of the cross draughts is high in relation to the exhaust air movement . 
The important conclusion is that the performance of correctly designed and operated down-draught systems for the knock-out of hot moulds is not unduly affected by cross draughts of the order usually present in foundries . 
Obviously , high velocity cross draughts , such as may be found when the knock-out is situated near large open doors , will seriously impair their performance . 
Nevertheless , cross draughts are so variable and unreliable that the assistance they may provide should not be considered when designing a system . 
Effect of Cross Draughts on the Exhaust Air Volume required for Cold Knock-out 
The effect of the cross draughts is to increase the strength of the exhaust air velocities on the windward side of the grid and to reduce those on the down-wind side . 
Since cross draughts not only diminish the exhaust air velocities on the down-wind side of the grid , but also blow the dust and fumes into this zone , it follows that the exhaust air volume must be increased by an amount that will counteract the fall in exhaust air velocities . 
The main distinction between the effects of cross draughts of normal velocity on thermal currents and cold air streams is that the former are deflected into exhaust air streams of unchanged or even higher velocities , while the latter are blown into weaker air streams , and therefore additional exhaust air volume is required . 
Relationship of Grid Size , Box Height and Exhaust Air Volume 
Examination of the results shown in Figs. 6.9 and 10 shows that the minimum exhaust air volume does not increase in direct proportion to the increase in the size of the grid . 
The proportional increase in air volume is , however , never greater than the corresponding increase in grid area . 
When considering these results it is important to remember that engineering methods of air flow measurement are not precise , and errors of 10 per cent . 
and even more , in some cases , may occur . 
Nevertheless , by considering a large number of test results , it is possible to distinguish two marked trends in the amount of exhaust air volume required by the 6-ft. x 4-ft. grid in relation to the 4-ft. 6-in. x 3-ft. 6-in. grid . 
( 1 ) Increase in exhaust air volume . 
The exhaust air volume required by the 6-ft. x 4-ft. grid with the 8-in. deep hot and cold moulds and the 16-in. deep cold moulds tested in the absence of appreciable cross draughts exceeded the volumes required by the 4-ft. 6-in. x 3-ft. 6-in. grid by between 25 and 40 per cent . 
( 2 ) Constant exhaust air volume . 
The exhaust air volume required by the 6-ft. x 4-ft. grid , with 16-in. deep hot and cold moulds tested in cross draughts of 75-100 f.p.m. was approximately equal to ( and in some cases even less than ) the volumes required by the 4-ft. 6-in. x 3-ft. 6-in. grid . 
Insufficient experimental data are available to provide a complete explanation of the conditions responsible for the similarity of exhaust air volumes measured between the two grids with the 16-in. deep boxes in 75-100 f.p.m. cross draughts . 
The many variable factors present during the tests produced complex air flow conditions which do not facilitate comparison , but the resultant effect of the following two factors emerges as a predominant influence : 
( a ) The effect of cross draughts on the sideways entrainment of dust-bearing air currents from the depressed velocity zone into relatively higher exhaust air velocities near to the down-wind top edge of the moulding box . 
( b ) The effect of the grid area and , therefore , grid velocity diminishes with increasing distance from the grid until the exhaust air velocities are almost identical , regardless of the size of the grid , as explained earlier . 
In practice , however , the number of possible variations in the factors controlling the distance from the grid at which air velocities become constant for a given exhaust air volume is so large that the distance must be calculated afresh for each individual case . 
In addition to the variation in the area of the vertical gaps at the sides of the grids and in the horizontal unblocked grid area , the pattern of grid blockage may be such that the zone above the grid is divided into separate regions so far apart that the exhaust streams found in them only lose their identity at a considerable height above the top of the moulding box . 
The important conclusion is that the effectiveness of down-draught systems of knock-out ventilation will not necessarily be improved by changes in the size and design of knock-out grids — regardless of exhaust air volume — if the depth of the box is too great . 
Field observations indicate that for the conditions described above , 11-in. or 12-in. is about the maximum permissible depth when knocking out hot , and that the blockage due to the box and sand should be less than 50 per cent . 
of the grid area . 
Selection and Performance of Down-Draught Systems 
Importance of the down-draught system — The ease with which a down-draught system of ventilation can be applied to a knock-out without interfering with other foundry operations frequently commends it to the planning engineer . 
The practical advantage of the absence of ventilating equipment above floor level is that all four sides of grids are available for the accommodation of foundry equipment , the movement of operators , boxes and castings , and no limitations are imposed upon the travel of cranes and hoists . 
The comfort of knock-out operators is greatly affected by radiant heat . 
The quantity of heat energy radiated from a surface depends upon its area , temperature , and radiation coefficient . 
Since no hood and baffles are fitted and the net area of the hot grid bars is small , the source of heat radiated to operators is effectively limited to the hot casting and the mould . 
Consequently , a down-draught system can give not only control of dust , but also less discomfort to the operators when dealing with a large number of very hot castings . 
Limitations in the application of down-draught systems — Down-draught systems can , as indicated by the experiments illustrated in Figs. 6.10 and 10a , and do , as shown by Test 1 in Table 2.2 , provide effective protection from the dust and fumes produced by relatively small castings in fairly shallow boxes . 
This system , therefore , finds the greatest application in highly mechanized foundries producing large quantities of light repetition castings . 
The down-draught system has , however , certain limitations and various factors must be considered before installing such a system . 
Depth of boxes — Thermal currents can not be reversed with economical exhaust air if the distance between the grid and the top of the boxes exceeds 12-in. , unless special provision is made . 
Boxes must always be knocked out at grid level and never turned over on rails above the grid . 
Size of grid — The larger the grid , the greater the area of boxes that can be knocked out and , consequently , the greater the distance between the side and centre of the boxes . 
The size of grids for hot moulds should not exceed 4-ft. 6-in. x 3-ft. 6-in. , or 6-ft. x 4-ft. in special cases . 
Shape of grid — The ratio of the grid length to width should be similar for both boxes and grid , so that exhaust air streams are concentrated around the sides of the box . 
Height of grid above the floor — The floor restricts the direction from which replacement air can approach a grid and acts as an air baffle , so that exhaust air velocities are highest when the grid is mounted level with the floor . 
Raised grids should not exceed 18-in. in height . 
Grid design — Green sand clogs between the bars of fixed grids and restricts the flow of exhaust air . 
A knock-out point should not be ventilated by a down-draught system unless sand is shaken through a vibrating grid at about the same rate as it is spilt from the box . 
Blockage of the grid — The blocked section of a grid should not greatly exceed the area of the box if the vibrating grid is efficient . 
The area of the box and spilt sand together should not exceed 50 per cent . 
of the grid if the exhaust air volumes given in Figs. 6.9 , 10 and 10a are to be used as the design basis . 
Experiments have shown that if the blockage is increased from 50 to 75 per cent. , the minimum exhaust air volumes required to control dust and fumes are increased by amounts up to 50 per cent. , or even more in some cases . 
Air seals — It is essential for knock-out units to be provided with effective air seals . 
The air seals at the sand transfer point between the hopper and belt must remain effective regardless of the rate at which sand spills from the hopper . 
Extraction of Sand and Fines 
In the down-draught system , air is exhausted through the sand falling into the hopper . 
Should this sand , or a large proportion of it , be completely dry , a considerable amount of the fines will be exhausted . 
With very high velocities the fines may be accompanied by fairly coarse grains . 
In consequence , the composition of the sand will be radically changed . 
The amount of material to be collected will be large and there may be abrasion of the ducting . 
The extraction of sand and fines can be reduced by consideration of the three following factors in design . 
Usually a combination of all three is necessary : 
( 1 ) The frequency of knocking-out in relation to the size of the hopper , rate of sand removal , and location of air ducts should be determined , so that the sand inside the hopper can never rise unduly close to the air inlets . 
The external angle of the base of the hopper should not be less than 60° . 
( 2 ) The velocity of the exhaust air close to the falling sand inside the hopper should be reduced by enlarged inlets . 
( 3 ) The air ducts in the hopper should be located and arranged so that sand does not fall directly into the exhaust inlet , and the openings should be protected by shields . 
In addition , the sand-to-metal ratio and the time between pouring and knock-out should be such that only part of the mould is completely dry by the time the knock-out is reached ( see Chapter 3 ) . 
If this condition can not be fulfilled a down-draught system should not be used . 
Sludging of Sand in the Exhaust Air Ducts 
Steam is released from hot moist sand moulds as they disintegrate and fall through the grid into the hopper . 
Should this steam exceed the amount which can be retained by the exhaust air , it will condense on the exhaust ducts . 
Sand and dust in the air stream will deposit on the moist surfaces or on any water at the bottom of the duct , forming a sludge which may eventually choke the duct to such an extent that efficient ventilation becomes impossible . 
The amount of water that can be retained by the air depends on the air volume and temperature . 
If the saturation level is exceeded , the moisture condenses to form droplets which are sufficiently small to remain in suspension as visible " steam , " but are readily deposited on objects with which they come into contact . 
The assumption takes account of the possibility that neither the deflection nor the slope at the ends of the beam is zero . 
The potential energy of the system is as follows : **f 
where b is the stiffness of the supports and K is a constant which depends upon the datum of the potential energy . 
Substituting for the { 15D 's by making use of equation ( 7.51 ) then yields : **f 
and for the potential energy to be stationary : **f 
whence : **f 
being the deflection of x = 0 , that is , at the load . 
Had an exact solution of this problem been carried-out there would have been seven simultaneous equations to solve in the seven unknown deflections { 15D1 , D2 , ... , 
D7 . 
The loss of accuracy due to adopting an approximate procedure is usually insignificant for purposes of engineering practice , i.e. a few per cent . 
Thus the correct value of d1 is 5.4 in . 
The considerable saving in labour achieved is usually much more important than a small loss of accuracy . 
In fact , it is possible in some instances , that without recourse to an approximate solution by an energy method , solution by manual activity would be too laborious to be practicable . 
CHAPTER 8 Some Uses of the Reciprocal Theorem 8:1 . 
INTRODUCTION 
One of the simplest statements of the reciprocal theorem which defines the reciprocal property of linear systems , specifies that the deflection of a point i of an elastic structure in a given direction due to the application of unit force in a given direction at another point j is equal to the deflection of j when unit force is applied at i . 
The deflection of j is measured in the direction of the line of action of the unit force while the unit force is applied at i in the line in which the deflection due to its presence at j was measured . 
This is manifest when the flexibility coefficients of linear structures are calculated , since then it is found that aij = aji as shown in Chapter 2 . 
It is also manifest when the stiffness coefficients are calculated . 
Further proof of the reciprocal theorem is hardly necessary . 
A simple statement of the theorem on these lines was made by J. Clerk Maxwell in his well-known paper on the analysis of frameworks ( 1864 ) but Clebsch had actually noted the reciprocal property of stiffness coefficients in his book published some two years earlier . 
Later Betti ( 1872 ) and Rayleigh ( 1873 ) made important general contributions to the theorem independently , which led to its coming to occupy an important place in the physics of linear systems . 
For the purpose of structural analysis the reciprocal theorem provides useful devices for the construction of influence lines for deflections and forces in frameworks whose elasticity is linear . 
8:2 . 
INFLUENCE LINES FOR DEFLECTION BY THE RECIPROCAL THEOREM 
For the purpose of illustrating this use of the reciprocal theorem it is sufficient to consider a simply supported beam with linear elasticity . 
Thus , if the influence line for the deflection of any point P of the beam shown in Fig. 8.1 is required ( that is , the curve whose ordinates represent the deflection of P as a concentrated unit load traverses the beam ) , by the reciprocal theorem it is merely necessary to consider the deflected shape of the beam due to unit load at P. The reason for this is that the deflection at any other point Q of the beam due to unit load at P is : **f 
where aQP is the relevant flexibility coefficient . 
Since this is equal to the deflection of P due to unit load at Q , i.e. : **f 
it follows that the deformed shape of the beam caused by unit load at P represents the variation of aQP = aPQ over the length of the beam which is the influence line for the deflection of P. By similar reasoning the influence line for the deflection of any point of an elastic linear structure , in a given direction , is represented by the deformed shape of the structure due to unit load applied in the specified direction at the point in question . 
A convenient means of using this principle to practical advantage is afforded by scale models . 
Such models need not be to scale in every detail ; for plane frameworks it is merely necessary that they are made of material which obeys Hooke 's Law of linear elasticity , to a chosen layout scale . 
Then , for portal frameworks whose members deform primarily in bending , it is sufficient for the ratios of the second moments of area of the members to be the same as in the actual framework . 
The shape of the required influence line to scale can be obtained by applying a force to the model at the point in question , in the specified direction . 
The scale factor for the ordinates of the influence line so obtained can be found either by scaling the force applied to the model or by calculating the deflection of the actual framework at the point in question due to unit load applied there . 
8:3 . 
INFLUENCE LINES FOR FORCES BY THE RECIPROCAL THEOREM 
A cantilever with a rigid prop at its " free " end , as one of the simplest statically-indeterminate systems , is suitable for demonstrating this use of the reciprocal theorem . 
In order to obtain the influence line for the force exerted by the prop , suppose first of all that unit concentrated load acts at any point Q of the span , as shown in Fig. 8.2(a) . 
If the prop is absent the deflection of the end of the cantilever due to this load is : **f 
so that the force which the prop must exert in restoring zero deflection at this point is : **f 
where the flexibility coefficients aPQ and aPP refer to the cantilever . 
Therefore , by equations ( 8.3 ) and ( 8.4 ) : **f 
Now the ratio aPQ/aPP can be obtained by considering an arbitrary small displacement { 15D7P of the end of the unloaded cantilever due to an arbitrary force R7P , as shown in Fig. 8.2(b) , since : **f 
while the resulting deflection of any other point Q is : **f 
so that : **f 
Therefore , by equation ( 8.5 ) : **f 
The significance of this result is that the deflection curve of the cantilever due to an arbitrary small displacement of P represents to scale the influence line for the load on the prop at P. This is in accordance with Mu " ller-Breslau 's principle that the influence line for the force in a member or upon a support of a linear statically-indeterminate framework is represented to scale by the change in shape of the framework due to a small displacement within the member or at the support . 
For the purpose of using the principle for the influence line for the bending moment at any point , the small displacement introduced there must be of the angular kind . 
It can be shown by virtual work that Mu " ller-Breslau 's principle also applies to statically-determinate systems which are not subject to gross distortion under load . 
Mu " ller-Breslau 's principle would be of very little practical value without scale model techniques . 
The procedure prescribed by the principle can be applied physically to a scale model for the purpose of obtaining influence lines to scale and affords an effective method of " model analysis " of frameworks . 
Such models must be made of material with linear elasticity to a definite length scale . 
Thus , if a model of the propped cantilever is made s times smaller than the actual , a small displacement **f at P corresponds to a small displacement **f at P of the actual system . 
Similarly , any other point of the model Q suffers a displacement which may be multiplied by the scale factor s to obtain the corresponding displacement of the point Q of the actual cantilever due to the displacement of P of **f . 
Also the deformed shape of the model represents the influence line for the load on the prop of the actual system to scale . 
Therefore , with reference to equations ( 8.8 ) and ( 8.9 ) : **f 
so that : **f 
and the scale factor does not appear in the final result obtained by the model in respect of influence lines for forces , because the ratios of model displacements of the linear kind are identical to the ratios of corresponding displacements of the actual structure . 
It is relatively easy to construct suitable models of frameworks whose members deform primarily in bending , such as portals , because then it is merely necessary for the ratios of the second moments of area of the various members to be correct . 
The actual scale factor in respect of second moment of area is immaterial and so models can be cut from , say , sheet celluloid , which obeys Hooke 's Law . 
Beggs pioneered the use of this kind of model . 
8:4 . 
EXAMPLE OF MODEL ANALYSIS 
The steel portal framework shown in Fig. 8.3 has encastre2 stanchion feet and the second moments of area of AB , BC , and CD are I , 2I and I , respectively . 
In order to obtain the influence lines for the redundants , chosen to be the reactions R1 , R2 and R3 at the foot A , a scale model may be used . 
The model must be made of material which has linear elasticity in accordance with Hooke 's Law ( e.g. , it can be cut from sheet Xylonite celluloid ) , to a layout scale factor s and the ratios of the second moments of area of the model members AB , BC and CD must be 1 : 2 : 1 . 
The required influence lines are found by subjecting the model , mounted to reproduce the encastre2 conditions at A and D , to small displacements horizontally ( for the influence line for R1 ) , vertically ( for R2 ) and rotationally ( for R3 ) at A , in turn , and recording the resulting changes in shape of the model . 
It is important for each displacement to be applied at A separately without movement in any other direction . 
Suppose the influence lines so obtained are as shown in Fig. 8.4 and that it is desired to determine the magnitudes of the reactions at A caused by the loading shown in Fig. 8.3 . 
Then using subscripts m to denote that the displacements are obtained from the model : **f 
which are independent of the scale of the model . 
For R3 , however , the scale of the model enters into the calculations and for this reason it is desirable to refer the model displacements to the corresponding values for the actual structure . 
Thus , if the foot A of the actual framework were rotated through th radians the resulting deflections would be s times those of the model when its foot A is rotated through the same angle . 
Using the equivalent full-scale influence line ordinates then to obtain R3 gives : **f 
since th is **f . 
Again , for a uniformly distributed loading of intensity w over , say , CD , the corresponding values of the reactions at A are : **f 
where distance x along CD refers to the model , so that if a1 , a2 and a3 are the areas enclosed by the relevant portions of the influence lines of the model , respectively : **f 
and for practical purposes it is sufficiently accurate to assume that the influence lines are straight between measured ordinates . 
The influence line for the bending moment at a point within a member can be obtained similarly by cutting the model at the point in question and applying an angular displacement , as indicated in Fig. 8.5 . 
The required bending moment due to particular loading is then obtained from the influence line ordinates in a manner similar to that used for finding R3 . 
It is particularly important to measure the influence line ordinates correctly , as , for example , in Fig. 8.4 with respect to the line of FQ2 . 
Accuracy can also be improved by using positive and negative displacements , as shown in Figs. 10.20 and 10.21 . 
Use of scale models for the analysis of frameworks is always worth considering as an alternative to manual computation , especially for frameworks of simple form whose members are of non-uniform section for reasons of economy . 
Accuracy of model analysis tends to lie between 5% and 10% in relation to values calculated exactly on the basis of the same assumptions as those used in constructing the model . 
Two articles have appeared by Bichsel on electron microscopy ; one is concerned with an investigation of sub-grain structure in high purity aluminium , while the other is general , describing the application of oxide replica techniques and the examination of thin foils . 
The illustrations in all these papers are impressive scientifically and attractive aesthetically ; it is only a matter of time before they receive the attention of designers of wallpaper , floor coverings and similar goods . 
Single crystals continue to attract the experimenter ; McKinnon has studied the work-hardening of a super-purity aluminium crystal , and indicated that during stage 1 , that is the period of slip on ( 111 ) plane of maximum resolved shear stress , the rate of hardening is determined by the amount and type of uniformly distributed secondary slip . 
Greetham and Honeycombe have deformed single crystals of aluminium-4.5% copper given various ageing treatments after solution treatment . 
Under-aged crystals showed a marked yield point followed by a period of low hardening , while over-aged crystals and those treated at the optimum temperature , though showing no yield point , strain-hardened rapidly . 
By X-ray and metallographic study , Richards and Pugh have determined the sequences of behaviour of super-purity aluminium during rolling and annealing . 
Structures after various amounts of cold reduction are illustrated as photomicrographs and X-ray transmission patterns . 
Blade , Clare and Lamb have used levitation melting to provide ingots of zone-refined aluminium containing additions of various elements , which were then rolled to sheet for determination of recrystallisation temperatures . 
As little as 0.001 at . 
% of the addition elements was sufficient to produce most of the retardation of recrystallisation ; silicon , copper and magnesium each caused an increase of recrystallisation temperature of 50-100° C. , while for iron , chromium and manganese a figure of c. 200° C. is quoted . 
At temperatures varying from 195-500° C. , Ormerod and Tegart have subjected super-purity aluminium to torsion stresses , and determined torque values which are converted to shear stress , while specimen revolutions are converted to shear strain , the two being used to draw true stressstrain curves . 
Davies has performed stress-rupture tests on the aluminium-1% nickel alloy favoured for resistance to corrosion by high temperature water , and obtained 1,000 hour values of 0.75 at 350° C. , 1.8 at 250° C. , and 4.2 at 100° C. , the units being kgsq. mm. ; English eyes would have preferred tonssq. in . 
Corrosion and Protection 
No form of degeneration of metals is more insidious than corrosion , and the volume of work published on the subject is a measure of the seriousness with which it is viewed . 
Evans has produced a monumental volume of great authority on the corrosion and oxidation of metals in general , with an author index containing no less than 3,000 names . 
A fat volume , but the scribbling has been very well worth while , and as with Gibbon 's work it will well outlive the author . 
Another useful book is that written by Rogers , principally for the education of naval constructors who are responsible for the maintenance of ships of war ; aluminium receives its due meed of attention , with alarming illustrations of what happens when wrong procedures are adopted , and details of correct design and practice . 
The power of the corrosive enemy must be recognised and assessed ; Great Britain has the unenviable reputation of being a particularly aggressive place . 
Ambler has found that the distribution of chloride in the British atmosphere has the same general relation to distance from the sea as in West Africa , and that the corrosion of steel and zinc bears no relation to salinity ; encouragingly , he considers that the corrosion of his aluminium specimens was so small as to give high errors on cleaning . 
A new hazard has been added to corrosion testing . 
At Llanrhystyd , Ambler 's specimens were liable to be licked by cows on the landward side ; he states that this would not be expected to give low results , but this surely depends on the corrosivity of cow saliva as against the beneficial effects of regular cleaning . 
In continuing its work on the basic causes and mechanism of corrosion , the National Bureau of Standards in the U.S.A. has established that with large single crystals of high purity aluminium exposed to an acid mixture , configuration of etch pits differed according to crystallographic orientation , and the rates of attack varied radically from those observed in an alkali mixture . 
Edeleanu has studied the pitting mechanism , using 99.999% aluminium foil in sodium chloride solution , and demonstrated that the rate of attack per unit of active area inside a pit is a constant , and that changes in an external polarising current change the rate of pitting only by altering the active area . 
An electron micrograph of a pitting system illustrates effectively the frequent changes in direction of the attack . 
In a general summary of the causes of pitting and its effects , Robinson makes the cardinal point that to avoid it one must eliminate the chloride ion or inhibit it ; it is not always possible to adopt either of these admirable actions , so that pitting must sometimes be lived with and allowed for in design and selection of materials . 
Susceptibility to intercrystalline corrosion may be a less serious matter than proneness to stress-corrosion ; indeed , in the high strength Al-Zn-Mg-Cu alloys , stress-corrosion failure can occur when very little evidence of corrosive attack is to be detected . 
In developing tests for the susceptibility of this type of alloy to intercrystalline attack , Ketcham and Taylor do not mention stress-corrosion , and while their tests are no doubt of value , tests including stress application would be preferred . 
Silver is highly cathodic to aluminium , and alloys containing large additions of silver might be expected to be correspondingly low in corrosion resistance . 
This has been shown to be the case by Stadelmeier and Whitener ; in their aluminium-silver alloy , Ag2Al was precipitated on the grain boundaries , and in a refrigerator atmosphere samples were completely pulverised in four weeks . 
A Committee of the National Association of Corrosion Engineers has reported on its investigations of techniques applicable to the examination of aluminium corrosion products , including X-ray diffraction and fluorescence , thermal analysis , electrographic methods , spectrographic analysis , microscopic examination and quantitative and qualitative tests . 
Having purified water sufficiently for it to merit the application high-purity , the user is anxious to keep it so , and Knoedler and Gordon have assembled test data on many materials that may be used for containers , pipes , etc. , including steel sprayed with aluminium , and the same combination coated with a polyvinyl top coat . 
Commercially pure aluminium and aluminium-manganese alloy tanks were also used , and the water showed 0.035 parts per million of aluminium after 56 days ' storage ; a very low proportion . 
In comparing metals for compatibility with 90% hydrogen peroxide , Bloom and his co-workers award classification 1 only to pure aluminium , certain aluminium alloys and zirconium . 
A rocket fuel rejoicing in the name of unsymmetrical dimethylhydrazine has been successfully stored in aluminium containers for three years without ill effect , as reported by Raleigh and Derr . 
Many somewhat unusual chemicals are needed in conjunction with rocket engines , and Geiger , Schuler and Mowers have discussed material selection problems in the light of present knowledge . 
Aluminium is compatible with hydrogen peroxide , nitrogen tetroxide , liquid fluorine and inhibited red fuming nitric acid , amongst other rocket chemicals . 
Aylmore , Gregg and Jepson have studied the oxides formed when aluminium is heated in dry oxygen and interpreted their results as showing crystallisation of an initially formed amorphous layer . 
Using an A.C. bridge , Lorking measured the capacity and thus the thickness of non-porous oxide films on aluminium ; chloride ions in solution increased the permeability of the film , and this was detected by potential measurements . 
Since a general air of pessimism permeates the account by Capp and Philibert about ship corrosion , their remarks about trouble with aluminium are perhaps less unacceptable ; however , they seem to be ill-informed about developments since the war in such matters as riveting and boundary bar joints , and the general avoidance of bimetallic corrosion . 
The stupid things that are still done are exemplified in an account by Brooks of a floodlight from a fishing vessel , that had castings in an aluminium alloy containing 2 1/2% copper , was bolted together with brass bolts , and employed an absorbent fibre gasket . 
It seems hardly conceivable , but these things still happen , even in the second half of the twentieth century . 
In the aircraft industry , hazards are much more fully recognised ; Heath has shown how modern aircraft design is being modified to provide access to all parts for inspection , to ensure that unobserved corrosion can not proceed to cause a catastrophe . 
This requirement in design is , of course , most important in modern aircraft from which long service lives are expected . 
Corrosion at welds has not proved a serious problem with aluminium since the dangers of flux entrapment were eliminated by the adoption of inert gas-shielded welding methods ; however , trouble with large gas-welded cooking pans in aluminium-2% magnesium alloy described by Latimer was not due to flux residues . 
" Knife-edge " attack along the sides of the welds was shown to be associated with the coarse structure of the partially fused zone , and the presence of continuous { 15b-phase on the grain boundaries of the heat-affected zones . 
This could be avoided by welding at a faster rate with less heat input , e.g. by tungsten-arc welding . 
Oldfield and Twigg investigating the staining of stainless steel tableware , tested blades in contact with galvanised iron and with aluminium in Sheffield tap water at 60° and 100° C. They concluded that aluminium containers are reasonably safe for trays or baskets for washing stainless steel cutlery , but galvanised iron can cause staining . 
Aluminium-magnesium-silicon alloy ( similar to H9-P ) pipe , TIG welded , and used for sour gas was inspected by Flournoy after being buried for six years without protection in a soil of sandy loam and broken caliche . 
Where failure had occurred , it was by pitting from the outside , and chlorides were detected in the corrosion product . 
This experience shows that aluminium is resistant to sour gas , and may be installed bare underground if protection is afforded at local spots of high corrosivity . 
If one keeps the anti-freeze in the cooling system of one 's car from year to year , one runs the risk of corrosion of the cast-iron parts of the circuit , due to increase in acid content and reduction of inhibitor content of the cooling liquid . 
This has been shown by Collins and Higgins , who also state that the danger of corrosion of other metals by the deteriorated anti-freeze is slight ; only occasionally has slight pitting been seen with aluminium , and no corrosion necessitating replacement has resulted . 
Investigating the special case of hypereutectic aluminium-silicon alloys under conditions related to car engine cooling systems , Craig and Woods have shown that such alloys , even when coupled to copper , are corroded to a negligible extent if there are suitable inhibitors in the coolant ; in general , hypereutectic aluminium-silicon alloys are more corrosion resistant than cast iron . 
Sundararajan and Char , continuing their studies of inhibition of the corrosion of aluminium , have assessed the effects of acridine , nicotinic acid , dextrin , thiourea and tannic acid in dilute hydrochloric acid ; all were efficient . 
In a second paper these authors describe polarisation studies in acid and alkaline solutions , with thiourea and dextrin as inhibitors , and conclude that cathodic protection is possible in acid solutions in the potential range -0.55 to -0.80 V. In both these papers one meets again the curious material previously described by Sundararajan and Char , namely 92% pure aluminium , containing 3% Fe , 4% Mn , 1% Si ; doubts about decimal points return more strongly than ever . 
Using some impressive mathematics , Bauer and Eddy have compared various possible anode materials for the protection of water tanks . 
One interesting factor affecting choice is whether or not the water freezes and breaks the anode or suspension ; if it does , aluminium is used , because of its cheapness . 
Chemical conversion coatings have been summarised by Ayres , considering them principally from the point of view of corrosion resistance , which is conferred by low chemical activity and solubility . 
Wells and Pinner have surveyed recent advances in chemical and electrolytic polishing , on all relevant metals including aluminium . 
This particular detecting element illustrates why the plant engineer is slow to take up new ideas , for at first sight to introduce microwave generating and detecting equipment into a power station fills the plant engineer with horror . 
It is only when the equipment can be made rugged and utterly reliable that he will consider using it at all . 
Nowadays engineers tend to use detecting elements which give an electrical output . 
The reason for this is that it is a matter of extreme simplicity to amplify the signal to any degree which is necessary . 
Moreover , it is very easy to transmit the signal from one part of the plant to another without serious loss . 
Detectors having an electrical output are therefore of growing importance at the present time , although in many cases a mechanical output is still quite satisfactory . 
Pneumatic Devices 
It is surprising that so little use is made of pneumatic devices for measurement and control of small distances . 
Work which has been done in the British Scientific Instrument Research Association has shown that pneumatic gauging is an almost ideal way of deciding if a sliver of a semiconducting material is of the right dimensions for manufacturing a transistor . 
Pneumatic bearings also have a considerable application which has not been developed outside gyroscopes : for example , a patent has recently been taken out covering the use of a pneumatic bearing for a glass polishing head . 
Passing on to optical detecting elements , which are now beginning to receive the attention they deserve as a result of the application of electronic devices to replace the human eye , these are coming more and more into favour as on line instruments . 
The nondispersive infra-red spectrometer is a good example , while the automatic saccharimeter developed at the National Physical Laboratory has a good future , but it is when one comes to consider the more sophisticated optical electronic instruments that one finds the numerous advantages of utilising the visible and near visible portions of the electromagnetic spectrometer . 
The Hilger &Watts automatic spectrographs are now well known and are in constant use in the iron and steel industries , while optical methods are beginning to be used in the guidance systems of many of our guided missiles . 
The importance of electrical detecting elements has already been stressed . 
Of these , the piezo electric effect is the best known and most used , apart from the obvious conventional cases of the thermocouple and the resistance thermometer . 
The piezo electric effect can be used to launch ultrasonic waves in a liquid or in a slurry , and the resulting phenomena are only now being investigated on an industrial basis . 
Nucleonic instruments tend to be largely electronic devices . 
The detecting element itself generally uses a nucleonic phenomenon , but the remainder of the apparatus is electronic . 
The reason for this is that nucleonic detection usually takes place in a very short space of time and , of course , the big advantage of electronics is its speed of response . 
The preceding paragraph gives some general reflections on detecting elements . 
A book could easily be written on this subject without exhausting the possibilities . 
Mechanical , hydraulic , pneumatic and electrical amplifiers are all in use in automatic control systems , and these represent the second class of component into which the system can be resolved . 
Mechanical amplifiers are exemplified by levers , while hydraulic amplifiers are exemplified by transference of a pressure or a flow from a wide tube to a narrow one . 
Pneumatic amplifiers operate in much the same way as hydraulic amplifiers , but offer greater diversity in their application . 
It should be noted that in none of these cases is there any real gain in the energy of the signal . 
For example , a lever increases the movement which is available to the observer , but it does so at the expense of the effort which is available at the end of the lever . 
The same is true of the hydraulic and pneumatic amplifiers which have been mentioned . 
Nevertheless , amplifiers have been made which correspond exactly to the electronic amplifier : the signal strength is actually increased at the expense of a reservoir of gas or liquid . 
Electronic amplifiers are essentially devices which transform part of the direct current available from the power supply to signal current , which can then be used to perform an operation . 
The third element of a control system is the transmission itself . 
At the present time the transmission is very often done hydraulically or pneumatically , but electrical systems are gradually coming into use , subject , of course , to the stringent conditions of intrinsic safety . 
Where long runs are required , electrical transmission is obviously to be preferred . 
The Use of Computers 
The next item in the control system has gained considerable notoriety and is sometimes thought by the uninitiated to be the principal component . 
It is the data logger or computer . 
Computers were originally manufactured in analogue form to solve certain complex differential equations and , in the first instance , they were mechanically operated . 
Thereafter , electronic computers came in , operated digitally , and since then there has been competition between the analogue computer and the digital computer . 
To a certain limited extent the analogue computers are very useful for the examination of plant characteristics , and such computers can be used to advantage when a new plant is being set up which is to be automatically controlled throughout . 
On the other hand , where extreme accuracy is required the digital computer is the only one to use and electronic digital computers are employed to advantage in performing difficult calculations in optics , in stresses and strains in aircraft , and in a multitude of other problems . 
So far as process control is concerned , after the preliminary investigation has been carried out by means of an analogue computer , the equipment to be used on the plant should be as simple as possible and should comprise a detecting element , a data logger and a controller , the third being connected , of course , by transmission lines . 
The data logger is usually called upon to perform one or two simple operations and , as such , it is not worth while using a general purpose electronic digital computer to do the job . 
It is therefore the writer 's opinion that general purpose computers have no long term significance so far as process or machine tool control is concerned . 
Rather the data loggers and computers which will be used in these circumstances will be small black boxes , designed to do specific jobs . 
It will be seen that the problem of the computer is in no way related to the problem of the detecting element . 
When we are concerned with the right kind of detecting element to use for a particular purpose , this takes us into the background of science to examine all the various phenomena and decide on the right device . 
On the other hand , so far as data loggers and computers are concerned it is a matter of straightforward engineering , for the circuits and devices to be used to perform the various specific tasks are all well understood . 
There is only one case where this may not be completely true , and that is where extreme speed is required in the computer , but this occurs so seldom in process control or machine tool control that it is hardly worth considering . 
The Controller 
The last element in the automatic control system is the controller itself . 
This has to be a mechanical device since it is applied to the line and changes certain parameters therein . 
Controllers nowadays are usually described as " three term " , meaning that they have a proportional control , a control which is determined by the rate of change of the signal , and a control which is determined by the integral of the signal . 
Three term controllers require careful setting up , and to make the best use of them an exhaustive analysis of the plant is necessary , but there is no doubt that three term control is essential in most cases if the plant is to operate at optimum efficiency . 
The necessity for the three term controller is to be found in the mode of variation of any particular parameter . 
For example , if we are concerned with temperature measurement and the temperature should suddenly shoot up , then some degree of anticipation is given to the controller by means of the rate of change of the signal . 
On the other hand should the parameter vary slightly between fairly wide limits over a long period of time , then it is very difficult to maintain it at the desired value unless an integral of the signal is used in the control system . 
No doubt more complex controllers could be manufactured and may be used in the future , but in the meantime the rate of change , the signal itself , and the integral of the signal give sufficient control . 
The Instrumentation of Reactors and Conventional Electrical Power Units 
Whether coal or uranium is used as the fuel , the power unit must always contain certain basic automatic controls . 
At the present moment the output of any station is in the form of electricity , which usually comes from a turbogenerator . 
Certain conventional instrumental controls are necessary at this end , but with the increasing use of reactors as power producing units , a completely new set of problems has been posed to the industrial instrument manufacturer . 
Apart from the measurement of such novel parameters as the neutron flux in the reactor , the control of temperature has become of major importance . 
An elegant solution to this problem is not yet in sight , but reactors are able to operate using a very large number of detecting elements which measure temperature . 
One of the outstanding problems of reactor instrumentation is the measurement of flux of intermediate energy neutrons . 
The British Scientific Instrument Research Association began an investigation of this problem some three years ago and the results so far achieved are promising . 
As might have been expected , on the way towards the solution of the set problem ( the measurement of flux of intermediate energy neutrons ) many other problems have been brought to the notice of the Association and have been solved . 
It is probable that the work at present in progress on new types of phosphors will result in a new set of instruments becoming available to the reactor engineer . 
If this is so , the economics of reactor manufacture and operation will need to be completely revised . 
Power Units in Industry 
Almost every big factory in the country produces a large amount of steam , which is then used for many purposes . 
These power units are all very similar and one would expect that their instrumentation would be well known and well defined . 
This is not the case , however . 
Apart from the measurement and control of fuel , steam pressure , water , and alkalinity or acidity , there are many other factors which must be measured in an economic power plant . 
The air to fuel ratio , the carbon monoxide content in the flue gases , and the smoke issuing from the chimney must all be controlled , and almost every factory has its individual system . 
There is certainly room here for a large amount of standardisation and , among smaller firms , for education in the value of adequate instrumentation . 
Future Trends 
It is a difficult matter at this juncture to specify the future trends of instrumentation among our basic industries , and so it may be well to deal , first of all , with those matters which are well defined . 
There is no doubt that large chemical plants could use to advantage on line instruments to perform simple chemical analyses , but in many cases progress is at a standstill because it is very difficult to imagine a detecting element which can be successfully applied to a plant . 
Another trend which has been mentioned above is towards the small special purpose computer . 
The general purpose machine usually contains much more than is necessary to perform its operation on the plant , and it is only by cutting out these unnecessary devices that the computer can be made an economic proposition . 
This trend is fairly certain . 
The other trend which appears to be well established is towards the detecting element having an electrical output . 
The ultimate concentration in the liquid oxygen will , therefore , depend on the equilibrium constant for the impurity when present in low concentration in liquid oxygen . 
Also , if the solubility is low , precipitation may occur before the concentration in the exit gas reaches the required value , and accumulation of the impurity as a solid will occur . 
Table 3 shows the results of calculations for a number of trace impurities in which , for different assumed concentrations in the inlet air , the concentration in the liquid oxygen in the evaporator for steady state operation has been determined for gaseous oxygen production . 
It must be appreciated that the figures for the concentration build up are dependent on the accuracy of the equilibrium data , which are uncertain , but the table does give an indication of the order of magnitude to be expected . 
It is important to note that where high concentrations are theoretically possible in the plant evaporator the time required to build them up may be considerable , thus easily allowing steps to be taken to prevent such accumulations occurring . 
Before discussing the methods which are adopted in practice to achieve this , we shall consider in a little more detail the effect of impurities in the air intake . 
Effect of trace impurities in the air feed 
There has been a considerable amount of work carried out in recent years on the effect of trace impurities in the air feed . 
Not all of it has been convincing , and certain aspects are still by no means clear . 
It is impossible to do more than briefly review available information and data here . 
In considering the relative significance of trace impurities , particularly hydrocarbons , it should be borne in mind that small concentrations of hydrocarbons dissolved in liquid oxygen do not necessarily present a hazard . 
This depends on the susceptibility to detonation of the hydrocarbon solution , and on the explosive limits . 
Data are incomplete for such solutions , but generally if the percentage by weight of the hydrocarbon in homogeneous solution is less than 2% , detonation can not be initiated . 
In practice , it is obviously undesirable to operate near such a limit . 
LIGHT HYDROCARBONS , CARBON MONOXIDE , AND HYDROGEN 
In general , the C1 and C2 hydrocarbons such as methane , ethane , and ethylene , ( but excluding acetylene ) which have relatively low boiling points , do not normally present any hazard if present as traces in the air intake to a plant since they are appreciably soluble in liquid oxygen , and their equilibrium constants in admixture with this are relatively high . 
This means that they will not tend to accumulate in , for example , the oxygen evaporator to any dangerous concentration under likely operating conditions . 
Carbon monoxide and hydrogen in trace quantities present no hazard since hydrogen is incondensible at the temperatures involved and is removed with the atmospheric inert gases , helium and neon , at a suitable vent-point in the plant . 
Carbon monoxide is similar to nitrogen in properties and is , in fact , more volatile than oxygen . 
It therefore presents no hazard in trace concentrations . 
HIGHER HYDROCARBONS AND ACETYLENICS 
Hydrocarbon impurities under the rather arbitrary classification of higher hydrocarbons and acetylenics can arise from three possible sources . 
The first is physical carry-over of hydrocarbon oil from , for example , an oil-lubricated expansion engine . 
This can accumulate as a solid in an oxygen evaporator unless provision is made in the plant design to prevent such an occurrence . 
The second source is from atmospheric contamination . 
The third is oxidation or thermal cracking of compressor lubricating oils where a reciprocating compressor is used . 
By the use of relatively low interstage pressure ratios ( 3/1 or less ) and by the use of lubricating oils of high stability , contamination from this source can be reduced to very small proportions . 
The problem does not arise with turbocompressors . 
The higher hydrocarbons and acetylenics have low vapour pressures at liquid oxygen temperature and are , therefore relatively non-volatile . 
When combined with a low solubility , as in the case of acetylene , accumulation as a precipitated solid can occur . 
It is for this reason that acetylene is one of the most dangerous of hydrocarbon contaminants . 
Its solubility in liquid oxygen at its normal boiling point is approximately 6 parts per million and its K-value ( defined as the ratio of the mol-fraction of hydrocarbon in the gas phase to the mol-fraction in the liquid phase under equilibrium conditions ) is between 1/15 and 1/70 , depending on the data used , for oxygen evaporator conditions . 
Whilst solid acetylene itself is more stable than usually realised , when mixed with liquid oxygen it is detonated relatively easily . 
It has also been shown that when a solid acetyleneliquid oxygen mixture contains fine inert solid particles , then the susceptibility of the mixture to detonation as measured by an impact sensitivity test is high . 
It has also been stated by Karwat that an incrustation of solid acetylene on oxygen evaporator tubes , which can be wetted by splashing with liquid , represents a particularly dangerous condition . 
It should be appreciated that whilst the amount of acetylene which can accumulate in a plant may not always in itself be sufficient to cause a serious explosion , it can , however , act as a trigger or detonator for the explosion of larger amounts of carbonaceous material if these should be allowed to accumulate . 
It is interesting to note that recently it has been pointed out by Karwat that propane may , under certain conditions , present a rather greater hazard than has perhaps hitherto been recognised , mainly due to the fact that although its solubility in liquid oxygen is relatively high ( circa 50 000 parts per million of oxygen ) its equilibrium constant is very low . 
Even traces in the air feed can , therefore , accumulate in the oxygen evaporator unless removed . 
The higher molecular weight hydrocarbons do not normally cause appreciable difficulty because they are almost completely non-volatile at low temperatures and are removed in the purification or heat exchanger system . 
NON-HYDROCARBON IMPURITIES 
The main non-hydrocarbon impurities which are likely to pass through the heat exchanger system and initial purification on air separation plants are nitrous oxide , ozone , and oxides of nitrogen , in particular , nitric oxide . 
These impurities will also tend to concentrate in the oxygen evaporator , in particular nitrous oxide because of its low equilibrium constant . 
It has a low solubility ( circa 100 v.p.m. ) and there have been suggestions that mixed crystals of nitrous oxide and acetylene may form from saturated solutions arising in air separation plants which can be easily detonated when the acetylene content of the mixed crystals is high enough . 
Whilst fully conclusive evidence is not available , there are indications that the presence of ozone or oxides of nitrogen , ( or both ) in the presence of acetylene or other hydrocarbons may increase the susceptibility to explosion . 
Further information is required to elucidate fully the possible role of these contaminants . 
SOLID PARTICLES 
A factor that is not always mentioned when discussing the safety of air separation plants is the importance of strict cleanliness during plant assembly to avoid the introduction anywhere into the low temperature system of possible carbonaceous material , i.e. carbonaceous dust , cloth fibres etc. , since they can constitute a hazard if they accumulate in sufficient quantity at a particular point where a high oxygen concentration exists . 
Safety measures 
We shall now briefly review the various methods which have been or are used to control impurity build up in air separation plants . 
It is important to stress that the degree of protection which is employed may frequently be influenced by the amount of contamination of the atmosphere in the vicinity of the plant . 
PURIFICATION OF THE AIR ENTERING THE PLANT 
An obvious method , if practicable , is to eliminate impurities in the air entering the air separation unit . 
One approach to this problem is the use of catalytic purifiers after the air compressor in which the heat of compression is used , partly at least , to raise the air to a temperature at which the hydrocarbon impurities present can be catalytically oxidised . 
For example , in an installation in America a Hopcalite catalyst has been used . 
Whilst for heavily contaminated atmospheres this initial purification may have advantages , it is relatively costly and also will not completely remove all trace impurities which will , therefore , nevertheless require treatment and removal at a later stage . 
A further disadvantage is that if used with a reciprocating compressor , oil contamination of the catalyst and loss of activity can occur if it is used directly after one of the compression stages . 
A different method of reducing the contamination in the air intake , particularly in industrialised areas , is the use of alternative suction lines , sometimes of considerable length , leading outside the contaminated area . 
These may be changed over depending on wind direction and the intensity of local contamination . 
This again does not eliminate contamination but it can reduce it appreciably . 
REMOVAL OF IMPURITIES IN THE HEAT EXCHANGER SYSTEM 
The removal of the less volatile trace constituents in the air-feed can take place in the heat exchanger system to some extent depending on their concentration , physical properties , the type of heat exchanger system , and the air pressure . 
For example , in a plant using regenerators in which the air is cooled at approximately 5 atm abs almost to its dew point ( approximately -173° C ) , acetylene may be condensed in the regenerator packing and resublimed in the nitrogen of the next cooling cycle if the concentration in the inlet air exceeds approximately 0.6 v.p.m . 
This is a valuable safeguard of such plants . 
In plants operating with higher pressures , e.g. fluid-producing plants , the effect of the superimposed air pressure in raising the vapour pressure of condensible impurities reduces , or may eliminate the possible deposition of impurities in the heat exchanger system . 
REMOVAL AT LOW TEMPERATURES 
One of the simplest methods of reducing the build-up of contaminants in the oxygen evaporator , which is the crucial part of the plant , is to provide a continuous purge of liquid . 
This has been practised since early days , but by itself is not an entirely satisfactory operation since it is only palliative , can easily be misapplied , or not operated , and also imposes an additional refrigeration load due to liquid withdrawn and rejected . 
The next step was to use an additional small condenser built away from the main plant condenser which was operated in series as far as the oxygen flow was concerned . 
The basic elements are shown in Fig. 4 . 
A small purge was led away from the additional condenser and rejected . 
The net result is a relatively large purge from the main plant condenser , and an appreciable accumulation of impurities in the additional condenser . 
This , however , is small and suitably protected , so that if , in fact , an explosion should occur , relatively little damage is done . 
Whilst the above arrangement together with correct condenser design has been largely used in the past , the tendency today is undoubtedly towards the use of adsorption of the impurities from one or more of the process streams . 
Silica gel is the adsorbent commonly used . 
There are a number of places at which one can apply such a clean-up system and they will be briefly mentioned . 
Fig. 5 shows a hypothetical and simplified plant flow diagram in which the various positions in which such adsorbers can be used is indicated . 
For illustration , the plant cycle shown is a low pressure plant using regenerators and producing gaseous oxygen . 
Adsorption from the gas phase at or near the saturation temperature has attractions and silica gel adsorbers placed after the regenerators on low pressure plants provide a very effective clean up . 
The adsorbers are , however , large and relatively costly . 
The effect when a number of impurities are present on their individual adsorptive capacities under dynamic conditions , must be allowed for , i.e. the occurrence of sorption displacement has to be considered . 
For example , Karwat showed that in solution in liquid oxygen trace impurities reached their " break point " in a silica gel adsorber in the order of ethanepropanenitrous oxide + ethylenecarbon dioxidepropylene and acetylene , whereas in gas phase adsorbers the order of break through was ethaneethylene and nitrous oxidepropane , and then acetylene and propylene . 
Another generalization presented in Chapter 6 was the application of the technique to large structural assemblies in which we provide also for the so-called interaction or external redundancies . 
As far as the practical side of the cut-out technique is concerned this was discussed in connexion with windows , doors , wing-fuselage interpenetrations , floors , partial removals of rings , etc . 
Now , we may consider the cut-out process as a special case of the more general modification technique and this was , in fact , usually our approach to the presentation of the relevant theory . 
However , we did also mention that there is an essential difference between the cut-out and modification techniques in their practical application . 
This is immediately evident if we have to apply these respective procedures to a large number of elements which may be taken to form a sub-system . 
Thus , when the flexibilities of the elements of the sub-system have to be modified it is obvious that we have to include all stresses specified in the elements to be altered in the matrix b1h and other relevant matrices of the sub-systems . 
But this is not so if we wish to eliminate the sub-system . 
Here we may achieve its effective removal by detaching it along its boundary in the parent regularized structure , leaving only a statically determinate connexion . 
Hence , in this approach , we actually cut only the redundant members of this connexion without having , at the same time , to break it up internally if it is itself redundant . 
On the other hand , it is perfectly legitimate to carry out , in addition , these internal eliminations , but this extends inevitably the amount of work involved and the order of magnitude of the matrix to be inverted . 
But on no account can we cut beyond this stage for we would then create a kinematic mechanism which means mathematically linearly dependent rows in b1h and a consequent singularity of the process . 
Thus , we see that in the case of the elimination of sub-systems there is no unique number of cut-outs and , furthermore , no unique position of these cut-outs . 
We may achieve a minimum of eliminations by removing only the redundancies along the boundary and we may reach a maximum of eliminations by cutting also the internal redundancies . 
These subtle considerations are dealt with in great detail in Section 36 and illustrated on a wide range of examples showing the alternative ways we can view and solve these problems . 
Prior to this we summarize for the convenience of the reader in Section 35 the basic theory of the modification and cut-out procedures as developed in a number of sections of this book and take this opportunity to generalize slightly the presentation . 
We hope that this joint account of theory and solutions to specimen problems will contribute to a deepening of the understanding of the cut-out technique and of its applications to practical cases . 
The concluding section of this chapter generalizes the matrix programme for the bending moments in the rings put forward in Section 12 . 
The reader will remember that the method given there ignored any discontinuity of the bending moments at the vertices . 
Now , this may be a too rough approximation when large loads ( e.g. at wing fuselage attachments ) are applied at the external vertices or other points of the rings . 
The necessary simple theory is developed in Section 37. 33 . 
Techniques to Improve the Conditioning of the D Matrix 
First a word of apology to our mathematically more knowledgeable readers . 
We are only too conscious that , in our repeated references to the conditioning of the D matrix , we have been guilty of imprecise language , not having really defined mathematically what we mean by the conditioning of a set of linear equations in the unknown redundancies . 
Indeed , our whole approach to this matter was rather of applying the terminologies well- or ill-conditioned as qualitative terms of praise or abuse to a system of equations . 
Now , ill-conditioning can , in fact , be expressed by various mathematical measures . 
Unfortunately , most of these precise measures involve as long computations as the solution itself of the simultaneous equations and are not , hence , very useful in practice for giving advance warning . 
We refer the interested reader to the papers of Todd , Turing , and Johannes von Neumann cum Goldstine . 
Even the relatively simple rule that ill conditioning is present when the value of the determinant **f is small ( more precisely we should state that **f is small compared with the individual terms of expansion of **f in the co-factors of the elements of any chosen row or column ) is not of much value in computational work . 
Nevertheless , in structural problems it is usually possible to adopt a simple measure sufficient for practical purposes . 
To fix ideas , consider a fuselage with two bays where only one set of primary redundancies Y arises at the intermediate frame station . 
Having introduced — for reasons connected exclusively with the application of the digital computer — the inversion technique of Eqs. ( 4 , 21 , 44 ) for the direct determination of the complete b1l , b1q matrices , and hence also of b1r , we are necessarily faced with self-equilibrating systems which are spread over the complete cross-section or , at least , over the main ( outer ) periphery . 
To express then with a high degree of accuracy ( from the practical computational point of view , which is the only one which interests us ) any arbitrary self-equilibrating stress system in terms of the b1l , b1q , b1r distributions , it is mandatory that the columns of these matrices — each of which corresponds to a redundancy — be not even remotely linearly dependent . 
This is evidently achieved when the flange loads , field forces and ring bending moments due to Y exhibit an increasing waviness with increasing order of redundancy . 
The search for such distributions brought us , more or less inevitably , to the selection of the trigonometrical matrix { 15Ol as a transformation matrix Al defining the redundancies . 
As we know from Chapter 4 and a large number of other similar computations , it appears that for the cross-sections commonly occurring in practice the flange loads and field forces based on { 15Ol do indeed retain the full waviness of { 15Ol , although naturally they are not any longer orthogonal as in the uniform circular cylinder . 
If the rings or frames were now rigid this characteristic waviness would ensure the precise determination of the redundancies and we then say that the associated equations are well conditioned . 
For the associated matrix Dyy — which in the present case where Dyyr is zero reduces to **f 
we observe that the diagonal terms dii must be strongly preponderant , the non-diagonal dij being the smaller the better the waviness of { 15Ol is retained . 
It is now possible to give the conditioning some measure by the degree of satisfaction of the condition **f 
which is the generalization of the simple requirement usually quoted for 2 x 2 matrices . 
From the strictly mathematical point of view the inequality ( 2 ) ought to be defined more rigorously to express a sufficient condition theoretically acceptable ; at the same time we know that it is not a necessary prerequisite for good conditioning . 
Nevertheless , for us engineers the relation ( 2 ) yields for structural matrices a sufficient measure for satisfactory conditioning . 
We must interpolate here in our main argument and refer briefly to the method of establishing systems of redundancies previously advocated by us in Ref. ( 30 ) . 
Contrary to what we put forward in the present treatise , we suggested there that it is advantageous to select systems of a distinctly local character . 
Clearly then condition ( 2 ) still holds and is the better satisfied the less overlapping there is between the self-equilibrating systems . 
For reasons set out in the introduction and subsequently , we preferred here the method of direct inversion for the determination of b1 . 
Considering next the more realistic case of fuselages with rings of finite stiffness , we find that the matrix Dyyr becomes of paramount importance ( this being at least so for the lower order redundancies ) and Eq . 
( 1 ) must be written as **f 
We noted in Chapter 5 that the internal ring forces b1r are much more prone to lose their full waviness when the cross-section departs significantly from the circular shape . 
It is inevitable , in such instances , that the off-diagonal terms dijr ( elements of the matrix Dr ) may become of similar order to diir and/or djjr so that the measure of conditioning , Eq . 
( 2 ) , will consequently deteriorate and yield , in extreme cases of severe loss of waviness , a positive value only slightly above zero ( of course , it can never become negative in structural problems ) . 
Such unfavourable conditions may prevail only in a few isolated spots of the Dyy matrix and we observed in Chapter 5 , p. 195 , that they do not seem , in our experience , to affect appreciably the accuracy of the solution , as long as these " Scho " nheitsfehler " are within **f 
On the other hand , as these unfavourable patches spread , the solution of the equations in the redundancies becomes increasingly inaccurate due to the limited number of digits available and the rapid accumulation of errors . 
Naturally , all methods of inversion or direct solution of equations are not equally sensitive to this danger in each specific case . 
Although such pronounced ill-conditioning should not often occur in practice , it remains a distinct even if remote possibility . 
We are thinking here of double cell cross-sections with doubly-connected rings of unfavourable shape — for which the conditioning of the symmetrical higher modes deteriorates rapidly — and the rather box-like cross-sections of fuselages specially designed for bulky loads . 
Our unavoidably superficial account leaves many extremely difficult questions unanswered ; in particular , the precise or statistical correlation between order and spread of bad patches , on the one hand , and loss of the accuracy of the solution on the other must unfortunately be ignored . 
An interesting practical point concerns the acceptable degree of inaccuracy in a solution due to such or other causes of errors . 
The practising engineer may often , and rightly so , consider a solution as satisfactory , although to us primarily interested in this instance to develop new methods , it may appear unacceptable . 
We referred to this issue in the introduction to this chapter when we discussed the application of the four-flange systems as redundancies . 
Now , for the reasons stated there and here , we must reject such a narrow utilitarian outlook and seek , in fact , a system of redundancies even better than that based on { 15Ol , if the conditioning of the latter should prove to us unsatisfactory . 
However , quite apart from the purely technical reasons , which demand such an extension of our original method , it is also perfectionism — a close companion of any intense research activity — which induces us to search for a more appropriate transformation matrix Al . 
Before we proceed to the examination of this question , we must first conclude the bird 's eye view of our theme . 
The discussion of the previous paragraphs was concerned with the so-called conditioning of the matrix D in the case of a single set of the primary redundancies Ya . 
When the fuselage extends over more than two bays , there arises at each intermediate frame station i a set of redundancies Yi . 
It is evident that our previous account is still applicable to the submatrices Dii in the leading diagonal of Dyy . 
We denote the conditioning of these matrices as peripheral to differentiate from another type presently to be mentioned . 
Now , when a satisfactory conditioning of the leading diagonal submatrices has been achieved this will also apply , in general , to each of the other submatrices ( in the secondary diagonals ) of the five-band supermatrix Dyy . 
Only a very violent change of cross-section could , { 6in extremis , give rise to a significant ill-conditioning in these submatrices . 
However , from the point of view of the overall conditioning of the complete Dyy matrix , another possible source of ill-conditioning has to be looked for . 
Thus , if the off-diagonal submatrices , say , Di , i+1 ( or Di , i+2 ) arising from the coupling of the sets Yi and Yi+1 ( or Yi+2 ) were proportional to Dii , the proportionality factor being only slightly smaller than unity , then it is evident from what we said previously in the peripheral kind of conditioning , that a new kind of ill-conditioning , conveniently denoted as a longitudinal one , could originate .