George Paget Thomson-Nobel Lecture Ever since last Novem ber, I have been wanting to ex press in person my gratit ude to the generas ity of Alfred Nobel, to w hom i ow e it t hat I am privileged be here today, es pecial y since ill ness prevented me from doi ng so at the proper time. the idealism w hic h permeated his char acter led him to make his magnifice nt foundation for the benefit of a cl ass of men with w hose aims and view poi nt his ow n scienti fic instincts and a bility had made him naturally his successful in the first as in t he second, is due to the manner in w hich his wishes have been carried out. The Sw edis h peo ple under the le adershipof the Royal Family, and through the medium of the Royal Academy of Sciences, have made the Nobel Prizes one of the chief causes of the growth of the prestige of science in the eyes of the world, w hich is a feat ure of our time. As a recipient of Nobel's generosity I ow e since rest thanks to them as well as The goddess of le ning is fa bled to have s rung full -grow n from the brain o Zeus, but it is seldom that a scientific conce ption is born in its final form or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that come after. The electron is no exception. have realized it, his wor k on electrol ysis, by s howing the o uti the first step. Clerk Maxwell in 1873 used t he phrase a 'molec ule of electricity and von Helmholtz in 1881 s pea king of Faradays wor k said "If we accept the hypothesis that elementary substances are composed of atoms, we cannot well avoid concluding that electricity also is div ided into elementary porti ons w hich behave like atoms of electricity. The hypothetical atom received a name in the same year when Johnstone Stoney of Dublin christened lectron charge. last year of the nineteenth century saw the electron take a leading place amongst the conceptions of physics. It acquired not only mass but uni versality, it was not only electricity but an essential part of all matter. If among the many names associated with this advance I mention hat of].J. Thomson I hope you will forgi ve a nat ural pride. It is tothe great work of Bohr that we owe the demonstration of the connection between electrons and antum whic h gave the electron a dy namics of its own. A few years later, Goudsmit and Uhlenbeck, following on an earlier s ug gestion by A.H. pt on s how ed that it was necessary to suppose that the electron had s pin. Yet even with the properties of char ge, mass, s pin and a s pecial mechanics to help it, the electron was unable to carry the burden of explaining the large and detailed ch had accumulated. L. heory of radiation, associated with a system of w aves. It is with these w aves, formul ated more precisely by Schr tt inger, and modified by Dirac to cover the idea of s pin, rest of my lecture will deal The first published experiments to confim de Broglie,s theory were thase of Davisson and Germer, but perhaps you will allow me to describe instead those to which my pupils and I were led by de Broglie,s epoch-making conception. A narrow beam of cathode r ays was transmitted through a thin film of matter. In the earliest ex periment of the late Mr. Reid this film was of cellu oid, in my ow n experiment of metal. In both, the thickness was of the order of 10cm. The scatte red beam was received on a phot ogr aphic plate normal the beam, and when developed showed a pattern o rings, recalling optical halos and the Debye-Scherrer rin ence phe nomenon is at once suggested. This would occur if each atom of the fllm scatter ed in phase a wavelet from an advancing wave associated with the electrons formi ng the cat hode rays. since the atoms in each small crystal ofthe metal are regul arly spaced, the phases of the wavel ets scattered in ay fixed direction will have a definite rel ationshi pto one another. In some directions they will agree in phase and uild up a str ong scattered wave, in others they will destroy one anot her by interference. the strong wav es are analogous to the beams of light diffracted by an optical grating. At the time, the arm angem ent of the at oms in cellul oid was not known with certai nty and only general concl usions could be drawn, but for t he m etals it had been determined previously by the use of x-rays. Accor ding to de Broglie's theory the wavelengt h ass ociated with an electron is hmv w hic h for the electrons used(cat hode oto 60,000 wolts energy )comes out from 8 X 10-to 5x 10-cm. I do not wishto trouble you with detail ed figures and it will be enough to say t hat the patterns on the photogr aphic pl ates agreed quantitatively, in all cases, with
George Paget Thomson – Nobel Lecture Nobel Lecture, June 7, 1938 Electronic waves Ever si nce l ast Novem ber, I hav e been wanting to express i n person my gratit ude to t he generosit y o f Alfr ed Nobel, to w hom I ow e it t hat I am privileged to be her e t oday, es peciall y si nce ill ness pr evented m e from doi ng so at t he pr oper tim e. The idealism w hic h perm eated his c har acter l ed him to make his magni ficent foundation for t he bene fit o f a cl ass of men with w hose aims and view poi nt his ow n scienti fic insti ncts and ability had m ade him natur ally sympat hetic, but he was c ertai nly at least as muc h concer ned wit h hel ping science as a w hol e, as i ndi vidual scientists. That his foundation has been as successful in t he first as in t he second, is due to t he manner i n w hich his wishes hav e been carri ed out. The Sw edis h people, under the leade rshi p o f t he Royal Family, and through the medium of the Royal Academy of Sciences, have made the Nobel Prizes one of the chief causes of the growth of the prestige o f science i n t he eyes o f the worl d, w hich is a feat ure o f our tim e. As a r ecipi ent of Nobel's generosity I ow e since rest thanks to t hem as w ell as to him. The goddess o f lear ning is fabled t o have s pr ung full -gr ow n from the brai n of Zeus, but it is sel dom that a scienti fic conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that come after. The electron is no exception. Although F araday does not seem to have r ealized it, his wor k on electrol ysis, by s howi ng the unit ary c har acter of t he charges on at oms i n sol ution, was the first step. Cle rk M axwell i n 1873 used t he phrase a "m olec ule of electricity" and von Helmholtz in 1881 s pea king of F araday's wor k said "I f we accept the hypothesis that elementary substances are composed of atoms, we cannot well avoid concluding that electricity also is divided into elementary porti ons w hich behav e lik e atoms of electricity." The hypothetical at om r eceiv ed a name i n the sam e y ear when Johnstone St oney of Dublin christened it "electron", but so far the only property implied was an electron charge. The last year of the nineteenth century saw the electron take a leading place amongst the conceptions of physics. It acquired not only mass but uni versalit y, it was not only el ectricity but an essential part o f all m atter. I f among the m any nam es associat ed with this advance I mention t hat o f J.J. Thomson I hope you will forgi ve a nat ural pri de. It is t o t he great wor k o f B ohr that we owe the demonstrati on o f the connection between electr ons and Planc k's quantum whic h gav e the el ectron a dynamics of its ow n. A few y ears l ater, Goudsmit and Uhlenbeck, foll owing on an earli er s ug gestion by A.H. Compt on s how ed t hat it was necessar y to suppose t hat t he el ectron had s pin. Yet ev en wit h the pr operties o f char ge, mass, s pin and a s pecial m echanics to help it, the electron was unable to carry the burden of explaining the large and detailed mass of experimental data which had accumulated. L. de Brogli e, wor king origi nall y on a t heory of radiati on, produced as a ki nd o f by-pr oduct the conception t hat any particle and i n partic ular an el ectron, was associated wit h a system o f w aves. It is with these w av es, formul ated m ore pr ecisely by Schr 鰀 inger, and modifi ed by Dirac t o cover the i dea o f s pin, that the rest of my lecture will deal. The first published experiments to confirm de Broglie's theory were those of Davisson and Germer, but perhaps you will allow me to describe instead those to which my pupils and I were led by de Broglie's epoch-making conception. A narrow beam o f c athode r ays w as transmitted t hrough a thi n film o f m atter. I n t he earliest experim ent o f t he late Mr. Reid t his film w as o f c ellul oid, in my ow n experiment of metal. In bot h, t he t hickness was of the orde r o f 10-6 cm. The scatte red beam was r eceiv ed on a phot ogr aphic plate normal to the beam, and when developed showed a pattern of rings, recalling optical halos and the Debye-Scherrer rings well known in the corresponding experiment wit h X-r ays. A n i nterference phenom enon is at onc e suggested. This would occur if eac h atom of the film scatter ed i n phase a wavel et fr om an advancing wave associated wit h t he electrons formi ng the cat hode r ays. Si nce t he atoms i n each small cr ystal o f t he metal are regul arly spac ed, t he phases of the wavel ets scattered i n any fix ed di rection will have a defi nite rel ationshi p t o one anothe r. In som e directions t hey will agree i n phase and buil d up a str ong scattered wave, in others t hey will destroy one anot her by int erference. The strong wav es are analogous to t he beams o f li ght diffracted by an optic al gr ating. At t he tim e, the arr angem ent of the at oms in cellul oid was not known with c ertai nty and only general c oncl usions could be dr awn, but for t he m etals it had been determi ned pre viously by the use of X-rays. Accor ding to de Br ogli e's theor y t he w av elengt h ass ociated wit h an electron is h/mv w hic h for the el ectrons used (cat hode rays of 20 to 60,000 volts ener gy ) comes out fr om 8 X 10- 9 to 5 X 10- 9 cm. I do not wish t o troubl e you wit h detail ed figures and it will be enough to say t hat t he patter ns on the photogr aphic pl ates agreed quantitati vely, i n all cases, with t he distribution o f str ong
scattered waves calculated by the met hod I haveindicated Theagreement is good tot he accuracy of the experiments which was about 1%. There is no ustatle constant. and the patterns reprodue not merely the general features of the x-ray pattems but detalls due to special arranoements of the adjustable constant, and the patterns reproduce not merely the general features of the X-ray pattemns but details due to special a s or crystals in the films which were known to occur from previous investigation by X-rays. Later work has amply confirmed this conclusion, and many houeande ot nhet ooranhe have heen taken in my and ot her laberatoree withot any dicacreement with the therry hel found The thousands of phot ographs have been taken in m and ot her la boratories without any dis greement with the theory bei ng foun d. increased with the improvement of the apparatus, perhaps the most accurate work being that of v. Friesen of Uppsala who has used the method in a pre of e in which he acy of I in 1,00 Before discussing the thegretic al mplic ations of theseres utsthere are two mad ncat ns ofthe ex peri ments w hich s hould be mentioned. In the one, the electrons after passing throughthe film are subject to a uniform magnetic field which defl ects them. It is found that the el ectrons whoseimpact onthe Mate forms thering patt ern are deflected equally with those which have passed through holes in the flm. Thusthe pattem is duetoelectrons which have plate f ms ering pattern are de flected equally with thos e which assed through holes in the us the patter is d oelectrons which preserved uncha nged the propert y of being def ected by a magnet. This distinguishes theeffect from anything produced by X-rays and shows that it is ate roety electre. the other noit k a maticat to awid the need foe menarln the verv thin flms whch are needed to transmit th electrons, an appar atus has been devised to w ork by reflection the electrons strikingt he diffr acting s urface at a sm all glancing angle. It appears par atu tingsurrace appears that in many cases the patterns so obtained are really due to electrons transmitted through small projections on the surface. In other cases, for example to a great variety of phenomena with success, but owling lar gely to mat hem atical afficulties there are not mamy cases in w hich an accurate com parison ety nenom nsuccess rgely to mat hemati ere are nany cases in wh an accurate com parison is possible betw eentheory and experiment. The diffraction of fast electrons by crystals is by farthe s everest numerical test which has been made and theratre Imootant to cee tist what cocie lone the evre a ent between theory and these experiments permits The calculations sofar are identical with those in the corresponding case of the diffraction of X-rays. The only assumption made in determining the drections of the difracted heame le that we hawe to deal with a traln of wave conelderahle denth and with nlane wave. etendin owera directions of the difracted beams is that e to deal with a train of wave of considerable depth and with a plan -tront ling over a considerable num ber of atoms. The minimum extension oft he wave system sideways and frontways can be found I fromthe s har pness oft he lines. Taking Frlecend's fouree t at leact waves from back to frot ower a froot of more than 2ach way But the real trouble comes when weconsider the physical mea ning of the waves. In, as we have seen, the electrons acke nthe photographic plate at those places w rong. Following Bohr, Born, and Schr inger, we can express this by saying that the intensity of the waves at any place measures the probability of an electron m ani festing itselfthere. This view is strengt hened by meas urements ofthe relative int ensnes ings, w hichagree well withalc dations by Mott based onsSche ingrs equation. Such a view, how ever sucessful as formal statement satvanlance with all ordnan ldess why shoud atile in cetain daces aseclated with of waves why should wavee odure efecte with all ordinary ideas. Why should a particle appear only in certain places associated with a set of waves? why should waves eftects only through the medium of particles? For it must be emphasized that in theseexperiments each electron only sensitizes the photographic plate inone minute he in that redlonit the reg of pe he energy is distri buted throughout the w aves as in a sound or wat er wave, the wave is only effective in the one place where the electron appears. The rest w, the wave is nroug aves as a sound of it is kind of Once the particle has appeared the wave disappears like dream when the sleeper wakes. Yet the motion of the electron, ulike that ofa Newtonian particle, is infuenced by what he ppers ov er the whole front of the wave, ashown by the effct of the size of the crystals in point of view is fundamental, and we have to face a break wit h ordi nary m echanical ideas. Particles have not a unique track, the energy in these waves is not continuously distributed. probebility not determinism governs nature. have not a unique track, the energy in these waves is not continuously distributed, probability not determinism governs nature. But while emphasizing this fundamental change in outlook which I believe to represent an advance in physical conceptions, I should like to point out aueral wave inwhich the hencmen the old on the s harpness of the diffr acted beams, which we have just mentioned. On the wave theory it is sim ply an example of the factthat a diff ractiongr atin themhertth the chmecetthe dutteted heame douhled ingp Double the num ber of the lines and the shar pness ofthe diffracted b is doubled also. However if there are already many lines, the angular change is small. But imagine a perticle acted on by the material which forms the slits of the grating, and sunse the forces surh asto deflect it into one of the difracted beams. The forces due to the material round the slits near the oe throuh whlch t e of the diffracted beams. The forces due to the material round the slits through which it sses will be the most im partant, an increase in the num ber ofslits will affect the motion but the angular ection due to add ing successive slits wil passe e most im portant, an rease in the num ber he motion but e angular der e dding successives ts will diminish as the numbers increase. The law is of a similar character, though no simple law of force would reproduce the wave effect quantitatively. Similarty for the length of the wave train It this were limited by a shutter mowving so quickly as to let only a shart wave train pass through, the wave Similar or the gth of the wave tra n. this e limited by a shutter kly as to let only as ive train pass n, the w theory woud requ rethat the velocity ofthe particle would be uncertain over a range increasing with the s hort ness ofthe wave train, and corresponding
scattered w av es calcul ated by the met hod I hav e i ndicat ed. The agreement is good to t he accur acy o f the experiments whic h was about 1%. Ther e is no adjustable constant, and the patterns reproduce not merely the general features of the X-ray patterns but details due to special arrangements of the crystals in the films which were known to occur from previous investigation by X-rays. Later work has amply confirmed this conclusion, and many thousands of phot ogr aphs hav e been tak en in my own and ot her labor atories without any disagreement with the theor y bei ng foun d. The accur acy has increased with the improvement of the apparatus, perhaps the most accurate work being that of v. Friesen of Uppsala who has used the method in a precision determination of e in which he reaches an accuracy of I in 1,000. Before discussing the theoretic al implic ations of t hes e res ults t her e ar e two modi fications o f the experiments w hich s houl d be mentioned. I n t he one, t he electrons a fter passing thr ough t he film are subject to a uniform m agnetic fiel d w hich defl ects them. It is found t hat the el ectrons whose impact on t he plate forms t he ri ng patt ern are de flected equally with t hos e whic h have passed through holes i n the film. Thus t he patte rn is due t o electr ons w hich have preser ved unc hanged the propert y o f bei ng defl ected by a m agnet. This distinguishes the e ffect from anyt hing produced by X - rays and shows that it is a true property of electrons. The other point is a practical one, to avoid the need for preparing the very thin films which are needed to transmit the electrons, an appar atus has been devised t o w ork by r efl ection, the el ectrons striki ng t he di ffr acting s urface at a sm all glancing angl e. It appears t hat in many cases the patterns so obtained are really due to electrons transmitted through small projections on the surface. In other cases, for example when the cleavage surface of a crystal is used, true reflection occurs from the Bragg planes. The theor y o f de B roglie i n t he form given t o it by Sc hr 鰀 inge r is now known as w ave mec hanics and is t he basis o f at omic physics. It has been applied to a great v ariety o f phenomena with s uccess, but owi ng lar gel y to mat hem atical difficulti es there are not many cases i n w hic h an accurate com parison is possi ble betw een t heory and experim ent. The di ffr action o f fast electr ons by crystals is by fa r t he s ever est num erical test w hich has been made and it is therefore important to see just what conclusions the excellent agreement between theory and these experiments permits us to draw. The calculations so far are identical with those in the corresponding case of the diffraction of X-rays. The only assumption made in determining the directions of the diffracted beams is that we have to deal with a train of wave of c onsiderable depth and with a plane wave-front extending over a considerable num be r of atoms. The mi nim um ext ensi on of t he wave system sideways and frontways can be found from t he s har pness of t he li nes. Taking v. Friesen's figures, it is at least 225 waves from back to front over a front of more than 200 ?each way. But the real trouble c omes w hen we c onsi der the physical meani ng of the waves. In fact, as w e hav e seen, t he electrons bl acke n t he photogr aphic pl ate at thos e pl aces w her e the waves woul d be stro ng. F ollowi ng Bohr, Born, and Schr 鰀 i nger, we can express t his by sayi ng that the i ntensity o f t he waves at any pl ace measur es the pr obability of an electr on m ani festi ng itsel f there. This vi ew is strengt hened by meas urem ents of t he r elativ e int ensities of t he rings, w hich agr ee well wit h calc ulations by Mott based on Sc hr 鰀 inge r's equati on. S uch a view, how ever s uccessful as a formal stat ement is at v ariance with all ordinary ideas. Why should a particle appear only in certain places associated with a set of waves? Why should waves produce effects only through the medium o f pa rticles? For it m ust be emphasized that in t hese experiments eac h el ectron only sensitizes t he photographic plate i n one mi nute regi on, but in that region it has the sam e pow ers o f penetr ation and photographic action as if it had neve r been diffract ed. W e cannot s uppos e that t he ene rgy is distri buted t hroughout t he w aves as in a sound or wat er wave, the wav e is only effectiv e i n the one place where t he electron appea rs. The rest of it is a kind of phantom. Once the particle has appeared the wave disappears like a dream when the sleeper wakes. Yet the motion of the electron, unli ke t hat o f a Newtonian particle, is i nfluenced by what happens ov er t he w hol e front of the wave, as is shown by t he e ffect of t he size of t he crystals on t he sharpness of the patter ns. The di fference in point o f view is fundam ental, and we have to face a break wit h ordi nar y m echanical ideas. Particles have not a unique track, the energy in these waves is not continuously distributed, probability not determinism governs nature. But while emphasizing this fundamental change in outlook, which I believe to represent an advance in physical conceptions, I should like to point out several ways i n w hich the new phenomena fit the ol d fr amew ork better t han is o ften r ealized. Tak e t he case o f t he infl uence of the size o f t he crystals on t he s har pness of t he diffr acted beams, w hich w e hav e just mentioned. O n the wav e theor y it is sim ply an ex ampl e o f the fac t t hat a di ffraction gr ating with only a few li nes has a poor r esolvi ng power. Double the num ber o f t he li nes and the shar pness o f t he diffr acted beams is doubled also. However i f there are already many lines, the angular change is small. But imagine a particle acted on by the material which forms the slits of the grating, and suppose the forces such as to deflect it into one of the diffracted beams. The forces due to the material round the slits near the one through which it passes will be the m ost im port ant, an incr ease in the num ber o f slits will a ffect the moti on but t he angular defl ection due to addi ng successiv e slits will diminish as the numbers increase. The law is of a similar character, though no simple law of force would reproduce the wave effect quantitatively. Similarly for the length of the wave train. If this were limited by a shutter moving so quickly as to let only a short wave train pass through, the wave theor y woul d requi re t hat the v elocity of t he particl e would be uncertai n over a range i ncreasing with t he s hort ness o f t he wave tr ain, and corr esponding
to the range of wavelengths shown by a Fourier analysis of the train. But the motion of the shutter might well be expected to alter the velocity of particle passing through, Just before it clased. this initi al motion wit hout astur bi ng it ho pelessly. There seems no reas on why those w ho prefer it s houl motion of particles governed by laws which sim ulate the character of waves, but besides the rat her arti ficial character of the law of motion, one has to ascribe importance to the detailed initial conditions of the motion which, as far as our present knowledge goes, are necessar ily incapable of being determined. I am predisposed by nature in favour of the most mechanical explanations possible, but I feel that this view is rather clumsy and that it might be best, as it is certai nly safer, to keep strictly to the facts and re gar d the wave equati on as merely a way of predicting the result of ex perime Nevertheless, the view I have sketched is often a help in thinking of these problems. We are curiously near the position whic h Newton an that of his rivals an Those that are averse from assenting to any new Discoveries, but such as they can explain by an Hypothesis, may for the pres ent suppose, that as Stones by falling upon w ater put the w ater into an undulati ng Moti on, and all B odes by percussion excite vi brations in the Air: so the Rays of ught, by impinging on any refracting or reflecting Surface, excite vibrations in the refracting or reflecting Medium or Substance, muc h after the manner that vibrations are propagated in the Air for ca using sound, and move taster thant he Rays so as to overtake them; and that when any Ray is in that part of the vibration which conspires with its Motion, it easily breaks through a refracting surface, but when it is in the contrary part of the vibration which impedes its Motion, it is easily reflected; and, by conseque nce, that every Ray is s uccessivel y dispos ed to be easily ref ect ed, or easily transmitted, by ery vibration which overtakes it. But not here consider Although the experiments in diffraction confirm so beautifully the de Broglie-Schr t inger wave theory the position is less satisfactory as regards th On this theory the electron possesses magnetic properties and the wave requires four quantities instead of one for its specification. This satis fies those needs of spectroscopy which led to the inventi on of the spi ng electron. It suggests however that electronic waves could be pol arized and that the polariz ed waves might int eract wit h matter in an anis tropic manner. In fact detailed calculations by Mott indicate th if Dirac electrons of 140 kv energy are scattered twice through 90 by the nuclei of gold atoms the intensity of the scattered beam will dinter by 16% according to whether the two scatterings are in the same or in opposite drections. Experiments by Dymond and by myself have established independently that no eftect of this order of magnitude exists, when the scattering is done by gold foils. while there is a slight possibility that th circumnuclear electrons, or the or ganization of the atoms into crystals might effect the res ut, it seems very unlikely. Some of the theor ists ha ve arrived at results conflicting with Mott nderstand that their wok has been found to contain errors. At present there seems no explanation of this repancy which throws doubt on the validity of the Dirac equations in spite of their success in predicting the positive el ectron. I shoul d be sorry to leave you with the im pression t hat electron di ffraction w as of interest only to those concerned with the fundamentals of physics. It has im portant practical applications to the study of s urface effects. You know how x-ray diffraction has made it possi ble to determine the arrangement of the atoms in a great variety of s olds and even liquids. x-rays are very penetrating, and any structure pec liar to the surface of a body will be likely to be overlooked, for its effect is swamped in that of t he m uch greater mass of underlying material. Electrons only affect lay ers of a few atoms, or at most ens of atoms, in thic kness, and so are emi ne ntly s uited for the pur pose. The position of the beams diffracted from a surface enables us, at least in may cases,to deter mine the arrangeme nt of the atoms in the sur face. Among the many cases which ha ve alre ady been st ud ed I have only time to refer to one, the state of the surface of polished metals. Many years ago sir George Beil by suggested that this resembled a s upercodle d liquid which had flowed under the stress of polishing. A senes of ex periments by electron dif fracti on carried out at the Im perial Coll ege in London has confirm ed this conclusi on The most recent work due to Dr. Coc hrane has shown that though t his am orphous i ayer is sta ble at ordi nary tem perature as long as it remains fixed to recrystalize after a few hours. Work by Professor Finch on these lines has led to valuable conclusions as to the wear on the surtaces o cylinders and pistons in petrol engines. It is in keeping with the unive rsal character of physical science t hat this single small branch of it should touc h on the one hand on the fundam ent als scientific philasophy and on the other, questions of everyday li
to the range of wavelengths shown by a Fourier analysis of the train. But the motion of the shutter might well be expected to alter the velocity of a particle passing through, just before it closed. Agai n, on the new view it is purel y a matter o f chance in whic h o f t he di ffr acted beams of di fferent or ders an el ectron appears. I f the phenomenon w ere expr essed as t he classical m otion o f a particle, t his woul d hav e to depend on the i nitial m otion of the particle, and t here is no possi bility of determi ning this initi al m otion wit hout distur bi ng it hopelessly. Ther e seems no reas on why t hose w ho pre fe r it s houl d not regar d t he di ffr action o f electr ons as t he motion o f pa rticles gov erned by l aws w hich sim ulat e t he c har ac ter o f waves, but besides the rat her arti ficial cha racter o f t he l aw of moti on, one has to ascribe importance to the detailed initial conditions of the motion which, as far as our present knowledge goes, are necessar ily incapable of being determined. I am predisposed by nature in favour of the most mechanical explanations possible, but I feel that this view is rather clumsy and that it might be best, as it is certai nly safer, to keep strictly t o the facts and regar d the wave equati on as m erely a w ay of pr edicting t he r esult of experiments. Nevertheless, the view I have sketched is often a help in thinking of these problems. We are curiously near the position whic h Newton took over his theory of optics, long despised but now seen to be far nearer the truth than that of his rivals and successors. "Those that are averse from assenting to any new Discoveries, but such as they can explain by an Hypothesis, may for the pres ent suppose, that as Stones by falling upon w ater put the W ater i nto an undulati ng Moti on, an d all B odies by percussi on excite vi brati ons i n t he Air: so t he Rays of Li ght, by impinging on any refracting or reflecting Surface, excite vibrations in the refracting or reflecting Medium or Substance, muc h after the manner that vibrati ons are pr opagated i n t he Air for causing S ound, and mov e faster than t he Rays so as to ov ertak e t hem; and that when any R ay is in that part o f the vibration which conspires with its Motion, it easily breaks through a refracting Surface, but when it is in the contrary part of the vibration which impedes its Moti on, it is easily re flected; and, by consequence, t hat ev ery Ray is s uccessivel y dispos ed to be easily refl ect ed, or easil y tr ansmitted, by every vibration which overtakes it. But whether this Hypothesis be true or false I do not here consider." Although the experiments in diffraction confirm so beautifully the de Broglie-Schr 鰀 inger wave theory, the position is less satisfactory as regards the extended theory due to Dirac. On this theory the electron possesses magnetic properties and the wave requires four quantities instead of one for its specificati on. This satis fies t hos e needs o f spectroscopy whic h l ed to the i nv enti on o f t he spi nni ng electron. It suggests however that el ectronic waves coul d be pol arized and t hat the polariz ed wav es mi ght int eract wit h matter in an anis otropic manner. I n fact detailed c alculati ons by M ott i ndicat e t hat if Dirac electrons of 140 kV energy are scattered twice through 90° by the nuclei of gold atoms the intensity of the scattered beam will differ by 16% according to whether the two scatterings are in the same or in opposite directions. Experiments by Dymond and by myself have established independently that no effect of this order of magnitude exists, when the scattering is done by gold foils. While there is a slight possibility that the circumnuclea r electr ons, or the or ganizati on of t he atoms i nto cr ystals mi ght effect the res ult, it seems very unlik ely. Som e o f t he t heor ists have a rrived at results conflicting with Mott, but I understand that their work has been found to contain errors. At present there seems no explanation of this discrepancy which throws doubt on the validity of the Dirac equations in spite of their success in predicting the positive el ectron. I shoul d be s orry to l eav e you with the im pression t hat electr on di ffraction w as o f i nter est only t o t hose concer ned with the fundamentals o f physics. I t has im portant pr actical applications t o the st udy o f s urface effects. You know how X- ray di ffraction has m ade it possi ble t o dete rmine t he arrangement of t he at oms i n a great v ariety o f s olids and ev en liqui ds. X-rays a re ver y penetrati ng, and any structure pec uliar to the surface of a body will be lik ely to be overl ooked, for its e ffect is swamped i n that of t he m uch greater m ass of underl ying m aterial. Electrons only a ffect lay ers o f a few atoms, or at most tens o f at oms, i n thic kness, and so a re emi nently s uited for the pur pose. The position o f the beams diffracted from a sur face enables us, at l east in many cases, to determine t he arrangement of the atoms i n t he sur face. A mong the m any cases whic h have already been st udi ed I hav e onl y tim e to re fer to one, t he st ate of t he sur face o f polished metals. M any y ears ago Sir George Beil by suggested t hat t his r esembl ed a s upercoole d liqui d whic h had flowed under the stress o f polishi ng. A series of experim ents by electron diffracti on c arried out at the Im perial Coll ege in London has confirm ed t his conclusi on. The most recent work due t o Dr. Coc hrane has shown that though t his am orphous l aye r is stable at ordi nar y tem pe rature as long as it rem ains fix ed to the mass of the metal, it is unstable when removed, and recrystalizes after a few hours. Work by Professor Finch on these lines has led to valuable conclusions as to the wear on the surfaces of cylinders and pistons in petrol engines. It is in k eepi ng wit h t he unive rsal c har acter of physical science t hat this si ngl e sm all branch o f it shoul d touc h on the one hand on t he fundam ent als o f scientific philosophy and on the other, questions of everyday life