file which includes the original illustrations4 ,see #fecei-;h4htm or #fecei-;h4zip3 7https3_/_/www4gutenberg4org_/cache_/epu b_/#fecei_/pg#fecei-;images4html7 or 7https3_/_/www4gutenberg4org_/files_/#fe cei_/fecei-;h4zip7 ,images of the original pages are available through ,internet ,archive4 ,see https3_/_/archive4org_/details_/jamescle rkmaxwel#jj;glaziala ,transcriber's note3 ,text enclosed by underscores is in italics 7italics74 ,superscripts that cannot be represented directly are enclosed by curly brackets immediately after a caret character 7example3 nth74 ,some characters might not display properly in this ,,utf-#h text file 7e4g41 empty squares74 ,if so1 the reader should consult the html version or the original page images noted above4 ,illustration3 7cover7 ,the ,century ,science ,series ,edited by ,sir ,henry ,e4 ,roscoe1 ,d4,c4,l41 ,,ll4,d41 ,f4,r4,s4 ,,james ,,clerk ,,maxwell ,,and ,,modern ,,physics 99 99 99 99 99 99 ,the ,century ,science ,series4 ,,edited ,,by ,,sir ,,henry ,e4 ,,roscoe1 ,d4,c4,l41 ,f4,r4,s41 ,m4,p4 ,john ,dalton and the ,rise of ,modern ,chemistry4 ,by ,sir ,,henry ,e4 ,,roscoe1 ,f4,r4,s4 ,major ,rennell1 ,f4,r4,s41 and the ,rise of ,english ,geography4 ,by ,,clements ,r4 ,,markham1 ,c4,b41 ,f4,r4,s41 ,president of the ,royal ,geographical ,society4 ,justus von ,liebig3 his ,life and ,work 7#ahjc-ahgc74 ,by ,w4 ,a4 ,,shenstone1 ,f4,i4,c41 ,lecturer on ,chemistry in ,clifton ,college4 ,the ,herschels and ,modern ,astronomy4 ,by ,,agnes ,m4 ,,clerke1 ,author of 8,a ,popular ,history of ,astronomy during the #aith ,century10 c4 ,charles ,lyell and ,modern ,geology4 ,by ,rev4 ,professor ,t4 ,g4 ,,bonney1 ,f4,r4,s4 ,james ,clerk ,maxwell and ,modern ,physics4 ,by ,r4 ,t4 ,,glazebrook1 ,f4,r4,s41 ,fellow of ,trinity ,college1 ,cambridge4 ,in ,preparation4 ,michael ,faraday3 his ,life and ,work4 ,by ,professor ,,silvanus ,p4 ,,thompson1 ,f4,r4,s4 ,humphry ,davy4 ,by ,t4 ,e4 ,,thorpe1 ,f4,r4,s41 ,principal ,chemist of the ,government ,laboratories4 ,pasteur3 his ,life and ,work4 ,by ,m4 ,,armand ,,ruffer1 ,m4,d41 ,director of the ,british ,institute of ,preventive ,medicine4 ,charles ,darwin and the ,origin of ,species4 ,by ,,edward ,b4 ,,poulton1 ,m4,a41 ,f4,r4,s41 ,hope ,professor of ,zoology in the ,university of ,oxford4 ,hermann von ,helmholtz4 ,by ,a4 ,w4 ,r,,cker1 ,f4,r4,s41 ,professor of ,physics in the ,royal ,college of ,science1 ,london4 ,,cassell ,,company1 ,,limited1 ,london2 ,paris ,melbourne4 99 99 99 99 99 99 ,illustration3 ,j4 ,clerk ,maxwell 7,from a ,photograph of the ,picture by ,g4 ,lowes ,dickinson1 ,esq41 in the ,hall of ,trinity ,college1 ,cambridge47 ,the ,century ,science ,series ,,james ,,clerk ,,maxwell ,,and ,,modern ,,physics by ,r4 ,t4 ,,glazebrook1 ,f4,r4,s4 ,fellow of ,trinity ,college1 ,cambridge ,university ,lecturer in ,mathematics1 and ,assistant ,director of the ,cavendish ,laboratory ,cassell and ,company1 ,limited ,london1 ,paris ,melbourne #ahif ,all ,rights ,reserved ,illustration ,,preface4 ,the task of giving some account of ,maxwell's work--of describing the share that he has taken in the advance of ,physical ,science during the latter half of this nineteenth century--has proved no light labour4 ,the problems which he attacked are of such magnitude and complexity1 that the attempt to explain them and their importance1 satisfactorily1 without the aid of symbols1 is almost foredoomed to failure4 ,however1 the attempt has been made1 in the belief that there are many who1 though they cannot follow the mathematical analysis of ,maxwell's work1 have sufficient general knowledge of physical ideas and principles to make an account of ,maxwell and of the development of the truths that he discovered1 subjects of intelligent interest4 ,maxwell's life was written in #ahhb by two of those who were most intimately connected with him1 ,professor ,lewis ,campbell and ,dr4 ,garnett4 ,many of the biographical details of the earlier part of this book are taken from their work4 ,my thanks are due to them and to their publishers1 ,messrs4 ,macmillan1 for permission to use any of the letters which appear in their biography4 ,i trust that my brief account may be sufficient to induce many to read ,professor ,campbell's 8,life and ,letters10 with a view of learning more of the inner thoughts of one who has left so strong an imprint on all he undertook1 and was so deeply loved by all who knew him4 ,r4 ,t4 ,g4 ,cambridge1 ,december1 #ahie4 ,,contents4 ,,chapter ,,page ,i4 ,,early ,,life #i ,,ii4 ,,undergraduate ,,life ,,at ,,cambridge #bh ,,iii4 ,,early ,,researches--,,professor ,,at ,,aberdeen #ch ,,iv4 ,,professor ,,at ,,king',s ,,college1 ,,london--,,life ,,at ,,glenlair #ed ,v4 ,,cambridge--,,professor ,,or ,,physics #fj ,,vi4 ,,cambridge--,,the ,,cavendish ,,laboratory #gc ,,vii4 ,,scientific ,,work--,,colour ,,vision #ic ,,viii4 ,,scientific ,,work--,,molecular ,,theory #ajh ,,ix4 ,,scientific ,,work--,,electrical ,,theories #adh ,x4 ,,development ,,of ,,maxwell',s ,,theory #bjb ,,james ,,clerk ,,maxwell ,,and ,,modern ,,physics4 ,,chapter ,i4 ,,early ,,life4 8,one who has enriched the inheritance left by ,newton and has consolidated the work of ,faraday--one who impelled the mind of ,cambridge to a fresh course of real investigation--has clearly earned his place in human memory40 ,it was thus that ,professor ,lewis ,campbell and ,mr4 ,garnett began in #ahhb their life of ,james ,clerk ,maxwell4 ,the years which have passed1 since that date1 have all tended to strengthen the belief in the greatness of ,maxwell's work and in the fertility of his genius1 which has inspired the labours of those who1 not in ,cambridge only1 but throughout the world1 have aided in developing the seeds sown by him4 ,my object in the following pages will be to give some very brief account of his life and writings1 in a form which may1 ,i hope1 enable many to realise what ,physical ,science owes to one who was to me a most kind friend as well as a revered master4 ,the ,clerks of ,penicuik1 from whom ,clerk ,maxwell was descended1 were a distinguished family4 ,sir ,john ,clerk1 the great-great-grandfather of ,clerk ,maxwell1 was a ,baron of the ,exchequer in ,scotland from #agjg to #agee2 he was also one of the ,commissioners of the ,union1 and was in many ways an accomplished scholar4 ,his second son ,george married a first cousin1 ,dorothea ,maxwell1 the heiress of ,middlebie in ,dumfriesshire1 and took the name of ,maxwell4 ,by the death of his elder brother ,james in #aghb ,george ,clerk ,maxwell succeeded to the baronetcy and the property of ,penicuik4 ,before this time he had become involved in mining and manufacturing speculations1 and most of the ,middlebie property had been sold to pay his debts4 ,the property of ,sir ,george ,clerk ,maxwell descended in #agih to his two grandsons1 ,sir ,george ,clerk and ,mr4 ,john ,clerk ,maxwell4 ,it had been arranged that the younger of the two was to take the remains of the ,middlebie property and to assume with it the name of ,maxwell4 ,sir ,george ,clerk was member for ,midlothian1 and held office under ,sir ,robert ,peel4 ,john ,clerk ,maxwell was the father of ,james ,clerk ,maxwell1 the subject of this sketch4#a ,john ,clerk ,maxwell lived with his widowed mother in ,edinburgh until her death in #ahbd4 ,he was a lawyer1 and from time to time did some little business in the courts4 ,at the same time he maintained an interest in scientific pursuits1 especially those of a practical nature4 ,professor ,campbell tells us of an endeavour to devise a bellows which would give a continuous draught of air4 ,in #ahca he contributed to the ,edinburgh ,medical and ,philosophical ,journal a paper entitled 8,outlines of a ,plan for combining ,machinery with the ,manual ,printing ,press40 ,in #ahbf ,john ,clerk ,maxwell married ,miss ,frances ,cay1 of ,north ,charlton1 ,northumberland4 ,for the first few years of their married life their home was in ,edinburgh4 ,the old estate of ,middlebie had been greatly reduced in extent1 and there was not a house on it in which the laird could live4 ,however1 soon after his marriage1 ,john ,clerk ,maxwell purchased the adjoining property of ,glenlair and built a mansion-house for himself and his wife4 ,mr4 ,maxwell superintended the building work4 ,the actual working plans for some further additions made in #ahdc were his handiwork4 ,a garden was laid out and planted1 and a dreary stony waste was converted into a pleasant home4 ,for some years after he settled at ,glenlair the house in ,edinburgh was retained by ,mr4 ,maxwell1 and here1 on ,june #ac1 #ahca1 was born his only son1 ,james ,clerk ,maxwell4 ,a daughter1 born earlier1 died in infancy4 ,glenlair1 however1 was his parents' home1 and nearly all the reminiscences we have of his childhood are connected with it4 ,the laird devoted himself to his estates and to the education of his son1 taking1 however1 from time to time his full share in such county business as fell to him4 ,glenlair in #ahcj was very much in the wilds2 the journey from ,edinburgh occupied two days4 8,carriages in the modern sense were hardly known to the ,vale of ,urr4 ,a sort of double gig with a hood was the best apology for a travelling coach1 and the most active mode of locomotion was in a kind of rough dog-cart known in the family speech as a hurly40#b ,mrs4 ,maxwell writes thus#c1 when the boy was nearly three years old1 to her sister1 ,miss ,jane ,cay3-- 8,he is a very happy man1 and has improved much since the weather got moderate4 ,he has great work with doors1 locks1 keys1 etc41 and #8,show me how it doos' is never out of his mouth4 ,he also investigates the hidden course of streams and bell-wires--the way the water gets from the pond through the wall and a pend or small bridge and down a drain into ,water ,orr1 then past the smiddy and down to the sea1 where ,maggy's ships sail4 ,as to the bells1 they will not rust2 he stands sentry in the kitchen and ,mag runs through the house ringing them all by turns1 or he rings and sends ,bessy to see and shout to let him know2 and he drags papa all over to show him the holes where the wires go through40 ,to discover 8how it doos0 was thus early his aim4 ,his cousin1 ,mrs4 ,blackburn1 tells us that throughout his childhood his constant question was1 8,what's the go of that8 ,what does it do80 ,and if the answer were too vague or inconclusive1 he would add1 8,but what's the particular go of that80 ,professor ,campbell's most interesting account of these early years is illustrated by a number of sketches of episodes in his life4 ,in one ,maxwell is absorbed in watching the fiddler at a country dance2 in another he is teaching his dog some tricks2 in a third he is helping a smaller boy in his efforts to build a castle4 ,together with his cousin1 ,miss ,wedderburn1 he devised a number of figures for a toy known as a magic disc1 which afterwards developed into the zoetrope or wheel of life1 and in which1 by means of an ingenious contrivance of mirrors1 the impression of a continuous movement was produced4 ,this happy life went on until his mother's death in ,december1 #ahci2 she died1 at the age of forty-eight1 of the painful disease to which her son afterwards succumbed4 ,when ,james1 being then eight years old1 was told that she was now in heaven1 he said3 8,oh1 ,i'm so glad6 ,now she'll have no more pain40 ,after this his aunt1 ,miss ,jane ,cay1 took a mother's place4 ,the problem of his education had to be faced1 and the first attempts were not successful4 ,a tutor had been engaged during ,mrs4 ,maxwell's last illness1 and he1 it seems1 tried to coerce ,clerk ,maxwell into learning2 but such treatment failed1 and in #ahda1 when ten years old1 he began his school-life at the ,edinburgh ,academy4 ,school-life at first had its hardships4 ,maxwell's appearance1 his first day at school1 in ,galloway home-spun and square-toed shoes with buckles1 was more than his fellows could stand4 8,who made those shoes80 they asked#d2 and the reply they received was-- 8,div ye ken 'twas a man1 ,and he lived in a house1 ,in whilk was a mouse40 ,he returned to ,heriot ,row that afternoon1 says ,professor ,campbell1 8with his tunic in rags and wanting the skirt1 his neat frill rumpled and torn--himself excessively amused by his experiences and showing not the slightest sign of irritation40 ,no4 #ca1 ,heriot ,row1 was the house of his widowed aunt1 ,mrs4 ,wedderburn1 ,mr4 ,maxwell's sister2 and this1 with occasional intervals when he was with ,miss ,cay1 was his home for the next eight or nine years4 ,mr4 ,maxwell himself1 during this period1 spent much of his time in ,edinburgh1 living with his sister during most of the winter and returning to ,glenlair for the spring and summer4 ,much of what we know of ,clerk ,maxwell's life during this period comes from the letters which passed between him and his father4 ,they tell us of the close intimacy and affection which existed between the two1 of the boy's eager desire to please and amuse his father in the dull solitude of ,glenlair1 and his father's anxiety for his welfare and progress4 ,professor ,campbell was his schoolfellow1 and records events of those years in which he shared1 which bring clearly before us what ,clerk ,maxwell was like4 ,thus he writes#e3-- 8,he came to know ,swift and ,dryden1 and after a while ,hobbes1 and ,butler's #8,hudibras4' ,then1 if his father was in ,edinburgh1 they walked together1 especially on the ,saturday half-holiday1 and #8viewed' ,leith ,fort1 or the preparations for the ,granton railway1 or the stratification of ,salisbury ,crags--always learning something new1 and winning ideas for imagination to feed upon4 ,one ,saturday1 ,february #ab1 #ahdb1 he had a special treat1 being taken #8to see electro-magnetic machines4'0 ,and again1 speaking of his school-life3-- 8,but at school also he gradually made his way4 ,he soon discovered that ,latin was worth learning1 and the ,greek ,delectus interested him when we got so far4 ,and there were two subjects in which he at once took the foremost place1 when he had a fair chance of doing so2 these were ,scripture ,biography and ,english4 ,in arithmetic as well as in ,latin his comparative want of readiness kept him down4 8,on the whole he attained a measure of success which helped to secure for him a certain respect2 and1 however strange he sometimes seemed to his companions1 he had three qualities which they could not fail to understand--agile strength of limb1 imperturbable courage1 and profound good-nature4 ,professor ,james ,muirhead remembers him as #8a friendly boy1 though never quite amalgamating with the rest4' ,and another old class-fellow1 the ,rev4 ,w4 ,macfarlane of ,lenzie1 records the following as his impression3--#8,clerk ,maxwell1 when he entered the ,academy1 was somewhat rustic and somewhat eccentric4 ,boys called him 8,dafty10 and used to try to make fun of him4 ,on one occasion ,i remember he turned with tremendous vigour1 with a kind of demonic force1 on his tormentors4 ,i think he was let alone after that1 and gradually won the respect even of the most thoughtless of his schoolfellows4'0 ,the first reference to mathematical studies occurs1 says ,professor ,campbell1 in a letter to his father written soon after his thirteenth birthday4#f 8,after describing the ,virginian ,minstrels1 and betwixt inquiries after various pets at ,glenlair1 he remarks1 as if it were an ordinary piece of news1 #8,i have made a tetrahedron1 a dodecahedron1 and two other hedrons1 whose names ,i don't know4' ,we had not yet begun geometry1 and he had certainly not at this time learnt the definitions in ,euclid2 yet he had not merely realised the nature of the five regular solids sufficiently to construct them out of pasteboard with approximate accuracy1 but had further contrived other symmetrical polyhedra derived from them1 specimens of which 7as improved in #ahdh7 may be still seen at the ,cavendish ,laboratory4 8,who first called his attention to the pyramid1 cube1 etc41 ,i do not know4 ,he may have seen an account of them by chance in a book4 ,but the fact remains that at this early time his fancy1 like that of the old ,greek geometers1 was arrested by these types of complete symmetry2 and his imagination so thoroughly mastered them that he proceeded to make them with his own hand4 ,that he himself attached more importance to this moment than the letter indicates is proved by the care with which he has preserved these perishable things1 so that they 7or those which replaced them in #ahdh7 are still in existence after thirty-seven years40 ,the summer holidays were spent at ,glenlair4 ,his cousin1 ,miss ,jemima ,wedderburn1 was with him1 and shared his play4 ,her skilled pencil has left us many amusing pictures of the time1 some of which are reproduced by ,professor ,campbell4 ,there were expeditions and picnics of all sorts1 and a new toy known as 8the devil on two sticks0 afforded infinite amusement4 ,the winter holidays usually found him at ,penicuik1 or occasionally at ,glasgow1 with ,professor ,blackburne or ,professor ,w4 ,thomson 7now ,lord ,kelvin74 ,in ,october1 #ahdd1 ,maxwell was promoted to the rector's class-room4 ,john ,williams1 afterwards ,archdeacon of ,cardigan1 a distinguished ,baliol man1 was rector1 and the change was in many ways an important one for ,maxwell4 ,he writes to his father3 8,i like ,p---- better than ,b----4 ,we have lots of jokes1 and he speaks a great deal1 and we have not so much monotonous parsing4 ,in the ,english ,milton is better than the ,history of ,greece44440 ,p---- was the boys' nickname for the rector2 ,b---- for ,mr4 ,carmichael1 the second master4 ,this#g is the account of ,maxwell's first interview with the rector3-- ,rector3 8,what part of ,galloway do you come from80 ,j4 ,c4 ,m43 8,from the ,vale of ,urr4 ,ye spell it o1 err1 err1 or oo1 err1 err40 ,the study of geometry was begun1 and in the mathematical master1 ,mr4 ,gloag1 ,maxwell found a teacher with a real gift for his task4 ,it was here that ,maxwell's vast superiority to many who were his companions at once showed itself4 8,he seemed10 says ,professor ,campbell1 8to be in the heart of the subject when they were only at the boundary2 but the boyish game of contesting point by point with such a mind was a most wholesome stimulus1 so that the mere exercise of faculty was a pure joy4 ,with ,maxwell the first lessons of geometry branched out at once into inquiries which became fruitful40 ,in ,july1 #ahde1 he writes3-- 8,i have got the #aath prize for ,scholarship1 the #ast for ,english1 the prize for ,english verses1 and the ,mathematical ,medal4 ,i tried for ,scripture knowledge1 and ,hamilton in the #gth has got it4 ,we tried for the ,medal on ,thursday4 ,i had done them all1 and got home at half-past two2 but ,campbell stayed till four4 ,i was rather tired with writing exercises from nine till half-past two4 8,campbell and ,i went #8once more unto the b7r7each' to-day at ,portobello4 ,i can swim a little now4 ,campbell has got #f prizes4 ,he got a letter written too soon1 congratulating him upon my medal2 but there is no rivalry betwixt us1 as ,b---- ,carmichael says40 ,after a summer spent chiefly at ,glenlair1 he returned with his father to ,edinburgh for the winter1 and began1 at the age of fourteen1 to go to the meetings of the ,royal ,society of ,edinburgh4 ,at the ,society of ,arts he met ,mr4 ,r4 ,d4 ,hay1 the decorative painter1 who had interested himself in the attempt to reduce beauty in form and colour to mathematical principles4 ,clerk ,maxwell was interested in the question how to draw a perfect oval1 and devised a method of drawing oval curves which was referred by his father to ,professor ,forbes for his criticism and suggestions4 ,after discussing the matter with ,professor ,kelland1 ,professor ,forbes wrote as follows#h3-- 8,,my ,,dear ,,sir1--,i am glad to find to-day1 from ,professor ,kelland1 that his opinion of your son's paper agrees with mine1 namely1 that it is most ingenious1 most creditable to him1 and1 we believe1 a new way of considering higher curves with reference to foci4 ,unfortunately1 these ovals appear to be curves of a very high and intractable order1 so that possibly the elegant method of description may not lead to a corresponding simplicity in investigating their properties4 ,but that is not the present point4 ,if you wish it1 ,i think that the simplicity and elegance of the method would entitle it to be brought before the ,royal ,society4--,believe me1 my dear sir1 yours truly1 8,,james ,d4 ,,forbes40 ,in consequence of this1 ,clerk ,maxwell's first published paper was communicated to the ,royal ,society of ,edinburgh on ,april #fth1 #ahdf1 when its author was barely fifteen4 ,its title is as follows3 8,on the ,description of ,oval ,curves and those having a ,plurality of ,foci4 ,by ,mr4 ,clerk ,maxwell1 ,junior4 ,with ,remarks by ,professor ,forbes4 ,communicated by ,professor ,forbes40 ,the notice in his father's diary runs3 8,m4 #f ,ap41 #ahdf4 ,royal ,society with ,jas4 ,professor ,forbes gave acct4 of ,james's ,ovals4 ,met with very great attention and approbation generally40 ,this was the beginning of the lifelong friendship between ,maxwell and ,forbes4 ,the curves investigated by ,maxwell have the property that the sum found by adding to the distance of any point on the curve from one focus a constant multiple of the distance of the same point from a second focus is always constant4 ,the curves are of great importance in the theory of light1 for if this constant factor expresses the refractive index of any medium1 then light diverging from one focus without the medium and refracted at a surface bounding the medium1 and having the form of one of ,maxwell's ovals1 will be refracted so as to converge to the second focus4 ,about the same time he was busy with some investigations on the properties of jelly and gutta-percha1 which seem to have been suggested by ,forbes' 8,theory of ,glaciers40 ,he failed to obtain the ,mathematical ,medal in #ahdf--possibly on account of these researches--but he continued at school till #ahdg1 when he left1 being then first in mathematics and in ,english1 and nearly first in ,latin4 ,in #ahdg he was working at magnetism and the polarisation of light4 ,some time in that year he was taken by his uncle1 ,mr4 ,john ,cay1 to see ,william ,nicol1 the inventor of the polarising prism1 who showed him the colours exhibited by polarised light after passing through unannealed glass4 ,on his return1 he made a polariscope with a glass reflector4 ,the framework of the first instrument was of cardboard1 but a superior article was afterwards constructed of wood4 ,small lenses mounted on cardboard were employed when a conical pencil was needed4 ,by means of this instrument he examined the figures exhibited by pieces of unannealed glass1 which he prepared himself2 and1 with a camera lucida and box of colours1 he reproduced these figures on paper1 taking care to sketch no outlines1 but to shade each coloured band imperceptibly into the next4 ,some of these coloured drawings he forwarded to ,nicol1 and was more than repaid by the receipt shortly afterwards of a pair of prisms prepared by ,nicol himself4 ,these prisms were always very highly prized by ,maxwell4 ,once1 when at ,trinity1 the little box containing them was carried off by his bed-maker during a vacation1 and destined for destruction4 ,the bed-maker died before term commenced1 and it was only by diligent search among her effects that the prisms were recovered4#i ,after this they were more carefully guarded1 and they are now1 together with the wooden polariscope1 the bits of unannealed glass1 and the water-colour drawings1 in one of the showcases at the ,cavendish ,laboratory4 ,about this time1 ,professor ,p4 ,g4 ,tait and he were schoolfellows at the ,academy1 acknowledged as the two best mathematicians in the school4 ,it was thought desirable1 says ,professor ,campbell1 that 8we should have lessons in physical science1 so one of the classical masters gave them out of a text-book4444 ,the only thing ,i distinctly remember about these hours is that ,maxwell and ,p4 ,g4 ,tait seemed to know much more about the subject than our teacher did40 ,an interesting account of these days is given by ,professor ,tait in an obituary notice on ,maxwell printed in the 8,proceedings of the ,royal ,society of ,edinburgh1 #ahgi-hj10 from which the following is taken3-- 8,when ,i first made ,clerk ,maxwell's acquaintance1 about thirty-five years ago1 at the ,edinburgh ,academy1 he was a year before me1 being in the fifth class1 while ,i was in the fourth4 8,at school he was at first regarded as shy and rather dull4 ,he made no friendships1 and he spent his occasional holidays in reading old ballads1 drawing curious diagrams1 and making rude mechanical models4 ,this absorption in such pursuits1 totally unintelligible to his schoolfellows 7who were then quite innocent of mathematics71 of course procured him a not very complimentary nickname1 which ,i know is still remembered by many ,fellows of this ,society4 ,about the middle of his school career1 however1 he surprised his companions by suddenly becoming one of the most brilliant among them1 gaining high1 and sometimes the highest1 prizes for scholarships1 mathematics1 and ,english verse composition4 ,from this time forward ,i became very intimate with him1 and we discussed together1 with schoolboy enthusiasm1 numerous curious problems1 among which ,i remember particularly the various plane sections of a ring or tore1 and the form of a cylindrical mirror which should show one his own image unperverted4 ,i still possess some of the ,,mss4 we exchanged in #ahdf and early in #ahdg4 ,those by ,maxwell are on #8,the ,conical ,pendulum1' #8,descartes' ,ovals1' #8,meloid and ,apioid1' and #8,trifocal ,curves4' ,all are drawn up in strict geometrical form and divided into consecutive propositions4 ,the three latter are connected with his first published paper1 communicated by ,forbes to this society and printed in our #8,proceedings1' vol4 ii41 under the title1 #8,on the ,description of ,oval ,curves and those having a ,plurality of ,foci' 7#ahdf74 ,at the time when these papers were written he had received no instruction in mathematics beyond a few books of ,euclid and the merest elements of algebra40 ,in ,november1 #ahdg1 ,clerk ,maxwell entered the ,university of ,edinburgh1 learning mathematics from ,kelland1 natural philosophy from ,j4 ,d4 ,forbes1 and logic from ,sir ,w4 ,r4 ,hamilton4 ,at this time1 according to ,professor ,campbell#aj-- 8he still occasioned some concern to the more conventional amongst his friends by the originality and simplicity of his ways4 ,his replies in ordinary conversation were indirect and enigmatical1 often uttered with hesitation and in a monotonous key4 ,while extremely neat in his person1 he had a rooted objection to the vanities of starch and gloves4 ,he had a pious horror of destroying anything1 even a scrap of writing-paper4 ,he preferred travelling by the third class in railway journeys1 saying he liked a hard seat4 ,when at table he often seemed abstracted from what was going on1 being absorbed in observing the effects of refracted light in the finger-glasses1 or in trying some experiment with his eyes--seeing round a corner1 making invisible stereoscopes1 and the like4 ,miss ,cay used to call his attention by crying1 #8,jamsie1 you're in a prop4' ,he never tasted wine2 and he spoke to gentle and simple in exactly the same tone4 ,on the other hand1 his teachers--,forbes above all--had formed the highest opinion of his intellectual originality and force2 and a few experienced observers1 in watching his devotion to his father1 began to have some inkling of his heroic singleness of heart4 ,to his college companions1 whom he could now select at will1 his quaint humour was an endless delight4 ,his chief associates1 after ,i went to the ,university of ,glasgow1 were my brother1 ,robert ,campbell 7still at the ,academy71 ,p4 ,g4 ,tait1 and ,allan ,stewart4 ,tait went to ,peterhouse1 ,cambridge1 in #ahdh1 after one session of the ,university of ,edinburgh2 ,stewart to the same college in #ahdi2 ,maxwell did not go up until #ahej40 ,during this period he wrote two important papers4 ,the one1 on 8,rolling ,curves10 was read to the ,royal ,society of ,edinburgh by ,professor ,kelland--78it was not thought proper for a boy in a round jacket to mount the rostrum07--in ,february1 #ahdi2 the other1 on 8,the ,equilibrium of ,elastic ,solids10 appeared in the spring of #ahej4 ,the vacations were spent at ,glenlair1 and we learn from letters to ,professor ,campbell and others how the time was passed4 8,on ,saturday10 he writes#aa--;,april #bfth1 #ahdh1 just after his arrival home--8the natural philosophers ran up ,arthur's ,seat with the barometer4 ,the ,professor set it down at the top4444 ,he did not set it straight1 and made the hill grow fifty feet2 but we got it down again40 ,in a letter of ,july in the same year he describes his laboratory3-- 8,i have regularly set up shop now above the wash-house at the gate1 in a garret4 ,i have an old door set on two barrels1 and two chairs1 of which one is safe1 and a skylight above which will slide up and down4 8,on the door 7or table7 there is a lot of bowls1 jugs1 plates1 jam pigs1 etc41 containing water1 salt1 soda1 sulphuric acid1 blue vitriol1 plumbago ore2 also broken glass1 iron1 and copper wire1 copper and zinc plate1 bees' wax1 sealing wax1 clay1 rosin1 charcoal1 a lens1 a ,smee's galvanic apparatus1 and a countless variety of little beetles1 spiders1 and wood lice1 which fall into the different liquids and poison themselves4 ,i intend to get up some more galvanism in jam pigs2 but ,i must first copper the interiors of the pigs1 so ,i am experimenting on the best methods of electrotyping4 ,so ,i am making copper seals with the device of a beetle4 ,first1 ,i thought a beetle was a good conductor1 so ,i embedded one in wax 7not at all cruel1 because ,i slew him in boiling water1 in which he never kicked71 leaving his back out2 but he would not do4 ,then ,i took a cast of him in sealing wax1 and pressed wax into the hollow1 and blackleaded it with a brush2 but neither would that do4 ,so at last ,i took my fingers and rubbed it1 which ,i find the best way to use the blacklead4 ,then it coppered famously4 ,i melt out the wax with the lens1 that being the cleanest way of getting a strong heat1 so ,i do most things with it that need heat4 ,to-day ,i astonished the natives as follows4 ,i took a crystal of blue vitriol and put the lens to it1 and so drove off the water1 leaving a white powder4 ,then ,i did the same to some washing soda1 and mixed the two white powders together1 and made a small native spit on them1 which turned them green by a mutual exchange1 thus3--#a4 ,sulphate of copper and carbonate of soda4 #b4 ,sulphate of soda and carbonate of copper 7blue or green740 ,of his reading he says3--8,i am reading ,herodotus' #8,euterpe1' having taken the turn--that is to say that sometimes ,i can do props41 read ,diff4 and ,int4 ,calc41 ,poisson1 ,hamilton's dissertation1 etc40 ,in ,september he was busy with polarised light4 8,we were at ,castle ,douglas yesterday1 and got crystals of saltpetre1 which ,i have been cutting up into plates to-day in hopes to see rings40 ,in ,july1 #ahdi1 he writes#ab3-- 8,i have set up the machine for showing the rings in crystals1 which ,i planned during your visit last year4 ,it answers very well4 ,i also made some experiments on compressed jellies in illustration of my props4 on that subject4 ,the principal one was this3--,the jelly is poured while hot into the annular space contained between a paper cylinder and a cork2 then1 when cold1 the cork is twisted round and the jelly exposed to polarised light1 when a transverse cross1 ,x1 not 1 appears1 with rings as the inverse square of the radius1 all which is fully verified4 ,hip6 etc4 ,q4,e4,d40 ,and again on ,march #bbnd1 #ahej3-- 8,at ,practical ,mechanics ,i have been turning ,devils of sorts4 ,for private studies ,i have been reading ,young's #8,lectures1' ,willis's #8,principles of ,mechanism1' ,moseley's #8,engineering and ,mechanics1' ,dixon on #8,heat1' and ,moigno's #8,rpertoire d',optique4' ,this last is a very complete analysis of all that has been done in the optical way from ,fresnel to the end of #ahdi1 and there is another volume a-coming which will complete the work4 ,there is in it1 besides common optics1 all about the other things which accompany light1 as heat1 chemical action1 photographic rays1 action on vegetables1 etc4 8,my notions are rather few1 as ,i do not entertain them just now4 ,i have a notion for the torsion of wires and rods1 not to be made till the vacation2 of experiments on the action of compression on glass1 jelly1 etc41 numerically done up2 of papers for the ,physico-,mathematical ,society 7which is to revive in earnest next session672 on the relations of optical and mechanical constants1 their desirableness1 etc42 and suspension bridges1 and catenaries1 and elastic curves4 ,alex4 ,campbell1 ,agnew1 and ,i are appointed to read up the subject of periodical shooting stars1 and to prepare a list of the phenomena to be observed on the #ith ,august and #acth ,november4 ,the society's barometer is to be taken up ,arthur's ,seat at the end of the session1 when ,forbes goes up1 and ,all students are invited to attend1 so that the existence of the society may be recognised40 ,it was at last settled that he was to go up to ,cambridge4 ,tait had been at ,peterhouse for two years1 while ,allan ,stewart had joined him there in #ahdi1 and after much discussion it was arranged that ,maxwell should enter at the same college4 ,of this period of his life ,tait writes as follows3-- 8,the winter of #ahdg found us together in the classes of ,forbes and ,kelland1 where he highly distinguished himself4 ,with the former he was a particular favourite1 being admitted to the free use of the class apparatus for original experiments4 ,he lingered here behind most of his former associates1 having spent three years at the ,university of ,edinburgh1 working 7without any assistance or supervision7 with physical and chemical apparatus1 and devouring all sorts of scientific works in the library4 ,during this period he wrote two valuable papers1 which are published in our #8,transactions1' on #8,the ,theory of ,rolling ,curves' and on #8,the ,equilibrium of ,elastic ,solids4' ,thus he brought to ,cambridge1 in the autumn of #ahej1 a mass of knowledge which was really immense for so young a man1 but in a state of disorder appalling to his methodical private tutor4 ,though that tutor was ,william ,hopkins1 the pupil to a great extent took his own way1 and it may safely be said that no high wrangler of recent years ever entered the ,senate ,house more imperfectly trained to produce #8paying' work than did ,clerk ,maxwell4 ,but by sheer strength of intellect1 though with the very minimum of knowledge how to use it to advantage under the conditions of the examination1 he obtained the position of ,second ,wrangler1 and was bracketed equal with the ,senior ,wrangler in the higher ordeal of the ,smith's ,prizes4 ,his name appears in the ,cambridge #8,calendar' as ,maxwell of ,trinity1 but he was originally entered at ,peterhouse1 and kept his first term there1 in that small but most ancient foundation which has of late furnished ,scotland with the majority of the professors of mathematics and natural philosophy in her four universities40 ,while ,w4 ,d4 ,niven1 in his preface to ,maxwell's collected works 7p4 xii471 says3-- 8,it may readily be supposed that his preparatory training for the ,cambridge course was far removed from the ordinary type4 ,there had indeed for some time been practically no restraint upon his plan of study1 and his mind had been allowed to follow its natural bent towards science1 though not to an extent so absorbing as to withdraw him from other pursuits4 ,though he was not a sportsman--indeed1 sport so-called was always repugnant to him--he was yet exceedingly fond of a country life4 ,he was a good horseman and a good swimmer4 ,whence1 however1 he derived his chief enjoyment may be gathered from the account which ,mr4 ,campbell gives of the zest with which he quoted on one occasion the lines of ,burns which describe the poet finding inspiration while wandering along the banks of a stream in the free indulgence of his fancies4 ,maxwell was not only a lover of poetry1 but himself a poet1 as the fine pieces gathered together by ,mr4 ,campbell abundantly testify4 ,he saw1 however1 that his true calling was science1 and never regarded these poetical efforts as other than mere pastime4 ,devotion to science1 already stimulated by successful endeavour2 a tendency to ponder over philosophical problems2 and an attachment to ,english literature1 particularly to ,english poetry--these tastes1 implanted in a mind of singular strength and purity1 may be said to have been the endowments with which young ,maxwell began his ,cambridge career4 ,besides this1 his scientific reading1 as we may gather from his papers to the ,royal ,society of ,edinburgh referred to above1 was already extensive and varied4 ,he brought with him1 says ,professor ,tait1 a mass of knowledge which was really immense for so young a man1 but in a state of disorder appalling to his methodical private tutor40 ,,chapter ,,ii4 ,,undergraduate ,,life ,,at ,,cambridge4 ,maxwell did not remain long at ,peterhouse2 before the end of his first term he migrated to ,trinity1 and was entered under ,dr4 ,thompson ,december #adth1 #ahej4 ,he appeared to the tutor a shy and diffident youth1 but presently surprised ,dr4 ,thompson by producing a bundle of papers--copies1 probably1 of those he had already published--and remarking1 8,perhaps these may show that ,i am not unfit to enter at your ,college40 ,the change was pressed upon him by many friends1 the grounds of the advice being that1 from the large number of high wranglers recently at ,peterhouse and the smallness of the foundation1 the chances of a ,fellowship there for a mathematical man were less than at ,trinity4 ,it was a step he never regretted2 the prospect of a ,fellowship had but little influence on his mind4 ,he found1 however1 at the larger college ampler opportunities for self-improvement1 and it was possible for him to select his friends from among men whom he otherwise would never have known4 ,the record of his undergraduate life is not very full2 his letters to his father have1 unfortunately1 been lost1 but we have enough in the recollections of friends still living to picture what it was like4 ,at first he lodged in ,king's ,parade with an old ,edinburgh schoolfellow1 ,c4 ,h4 ,robertson4 ,he attended the ,college lectures on mathematics1 though they were somewhat elementary1 and worked as a private pupil with ,porter1 of ,peterhouse4 ,his father writes to him1 ,november1 #ahej3 8,have you called on ,professors ,sedgwick1 at ,trin41 and ,stokes1 at ,pembroke8 ,if not1 you should do both4 ,stokes will be most in your line1 if he takes you in hand at all4 ,sedgwick is also a great ,don in his line1 and1 if you were entered in geology1 would be a most valuable acquaintance40 ,in his second year he became a pupil of ,hopkins1 the great coach2 he also attended ,stokes' lectures1 and the friendship which lasted till his death was thus begun4 ,in ,april1 #aheb1 he was elected a scholar1 and obtained rooms in ,college 7,g1 ,old ,court74 ,in ,june1 #aheb1 he came of age4 8,i trust you will be as discreet when major as you have been while minor10 writes his father the day before4 ,the next academic year1 ,october1 #aheb1 to ,june1 #ahec1 was a very busy one2 hard grind for the ,tripos occupied his time1 and he seems to have been thoroughly overstrained4 ,he was taken ill while staying near ,lowestoft with the ,rev4 ,c4 ,b4 ,tayler1 the uncle of a ,college friend4 ,his own account of the illness is given in a letter to ,professor ,campbell#ac1 dated ,july #adth1 #ahec4 8,you wrote just in time for your letter to reach me as ,i reached ,cambridge4 ,after examination1 ,i went to visit the ,rev4 ,c4 ,b4 ,tayler 7uncle to a ,tayler whom ,i think you have seen under the name of ,freshman1 etc41 and author of many tracts and other didactic works74 ,we had little expedites and walks1 and things parochial and educational1 and domesticity4 ,i intended to return on the #ahth ,june1 but on the #agth ,i felt unwell1 and took measures accordingly to be well again--i4e4 went to bed1 and made up my mind to recover4 ,but it lasted more than a fortnight1 during which time ,i was taken care of beyond expectation 7not that ,i did not expect much before74 ,when ,i was perfectly useless and could not sit up without fainting1 ,mr4 ,tayler did everything for me in such a way that ,i had no fear of giving trouble4 ,so did ,mrs4 ,tayler2 and the two nephews did all they could4 ,so they kept me in great happiness all the time1 and detained me till ,i was able to walk about and got back strength4 ,i returned on the #dth ,july4 8,the consequence of all this is that ,i correspond with ,mr4 ,tayler1 and have entered into bonds with the nephews1 of all of whom more hereafter4 ,since ,i came here ,i have been attending ,hop41 but1 with his approval1 did not begin full swing4 ,i am getting on1 though1 and the work is not grinding on the prepared brain40 ,during this period he wrote some papers for the ,cambridge and ,dublin ,mathematical ,journal which will be referred to again later4 ,he was also a member of a discussion society known as the 8,apostles10 and some of the essays contributed by him are preserved by ,professor ,campbell4 ,mr4 ,niven1 in his preface to the collected edition of ,maxwell's works1 suggests that the composition of these essays laid the foundation of that literary finish which is one of the characteristics of ,maxwell's scientific writings4 ,among his friends at the time were ,tait1 ,charles ,mackenzie of ,caius1 the missionary bishop of ,central ,africa1 ,henry and ,frank ,mackenzie of ,trinity1 ,droop1 third ,wrangler in #ahed2 ,gedge1 ,isaac ,taylor1 ,blakiston1 ,f4 ,w4 ,farrar1#ad ,h4 ,m4 ,butler1#ae ,hort1 ,v4 ,lushington1 ,cecil ,munro1 ,g4 ,w4 ,h4 ,tayler1 and ,w4 ,n4 ,lawson4 ,some of these who survived him have given to ,professor ,campbell their recollections of these undergraduate days1 which are full of interest4 ,thus ,mr4 ,lawson writes#af3-- 8,there must be many of his quaint verses about1 if one could lay hands on them1 for ,maxwell was constantly producing something of the sort and bringing it round to his friends1 with a sly chuckle at the humour1 which1 though his own1 no one enjoyed more than himself4 8,i remember ,maxwell coming to me one morning with a copy of verses beginning1 #8,gin a body meet a body going through the air1' in which he had twisted the well-known song into a description of the laws of impact of solid bodies4 8,there was also a description which ,maxwell wrote of some ,university ceremony--,i forget what--in which somebody #8went before' and somebody #8followed after1' and #8in the midst were the wranglers1 playing with the symbols4' 8,these last words1 however meant1 were1 in fact1 a description of his own wonderful power4 ,i remember1 one day in lecture1 our lecturer had filled the black-board three times with the investigation of some hard problem in ,geometry of ,three ,dimensions1 and was not at the end of it1 when ,maxwell came up with a question whether it would not come out geometrically1 and showed how1 with a figure1 and in a few lines1 there was the solution at once4 8,maxwell was1 ,i daresay you remember1 very fond of a talk upon almost anything4 ,he and ,i were pupils 7at an enormous distance apart7 of ,hopkins1 and ,i well recollect how1 when ,i had been working the night before and all the morning at ,hopkins's problems1 with little or no result1 ,maxwell would come in for a gossip1 and talk on while ,i was wishing him far away1 till at last1 about half an hour or so before our meeting at ,hopkins's1 he would say1 #8,well1 ,i must go to old ,hop4's problems'2 and1 by the time we met there1 they were all done4 8,i remember ,hopkins telling me1 when speaking of ,maxwell1 either just before or just after his degree1 #8,it is not possible for that man to think incorrectly on physical subjects'2 and ,hopkins1 as you know1 had had1 perhaps1 more experience of mathematical minds than any man of his time40 ,the last clause is part of a quotation from a diary kept by ,mr4 ,lawson at ,cambridge1 in which1 under the date ,july #aeth1 #ahec1 he writes3-- 8,he 7,hopkins7 was talking to me this evening about ,maxwell4 ,he says he is unquestionably the most extraordinary man he has met with in the whole range of his experience2 he says it appears impossible for ,maxwell to think incorrectly on physical subjects2 that in his analysis1 however1 he is far more deficient4 ,he looks upon him as a great genius with all its eccentricities1 and prophesies that one day he will shine as a light in physical science--a prophecy in which all his fellow-students strenuously unite40 ,how many who have struggled through the 8,electricity and ,magnetism0 have realised the truth of the remark about the correctness of his physical intuitions and the deficiency at times of his analysis6 ,dr4 ,butler1 a friend of these early days1 preached the ,university sermon on ,november #afth1 #ahgi1 ten days after ,maxwell's death1 and spoke thus3-- 8,it is a solemn thing--even the least thoughtful is touched by it--when a great intellect passes away into the silence and we see it no more4 ,such a loss1 such a void1 is present1 ,i feel certain1 to many here to-day4 ,it is not often1 even in this great home of thought and knowledge1 that so bright a light is extinguished as that which is now mourned by many illustrious mourners1 here chiefly1 but also far beyond this place4 ,i shall be believed when ,i say in all simplicity that ,i wish it had fallen to some more competent tongue to put into words those feelings of reverent affection which are1 ,i am persuaded1 uppermost in many hearts on this ,sunday4 ,my poor words shall be few1 but believe me they come from the heart4 ,you know1 brethren1 with what an eager pride we follow the fortunes of those whom we have loved and reverenced in our undergraduate days4 ,we may see them but seldom1 few letters may pass between us1 but their names are never common names4 ,they never become to us only what other men are4 ,when ,i came up to ,trinity twenty-eight years ago1 ,james ,clerk ,maxwell was just beginning his second year4 ,his position among us--,i speak in the presence of many who remember that time--was unique4 ,he was the one acknowledged man of genius among the undergraduates4 ,we understood even then that1 though barely of age1 he was in his own line of inquiry not a beginner but a master4 ,his name was already a familiar name to men of science4 ,if he lived1 it was certain that he was one of that small but sacred band to whom it would be given to enlarge the bounds of human knowledge4 ,it was a position which might have turned the head of a smaller man2 but the friend of whom we were all so proud1 and who seemed1 as it were1 to link us thus early with the great outside world of the pioneers of knowledge1 had one of those rich and lavish natures which no prosperity can impoverish1 and which make faith in goodness easy for others4 ,i have often thought that those who never knew the grand old ,adam ,sedgwick and the then young and ever-youthful ,clerk ,maxwell had yet to learn the largeness and fulness of the moulds in which some choice natures are framed4 ,of the scientific greatness of our friend we were most of us unable to judge2 but anyone could see and admire the boy-like glee1 the joyous invention1 the wide reading1 the eager thirst for truth1 the subtle thought1 the perfect temper1 the unfailing reverence1 the singular absence of any taint of the breath of worldliness in any of its thousand forms4 8,brethren1 you may know such men now among your college friends1 though there can be but few in any year1 or indeed in any century1 that possess the rare genius of the man whom we deplore4 ,if it be so1 then1 if you will accept the counsel of a stranger1 thank ,god for ,his gift4 ,believe me when ,i tell you that few such blessings will come to you in later life4 ,there are blessings that come once in a lifetime4 ,one of these is the reverence with which we look up to greatness and goodness in a college friend--above us1 beyond us1 far out of our mental or moral grasp1 but still one of us1 near to us1 our own4 ,you know1 in part at least1 how in this case the promise of youth was more than fulfilled1 and how the man who1 but a fortnight ago1 was the ornament of the ,university1 and--shall ,i be wrong in saying it8--almost the discoverer of a new world of knowledge1 was even more loved than he was admired1 retaining after twenty years of fame that mirth1 that simplicity1 that child-like delight in all that is fresh and wonderful which we rejoice to think of as some of the surest accompaniment of true scientific genius4 8,you know1 also1 that he was a devout as well as thoughtful ,christian4 ,i do not note this in the triumphant spirit of a controversialist4 ,i will not for a moment assume that there is any natural opposition between scientific genius and simple ,christian faith4 ,i will not compare him with others who have had the genius without the faith4 ,christianity1 though she thankfully welcomes and deeply prizes them1 does not need now1 any more than when ,st4 ,paul first preached the ,cross at ,corinth1 the speculations of the subtle or the wisdom of the wise4 ,if ,i wished to show men1 especially young men1 the living force of the ,gospel1 ,i would take them not so much to a learned and devout ,christian man to whom all stores of knowledge were familiar1 but to some country village where for fifty years there had been devout traditions and devout practice4 ,there they would see the ,gospel lived out2 truths1 which other men spoke of1 seen and known2 a spirit not of this world1 visibly1 hourly present2 citizenship in heaven daily assumed and daily realised4 ,such characters ,i believe to be the most convincing preachers to those who ask whether ,revelation is a fable and ,god an unknowable4 ,yes1 in most cases--not1 ,i admit1 in all--simple faith1 even peradventure more than devout genius1 is mighty for removing doubts and implanting fresh conviction4 ,but having said this1 we may well give thanks to ,god that our friend was what he was1 a firm ,christian believer1 and that his powerful mind1 after ranging at will through the illimitable spaces of ,creation and almost handling what he called #8the foundation-stones of the material universe1' found its true rest and happiness in the love and the mercy of ,him whom the humblest ,christian calls his ,father4 ,of such a man it may be truly said that he had his citizenship in heaven1 and that he looked for1 as a ,saviour1 the ,lord ,jesus ,christ1 through whom the unnumbered worlds were made1 and in the likeness of whose image our new and spiritual body will be fashioned40 ,the ,tripos came in ,january1 #ahed4 8,you will need to get muffetees for the ,senate ,room4 ,take your plaid or rug to wrap round your feet and legs10 was his father's advice--advice which will appeal to many who can remember the ,senate ,house as it felt on a cold ,january morning4 ,maxwell had been preparing carefully for this examination4 ,thus to his aunt1 ,miss ,cay1 in ,june1 #ahec1 he writes3--8,if anyone asks how ,i am getting on in mathematics1 say that ,i am busy arranging everything so as to be able to express all distinctly1 so that examiner may be satisfied now and pupils edified hereafter4 ,it is pleasant work and very strengthening1 but not nearly finished40 ,still1 the illness of ,july1 #ahec1 had left some effect4 ,professor ,baynes states that he said that on entering the ,senate ,house for the first paper he felt his mind almost a blank1 but by-and-by his mental vision became preternaturally clear4 ,the moderators were ,mackenzie of ,caius1 whose advice had been mainly instrumental in leading him to migrate to ,trinity1 ,wm4 ,walton of ,trinity1 ,wolstenholme of ,christ's1 and ,percival ,frost of ,st4 ,john's4 ,when the lists were published1 ,routh of ,peterhouse was senior1 ,maxwell second4 ,the examination for the ,smith's ,prizes followed in a few days1 and then ,routh and ,maxwell were declared equal4 ,in a letter to ,miss ,cay#ag of ,january #acth1 while waiting for the three days' list1 he writes3-- 8,all my correspondents have been writing to me1 which is kind1 and have not been writing questions1 which is kinder4 ,so ,i answer you now1 while ,i am slacking speed to get up steam1 leaving ,lewis and ,stewart1 etc41 till next week1 when ,i will give an account of the five days4 ,there are a good many up here at present1 and we get on very jolly on the whole2 but some are not well1 and some are going to be plucked or gulphed1 as the case may be1 and others are reading so hard that they are invisible4 ,i go to-morrow to breakfast with shaky men1 and after food ,i am to go and hear the list read out1 and whether they are through1 and bring them word4 ,when the honour list comes out the poll men act as messengers4 ,bob ,campbell comes in occasionally of an evening now1 to discuss matters and vary sports4 ,during examination ,i have had men at night working with gutta-percha1 magnets1 etc4 ,it is much better than reading novels or talking after #e hours' hard writing40 ,his father1 on hearing the news1 wrote from ,edinburgh3-- 8,i heartily congratulate you on your place in the list4 ,i suppose it is higher than the speculators would have guessed1 and quite as high as ,hopkins reckoned on4 ,i wish you success in the ,smith's ,prizes2 be sure to write me the result4 ,i will see ,mrs4 ,morrieson1 and ,i think ,i will call on ,dr4 ,gloag to congratulate him4 ,he has at least three pupils gaining honours40 ,his friends in ,edinburgh were greatly pleased4 8,i get congratulations on all hands10 his father writes1#ah 8including ,professor ,kelland and ,sandy ,fraser and all others competent4444 ,to-night or on ,monday ,i shall expect to hear of the ,smith's ,prizes40 ,and again1 ,february #fth1 #ahed3--8;,george ,wedderburn came into my room at #b a4m4 yesterday morning1 having seen the ,saturday ,times1 received by the express train4444 ,as you are equal to the ,senior in the champion trial1 you are very little behind him40 ,or again1 ,march #eth1 #ahed3-- 8,aunt ,jane stirred me up to sit for my picture1 as she said you wished for it and were entitled to ask for it qua ,wrangler4 ,i have had four sittings to ,sir ,john ,watson ,gordon1 and it is now far advanced2 ,i think it is very like4 ,it is kitcat size1 to be a companion to ,dyce's picture of your mother and self1 which ,aunt ,jane says she is to leave to you40 ,and now the long years of preparation were nearly over4 ,the cunning craftsman was fitted with his tools2 he could set to work to unlock the secrets of ,nature2 he was free to employ his genius and his knowledge on those tasks for which he felt most fitted4 ,,chapter ,,iii4 ,,early ,,researches4--,,professor ,,at ,,aberdeen4 ,from this time on ,maxwell's life becomes a record of his writings and discoveries4 ,it will1 however1 probably be clearest to separate as far as possible biographical details from a detailed account of his scientific work1 leaving this for consecutive treatment in later chapters1 and only alluding to it so far as may prove necessary to explain references in his letters4 ,he continued in ,cambridge till the ,long ,vacation of #ahed1 reading ,mill's 8,logic40 8,i am experiencing the effects of ,mill10 he writes1 ,march #beth1 #ahed1 8but ,i take him slowly4 ,i do not think him the last of his kind4 ,i think more is wanted to bring the connexion of sensation with science to light1 and to show what it is not40 ,he also read ,berkeley on 8,the ,theory of ,vision0 and 8greatly admired it40 ,about the same time he devised an ophthalmoscope4#ai 8,i have made an instrument for seeing into the eye through the pupil4 ,the difficulty is to throw the light in at that small hole and look in at the same time2 but that difficulty is overcome1 and ,i can see a large part of the back of the eye quite distinctly with the image of the candle on it4 ,people find no inconvenience in being examined1 and ,i have got dogs to sit quite still and keep their eyes steady4 ,dogs' eyes are very beautiful behind--a copper-coloured ground1 with glorious bright patches and networks of blue1 yellow1 and green1 with blood-vessels great and small40 ,after the vacation he returned to ,cambridge1 and the letters refer to the colour-top4 ,thus to ,miss ,cay1 ,november #bdth1 #ahed1 p4 #bjh3-- 8,i have been very busy of late with various things1 and am just beginning to make papers for the examination at ,cheltenham1 which ,i have to conduct about the #aath of ,december4 ,i have also to make papers to polish off my pups4 with4 ,i have been spinning colours a great deal1 and have got most accurate results1 proving that ordinary people's eyes are all made alike1 though some are better than others1 and that other people see two colours instead of three2 but all those who do so agree amongst themselves4 ,i have made a triangle of colours by which you may make out everything4 8,if you can find out any people in ,edinburgh who do not see colours 7,i know the ,dicksons don't71 pray drop a hint that ,i would like to see them4 ,i have put one here up to a dodge by which he distinguishes colours without fail4 ,i have also constructed a pair of squinting spectacles1 and am beginning operations on a squinting man40 ,a paper written for his own use originally some time in #ahed1 but communicated as a parting gift to his friend ,farrar1 who was about to become a master at ,marlborough1 gives us some insight into his view of life at the age of twenty-three4 8,he that would enjoy life and act with freedom must have the work of the day continually before his eyes4 ,not yesterday's work1 lest he fall into despair2 nor to-morrow's1 lest he become a visionary--not that which ends with the day1 which is a worldly work2 nor yet that only which remains to eternity1 for by it he cannot shape his actions4 8,happy is the man who can recognise in the work of to-day a connected portion of the work of life and an embodiment of the work of ,eternity4 ,the foundations of his confidence are unchangeable1 for he has been made a partaker of ,infinity4 ,he strenuously works out his daily enterprises because the present is given him for a possession4 8,thus ought ,man to be an impersonation of the divine process of nature1 and to show forth the union of the infinite with the finite1 not slighting his temporal existence1 remembering that in it only is individual action possible2 nor yet shutting out from his view that which is eternal1 knowing that ,time is a mystery which man cannot endure to contemplate until eternal ,truth enlighten it40 ,his father was unwell in the ,christmas vacation of that year1 and he could not return to ,cambridge at the beginning of the ,lent term4 8,my steps10 he writes#bj to ,c4 ,j4 ,munro from ,edinburgh1 ,february #aith1 #ahee1 8will be no more by the reedy and crooked till ,easter term4444 ,i should like to know how many kept bacalaurean weeks go to each of these terms1 and when they begin and end4 ,overhaul the ,calendar1 and when found make note of40 ,he was back in ,cambridge for the ,may term1 working at the motion of fluids and at his colour-top4 ,a paper on 8,experiments on ,colour as ,perceived by the ,eye0 was communicated to the ,royal ,society of ,edinburgh on ,march #aith1 #ahee4 ,the experiments were shown to the ,cambridge ,philosophical ,society in ,may following1 and the results are thus described in two letters#ba to his father1 ,saturday1 ,may #eth1 #ahee3 8,the ,royal ,society have been very considerate in sending me my paper on #8,colours' just when ,i wanted it for the ,philosophical here4 ,i am to let them see the tricks on ,monday evening1 and ,i have been there preparing their experiments in the gaslight4 ,there is to be a meeting in my rooms to-night to discuss ,adam ,smith's #8,theory of ,moral ,sentiments1' so ,i must clear up my litter presently4 ,i am working away at electricity again1 and have been working my way into the views of heavy ,german writers4 ,it takes a long time to reduce to order all the notions one gets from these men1 but ,i hope to see my way through the subject and arrive at something intelligible in the way of a theory4444 8,the colour trick came off on ,monday1 #gth4 ,i had the proof-sheets of my paper1 and was going to read2 but ,i changed my mind and talked instead1 which was more to the purpose4 ,there were sundry men who thought that blue and yellow make green1 so ,i had to undeceive them4 ,i have got ,hay's book of colours out of the ,univ4 ,library1 and am working through the specimens1 matching them with the top4 ,i have a new trick of stretching the string horizontally above the top1 so as to touch the upper part of the axis4 ,the motion of the axis sets the string a-vibrating in the same time with the revolutions of the top1 and the colours are seen in the haze produced by the vibration4 ,thomson has been spinning the top1 and he finds my diagram of colours agrees with his experiments1 but he doubts about browns1 what is their composition4 ,i have got colcothar brown1 and can make white with it1 and blue and green2 also1 by mixing red with a little blue and green and a great deal of black1 ,i can match colcothar exactly4 8,i have been perfecting my instrument for looking into the eye4 ,ware has a little beast like old ,ask1 which sits quite steady and seems to like being looked at1 and ,i have got several men who have large pupils and do not wish to let me look in4 ,i have seen the image of the candle distinctly in all the eyes ,i have tried1 and the veins of the retina were visible in some2 but the dogs' eyes showed all the ramifications of veins1 with glorious blue and green network1 so that you might copy down everything4 ,i have shown lots of men the image in my own eye by shutting off the light till the pupil dilated and then letting it on4 8,i am reading ,electricity and working at ,fluid ,motion1 and have got out the condition of a fluid being able to flow the same way for a length of time and not wriggle about40 ,the ,british ,association met at ,glasgow in ,september1 #ahee1 and ,maxwell was present1 and showed his colour-top at ,professor ,ramsay's house to some of those interested4 ,letters#bb to his father about this time describe some of the events of the meeting and his own plans for the term4 8,we had a paper from ,brewster on #8,the theory of three colours in the spectrum1' in which he treated ,whewell with philosophic pity1 commending him to the care of ,prof4 ,wartman of ,geneva1 who was considered the greatest authority in cases of his kind--cases1 in fact1 of colour-blindness4 ,whewell was in the room1 but went out and avoided the quarrel2 and ,stokes made a few remarks1 stating the case not only clearly but courteously4 ,however1 ,brewster did not seem to see that ,stokes admitted his experiments to be correct1 and the newspapers represented ,stokes as calling in question the accuracy of the experiments4 8,i am getting my electrical mathematics into shape1 and ,i see through some parts which were rather hazy before2 but ,i do not find very much time for it at present1 because ,i am reading about heat and fluids1 so as not to tell lies in my lectures4 ,i got a note from the ,society of ,arts about the platometer1 awarding thanks and offering to defray the expenses to the extent of #aj1 on the machine being produced in working order4 ,when ,i have arranged it in my head1 ,i intend to write to ,james ,bryson about it4 8,i got a long letter from ,thomson about colours and electricity4 ,he is beginning to believe in my theory about all colours being capable of reference to three standard ones1 and he is very glad that ,i should poach on his electrical preserves4 8444 ,it is difficult to keep up one's interest in intellectual matters when friends of the intellectual kind are scarce4 ,however1 there are plenty friends not intellectual who serve to bring out the active and practical habits of mind1 which overly-intellectual people seldom do4 ,wherefore1 if ,i am to be up this term1 ,i intend to addict myself rather to the working men who are getting up classes than to pups41 who are in the main a vexation4 ,meanwhile1 there is the examination to consider4 8,you say ,dr4 ,wilson has sent his book4 ,i will write and thank him4 ,i suppose it is about colour-blindness4 ,i intend to begin ,poisson's papers on electricity and magnetism to-morrow4 ,i have got them out of the library4 ,my reading hitherto has been of novels--#8,shirley' and #8,the ,newcomes1' and now #8,westward ,ho4' 8,macmillan proposes to get up a book of optics with my assistance1 and ,i feel inclined for the job4 ,there is great bother in making a mathematical book1 especially on a subject with which you are familiar1 for in correcting it you do as you would to pups4--look if the principle and result is right1 and forget to look out for small errors in the course of the work4 ,however1 ,i expect the work will be salutary1 as involving hard work1 and in the end much abuse from coaches and students1 and certainly no vain fame1 except in ,macmillan's puffs4 ,but1 if ,i have rightly conceived the plan of an educational book on optics1 it will be very different in manner1 though not in matter1 from those now used40 ,the examination referred to was that for a ,fellowship at ,trinity1 and ,maxwell was elected on ,october #ajth1 #ahee4 ,he was immediately asked to lecture for the ,college1 on hydrostatics and optics1 to the upper division of the third year1 and to set papers for the questionists4 ,in consequence1 he declined to take pupils1 in order to have time for reading and doing private mathematics1 and for seeing the men who attended his lectures4 ,in ,november he writes3 8,i have been lecturing two weeks now1 and the class seems improving2 and they come and ask questions1 which is a good sign4 ,i have been making curves to show the relations of pressure and volume in gases1 and they make the subject easier40 ,still1 he found time to attend ,professor ,willis's lectures on mechanism and to continue his reading4 8,i have been reading10 he writes1 8old books on optics1 and find many things in them far better than what is new4 ,the foreign mathematicians are discovering for themselves methods which were well known at ,cambridge in #agbj1 but are now forgotten40 ,the 8,poisson0 was read to help him with his own views on electricity1 which were rapidly maturing1 and the first of that great series of works which has revolutionised the science was published on ,december #ajth1 #ahee1 when his paper on 8,faraday's ,lines of ,force0 was read to the ,cambridge ,philosophical ,society4 ,the next term found him back in ,cambridge at work on his lectures1 full of plans for a new colour top and other matters4 ,early in ,february he received a letter from ,professor ,forbes1 telling him that the ,professorship of ,natural ,philosophy in ,marischal ,college1 ,aberdeen1 was vacant1 and suggesting that he should apply4 ,he decided to be a candidate if his father approved4 8,for my own part10 he writes1 8,i think the sooner ,i get into regular work the better1 and that the best way of getting into such work is to profess one's readiness by applying for it40 ,on the #bjth of ,february he writes3 8,however1 wisdom is of many kinds1 and ,i do not know which dwells with wise counsellors most1 whether scientific1 practical1 political1 or ecclesiastical4 ,i hear there are candidates of all kinds relying on the predominance of one or other of these kinds of wisdom in the constitution of the ,government40 ,the second part of the paper on 8,faraday's ,lines of ,force0 was read during the term4 ,writing on the #dth of ,march1 he expresses the hope soon to be able to write out fully the paper4 8,i have done nothing in that way this term10 he says1 8but am just beginning to feel the electrical state come on again40 ,his father was working at ,edinburgh in support of his candidature for ,aberdeen1 and when1 in the middle of ,march1 he returned ,north1 he found everything well prepared4 ,the two returned to ,glenlair together after a few days in ,edinburgh1 and ,maxwell was preparing to go back to ,cambridge1 when1 on the #bnd of ,april1 his father died suddenly4 ,writing to ,mrs4 ,blackburn1 he says3 8,my father died suddenly to-day at twelve o'clock4 ,he had been giving directions about the garden1 and he said he would sit down and rest a little1 as usual4 ,after a few minutes ,i asked him to lie down on the sofa1 and he did not seem inclined to do so2 and then ,i got him some ether1 which had helped him before4 ,before he could take any he had a slight struggle1 and all was over4 ,he hardly breathed afterwards40 ,almost immediately after this1 ,maxwell was appointed to ,aberdeen4 ,his father's death had frustrated some at least of the intentions with which he had applied for the post4 ,he knew the old man would be glad to see him the occupant of a ,scotch chair4 ,he hoped1 too1 to be able to live with his father at ,glenlair for one half the year2 but this was not to be4 ,no doubt the laboratory and the freedom of the post1 when compared with the routine work of preparing men for the ,tripos1 had their inducements2 still1 it may be doubted if the choice was a wise one for him4 ,the work of drilling classes1 composed1 for the most part1 of raw untrained lads1 in the elements of physics and mechanics was1 as ,niven says in his preface to the collected works1 not that for which he was best fitted2 while at ,cambridge1 had he stayed1 he must always have had among his pupils some of the best mathematicians of the time2 and he might have founded some ten or fifteen years before he did that ,cambridge ,school of ,physicists which looks back with so much pride to him as their master4 ,leave-taking at ,trinity was a sad task4 ,he writes#bc thus1 ,june #dth1 to ,mr4 ,r4 ,b4 ,litchfield3-- 8,on ,thursday evening ,i take the ,north-,western route to the ,north4 ,i am busy looking over immense rubbish of papers1 etc41 for some things not to be burnt lie among much combustible matter1 and some is soft and good for packing4 8,it is not pleasant to go down to live solitary1 but it would not be pleasant to stay up either1 when all one had to do lay elsewhere4 ,the transition state from a man into a ,don must come at last1 and it must be painful1 like gradual outrooting of nerves4 ,when it is done there is no more pain1 but occasional reminders from some suckers1 tap-roots1 or other remnants of the old nerves1 just to show what was there and what might have been40 ,the summer of #ahef was spent at ,glenlair1 where various friends were his guests--,lushington1 ,mac,lennan1 the two cousins ,cay1 and others4 ,he continued to work at optics1 electricity1 and magnetism1 and in ,october was busy with 8a solemn address or manifesto to the ,natural ,philosophers of the ,north1 which needed coffee and anchovies and a roaring hot fire and spread coat-tails to make it natural40 ,this was his inaugural lecture4 ,in ,november he was at ,aberdeen4 ,letters#bd to ,miss ,cay1 ,professor ,campbell1 and ,c4 ,j4 ,munro tell of the work of the session4 ,the last is from ,glenlair1 dated ,may #bjth1 #aheg1 after work was over4 8,the session went off smoothly enough4 ,i had ,sun1 all the beginning of optics1 and worked off all the experimental part up to ,fraunhofer's lines1 which were glorious to see with a water-prism ,i have set up in the form of a cubical box1 five inch side4444 8,i succeeded very well with heat4 ,the experiments on latent heat came out very accurate4 ,that was my part1 and the class could explain and work out the results better than ,i expected4 ,next year ,i intend to mix experimental physics with mechanics1 devoting ,tuesday and ,,thursday 7what would ,stokes say87 to the science of experimenting accurately4444 8,last week ,i brewed chlorophyll 7as the chemists word it71 a green liquor1 which turns the invisible light red4444 8,my last grind was the reduction of equations of colour which ,i made last year4 ,the result was eminently satisfactory40 ,another letter1#be ,june #eth1 #aheg1 also to ,munro1 refers to the work of the ,university ,commission and the new statutes4 8,i have not seen ,article #g1 but ,i agree with your dissent from it entirely4 ,on the vested interest principle1 ,i think the men who intended to keep their fellowships by celibacy and ordination1 and got them on that footing1 should not be allowed to desert the virgin choir or neglect the priestly office1 but on those principles should be allowed to live out their days1 provided the whole amount of souls cured annually does not amount to #bj in the ,king's ,book4 ,but my doctrine is that the various grades of ,college officers should be set on such a basis that1 although chance lecturers might be sometimes chosen from among fresh fellows who are going away soon1 the reliable assistant tutors1 and those that have a plain calling that way1 should1 after a few years1 be elected permanent officers of the ,college1 and be tutors and deans in their time1 and seniors also1 with leave to marry1 or1 rather1 never prohibited or asked any questions on that head1 and with leave to retire after so many years' service as seniors4 ,as for the men of the world1 we should have a limited term of existence1 and that independent of marriage or #8parsonage4'0 ,it was more than twenty years before the scheme outlined in the above letter came to anything2 but1 at the time of ,maxwell's death in #ahgi1 another ,commission was sitting1 and the plan suggested by ,maxwell became the basis of the statutes of nearly all the colleges4 ,for the winter session of #aheg-eh he was again at ,aberdeen4 ,the ,adams ,prize had been established in #ahdh by some members of ,st4 ,john's ,college1 and connected by them with the name of ,adams 8in testimony of their sense of the honour he had conferred upon his ,college and the ,university by having been the first among the mathematicians of ,europe to determine from perturbations the unknown place of a disturbing planet exterior to ,uranus40 ,professor ,challis1 ,dr4 ,parkinson1 and ,sir ,william ,thomson1 the examiners1 had selected as the subject for the prize to be awarded in #aheg the 8,motions of ,saturn's ,rings40 ,for this ,maxwell had decided to compete1 and his letters at the end of #aheg tell of the progress of the task4 ,thus1 writing#bf to ,lewis ,campbell from ,glenlair on ,august #bhth1 he says3-- 8,i have been battering away at ,saturn1 returning to the charge every now and then4 ,i have effected several breaches in the solid ring1 and now ,i am splash into the fluid one1 amid a clash of symbols truly astounding4 ,when ,i reappear it will be in the dusky ring1 which is something like the state of the air supposing the siege of ,sebastopol conducted from a forest of guns #ajj miles one way1 and #cj1jjj miles the other1 and the shot never to stop1 but go spinning away round a circle1 radius #agj1jjj miles40 ,and again#bg to ,miss ,cay on the #bhth of ,november3-- 8,i have been pretty steady at work since ,i came4 ,the class is small and not bright1 but ,i am going to give them plenty to do from the first1 and ,i find it a good plan4 ,i have a large attendance of my old pupils1 who go on with the higher subjects4 ,this is not part of the ,college course1 so they come merely from choice1 and ,i have begun with the least amusing part of what ,i intend to give them4 ,many had been reading in summer1 for they did very good papers for me on the old subjects at the beginning of the month4 ,most of my spare time ,i have been doing ,saturn's rings1 which is getting on now1 but lately ,i have had a great many long letters to write--some to ,glenlair1 some to private friends1 and some all about science4444 ,i have had letters from ,thomson and ,challis about ,saturn--from ,hayward1 of ,durham ,university1 about the brass top1 of which he wants one4 ,he says that the earth has been really found to change its axis regularly in the way ,i supposed4 ,faraday has also been writing about his own subjects4 ,i have had also to write ,forbes a long report on colours2 so that for every note ,i have got ,i have had to write a couple of sheets in reply1 and reporting progress takes a deal of writing and spelling40 ,he devised a model 7now at the ,cavendish ,laboratory7 to exhibit the motions of the satellites in a disturbed ring1 8for the edification of sensible image-worshippers40 ,the essay was awarded the prize1 and secured for its author great credit among scientific men4 ,in another letter1 written during the same session1 he says3 8,i find my principal work here is teaching my men to avoid vague expressions1 as #8a certain force1' meaning uncertain2 may instead of must2 will be instead of is2 proportional instead of equal40 ,the death1 during the autumn1 of his ,college friend ,pomeroy1 from fever in ,india1 was a great blow to him2 his letters at the time show the depth of his feelings and his beliefs4 ,the question of the fusion of the two ,colleges at ,aberdeen1 ,king's ,college and the ,marischal ,college1 was coming to the fore4 8,know all men10 he says1 in a letter to ,professor ,campbell1 8that ,i am a ,fusionist40 ,in ,february1 #aheh1 he was still engaged on ,saturn's rings1 while hard at work during the same time with his classes4 ,he had established a voluntary class for his students of the previous year1 and was reading with them ,newton's 8,lunar ,theory and ,astronomy40 ,this was followed by 8,electricity and ,magnetism10 ,faraday's book being the backbone of everything1 8as he himself is the nucleus of everything electric since #ahcj40 ,in ,february1 #aheh1 he announced his engagement to ,katherine ,mary ,dewar1 the daughter of the ,principal of ,marischal ,college4 8,dear ,aunt0 7he says1#bh ,february #ahth1 #aheh71 8this comes to tell you that ,i am going to have a wife4444 8,don't be afraid2 she is not mathematical1 but there are other things besides that1 and she certainly won't stop mathematics4 ,the only one that can speak as an eye-witness is ,johnnie1 and he only saw her when we were both trying to act the indifferent4 ,we have been trying it since1 but it would not do1 and it was not good for either40 ,the wedding took place early in ,june4 ,professor ,campbell has preserved some of the letters written by ,maxwell to ,miss ,dewar1 and these contain 8the record of feelings which in the years that followed were transfused in action and embodied in a married life which can only be spoken of as one of unexampled devotion40 ,the project for the fusion of the two ,colleges1 to which reference has been made1 went on1 and the scheme was completed in #ahfj4 ,the two ,colleges were united to form the ,university of ,aberdeen1 and the new chair of ,natural ,philosophy thus created was filled by the appointment of ,david ,thomson1 ,professor of ,natural ,philosophy in ,king's ,college1 and ,maxwell's senior4 ,mr4 ,w4 ,d4 ,niven1 in his preface to ,maxwell's works1 when dealing with this appointment1 writes3-- 8,professor ,thomson1 though not comparable to ,maxwell as a physicist1 was nevertheless a remarkable man4 ,he was distinguished by singular force of character and great administrative faculty1 and he had been prominent in bringing about the fusion of the ,colleges4 ,he was also an admirable lecturer and teacher1 and had done much to raise the standard of scientific education in the north of ,scotland4 ,thus the choice made by the ,commissioners1 though almost inevitable1 had the effect of making it appear that ,maxwell failed as a teacher4 ,there seems1 however1 to be no evidence to support such an inference4 ,on the contrary1 if we may judge from the number of voluntary students attending his classes in his last ,college session1 he would seem to have been as popular as a professor as he was personally estimable40 ,the question whether ,maxwell was a great teacher has sometimes been discussed4 ,i trust that the following pages will give an answer to it4 ,he was not a prominent lecturer4 ,as ,professor ,campbell says1#bi 8,between his students' ignorance and his vast knowledge it was difficult to find a common measure4 ,the advice which he once gave to a friend whose duty it was to preach to a country congregation1 #8,why don't you give it them thinner8' must often have been applicable to himself4444 ,illustrations of ignotum per ignotius1 or of the abstruse by some unobserved property of the familiar1 were multiplied with dazzling rapidity4 ,then the spirit of indirectness and paradox1 though he was aware of its dangers1 would often take possession of him against his will1 and1 either from shyness or momentary excitement1 or the despair of making himself understood1 would land him in #8chaotic statements1' breaking off with some quirk of ironical humour40 ,but teaching is not all done by lecturing4 ,his books and papers are vast storehouses of suggestions and ideas which the ablest minds of the past twenty years have been since developing4 ,to talk with him for an hour was to gain inspiration for a year's work2 to see his enthusiasm and to win his praise or commendation were enough to compensate for many weary struggles over some stubborn piece of apparatus which would not go right1 or some small source of error which threatened to prove intractable and declined to submit itself to calculation4 ,the sure judgment of posterity will confirm the verdict that ,clerk ,maxwell was a great teacher1 though lecturing to a crowd of untrained undergraduates was a task for which others were better fitted than he4 ,,chapter ,,iv4 ,,professor ,,at ,,king',s ,,college1 ,,london4--,,life ,,at ,,glenlair4 ,in #ahfj ,forbes resigned the chair of ,natural ,philosophy at ,edinburgh4 ,maxwell and ,tait were candidates1 and ,tait was appointed4 ,in the summer of the same year ,maxwell obtained the vacant ,professorship of ,natural ,philosophy at ,king's ,college1 ,london4 ,this he held to #ahfe1 and this period of his life is distinguished by the appearance of some of his most important papers4 ,the work was arduous2 the ,college course extended over nine months of the year2 there were as well evening lectures to artisans as part of his regular duties4 ,his life in ,london was useful to him in the opportunities it gave him for becoming personally acquainted with ,faraday and others4 ,he also renewed his intimacy with various ,cambridge friends4 ,he was at the celebrated ,oxford meeting of the ,british ,association in #ahfj1 where he exhibited his colour-box for mixing the colours of the spectrum4 ,in #ahei1 at the meeting at ,aberdeen1 he had read to ,section ,a his first paper on the 8,dynamical ,theory of ,gases10 published in the ,philosophical ,magazine for ,january1 #ahfj4 ,the second part of the paper1 dealing with the conduction of heat and other phenomena in a gas1 was published in ,july1 #ahfj1 after the ,oxford meeting4 ,a paper on the 8,theory of ,compound ,colours0 was communicated to the ,royal ,society by ,professor ,stokes in ,january1 #ahfj4 ,it contains the account of his colour-box in the form finally adopted 7most of the important parts of the apparatus are still at the ,cavendish ,laboratory71 and a number of observations by ,mrs4 ,maxwell and himself1 which will be more fully described later4 ,in ,november1 #ahfj1 he received for this work the ,rumford medal of the ,royal ,society4 ,the next year1 #ahfa1 is of great importance in the history of electrical science4 ,the ,british ,association met at ,manchester1 and a ,committee was appointed on ,standards of ,electrical ,resistance4 ,maxwell was not a member4 ,the committee reported at the ,cambridge meeting in #ahfb1 and were reappointed with extended duties4 ,maxwell's name1 among others1 was added1 and he took a prominent part in the deliberations of the committee1 which1 as their ,report#cj presented in #ahfc states1 came to the opinion1 8after mature consideration1 that the system of so-called absolute electrical units1 based on purely mechanical measurements1 is not only the best system yet proposed1 but is the only one consistent with our present knowledge both of the relations existing between the various electrical phenomena and of the connection between these and the fundamental measurements of time1 space1 and mass40 ,appendix ,c of this ,report1 8,on the ,elementary ,relations between ,electrical ,measurements10 bears the names of ,clerk ,maxwell and ,fleeming ,jenkin1 and is the foundation of everything that has been done in the way of absolute electrical measurement since that date2 while ,appendix ,d gives an account by the same two workers of the experiments on the absolute unit of electrical resistance made in the laboratory of ,king's ,college by ,maxwell1 ,fleeming ,jenkin1 and ,balfour ,stewart4 ,further experiments are described in the report for #ahfd4 ,the work thus begun was consummated during the year #ahid by the legalisation throughout the civilised world of a system of electrical units based on those described in these reports4 ,meanwhile1 ,maxwell's views on electro-magnetic theory were quietly developing4 ,papers on 8,physical ,lines of ,force10 which appeared in the ,philosophical ,magazine during #ahfa and #ahfb1 contain the germs of his theory--expressed at that time1 it is true1 in a somewhat material form4 ,in the paper published ,january1 #ahfb1 the now well-known relation between the ratio of the electric units and the velocity of light was established1 and his correspondence with ,fleeming ,jenkin and ,c4 ,j4 ,munro about this time relates in part to the experimental verification of this relation4 ,his experiments on this matter were published in the 8,philosophical ,transactions0 for #ahfh4 ,this electrical theory occupied his mind mainly during #ahfc and #ahfd4 ,in ,september of the latter year he writes#ca from ,glenlair to ,c4 ,hockin1 who had taken ,balfour ,stewart's place during the second series of experiments on the measurement of resistance4 8,i have been doing several electrical problems4 ,i have got a theory of #8electric absorption1' i4e41 residual charge1 etc41 and ,i very much want determinations of the specific induction1 electric resistance1 and absorption of good dielectrics1 such as glass1 shell-lac1 gutta-percha1 ebonite1 sulphur1 etc4 8,i have also cleared the electromagnetic theory of light from all unwarrantable assumption1 so that we may safely determine the velocity of light by measuring the attraction between bodies kept at a given difference of potential1 the value of which is known in electromagnetic measure4 8,i hope there will be resistance coils at the ,british ,association40 ,this work resulted in his greatest electrical paper1 8,a ,dynamical ,theory of the ,electromagnetic ,field10 read to the ,royal ,society ,december #hth1 #ahfd4 ,but the molecular theory of gases was still prominently before his mind4 ,in #ahfb1 writing#cb to ,h4 ,r4 ,droop1 he says3-- 8,some time ago1 when investigating ,bernoulli's theory of gases1 ,i was surprised to find that the internal friction of a gas 7if it depends on the collision of particles7 should be independent of the density4 8,stokes has been examining ,graham's experiments on the rate of flow of gases through fine tubes1 and he finds that the friction1 if independent of density1 accounts for ,graham's results2 but1 if taken proportional to density1 differs from those results very much4 ,this seems rather a curious result1 and an additional phenomenon1 explained by the #8collision of particles' theory of gases4 ,still one phenomenon goes against that theory--the relation between specific heat at constant pressure and at constant volume1 which is in air #adjh1 while it ought to be #accc40 ,and again#cc in the same year1 #bast ,april1 #ahfb1 to ,lewis ,campbell3-- 8,herr ,clausius of ,zrich1 one of the heat philosophers1 has been working at the theory of gases being little bodies flying about1 and has found some cases in which he and ,i don't tally4 ,so ,i am working it out again4 ,several experimental results have turned up lately rather confirmatory than otherwise of that theory4 8,i hope you enjoy the absence of pupils4 ,i find the division of them into smaller classes is a great help to me and to them2 but the total oblivion of them for definite intervals is a necessary condition for doing them justice at the proper time40 ,the experiments on the viscosity of gases1 which formed the ,bakerian ,lecture to the ,royal ,society read on ,february #hth1 #ahff1 were the outcome of this work4 ,his house in #h1 ,palace ,gardens1 ,kensington1 contained a large garret running the complete length4 8,to maintain the proper temperature a large fire was for some days kept up in the room in the midst of very hot weather4 ,kettles were kept on the fire and large quantities of steam allowed to flow into the room4 ,mrs4 ,maxwell acted as stoker1 which was very exhausting work when maintained for several consecutive hours4 ,after this the room was kept cool for subsequent experiments by the employment of a considerable amount of ice40 ,next year1 ,may1 #ahff1 was read his paper on the 8,dynamical ,theory of ,gases10 in which errors in his former papers1 which had been pointed out by ,clausius1 were corrected4 ,meanwhile he had resigned his ,london ,professorship at the end of the ,session of #ahfe1 and had been succeeded by ,professor ,w4 ,g4 ,adams4 ,for the next four years he lived chiefly at ,glenlair1 working at his theory of electricity1 occasionally1 as we shall see1 visiting ,london and ,cambridge1 and taking an active interest in the affairs of his own neighbourhood4 ,in #ahfe he had a serious illness1 through which he was nursed with great care by ,mrs4 ,maxwell4 ,his correspondence was considerable1 and absorbed much of his time4 ,much also was given to the study of ,english literature2 he was fond of reading ,chaucer1 ,milton1 or ,shakespeare aloud to ,mrs4 ,maxwell4 ,he also read much theological and philosophical literature1 and all he read helped only to strengthen that firm faith in the fundamentals of ,christianity in which he lived and died4 ,in #ahfg he and ,mrs4 ,maxwell paid a visit to ,italy1 which was a source of great pleasure to both4 ,his chief scientific work was the preparation of his 8,electricity and ,magnetism10 which did not appear till #ahgc2 the time was in the main one of quiet thought and preparation for his next great task1 the foundation of the ,school of ,physics in ,cambridge4 ,in #ahfh the principalship of the ,united ,college in the ,university of ,st4 ,andrews was vacant by the resignation of ,forbes1 and ,maxwell was invited by several of the professors to stand4 ,he1 however1 declined to submit his name to the ,crown4 ,,chapter ,v4 ,,cambridge4--,,professor ,,of ,,physics4 ,during his retirement at ,glenlair from #ahfe to #ahgj ,maxwell was frequently at ,cambridge4 ,he examined in the ,mathematical ,tripos in #ahff and #ahfg1 and again in #ahfi and #ahgj4 ,the regulations for the ,tripos had been in force practically unchanged since #ahdh1 and it was felt by many that the range of subjects included was not sufficiently extensive1 and that changes were urgently needed if ,cambridge were to retain its position as the centre of mathematical teaching4 ,natural ,philosophy was mentioned in the ,schedule1 but ,natural ,philosophy included only ,dynamics and ,astronomy1 ,hydrostatics and ,physical ,optics1 with some simple ,hydrodynamics and ,sound4 ,the subjects of ,heat1 ,electricity and ,magnetism1 the ,theory of ,elastic ,solids and ,vibrations1 ,vortex-,motion in ,hydrodynamics1 and much else1 were practically new since #ahdh4 ,stokes1 ,thomson1 and ,maxwell in ,england1 and ,helmholtz in ,germany1 had created them4 ,accordingly in ,june1 #ahfh1 a new plan of examinations was sanctioned by the ,senate to come into force in ,january1 #ahgc1 and these various subjects were explicitly included4 ,mr4 ,niven1 who was one of those examined by ,maxwell in #ahff1 writes in the preface to the collected works3-- 8,for some years previous to #ahff1 when ,maxwell returned to ,cambridge as ,moderator in the ,mathematical ,tripos1 the studies in the ,university had lost touch with the great scientific movements going on outside her walls4 ,it was said that some of the subjects most in vogue had but little interest for the present generation1 and loud complaints began to be heard that while such branches of knowledge as ,heat1 ,electricity1 and ,magnetism were left out of the ,tripos examination1 the candidates were wasting their time and energy upon mathematical trifles barren of scientific interest and of practical results4 ,into the movement for reform ,maxwell entered warmly4 ,by his questions in #ahff1 and subsequent years1 he infused new life into the examination2 he took an active part in drafting the new scheme introduced in #ahgc2 but most of all by his writings he exerted a powerful influence on the younger members of the ,university1 and was largely instrumental in bringing about the change which has been now effected40 ,but the ,university possessed no means of teaching these subjects1 and a ,syndicate or ,committee was appointed1 ,november #beth1 #ahfh1 8to consider the best means of giving instruction to students in ,physics1 especially in ,heat1 ,electricity and ,magnetism1 and the methods of providing apparatus for this purpose40 ,dr4 ,cookson1 ,master of ,st4 ,peter's ,college1 took an active part in the work of the ,syndicate4 ,professor ,stokes1 ,professor ,liveing1 ,professor ,humphry1 ,dr4 ,phear1 and ,dr4 ,routh were among the members4 ,maxwell himself was in ,cambridge that winter1 as ,examiner for the ,tripos1 and his work as ,moderator and ,examiner in the two previous years had done much to show the necessity of alterations and to indicate the direction which changes should take4 ,the ,syndicate reported ,february #bgth1 #ahfi4 ,they called attention to the ,report of the ,royal ,commission of #ahej4 ,the ,commissioners had 8prominently urged the importance of cultivating a knowledge of the great branches of ,experimental ,physics in the ,university02 and in page #aah of their ,report1 after commending the manner in which the subject of ,physical ,optics is studied in the ,university1 and pointing out that 8there is1 perhaps1 no public institution where it is better represented or prosecuted with more zeal and success in the way of original research10 they had stated that 8no reason can be assigned why other great branches of ,natural ,science should not become equally objects of attention1 or why ,cambridge should not become a great school of physical and experimental1 as it is already of mathematical and classical1 instruction40 ,and again the ,commissioners remark3 8,in a ,university so thoroughly imbued with the mathematical spirit1 physical study might be expected to assume within its precincts its highest and severest tone1 be studied under more abstract forms1 with more continual reference to mathematical laws1 and therefore with better hope of bringing them one by one under the domain of mathematical investigation than elsewhere40 ,after calling attention to these statements the ,report of the ,syndicate then continues3-- 8,in the scheme of ,examination for ,honours in the ,mathematical ,tripos approved by ,grace of the ,senate on the #bnd of ,june1 #ahfh1 ,heat1 ,electricity and ,magnetism1 if not introduced for the first time1 had a much greater degree of importance assigned to them than at any previous period1 and these subjects will henceforth demand a corresponding amount of attention from the candidates for ,mathematical ,honours4 ,the ,syndicate have limited their attention almost entirely to the question of providing public instruction in ,heat1 ,electricity and ,magnetism4 ,they recognise the importance and advantage of tutorial instruction in these subjects in the several colleges1 but they are also alive to the great impulse given to studies of this kind1 and to the large amount of additional training which students may receive through the instruction of a public ,professor1 and by knowledge gained in a well-appointed laboratory40 8,in accordance with these views1 and at an early period in their deliberations1 they requested the ,professors#cd of the ,university1 who are engaged in teaching ,mathematical and ,physical ,science1 to confer together upon the present means of teaching ,experimental ,physics1 especially ,heat1 ,electricity and ,magnetism1 and to inform them how the increased requirements of the ,university in this respect could be met by them40 8,the ,professors1 so consulted1 favoured the ,syndicate with a report on the subject1 which the ,syndicate now beg leave to lay before the ,senate4 ,it points out how the requirements of the ,university might be 8partially met10 but the ,professors state distinctly that they 8do not think that they are able to meet the want of an extensive course of lectures on ,physics treated as such1 and in great measure experimentally4 ,as ,experimental ,physics may fairly be considered to come within the province of one or more of the above-mentioned ,professors1 the ,syndicate have considered whether now or at some future time some arrangement might not be made to secure the effective teaching of this branch of science1 without having resort to the services of an additional ,professor4 ,they are1 however1 of opinion that such an arrangement cannot be made at the present time1 and that the exigencies of the case may be best met by founding a new professorship which shall terminate with the tenure of office of the ,professor first elected4 ,the services of a man of the highest attainments in science1 devoting his life to public teaching as such ,professor1 and engaged in original research1 would be of incalculable benefit to the ,university40 ,the ,report goes on to point out that a laboratory would be necessary1 and also apparatus4 ,it is estimated that #e1jjj would cover the cost of the laboratory1 and #a1cjj the necessary apparatus4 ,provision is also made for a demonstrator and a laboratory assistant1 and the ,report closes with a recommendation that a special ,syndicate of ,finance should be appointed to consider the means of raising the funds4 ,the ,professors in their ,report to the ,syndicate point out that teaching in ,experimental ,physics is needed for the ,mathematical ,tripos1 the ,natural ,sciences ,tripos1 certain ,special examinations1 and the first examination for the degree of ,m4,b4 ,it appeared to them clear that there was work for a new ,professor4 ,in ,may1 #ahfi1 the ,financial ,syndicate recommended by the above ,report was appointed 8to consider the means of raising the necessary funds for establishing a professor and demonstrator of ,experimental ,physics1 and for providing buildings and apparatus required for that department of science1 and further to consider other wants of the ,university1 and the sources from which those wants may be supplied40 ,the ,syndicate endeavoured to meet the expenditure by inquiry from the several ,colleges whether they would be willing to make contributions from their corporate funds1 but without success4 8,the answers of the ,colleges indicated such a want of concurrence in any proposal to raise contributions from the corporate funds of ,colleges by any kind of direct taxation that the ,syndicate felt obliged to abandon the notion of obtaining the necessary funds from this source1 and accordingly to limit the number of objects which they should recommend the ,senate to accomplish40 ,external authority was necessary before the colleges would submit to taxation for ,university purposes1 and it was left to the ,royal ,commission of #ahgg to carry into effect many of the suggestions made by the ,syndicate4 ,meanwhile they contented themselves with recommending means for raising an annual stipend of #ffj for the professor1 demonstrator1 and assistant1 and a capital sum of #e1jjj1 or thereabouts1 for the expenses of a building4 ,the ,syndicate's ,report was issued in an amended form in the ,may term of #ahgj1 and before any decision was taken on it the ,vice-,chancellor1 ,dr4 ,atkinson1 on ,october #acth1 #ahgj1 published 8the following munificent offer of his grace the ,duke of ,devonshire1 the ,chancellor of the ,university10 who had been chairman of the ,commission on ,scientific ,education4 8,holker ,hall1 ,grange1 ,lancashire4 8,,my ,,dear ,,mr4 ,,vice-,,chancellor1--,i have the honour to address you for the purpose of making an offer to the ,university1 which1 if you see no objection1 ,i shall be much obliged to you to submit in such manner as you may think fit for the consideration of the ,council and the ,university4 8,i find in the report dated ,february #bith1 #ahfi1 of the ,physical ,science ,syndicate1 recommending the establishment of a ,professor and ,demonstrator of ,experimental ,physics1 that the buildings and apparatus required for this department of science are estimated to cost #f1cjj4 8,i am desirous to assist the ,university in carrying this recommendation into effect1 and shall accordingly be prepared to provide the funds required for the building and apparatus as soon as the ,university shall have in other respects completed its arrangements for teaching ,experimental ,physics1 and shall have approved the plan of the building4 8,i remain1 my dear ,mr4 ,vice-,chancellor1 8,yours very faithfully1 8,,devonshire40 ,by his generous action the ,university was relieved from all expense connected with the building4 ,a ,grace establishing a ,professorship of ,experimental ,physics was confirmed by the ,senate ,february #ith1 #ahga1 and ,march #hth was fixed for the election4 ,meanwhile who was to be ,professor8 ,sir ,w4 ,thomson's name had been mentioned1 but he1 it was known1 would not accept the post4 ,maxwell was then applied to1 and at first he was unwilling to leave ,glenlair4 ,professor ,stokes1 the ,hon4 ,j4 ,w4 ,strutt 7,lord ,rayleigh71 ,mr4 ,blore of ,trinity1 and others wrote to him4 ,lord ,rayleigh's letter#ce is as follows3 8,cambridge1 #adth ,february1 #ahga4 8,when ,i came here last ,friday ,i found everyone talking about the new professorship1 and hoping that you would come4 ,thomson1 it seems1 has definitely declined4444 ,there is no one here in the least fit for the post4 ,what is wanted by most who know anything about it is not so much a lecturer as a mathematician who has actual experience in experimenting1 and who might direct the energies of the younger ,fellows and bachelors into a proper channel4 ,there must be many who would be willing to work under a competent man1 and who1 while learning themselves1 would materially assist him4444 ,i hope you may be induced to come2 if not1 ,i don't know who it is to be4 ,do not trouble to answer me about this1 as ,i believe others have written to you about it40 ,on the #aeth of ,february1 ,maxwell wrote to ,mr4 ,blore3-- 8,i had no intention of applying for the post when ,i got your letter1 and ,i have none now1 unless ,i come to see that ,i can do some good by it40 ,the letter continues3--8,the class of ,physical ,investigations1 which might be undertaken with the help of men of ,cambridge education1 and which would be creditable to the ,university1 demand in general a considerable amount of dull labour1 which may or may not be attractive to the pupils40 ,however1 on the #bdth of ,february1 ,mr4 ,blore wrote to the ,electoral ,roll3-- 8,i am authorised to give notice that ,mr4 ,john 7sic7 ,clerk ,maxwell1 ,f4,r4,s41 formerly ,professor of ,natural ,philosophy at ,aberdeen1 and at ,king's ,college1 ,london1 is a candidate for the professorship of ,experimental ,physics40 ,maxwell was elected without opposition4 ,writing#cf to his wife from ,cambridge1 #bjth ,march1 #ahga1 he says3-- 8,there are two parties about the professorship4 ,one wants popular lectures1 and the other cares more for experimental work4 ,i think there should be a gradation--popular lectures and rough experiments for the masses2 real experiments for real students2 and laborious experiments for first-rate men like ,trotter and ,stuart and ,strutt40 ,while in a letter#cg from ,glenlair to ,c4 ,j4 ,munro1 dated ,march #aeth1 #ahga1 he writes3--8,the ,experimental ,physics at ,cambridge is not built yet1 but we are going to try4 ,the desideratum is to set a ,don and a ,freshman to observe and register 7say7 the vibrations of a magnet together1 or the ,don to turn a watch and the ,freshman to observe and govern him40 ,in ,october he delivered his ,introductory ,lecture4 ,a few quotations will show the spirit in which he approached his task4 8,in a course of ,experimental ,physics we may consider either the ,physics or the ,experiments as the leading feature4 ,we may either employ the experiments to illustrate the phenomena of a particular branch of ,physics1 or we may make some physical research in order to exemplify a particular experimental method4 ,in the order of time1 we should begin1 in the ,lecture ,room1 with a course of lectures on some branch of ,physics aided by experiments of illustration1 and conclude1 in the ,laboratory1 with a course of experiments of research4 8,let me say a few words on these two classes of experiments--,experiments of ,illustration and ,experiments of ,research4 ,the aim of an experiment of illustration is to throw light upon some scientific idea so that the student may be enabled to grasp it4 ,the circumstances of the experiment are so arranged that the phenomenon which we wish to observe or to exhibit is brought into prominence1 instead of being obscured and entangled among other phenomena1 as it is when it occurs in the ordinary course of nature4 ,to exhibit illustrative experiments1 to encourage others to make them1 and to cultivate in every way the ideas on which they throw light1 forms an important part of our duty4 ,the simpler the materials of an illustrative experiment1 and the more familiar they are to the student1 the more thoroughly is he likely to acquire the idea which it is meant to illustrate4 ,the educational value of such experiments is often inversely proportional to the complexity of the apparatus4 ,the student who uses home-made apparatus1 which is always going wrong1 often learns more than one who has the use of carefully adjusted instruments1 to which he is apt to trust1 and which he dares not take to pieces4 8,it is very necessary that those who are trying to learn from books the facts of physical science should be enabled by the help of a few illustrative experiments to recognise these facts when they meet with them out of doors4 ,science appears to us with a very different aspect after we have found out that it is not in lecture-rooms only1 and by means of the electric light projected on a screen1 that we may witness physical phenomena1 but that we may find illustrations of the highest doctrines of science in games and gymnastics1 in travelling by land and by water1 in storms of the air and of the sea1 and wherever there is matter in motion4 8,if1 therefore1 we desire1 for our own advantage and for the honour of our ,university1 that the ,devonshire ,laboratory should be successful1 we must endeavour to maintain it in living union with the other organs and faculties of our learned body4 ,we shall therefore first consider the relation in which we stand to those mathematical studies which have so long flourished among us1 which deal with our own subjects1 and which differ from our experimental studies only in the mode in which they are presented to the mind4 8,there is no more powerful method for introducing knowledge into the mind than that of presenting it in as many different ways as we can4 ,when the ideas1 after entering through different gateways1 effect a junction in the citadel of the mind1 the position they occupy becomes impregnable4 ,opticians tell us that the mental combination of the views of an object which we obtain from stations no further apart than our two eyes is sufficient to produce in our minds an impression of the solidity of the object seen2 and we find that this impression is produced even when we are aware that we are really looking at two flat pictures placed in a stereoscope4 ,it is therefore natural to expect that the knowledge of physical science obtained by the combined use of mathematical analysis and experimental research will be of a more solid1 available1 and enduring kind than that possessed by the mere mathematician or the mere experimenter4 8,but what will be the effect on the ,university if men pursuing that course of reading which has produced so many distinguished ,wranglers turn aside to work experiments8 ,will not their attendance at the ,laboratory count not merely as time withdrawn from their more legitimate studies1 but as the introduction of a disturbing element1 tainting their mathematical conceptions with material imagery1 and sapping their faith in the formul of the text-books8 ,besides this1 we have already heard complaints of the undue extension of our studies1 and of the strain put upon our questionists by the weight of learning which they try to carry with them into the ,senate-,house4 ,if we now ask them to get up their subjects not only by books and writing1 but at the same time by observation and manipulation1 will they not break down altogether8 ,the ,physical ,laboratory1 we are told1 may perhaps be useful to those who are going out in ,natural ,science1 and who do not take in ,mathematics1 but to attempt to combine both kinds of study during the time of residence at the ,university is more than one mind can bear4 8,no doubt there is some reason for this feeling4 ,many of us have already overcome the initial difficulties of mathematical training4 ,when we now go on with our study1 we feel that it requires exertion and involves fatigue1 but we are confident that if we only work hard our progress will be certain4 8,some of us1 on the other hand1 may have had some experience of the routine of experimental work4 ,as soon as we can read scales1 observe times1 focus telescopes1 and so on1 this kind of work ceases to require any great mental effort4 ,we may1 perhaps1 tire our eyes and weary our backs1 but we do not greatly fatigue our minds4 8,it is not till we attempt to bring the theoretical part of our training into contact with the practical that we begin to experience the full effect of what ,faraday has called #8mental inertia'--not only the difficulty of recognising1 among the concrete objects before us1 the abstract relation which we have learned from books1 but the distracting pain of wrenching the mind away from the symbols to the objects1 and from the objects back to the symbols4 ,this1 however1 is the price we have to pay for new ideas4 8,but when we have overcome these difficulties1 and successfully bridged over the gulph between the abstract and the concrete1 it is not a mere piece of knowledge that we have obtained2 we have acquired the rudiment of a permanent mental endowment4 ,when1 by a repetition of efforts of this kind1 we have more fully developed the scientific faculty1 the exercise of this faculty in detecting scientific principles in nature1 and in directing practice by theory1 is no longer irksome1 but becomes an unfailing source of enjoyment1 to which we return so often that at last even our careless thoughts begin to run in a scientific channel4 8,our principal work1 however1 in the ,laboratory must be to acquaint ourselves with all kinds of scientific methods1 to compare them and to estimate their value4 ,it will1 ,i think1 be a result worthy of our ,university1 and more likely to be accomplished here than in any private laboratory1 if1 by the free and full discussion of the relative value of different scientific procedures1 we succeed in forming a school of scientific criticism and in assisting the development of the doctrine of method4 8,but admitting that a practical acquaintance with the methods of ,physical ,science is an essential part of a mathematical and scientific education1 we may be asked whether we are not attributing too much importance to science altogether as part of a liberal education4 8,fortunately1 there is no question here whether the ,university should continue to be a place of liberal education1 or should devote itself to preparing young men for particular professions4 ,hence1 though some of us may1 ,i hope1 see reason to make the pursuit of science the main business of our lives1 it must be one of our most constant aims to maintain a living connexion between our work and the other liberal studies of ,cambridge1 whether literary1 philological1 historical1 or philosophical4 8,there is a narrow professional spirit which may grow up among men of science just as it does among men who practise any other special business4 ,but surely a ,university is the very place where we should be able to overcome this tendency of men to become1 as it were1 granulated into small worlds1 which are all the more worldly for their very smallness8 ,we lose the advantage of having men of varied pursuits collected into one body if we do not endeavour to imbibe some of the spirit even of those whose special branch of learning is different from our own40 ,another expression of his views on the position of ,physics at the time will be found in his address to ,section ,a of the ,british ,association1 when ,president at the ,liverpool meeting of #ahgj4 ,,chapter ,,vi4 ,,cambridge--,,the ,,cavendish ,,laboratory4 ,but the laboratory was not yet built4 ,a ,syndicate1 of which ,maxwell was a member1 was appointed to consider the question of a site1 to take professional advice1 and to obtain plans and estimates4 ,professor ,maxwell and ,mr4 ,trotter visited various laboratories at home and abroad for the purpose of ascertaining the best arrangements4 ,mr4 ,w4 ,m4 ,fawcett was appointed architect2 the tender of ,mr4 ,john ,loveday1 of ,kebworth1 for the building at a cost of #h1dej1 exclusive of gas1 water1 and heating1 was accepted in ,march1 #ahgb1 and the building#ch was begun during the summer4 ,in the meantime ,maxwell began to lecture1 finding a home where he could4 8,lectures begin #bdth10 he writes from ,glenlair1 ,october #aith1 #ahgb4 8,laboratory rising1 ,i hear1 but ,i have no place to erect my chair1 but move about like the cuckoo1 depositing my notions in the ,chemical ,lecture-room #ast term2 in the ,botanical in ,lent1 and in ,comparative ,anatomy in ,easter40 ,it was not till ,june1 #ahgd1 that the building was complete1 and on the #afth the ,chancellor formally presented his gift of the ,cavendish ,laboratory to the ,university4 ,in the correspondence previous to this time it was spoken of as the ,devonshire ,laboratory4 ,the name ,cavendish commemorated the work of the great physicist of a century earlier1 whose writings ,maxwell was shortly to edit1 as well as the generosity of the ,chancellor4 ,in their letter of thanks to the ,duke of ,devonshire the ,university write3-- 8,unde vero conventius poterat illis artibus succurri quam e tua domo qu in ipsis jam pridem inclaruerat4 ,notum est ,henricum ,cavendish quem secutus est ,coulombius primum ita docuisse1 qu sit vis electrica ut eam numerorum modulis illustraret2 adhibitis rationibus quas hodie veras esse constat40 ,and they suggest the name as suitable for the building4 ,to this the ,chancellor replied1 after referring to the work of ,henry ,cavendish3 8,quod pono in officin ips nuncupand nomen ejus commemorare dignati sitis1 id grato animo accepi40 ,the building had cost far more than the original estimate1 but the ,chancellor's generosity was not limited1 and on ,july #bast1 #ahgd1 he wrote to the ,vice-,chancellor3-- 8,it is my wish to provide all instruments for the ,cavendish ,laboratory which ,professor ,maxwell may consider to be immediately required1 either in his lectures or otherwise40 ,maxwell prepared a list1 but explained while doing it that time and thought were necessary to secure the best form of instruments2 and he continues1 writing to the ,vice-,chancellor3 8,i think the ,duke fully understood from what ,i said to him that to furnish the ,laboratory will be a matter of several years' duration4 ,i shall consider myself1 however10 he says1 8at liberty to contribute to the ,laboratory any instruments which ,i have had constructed in former years1 and which may be found still useful1 and also from time to time to procure others for special researches40 ,in #ahgg in his annual report ,professor ,maxwell announced that the ,chancellor#ci had now 8completed his gift to the ,university by furnishing the ,cavendish ,laboratory with apparatus suited to the present state of science40 ,the stock of apparatus1 however1 was still small1 although ,maxwell in the most generous manner himself spent large sums in adding to it2 for the ,professor was most particular in procuring only expensive instruments by the best makers1 with such additional improvements as he could himself suggest4 ,in ,march1 #ahgd1 a ,demonstratorship of ,physics had been established1 and ,mr4 ,garnett of ,st4 ,john's ,college was appointed4 ,work began in the laboratory in ,october1 #ahgd4 ,at first the number of students was small4 ,only seventeen names appear in the ,natural ,sciences ,tripos#dj list for #ahgd1 and few of those did ,physics4 ,the fear alluded to by the ,professor in his introductory lecture1 that men reading for the ,mathematical ,tripos would not find time for attendance at the laboratory1 was justified4 ,one of the weaknesses of our ,cambridge plan has been the divorce between ,mathematics and experimental work1 encouraged by our system of examinations4 ,experimental knowledge is supposed not to be needed for the ,mathematical ,tripos2 the ,mathematics permitted in the ,natural ,sciences ,tripos are very simple2 thus it came about that few men while reading for the ,mathematical ,tripos attended the laboratory1 and this unfortunate result was intensified by the action of the ,university in #ahgg-gh1 when the regulations for the ,mathematical ,tripos were again altered4#da ,still there were pupils eager and willing to work1 though they were chiefly men who had already taken their ,b4,a4 degree1 and who wished to continue ,physical reading and research1 even though it involved 8a considerable amount of dull labour not altogether attractive40 ,my own work there began in #ahgf1 and it may be interesting if ,i recall my reminiscences of that time4 ,the first experiments ,i can recollect related to the measurement of electrical resistance4 ,i well remember ,maxwell explaining the principle of ,wheatstone's bridge1 and my own wish at the time that ,i had come to the laboratory before the ,tripos1 instead of afterwards4 ,lord ,rayleigh had1 during the examination1 set an easy question which ,i failed to do for want of some slight experimental knowledge1 and the first few words of ,maxwell's talk showed me the solution4 ,i did not attend his lectures regularly--they were given1 ,i think1 at an hour which ,i was obliged to devote to teaching2 besides1 there was his book1 the 8,electricity and ,magnetism10 into which ,i had just dipped before the ,tripos1 to work at4 ,chrystal and ,saunder were then busy at their verification of ,ohm's law4 ,they were using a number of the ,thomson form of tray ,daniell's cells1 and ,maxwell was anxious for tests of various kinds to be made on these cells2 these ,i undertook1 and spent some time over various simple measurements on them4 ,he then set me to work at some of the properties of a stratified dielectric1 consisting1 if ,i remember rightly1 of sheets of paraffin paper and mica4 ,by this means ,i became acquainted with various pieces of apparatus4 ,there were no regular classes and no set drill of demonstrations arranged for examination purposes2 these came later4 ,in ,maxwell's time those who wished to work had the use of the laboratory and assistance and help from him1 but they were left pretty much to themselves to find out about the apparatus and the best methods of using it4 ,rather later than this ,schuster came and did some of his spectroscope work4 ,j4 ,e4 ,h4 ,gordon was busy with the preliminary observations for his determination of ,verdet's constant1 and ,niven had various electrical experiments on hand2 while ,fleming was at work on the ,b4 ,a4 resistance coils4 ,my own tastes lay in the direction of optics4 ,maxwell was anxious that ,i should investigate the properties of certain crystals4 ,i think they were the chlorate of potash crystals1 about which ,stokes and ,rayleigh have since written2 but these crystals were to be grown1 a slow process which would1 he supposed1 take years2 and as ,i wished to produce a dissertation for the ,trinity ,fellowship examination in #ahgg1 that work had to be laid aside4 ,eventually ,i selected as a subject the form of the wave surface in a biaxial crystal1 and set to work in a room assigned to me4 ,the ,professor used to come in on most days to see how ,i was getting on4 ,generally he brought his dog1 which sometimes was shut up in the next room while he went to college4 ,dogs were not allowed in college1 and ,maxwell had an amusing way of describing how ,toby once wandered into ,trinity1 and by some doggish instinct discovered immediately1 to his intense amazement1 that he was in a place where no dogs had been since the college was4 ,toby was not always quiet in his master's absence1 and his presence in the next room was somewhat disturbing4 ,when difficulties occurred ,maxwell was always ready to listen4 ,often the answer did not come at once1 but it always did come after a little time4 ,i remember one day1 when ,i was in a serious dilemma1 ,i told him my long tale1 and he said3-- 8,well1 ,chrystal has been talking to me1 and ,garnett and ,schuster have been asking questions1 and all this has formed a good thick crust round my brain4 ,what you have said will take some time to soak through1 but we will see about it40 ,in a few days he came back with--8,i have been thinking over what you said the other day1 and if you do so-and-so it will be all right40 ,my dissertation was referred to him1 and on the day of the election1 when returning to ,cambridge for the admission1 ,i met him at ,bletchley station1 and well remember his kind congratulations and words of warm encouragement4 ,for the next year and a half ,i was working regularly at the laboratory and saw him almost daily during term time4 ,of these last years there really is but little to tell4 ,his own scientific work went on4 ,the 8,electricity and ,magnetism0 was written mostly at ,glenlair4 ,about the time of his return to ,cambridge1 in ,october1 #ahgb1 he writes#db to ,lewis ,campbell3-- 8,i am continually engaged in stirring up the ,clarendon ,press1 but they have been tolerably regular for two months4 ,i find nine sheets in thirteen weeks is their average4 ,tait gives me great help in detecting absurdities4 ,i am getting converted to quaternions1 and have put some in my book40 ,the book was published in #ahgc4 ,the ,text-book of ,heat was written during the same period1 while 8,matter and ,motion10 8a small book on a great subject10 was published in #ahgf4 ,in #ahgc and #ahgd he was one of the examiners for the ,natural ,sciences ,tripos1 and in #ahgc he was the first additional examiner for the ,mathematical ,tripos1 in accordance with the scheme which he had done so much to promote in #ahfh4 ,many of his shorter papers were written about the same time4 ,the ninth edition of the ,encyclopdia ,britannica was being published1 and ,professor ,baynes had enlisted his aid in the work4 ,the articles 8,atom10 8,attraction10 8,capillary ,action10 8,constitution of ,bodies10 8,diffusion10 8,ether10 8,faraday10 and others are by him4 ,he also wrote a number of papers for ,nature4 ,some of these are reviews of books or accounts of scientific men1 such as the notices of ,faraday and ,helmholtz1 which appeared with their portraits2 others again are original contributions to science4 ,among the latter many have reference to the molecular constitution of bodies4 ,two lectures--the first on 8,molecules10 delivered before the ,british ,association at ,bradford in #ahgc2 the second on the 8,dynamical ,evidence of the ,molecular ,constitution of ,bodies10 delivered before the ,chemical ,society in #ahge--were of special importance4 ,the closing sentences of the first lecture have been often quoted4 ,they run as follow3-- 8,in the heavens we discover by their light1 and by their light alone1 stars so distant from each other that no material thing can ever have passed from one to another2 and yet this light1 which is to us the sole evidence of the existence of these distant worlds1 tells us also that each of them is built up of molecules of the same kinds as those which we find on earth4 ,a molecule of hydrogen1 for example1 whether in ,sirius or in ,arcturus1 executes its vibrations in precisely the same time4 8,each molecule therefore throughout the universe bears impressed upon it the stamp of a metric system1 as distinctly as does the metre of the ,archives at ,paris1 or the double royal cubit of the temple of ,karnac4 8,no theory of evolution can be formed to account for the similarity of molecules1 for evolution necessarily implies continuous change1 and the molecule is incapable of growth or decay1 of generation or destruction4 8,none of the processes of ,nature1 since the time when ,nature began1 have produced the slightest difference in the properties of any molecule4 ,we are therefore unable to ascribe either the existence of the molecules or the identity of their properties to any of the causes which we call natural4 8,on the other hand1 the exact equality of each molecule to all others of the same kind gives it1 as ,sir ,john ,herschel has well said1 the essential character of a manufactured article1 and precludes the idea of its being eternal and self-existent4 8,thus we have been led along a strictly scientific path1 very near to the point at which ,science must stop--not that ,science is debarred from studying the internal mechanism of a molecule which she cannot take to pieces any more than from investigating an organism which she cannot put together4 ,but in tracing back the history of matter1 ,science is arrested when she assures herself1 on the one hand1 that the molecule has been made1 and1 on the other1 that it has not been made by any of the processes we call natural4 8,science is incompetent to reason upon the creation of matter itself out of nothing4 ,we have reached the utmost limits of our thinking faculties when we have admitted that because matter cannot be eternal and self-existent1 it must have been created4 8,it is only when we contemplate1 not matter in itself1 but the form in which it actually exists1 that our mind finds something on which it can lay hold4 8,that matter1 as such1 should have certain fundamental properties1 that it should exist in space and be capable of motion1 that its motion should be persistent1 and so on1 are truths which may1 for anything we know1 be of the kind which metaphysicians call necessary4 ,we may use our knowledge of such truths for purposes of deduction1 but we have no data for speculating as to their origin4 8,but that there should be exactly so much matter and no more in every molecule of hydrogen is a fact of a very different order4 ,we have here a particular distribution of matter--a collocation1 to use the expression of ,dr4 ,chalmers1 of things which we have no difficulty in imagining to have been arranged otherwise4 8,the form and dimensions of the orbits of the planets1 for instance1 are not determined by any law of nature1 but depend upon a particular collocation of matter4 ,the same is the case with respect to the size of the earth1 from which the standard of what is called the metrical system has been derived4 ,but these astronomical and terrestrial magnitudes are far inferior in scientific importance to that most fundamental of all standards which forms the base of the molecular system4 ,natural causes1 as we know1 are at work which tend to modify1 if they do not at length destroy1 all the arrangements and dimensions of the earth and the whole solar system4 ,but though in the course of ages catastrophes have occurred and may yet occur in the heavens1 though ancient systems may be dissolved and new systems evolved out of their ruins1 the molecules out of which these systems are built--the foundation stones of the material universe--remain unbroken and unworn4 ,they continue this day as they were created--perfect in number and measure and weight2 and from the ineffaceable characters impressed on them we may learn that those aspirations after accuracy in measurement1 and justice in action1 which we reckon among our noblest attributes as men1 are ours because they are essential constituents of the image of ,him who in the beginning created1 not only the heaven and the earth1 but the materials of which heaven and earth consist40 ,this was criticised in ,nature by ,mr4 ,c4 ,j4 ,munro1 and at a later time by ,clifford in one of his essays4 ,some correspondence with the ,bishop of ,gloucester and ,bristol on the authority for the comparison of molecules to manufactured articles is given by ,professor ,campbell1 and in it ,maxwell points out that the latter part of the article 8,atom0 in the ,encyclopdia is intended to meet ,mr4 ,munro's criticism4 ,in #ahgd the ,british ,association met at ,belfast1 under the presidency of ,tyndall4 ,maxwell was present1 and published afterwards in ,blackwood's ,magazine an amusing paraphrase of the president's address4 ,this1 with some other verses written at about the same time1 may be quoted here4 ,professor ,campbell has collected a number of verses written by ,maxwell at various times1 which illustrate in an admirable manner both the grave and the gay side of his character4 ,,british ,,association1 #ahgd4 ,notes of the ,president's ,address4 ,in the very beginnings of science1 the parsons1 who managed things then1 ,being handy with hammer and chisel1 made gods in the likeness of men2 ,till commerce arose1 and at length some men of exceptional power ,supplanted both demons and gods by the atoms1 which last to this hour4 ,yet they did not abolish the gods1 but they sent them well out of the way1 ,with the rarest of nectar to drink1 and blue fields of nothing to sway4 ,from nothing comes nothing1 they told us--naught happens by chance1 but by fate2 ,there is nothing but atoms and void1 all else is mere whims out of date6 ,then why should a man curry favour with beings who cannot exist1 ,to compass some petty promotion in nebulous kingdoms of mist8 ,but not by the rays of the sun1 nor the glittering shafts of the day1 ,must the fear of the gods be dispelled1 but by words1 and their wonderful play4 ,so treading a path all untrod1 the poet-philosopher sings ,of the seeds of the mighty world--the first-beginnings of things2 ,how freely he scatters his atoms before the beginning of years2 ,how he clothes them with force as a garment1 those small incompressible spheres6 ,nor yet does he leave them hard-hearted--he dowers them with love and with hate1 ,like spherical small ,british ,asses in infinitesimal state2 ,till just as that living ,plato1 whom foreigners nickname ,plateau1#dc ,drops oil in his whisky-and-water 7for foreigners sweeten it so72 ,each drop keeps apart from the other1 enclosed in a flexible skin1 ,till touched by the gentle emotion evolved by the prick of a pin3 ,thus in atoms a simple collision excites a sensational thrill1 ,evolved through all sorts of emotion1 as sense1 understanding1 and will 7,for by laying their heads all together1 the atoms1 as councillors do1 ,may combine to express an opinion to every one of them new74 ,there is nobody here1 ,i should say1 has felt true indignation at all1 ,till an indignation meeting is held in the ,ulster ,hall2 ,then gathers the wave of emotion1 then noble feelings arise1 ,till you all pass a resolution which takes every man by surprise4 ,thus the pure elementary atom1 the unit of mass and of thought1 ,by force of mere juxtaposition to life and sensation is brought2 ,so1 down through untold generations1 transmission of structureless gorms ,enables our race to inherit the thoughts of beasts1 fishes1 and worms4 ,we honour our fathers and mothers1 grandfathers and grandmothers too2 ,but how shall we honour the vista of ancestors now in our view8 ,first1 then1 let us honour the atom1 so lively1 so wise1 and so small2 ,the atomists next let us praise1 ,epicurus1 ,lucretius1 and all4 ,let us damn with faint praise ,bishop ,butler1 in whom many atoms combined ,to form that remarkable structure it pleased him to call--his mind4 ,last1 praise we the noble body to which1 for the time1 we belong1 ,ere yet the swift whirl of the atoms has hurried us1 ruthless1 along1 ,the ,british ,association--like ,leviathan worshipped by ,hobbes1 ,the incarnation of wisdom1 built up of our witless nobs1 ,which will carry on endless discussions when ,i1 and probably you1 ,have melted in infinite azure--in ,english1 till all is blue4 ,,molecular ,,evolution4 ,belfast1 #ahgd4 ,at quite uncertain times and places1 ,the atoms left their heavenly path1 ,and by fortuitous embraces ,engendered all that being hath4 ,and though they seem to cling together1 ,and form 8associations0 here1 ,yet1 soon or late1 they burst their tether1 ,and through the depths of space career4 ,so we who sat1 oppressed with science1 ,as ,british ,asses1 wise and grave1 ,are now transformed to wild ,red ,lions1#dd ,as round our prey we ramp and rave4 ,thus1 by a swift metamorphsis1 ,wisdom turns wit1 and science joke1 ,nonsense is incense to our noses1 ,for when ,red ,lions speak they smoke4 ,hail1 ,nonsense6 dry nurse of ,red ,lions1#de ,from thee the wise their wisdom learn2 ,from thee they cull those truths of science1 ,which into thee again they turn4 ,what combinations of ideas ,nonsense alone can wisely form6 ,what sage has half the power that she has1 ,to take the towers of ,truth by storm8 ,yield1 then1 ye rules of rigid reason6 ,dissolve1 thou too1 too solid sense6 ,melt into nonsense for a season1 ,then in some nobler form condense4 ,soon1 all too soon1 the chilly morning ,this flow of soul will crystallise2 ,then those who ,nonsense now are scorning ,may learn1 too late1 where wisdom lies4 ,,to ,,the ,,committee ,,of ,,the ,,cayley ,,portrait ,,fund4 #ahgd4 ,o wretched race of men1 to space confined6 ,what honour can ye pay to him1 whose mind ,to that which lies beyond hath penetrated8 ,the symbols he hath formed shall sound his praise1 ,and lead him on through unimagined ways ,to conquests new1 in worlds not yet created4 ,first1 ye ,determinants6 in ordered row ,and massive column ranged1 before him go1 ,to form a phalanx for his safe protection4 ,ye powers of the nth roots of -#a6 ,around his head in ceaseless#df cycles run1 ,as unembodied spirits of direction4 ,and you1 ye undevelopable scrolls6 ,above the host wave your emblazoned rolls1 ,ruled for the record of his bright inventions4 ,ye cubic surfaces6 by threes and nines ,draw round his camp your seven-and-twenty lines-- ,the seal of ,solomon in three dimensions4 ,march on1 symbolic host6 with step sublime1 ,up to the flaming bounds of ,space and ,time6 ,there pause1 until by ,dickinson depicted1 ,in two dimensions1 we the form may trace ,of him whose soul1 too large for vulgar space1 ,in n dimensions flourished unrestricted4 ,,in ,,memory ,,of ,,edward ,,wilson1 ,who repented of what was in his mind to write after section4 ,,rigid ,,body 7sings74 ,,gin a body meet a body ,flyin' through the air1 ,gin a body hit a body1 ,will it fly8 and where8 ,ilka impact has its measure1 ,ne'er a ane hae ,i2 ,yet a' the lads they measure me1 ,or1 at least1 they try4 ,gin a body meet a body ,altogether free1 ,how they travel afterwards ,we do not always see4 ,ilka problem has its method ,by analytics high2 ,for me1 ,i ken na ane o' them1 ,but what the waur am ,i8 ,another task1 which occupied much time1 from #ahgd to #ahgi1 was the edition of the works of ,henry ,cavendish4 ,cavendish1 who was great-uncle to the ,chancellor1 had published only two electrical papers1 but he had left some twenty packets of manuscript on ,mathematical and ,experimental ,electricity4 ,these were placed in ,maxwell's hands in #ahgd by the ,duke of ,devonshire4 ,niven1 in his preface to the collected papers dealing with this book1 writes thus3-- 8,this work1 published in #ahgi1 has had the effect of increasing the reputation of ,cavendish1 disclosing as it does the unsuspected advances which that acute physicist had made in the ,theory of ,electricity1 especially in the measurement of electrical quantities4 ,the work is enriched by a variety of valuable notes1 in which ,cavendish's views and results are examined by the light of modern theory and methods4 ,especially valuable are the methods applied to the determination of the electrical capacities of conductors and condensers1 a subject in which ,cavendish himself showed considerable skill both of a mathematical and experimental character4 8,the importance of the task undertaken by ,maxwell in connection with ,cavendish's papers will be understood from the following extract from his introduction to them3-- 8#8,it is somewhat difficult to account for the fact that though ,cavendish had prepared a complete description of his experiments on the charges of bodies1 and had even taken the trouble to write out a fair copy1 and though all this seems to have been done before #aggd1 and he continued to make experiments in electricity till #agha1 and lived on till #ahaj1 he kept his manuscript by him and never published it4 8#8,cavendish cared more for investigation than for publication4 ,he would undertake the most laborious researches in order to clear up a difficulty which no one but himself could appreciate or was even aware of1 and we cannot doubt that the result of his enquiries1 when successful1 gave him a certain degree of satisfaction4 ,but it did not excite in him that desire to communicate the discovery to others1 which in the case of ordinary men of science generally ensures the publication of their results4 ,how completely these researches of ,cavendish remained unknown to other men of science is shown by the external history of electricity4' 8,it will probably be thought a matter of some difficulty to place oneself in the position of a physicist of a century ago1 and to ascertain the exact bearing of his experiments4 ,but ,maxwell entered upon this undertaking with the utmost enthusiasm1 and succeeded in identifying himself with ,cavendish's methods4 ,he showed that ,cavendish had really anticipated several of the discoveries in electrical science which have been made since his time4 ,cavendish was the first to form the conception of and to measure ,electrostatic ,capacity and ,specific ,inductive ,capacity2 he also anticipated ,ohm's law40 ,during the last years of his life ,mrs4 ,maxwell had a serious and prolonged illness1 and ,maxwell's work was much increased by his duties as sick nurse4 ,on one occasion he did not sleep in a bed for three weeks1 but conducted his lectures and experiments at the laboratory as usual4 ,about this time some of those who had been 8,apostles0 in #ahec-eg revived the habit of meeting together for discussion4 ,the club1 which included ,professors ,lightfoot1 ,hort and ,westcott1 was christened the 8,eranus10 and three of ,maxwell's contributions to it have been preserved and are printed by ,professor ,campbell4 ,after the ,cavendish papers were finished1 ,maxwell had more time for his own original researches1 and two important papers were published in #ahgi4 ,the one on 8,stresses in ,rarefied ,gases arising from ,inequalities of ,temperature0 was printed in the ,royal ,society's ,transactions1 and deals with the ,theory of the ,radiometer2 the other on 8,boltzmann's ,theorem0 appears in the ,transactions of the ,cambridge ,philosophical ,society4 ,in the previous year he had delivered the ,rede lecture on 8,the ,telephone40 ,he also began to prepare a second edition of 8,electricity and ,magnetism40 ,his health gave way during the ,easter term of #ahgi2 indeed for two years previously he had been troubled with dyspeptic symptoms1 but had consulted no one on the subject4 ,he left ,cambridge as usual in ,june1 hoping that he would quickly recover at ,glenlair1 but he grew worse instead4 ,in ,october he was told by ,dr4 ,sanders of ,edinburgh that he had not a month to live4 ,he returned to ,cambridge in order to be under the care of ,dr4 ,paget1 who was able in some measure to relieve his most severe suffering but the disease1 of which his mother had died at the same age1 continued its progress1 and he died on ,november #eth4 ,his one care during his last illness was for those whom he left behind4 ,mrs4 ,maxwell was an invalid dependent on him for everything1 and the thought of her helplessness was the one thing which in these last days troubled him4 ,a funeral service took place in the chapel at ,trinity ,college1 and afterwards his remains were conveyed to ,scotland and interred in the family burying-place at ,corsock1 ,kirkcudbright4 ,a memorial edition of his works was issued by the ,cambridge ,university ,press in #ahij4 ,a portrait by ,lowes ,dickinson hangs in the hall of ,trinity ,college1 and there is a bust by ,boehm in the laboratory4 ,after his death ,mrs4 ,maxwell gave his scientific library to the ,cavendish ,laboratory1 and on her death she left a sum of about #f1jjj to found a scholarship in ,physics1 to be held at the laboratory4 99 99 99 99 99 ,the preceding pages contain some account of ,clerk ,maxwell's life as a man of science4 ,his character had other sides1 and any life of him would be incomplete without some brief reference to these4 ,his letters to his wife and to other intimate friends show throughout his life the depth of his religious convictions4 ,the high purpose evidenced in the paper given to the present ,dean of ,canterbury when leaving ,cambridge1 animated him continually1 and appears from time to time in his writings4 ,the student's evening hymn1 composed in #ahec when still an undergraduate1 expresses the same feelings-- ,through the creatures ,thou hast made ,show the brightness of ,thy glory1 ,be eternal truth displayed ,in their substance transitory1 ,till green earth and ocean hoary1 ,massy rock and tender blade1 ,tell the same unending story1 8,we are ,truth in form arrayed40 ,teach me so ,thy works to read ,that my faith1 new strength accruing1 ,may from world to world proceed1 ,wisdom's fruitful search pursuing1 ,till ,thy breath my mind imbuing1 ,i proclaim the eternal creed1 ,oft the glorious theme renewing1 ,god our ,lord is ,god indeed4 ,his views on the relation of ,science to ,faith are given in his letter#dg to ,bishop ,ellicott already referred to-- 8,but ,i should be very sorry if an interpretation founded on a most conjectural scientific hypothesis were to get fastened to the text in ,genesis1 even if by so doing it got rid of the old statement of the commentators which has long ceased to be intelligible4 ,the rate of change of scientific hypothesis is naturally much more rapid than that of ,biblical interpretations1 so that if an interpretation is founded on such an hypothesis1 it may help to keep the hypothesis above ground long after it ought to be buried and forgotten4 8,at the same time ,i think that each individual man should do all he can to impress his own mind with the extent1 the order1 and the unity of the universe1 and should carry these ideas with him as he reads such passages as the #ast chapter of the ,epistle to ,colossians 7see #8,lightfoot on ,colossians1' p4 #ahb71 just as enlarged conceptions of the extent and unity of the world of life may be of service to us in reading ,psalm viii41 ,heb4 ii4 #f1 etc40 ,and again in his letter#dh to the secretary of the ,victoria ,institute giving his reasons for declining to become a member-- 8,i think men of science as well as other men need to learn from ,christ1 and ,i think ,christians whose minds are scientific are bound to study science1 that their view of the glory of ,god may be as extensive as their being is capable of4 ,but ,i think that the results which each man arrives at in his attempts to harmonise his science with his ,christianity ought not to be regarded as having any significance except to the man himself1 and to him only for a time1 and should not receive the stamp of a society40 ,professor ,campbell and ,mr4 ,garnett have given us the evidence of those who were with him in his last days1 as to the strength of his own faith4 ,on his death bed he said that he had been occupied in trying to gain truth2 that it is but little of truth that man can acquire1 but it is something to know in whom we have believed4 ,,chapter ,,vii4 ,,scientific ,,work--,,colour ,,vision4 ,fifteen years only have passed since the death of ,clerk ,maxwell1 and it is almost too soon to hope to form a correct estimate of the value of his work and its relation to that of others who have laboured in the same field4 ,thus ,niven1 at the close of his obituary notice in the ,proceedings of the ,royal ,society1 says3 8,it is seldom that the faculties of invention and exposition1 the attachment to physical science and capability of developing it mathematically1 have been found existing in one mind to the same degree4 ,it would1 however1 require powers somewhat akin to ,maxwell's own to describe the more delicate features of the works resulting from this combination1 every one of which is stamped with the subtle but unmistakable impress of genius40 ,and again in the preface to ,maxwell's works1 issued in #ahij1 he wrote3 8,nor does it appear to the present editor that the time has yet arrived when the quickening influence of ,maxwell's mind on modern scientific thought can be duly estimated40 ,it is1 however1 the object of the present series to attempt to give some account of the work of men of science of the last hundred years1 and to show how each has contributed his share to our present stock of knowledge4 ,this task1 then1 remains to be done4 ,while attempting it ,i wish to express my indebtedness to others who have already written about ,maxwell's scientific work1 especially to ,mr4 ,w4 ,d4 ,niven1 whose preface to the ,maxwell papers has been so often referred to2 to ,mr4 ,garnett1 the author of ,part ,,ii4 of the 8,life of ,maxwell10 which deals with his contributions to science2 and to ,professor ,tait1 who in ,nature for ,february #eth1 #ahhj1 gave an account of ,clerk ,maxwell's work1 8necessarily brief1 but sufficient to let even the non-mathematical reader see how very great were his contributions to modern science0--an account all the more interesting because1 again to quote from ,professor ,tait1 8,i have been intimately acquainted with him since we were schoolboys together40 ,maxwell's main contributions to science may be classified under three heads--8,colour ,perception10 8,molecular ,physics10 and 8,electrical ,theories40 ,in addition to these there were other papers of the highest interest and importance1 such as the essay on 8,saturn's ,rings10 the paper on the 8,equilibrium of ,elastic ,solids10 and various memoirs on pure geometry and questions of mechanics1 which would1 if they stood alone1 have secured for their author a distinguished position as a physicist and mathematician1 but which are not the works by which his name will be mostly remembered4 ,the work on 8,colour ,perception0 was begun at an early date4 ,we have seen ,maxwell while still at ,edinburgh interested in the discussions about ,hay's theories4 ,his first published paper on the subject was a letter to ,dr4 ,g4 ,wilson1 printed in the ,transactions of the ,royal ,society of ,arts for #ahee2 but he had been mixing colours by means of his top for some little time previously1 and the results of these experiments are given in a paper entitled 8,experiments on ,colour10 communicated to the ,royal ,society of ,edinburgh by ,dr4 ,gregory1 and printed in their ,transactions1 vol4 xxi4 ,in the paper on 8,the ,theory of ,compound ,colours10 printed in the ,philosophical ,transactions for #ahfj1 ,maxwell gives a history of the theory as it was known to him4 ,he points out first the distinction between the optical properties and the chromatic properties of a beam of light4 8,the optical properties are those which have reference to its origin and propagation through media until it falls on the sensitive organ of vision20 they depend on the periods and amplitudes of the ether vibrations which compose the beam4 8,the chromatic properties are those which have reference to its power of exciting certain sensations of colour perceived through the organ of vision40 ,it is possible for two beams to be optically very different and chromatically alike4 ,the converse is not true2 two beams which are optically alike are also chromatically alike4 ,the foundation of the theory of compound colours was laid by ,newton4 ,he first shewed that 8by the mixture of homogeneal light colours may be produced which are like to the colours of homogeneal light as to the appearance of colour1 but not as to the immutability of colour and constitution of light40 ,two beams which differ optically may yet be alike chromatically2 it is possible by mixing red and yellow to obtain an orange colour chromatically similar to the orange of the spectrum1 but optically different to that orange1 for the compound orange can be analysed by a prism into its component red and yellow2 the spectrum orange is incapable of further resolution4 ,newton also solves the following problem3-- ,in a mixture of primary colours1 the quantity and quality of each being given to know the colour of the compound 7,optics1 ,book #a1 ,part #b1 ,prop4 #f71 and his solution is the following3--,he arranges the seven colours of the spectrum round the circumference of a circle1 the length occupied by each colour being proportional to the musical interval to which1 in ,newton's views1 the colour corresponded4 ,at the centre of gravity of each of these arcs he supposes a weight placed proportional to the number of rays of the corresponding colour which enter into the mixture under consideration4 ,the position of the centre of gravity of these weights indicates the nature of the resultant colour4 ,a radius drawn through this centre of gravity points out the colour of the spectrum which it most resembles2 the distance of the centre of gravity from the centre gives the fulness of the colour4 ,the centre itself is white4 ,newton gives no proof of this rule2 he merely says1 8,this rule ,i conceive to be accurate enough for practice1 though not mathematically accurate40 ,maxwell proved that ,newton's method of finding the centre of gravity of the component colours was confirmed by his observations1 and that it involves mathematically the theory of three elements of colour2 but the disposition of the colours on the circle was only a provisional arrangement2 the true relations of the colours could only be determined by direct experiment4 ,thomas ,young appears to have been the next1 after ,newton1 to work at the theory of colour sensation4 ,he made observations by spinning coloured discs much in the same way as that which was afterwards adopted by ,maxwell1 and he developed the theory that three different primary sensations may be excited in the eye by light1 while the colour of any beam depends on the proportions in which these three sensations are excited4 ,he supposes the three primary sensations to correspond to red1 green1 and violet4 ,a blue ray is capable of exciting both the green and the violet2 a yellow ray excites the red and the green4 ,any colour1 according to ,young's theory1 may be matched by a mixture of these three primary colours taken in proper proportion2 the quality of the colour depends on the proportion of the intensities of the components2 its brightness depends on the sum of these intensities4 ,maxwell's experiments were undertaken with the object of proving or disproving the physical part of ,young's theory4 ,he does not consider the question whether there are three distinct sensations corresponding to the three primary colours2 that is a physiological inquiry1 and one to which no completely satisfactory answer has yet been given4 ,he does show that by a proper mixture of any three arbitrarily chosen standard colours it is possible to match any other colour2 the words 8proper mixture10 however1 need1 as will appear shortly1 some development4 ,we may with advantage compare the problem with one in acoustics4 ,when a compound musical note consisting of a pure tone and its overtones is sounded1 the trained ear can distinguish the various overtones and analyse the sound into its simple components4 ,the same sensation cannot be excited in two different ways4 ,the eye has no such corresponding power4 ,a given yellow may be a pure spectral yellow1 corresponding to a pure tone in music1 or it may be a mixture of a number of other pure tones2 in either case it can be matched by a proper combination of three standard colours--this ,maxwell proved4 ,it may be1 as ,young supposed1 that if the three standard colours be properly selected they correspond exactly to three primary sensations of the brain4 ,maxwell's experiments do not afford any light on this point1 which still remains more than doubtful4 ,when ,maxwell began his work the theory of colours was exciting considerable interest4 ,sir ,david ,brewster had recently developed a new theory of colour sensation which had formed the basis of some discussions1 and in #aheb von ,helmholtz published his first paper on the subject4 ,according to ,brewster1 the three primitive colours were red1 yellow and blue1 and he supposed that they corresponded to three different kinds of objective light4 ,helmholtz pointed out that experiments up to that date had been conducted by mixing pigments1 with the exception of those in which the rotating disc was used1 and that it is necessary to make them on the rays of the spectrum itself4 ,he then describes a method of mixing the light from two spectra so as to obtain the combination of every two of the simple prismatic rays in all degrees of relative strength4 ,from these experiments results1 which at the time were unexpected1 but some of which must have been known to ,young1 were obtained4 ,among them it was shown that a mixture of red and green made yellow1 while one of green and violet produced blue4 ,in a later paper 7,philosophical ,magazine1 #ahed7 ,helmholtz described a method for ascertaining the various pairs of complementary colours--colours1 that is1 which when mixed will give white--which had been shown by ,grassman to exist if ,newton's theory were true4 ,he also gave a provisional diagram of the curve formed by the spectrum1 which ought to take the place of the circle in ,newton's diagram2 for this1 however1 his experiments did not give the complete data4 ,such was the state of the question when ,maxwell began4 ,his first colour-box was made in #aheb4 ,others were designed in #ahee and #ahef1 and the final paper appeared in #ahfj4 ,but before that time he had established important results by means of his rotatory discs and colour top4 ,in his own description of this he says3 8,the coloured paper is cut into the form of disc1 each with a hole in the centre and divided along a radius so as to admit of several of them being placed on the same axis1 so that part of each is exposed4 ,by slipping one disc over another we can expose any given portion of each colour4 ,these discs are placed on a top or teetotum1 which is spun rapidly4 ,the axis of the top passes through the centre of the discs1 and the quantity of each colour exposed is measured by graduations on the rim of the top1 which is divided into #ajj parts4 ,when the top is spun sufficiently rapidly1 the impressions due to each colour separately follow each other in quick succession at each point of the retina1 and are blended together2 the strength of the impression due to each colour is1 as can be shown experimentally1 the same as when the three kinds of light in the same relative proportions enter the eye simultaneously4 ,these relative proportions are measured by the areas of the various discs which are exposed4 ,two sets of discs of different radius are used2 the largest discs are put on first1 then the smaller1 so that the centre portion of the top shows the colour arising from the mixture of those of the smaller discs2 the outer portion1 that of the larger discs40 ,in experimenting1 six discs of each size are used1 black1 white1 red1 green1 yellow and blue4 ,it is found by experiment that a match can be arranged between any five of these4 ,thus three of the larger discs are placed on the top--say black1 yellow and blue--and two of the smaller discs1 red and green1 are placed above these4 ,then it is found that it is possible so to adjust the amount exposed of each disc that the two parts of the top appear when it is spun to be of the same tint4 ,in one series of experiments the chromatic effect of #dfh parts of black1 #bia of yellow1 and #bda of blue was found to be the same as that of #fff of red and #ccd of green2 each set of discs has a dirty yellow tinge4 ,now1 in this experiment1 black is not a colour2 practically no light reaches the eye from a dead black4 ,we have1 however1 to fill up the circumference of the top in some way which will not affect the impression on the retina arising from the mixture of the blue and yellow2 this we can do by using the black disc4 ,thus we have shown that #fff parts of red and #ccd parts of green produce the same chromatic effect as #bia of yellow and #bda of blue4 ,similarly in this manner a match can be arranged between any four colours and black1 the black being necessary to complete the circumference of the discs4 ,thus using ,a1 ,b1 ,c1 ,d to denote the various colours1 a1 b1 c1 d the amounts of each colour taken1 we can get a series of results expressed as follows3 a parts of ,a together with b parts of ,b match c parts of ,c together with d parts of ,d2 or we may write this as an equation thus3-- a ,a b ,b c ,c d ,d1 where the stands for 8combined with10 and the for 8matches in tint40 ,we may also write the above-- d ,d a ,a b ,b - c ,c1 or d parts of ,d can be matched by a proper combination of colours ,a1 ,b1 ,c4 ,the sign - shows that in order to make the match we have to combine the colour ,c with ,d2 the combination then matches a mixture of ,a and ,b4 ,in this way we can form a number of equations for all possible colours1 and if we like to take any three colours ,a1 ,b1 ,c as standards1 we obtain a result which may be written generally-- x ,x a ,a b ,b c ,c1 or x parts of ,x can be matched by a parts of ,a1 combined with b parts of ,b and c parts of ,c4 ,if the sign of one of the quantities a1 b1 or c is negative1 it indicates that that colour must be combined with ,x to match the other two4 ,now ,maxwell was able to show that1 if ,a1 ,b1 ,c be properly selected1 nearly every other colour can be matched by positive combinations of these three4 ,these three colours1 then1 are primary colours1 and nearly every other colour can be matched by a combination of the three primary colours4 ,experiments1 however1 with coloured discs1 such as were undertaken by ,young1 ,forbes and ,maxwell1 were not capable of giving satisfactory results4 ,the colours of the discs were not pure spectrum colours1 and varied to some extent with the nature of the incident light4 ,it was for this reason that ,helmholtz in #aheb experimented with the spectrum1 and that ,maxwell about the same time invented his colour box4 ,the principle of the latter was very simple4 ,suppose we have a slit ,s1 and some arrangement for forming a pure spectrum on a screen4 ,let there now be a slit ,r placed in the red part of the spectrum on the screen4 ,when light falls on the slit ,s1 only the red rays can reach ,r1 and hence conversely1 if the white source be placed at the other end of the apparatus1 so that ,r is illuminated with white light1 only red rays will reach ,s4 ,similarly1 if another slit be placed in the green at ,g1 and this be illuminated by white light1 only the green rays will reach ,s1 while from a third slit ,v in the violet1 violet light only can arrive at ,s4 ,thus by opening the three slits at ,v1 ,g and ,r simultaneously1 and looking through ,s1 the retina receives the impression of the three different colours4 ,the amount of light of each colour will depend on the breadth to which the corresponding slit is opened1 and the relative intensities of the three different components can be compared by comparing the breadths of the three slits4 ,any other colour which is allowed by some suitable contrivance to enter the eye simultaneously can now be matched1 provided the red1 green and violet are primary colours4 ,by means of experiments with the colour box ,maxwell showed conclusively that a match could be obtained between any four colours2 the experiments could not be carried out in quite the simple manner suggested by the above description of the principle of the box4 ,an account of the method will be found in ,maxwell's own paper4 ,it consisted in matching a standard white by various combinations of other colours4 ,the main object of his research1 however1 was to examine the chromatic properties of the different parts of the spectrum1 and to determine the form of the curve which ought to replace the circle in ,newton's diagram of colour4 ,maxwell adopted as his three standard colours3 red1 of about wave length #f1cjb2 green1 wave length #e1bha2 and violet1 #d1efi tenth metres4 ,on the scale of ,maxwell's instrument these are represented by the numbers #bd1 #dd and #fh4 ,let us take three points ,a1 ,b1 ,c at the corners of an equilateral triangle to represent on a diagram these three colours4 ,the position of any other colour on the diagram will be found by taking weights proportional to the amounts of the colours ,a1 ,b1 ,c required to make the match between ,a1 ,b1 ,c and the given colour2 these weights are placed at ,a1 ,b1 ,c respectively2 the position of their centre of gravity is the point required4 ,thus the position of white is given by the equation-- ,w #ahf 7#bd7 #cad 7#dd7 #cje 7#fh7 which means that weights proportional to #ahf1 #cad and #cje are to be placed at ,a1 ,b1 ,c respectively1 and their centre of gravity is to be found4 ,the point so found is the position of white4 ,any other colour is given by the equation-- ,x a 7#bd7 b 7#dd7 c 7#fh74 ,again1 the position on the diagram for all colours for which a1 b1 c are all positive lies within the triangle ,a ,b ,c4 ,if one of the coefficients1 say c1 is negative the same construction applies1 but the weight applied at ,c must be treated as acting in the opposite direction to those at ,a and ,b4 ,a mixture of the given colour and ,c matches a mixture of ,a and ,b4 ,it is clear that the point corresponding to ,x will then lie outside the triangle ,a ,b ,c4 ,maxwell showed that1 with his standards1 nearly all colours could be represented by points inside the triangle4 ,the colours he had selected as standards were very close to primary colours4 ,again1 he proved that any spectrum colour between red and green1 when combined with a very slight admixture of violet1 could be matched1 in the case of either ,mrs4 ,maxwell or himself1 by a proper mixture of the red and green4 ,the positions1 therefore1 of the spectrum colours between red and green lie just outside the triangle ,a ,b ,c1 being very close to the line ,a ,b1 while for the colours between green and violet ,maxwell obtained a curve lying rather further outside the side ,b ,c4 ,any spectrum colour between green and violet1 together with a slight admixture of red1 can be matched by a proper mixture of green and violet4 ,thus the circle of ,newton's diagram should be replaced by a curve1 which coincides very nearly with the two sides ,a ,b and ,b ,c of ,maxwell's figure4 ,strictly1 according to his observations1 the curve lies just outside these two sides4 ,the purples of the spectrum lie nearly along the third side1 ,c ,a1 of the triangle1 being obtained approximately by mixing the violet and the red4 ,to find the point on the diagram corresponding to the colour obtained by mixing any two or more spectrum colours we must1 in accordance with ,newton's rule1 place weights at the points corresponding to the selected colours1 and find the centre of gravity of these weights4 ,this1 then1 was the outcome of ,maxwell's work on colour4 ,it verified the essential part of ,newton's construction1 and obtained for the first time the true form of the spectrum curve on the diagram4 ,the form of this curve will of course depend on the eye of the individual observer4 ,thus ,maxwell and ,mrs4 ,maxwell both made observations1 and distinct differences were found in their eyes4 ,it appears1 however1 that a large majority of persons have normal vision1 and that matches made by one such person are accepted by most others as satisfactory4 ,some people1 however1 are colour blind1 and ,maxwell examined a few such4 ,in the case of those whom he examined it appeared as though vision was dichromatic1 the red sensation seemed to be absent2 nearly all colours could be matched by combinations of green and violet4 ,the colour diagram was reduced to the straight line ,b ,c4 ,other forms of colour blindness have since been investigated4 ,in awarding to ,maxwell the ,rumford medal in #ahfj1 ,major-,general ,sabine1 vice-president of the ,royal ,society1 after explaining the theory of colour vision and the possible method of verifying it1 said3 8,professor ,maxwell has subjected the theory to this verification1 and thereby raised the composition of colours to the rank of a branch of mathematical physics10 and he continues3 8,the researches for which the ,rumford medal is awarded lead to the remarkable result that to a very near degree of approximation all the colours of the spectrum1 and therefore all colours in nature which are only mixtures of these1 can be perfectly imitated by mixtures of three actually attainable colours1 which are the red1 green and blue belonging respectively to three particular parts of the spectrum40 ,it should be noticed in concluding our remarks on this part of ,maxwell's work that his results are purely physical4 ,they are not inconsistent with the physiological part of ,young's theory1 viz41 that there are three primary sensations of colour which can be transmitted to the brain1 and that the colour of any object depends on the relative proportions in which these sensations are excited1 but they do not prove that theory4 ,any physiological theory which can be accepted as true must explain ,maxwell's observations1 and ,young's theory does this2 but it is1 of course1 possible that other theories may explain them equally well1 and be more in accordance with physiological observations than ,young's4 ,maxwell has given us the physical facts which have to be explained2 it is for the physiologists to do the rest4 ,,chapter ,,viii4 ,,scientific ,,work--,,molecular ,,theory4 ,maxwell in his article 8,atom10 in the ninth edition of the ,encyclopdia ,britannica1 has given some account of ,modern ,molecular ,science1 and in particular of the molecular theory of gases4 ,of this science1 ,clausius and ,maxwell are the founders1 though to their names it has recently been shown that a third1 that of ,waterston1 must be added4 ,in the present chapter it is intended to give an outline of ,maxwell's contributions to molecular science1 and to explain the advances due to him4 ,the doctrine that bodies are composed of small particles in rapid motion is very ancient4 ,democritus was its founder1 ,lucretius--de ,rerum ,natur--explained its principles4 ,the atoms do not fill space2 there is void between4 8,quapropter locus est intactus inane vacansque1 ,quod si non esset1 null ratione moveri ,res possent2 namque officium quod corporis extat ,officere atque obstare1 id in omni tempore adesset ,omnibus4 ,haud igitur quicquam procedere posset ,principium quoniam cedendi nulla daret res40 ,according to ,boscovitch an atom is an indivisible point1 having position in space1 capable of motion1 and possessing mass4 ,it is also endowed with the power of exerting force1 so that two atoms attract or repel each other with a force depending on their distance apart4 ,it has no parts or dimensions3 it is a mere geometrical point without extension in space2 it has not the property of impenetrability1 for two atoms can1 it is supposed1 exist at the same point4 ,in modern molecular science according to ,maxwell1 8we begin by assuming that bodies are made up of parts each of which is capable of motion1 and that these parts act on each other in a manner consistent with the principle of the conservation of energy4 ,in making these assumptions we are justified by the facts that bodies may be divided into smaller parts1 and that all bodies with which we are acquainted are conservative systems1 which would not be the case unless their parts were also conservative systems4 8,we may also assume that these small parts are in motion4 ,this is the most general assumption we can make1 for it includes as a particular case the theory that the small parts are at rest4 ,the phenomena of the diffusion of gases and liquids through each other show that there may be a motion of the small parts of a body which is not perceptible to us4 8,we make no assumption with respect to the nature of the small parts--whether they are all of one magnitude4 ,we do not even assume them to have extension and figure4 ,each of them must be measured by its mass1 and any two of them must1 like visible bodies1 have the power of acting on one another when they come near enough to do so4 ,the properties of the body or medium are determined by the configuration of its parts40 ,these small particles are called molecules1 and a molecule in its physical aspect was defined by ,maxwell in the following terms3-- 8,a molecule of a substance is a small body1 such that if1 on the one hand1 a number of similar molecules were assembled together1 they would form a mass of that substance2 while on the other hand1 if any portion of this molecule were removed1 it would no longer be able1 along with an assemblage of other molecules similarly treated1 to make up a mass of the original substance40 ,we are to look upon a gas as an assemblage of molecules flying about in all directions4 ,the path of any molecule is a straight line1 except during the time when it is under the action of a neighbouring molecule2 this time is usually small compared with that during which it is free4 ,the simplest theory we could formulate would be that the molecules behaved like elastic spheres1 and that the action between any two was a collision following the laws which we know apply to the collision of elastic bodies4 ,if the average distance between two molecules be great compared with their dimensions1 the time during which any molecule is in collision will be small compared with the interval between the collisions1 and this is in accordance with the fundamental assumption just mentioned4 ,it is not1 however1 necessary to suppose an encounter between two molecules to be a collision4 ,one molecule may act on another with a force1 which depends on the distance between them1 of such a character that the force is insensible except when the molecules are extremely close together4 ,it is not difficult to see how the pressure exerted by a gas on the sides of a vessel which contains it may be accounted for on this assumption4 ,each molecule as it strikes the side has its momentum reversed--the molecules are here assumed to be perfectly elastic4 ,thus each molecule of the gas is continually gaining momentum from the sides of the vessel1 while it gives up to the vessel the momentum which it possessed before the impact4 ,the rate at which this change of momentum proceeds across a given area measures the force exerted on that area2 the pressure of the gas is the rate of change of momentum per unit of area of the surface4 ,again1 it can be shown that this pressure is proportional to the product of the mass of each molecule1 the number of molecules in a unit of volume1 and the square of the velocity of the molecules4 ,let us consider in the first instance the case of a jet of sand or water of unit cross section which is playing against a surface4 ,suppose for the present that all the molecules which strike the surface have the same velocity4 ,then the number of molecules which strike the surface per second1 will be proportional to this velocity4 ,if the particles are moving quickly they can reach the surface in one second from a greater distance than is possible if they be moving slowly4 ,again1 the number reaching the surface will be proportional to the number of molecules per unit of volume4 ,hence1 if we call v the velocity of each particle1 and ,n the number of particles per unit of volume1 the number which strike the surface in one second will be ,n v2 if m be the mass of each molecule1 the mass which strikes the surface per second is ,n m v2 the velocity of each particle of this mass is v1 therefore the momentum destroyed per second by the impact is ,n m v v1 or ,n m v1 and this measures the pressure4 ,hence in this case if p be the pressure p ,n m v4 ,in the above we assume that all the molecules in the jet are moving with velocity v perpendicular to the surface4 ,in the case of a crowd of molecules flying about in a closed space this is clearly not true4 ,the molecules may strike the surface in any direction2 they will not all be moving normal to the surface4 ,to simplify the case1 consider a cubical box filled with gas4 ,the box has three pairs of equal faces at right angles4 ,we may suppose one-third of the particles to be moving at right angles to each face1 and in this case the number per unit volume which we have to consider is not ,n1 but ,n4 ,hence the formula becomes p ,n m v4 ,moreover1 if be the density of the gas--that is1 the mass of unit volume--then ,nm is equal to 1 for m is the mass of each particle1 and there are ,n particles in a unit of volume4 ,hence1 finally1 p v4 ,or1 again1 if ,v be the volume of unit mass of the gas1 then ,v is unity1 or is equal to #a_/,v4 ,hence p,v v4 ,formul equivalent to these appear first to have been obtained by ,herapath about the year #ahaf 7,thomson's 8,annals of ,philosophy10 #ahaf74 ,the results only1 however1 were stated in that year4 ,a paper which attempted to establish them was presented to the ,royal ,society in #ahbj4 ,it gave rise to very considerable correspondence1 and was withdrawn by the author before being read4 ,it is printed in full in ,thomson's 8,annals of ,philosophy0 for #ahba1 vol4 i41 pp4 #bgc1 #cdj1 #dja4 ,the arguments of the author are no doubt open to criticism1 and are in many points far from sound4 ,still1 by considering the problem of the impact of a large number of hard bodies1 he arrived at a formula connecting the pressure and volume of a given mass of gas equivalent to that just given4 ,these results are contained in ,propositions viii4 and ix4 of ,herapath's paper4 ,in his next step1 however1 ,herapath1 as we know now1 was wrong4 ,one of his fundamental assumptions is that the temperature of a gas is measured by the momentum of each of its particles4 ,hence1 assuming this1 we have ,t m v1 if ,t represents the temperature3 and p ,n m v 7,n_/m7 7m v74 ,or1 again-- p ,n,tv 7,n_/m7,t4 ,these results are practically given in ,proposition viii41 ,corr4 7#a7 and 7#b71 and ,proposition ix4#di ,the temperature as thus defined by ,herapath is an absolute temperature1 and he calculates the absolute zero of temperature at which the gas would have no volume from the above results4 ,the actual calculation is of course wrong1 for1 as we know now by experiment1 the pressure is proportional to the temperature1 and not to its square1 as ,herapath supposed4 ,it will be seen1 however1 that ,herapath's formula gives ,boyle's law2 for if the temperature is constant1 the formula is equivalent to p ,v a constant4 ,herapath somewhat extended his work in his 8,mathematical ,physics0 published in #ahdg1 and applied his principles to explain diffusion1 the relation between specific heat and atomic weight1 and other properties of bodies4 ,he still1 however1 retained his erroneous supposition that temperature is to be measured by the momentum of the individual particles4 ,the next step in the theory was made by ,waterston4 ,his paper was read to the ,royal ,society on ,march #eth1 #ahdf4 ,it was most unfortunately committed to the ,archives of the ,society1 and was only disinterred by ,lord ,rayleigh in #ahib and printed in the ,transactions for that year4 ,in the account just given of the theory1 it has been supposed that all the particles move with the same velocity4 ,this is clearly not the case in a gas4 ,if at starting all the particles had the same velocity1 the collisions would change this state of affairs4 ,some particles will be moving quickly1 some slowly4 ,we may1 however1 still apply the theory by splitting up the particles into groups1 and1 supposing that each group has a constant velocity1 the particles in this group will contribute to the pressure an amount--p--equal to ,n m v1 where v is the velocity of the group and ,n the number of particles having that velocity4 ,the whole pressure will be found by adding that due to the various groups1 and will be given as before by p ,n m v1 where v is not now the actual velocity of the particles1 but a mean velocity given by the equation ,n v ,n v ,n v 444441 which will produce the same pressure as arises from the actual impacts4 ,this quantity v is known as the mean square of the molecular velocity1 and is so used by ,waterston4 ,in a paper in the ,philosophical ,magazine for #aheh ,waterston gives an account of his own paper of #ahdf in the following terms3--8,mr4 ,herapath unfortunately assumed heat or temperature to be represented by the simple ratio of the velocity instead of the square of the velocity1 being in this apparently led astray by the definition of motion generally received1 and thus was baffled in his attempts to reconcile his theory with observation4 ,if we make this change in ,mr4 ,herapath's definition of heat or temperature--viz41 that it is proportional to the vis-viva or square velocity of the moving particle1 not to the momentum or simple ratio of the velocity--we can without much difficulty deduce not only the primary laws of elastic fluids1 but also the other physical properties of gases enumerated above in the third objection to ,newton's hypothesis4 ,the paper from which the quotation is taken is on #8,the ,theory of ,sound4' ,in the ,archives of the ,royal ,society for #ahde-df there is a paper on #8,the ,physics of ,media that consist of perfectly 8,elastic ,molecules in a ,state of ,motion10' which contains the synthetical reasoning on which the demonstration of these matters rests4444 ,this theory does not take account of the size of the molecules4 ,it assumes that no time is lost at the impact1 and that if the impacts produce rotatory motion1 the vis viva thus invested bears a constant ratio to the rectilineal vis viva1 so as not to require separate consideration4 ,it does1 also1 not take account of the probable internal motion of composite molecules2 yet the results so closely accord with observation in every part of the subject as to leave no doubt that ,mr4 ,herapath's idea of the physical constitution of gases approximates closely to the truth40 ,in his introduction to ,waterston's paper 7,phil4 ,trans41 #ahib7 ,lord ,rayleigh writes3--8,impressed with the above passage1 and with the general ingenuity and soundness of ,waterston's views1 ,i took the first opportunity of consulting the ,archives1 and saw at once that the memoir justified the large claims made for it1 and that it marks an immense advance in the direction of the now generally received theory40 ,in the first section of the paper ,waterston's great advance consisted in the statement that the mean square of the kinetic energy of each molecule measures the temperature4 ,according to this we are thus to put in the pressure equation-- m v ,t1 the temperature1 and we have at once--p ,v ,n ,t4 ,now this equation expresses1 as we know1 the laws of ,boyle and ,gay ,lussac4 ,the second section discusses the properties of media1 consisting of two or more gases1 and arrives at the result that 8in mixed media the mean square molecular velocity is inversely proportional to the specific weights of the molecules40 ,this was the great law rediscovered by ,maxwell fifteen years later4 ,with modern notation it may be put thus3--,if m1 m be the masses of each molecule of two different sets of molecules mixed together1 then1 when a steady state has been reached1 since the temperature is the same throughout1 m v is equal to m v4 ,the average kinetic energy of each molecule is the same4 ,from this ,avogadros' law follows at once--for if p1 p be the pressures1 ,n1 ,n the numbers of molecules per unit volume-- p ,n m v1 p ,n m v4 ,hence1 if p1 is equal to p1 since m v is equal to m v1 we must have ,n equal to ,n1 or the number of molecules in equal volumes of two gases at the same pressure and temperature is the same4 ,the proof of this proposition given by ,waterston is not satisfactory4 ,on this point1 however1 we shall have more to say4 ,the third section of the paper deals with adiabatic expansion1 and in it there is an error in calculation which prevented correct results from being attained4 ,at the meeting of the ,british ,association at ,ipswich1 in #ahea1 a paper by ,j4 ,j4 ,waterston of ,bombay1 on 8,the ,general ,theory of ,gases10 was read4 ,the following is an extract from the ,proceedings3-- ,the author 8conceives that the atoms of a gas1 being perfectly elastic1 are in continual motion in all directions1 being constrained within a limited space by their collisions with each other1 and with the particles of surrounding bodies4 8,the vis viva of these motions in a given portion of a gas constitutes the quantity of heat contained in it4 8,he shows that the result of this state of motion must be to give the gas an elasticity proportional to the mean square of the velocity of the molecular motions1 and to the total mass of the atoms contained in unity of bulk0 7unit of volume7--that is to say1 to the density of the medium4 8,the elasticity in a given gas is the measure of temperature4 ,equilibrium of pressure and heat between two gases takes place when the number of atoms in unit of volume is equal and the vis viva of each atom equal4 ,temperature1 therefore1 in all gases is proportional to the mass of one atom multiplied by the mean square of the velocity of the molecular motions1 being measured from an absolute zero #dia below the zero of ,fahrenheit's thermometer40 ,it appears1 therefore1 from these extracts that the discovery of the laws that temperature is measured by the mean kinetic energy of a single molecule1 and that in a mixture of gases the mean kinetic energy of each molecule is the same for each gas1 is due to ,waterston4 ,they were contained in his paper of #ahdf1 and published by him in #ahea4 ,both these papers1 however1 appear to have been unnoticed by all subsequent writers until #ahib4 ,meanwhile1 in #ahdh1 ,joule's attention was called by his experiments to the question1 and he saw that ,herapath's result gave a means of calculating the mean velocity of the molecules of a gas4 ,for according to the result given above1 p v2 thus v #c p_/1 and p and being known1 we find v4 ,thus for hydrogen at freezing-point and atmospheric pressure ,joule obtains for v the value #f1jee feet per second1 or1 roughly1 six times the velocity of sound in air4 ,clausius was the next writer of importance on the subject4 ,his first paper is in 8,poggendorff's ,annalen10 vol4 c41 #aheg1 8,on the ,kind of ,motion we call ,heat40 ,it gives an exposition of the theory1 and establishes the fact that the kinetic energy of the translatory motion of a molecule does not represent the whole of the heat it contains4 ,if we look upon a molecule as a small solid we must consider the energy it possesses in consequence of its rotation about its centre of gravity1 as well as the energy due to the motion of translation of the whole4 ,clausius' second paper appeared in #ahei4 ,in it he considers the average length of the path of a molecule during the interval between two collisions4 ,he determines this path in terms of the average distance between the molecules and the distance between the centres of two molecules at the time when a collision is taking place4 ,these two papers appear to have attracted ,maxwell's attention to the matter1 and his first paper1 entitled 8,illustrations of the ,dynamical ,theory of ,gases10 was read to the ,british ,association at ,aberdeen and ,oxford in #ahei and #ahfj1 and appeared in the ,philosophical ,magazine1 ,january and ,july1 #ahfj4 ,in the introduction to this paper ,maxwell points out1 while there was then no means of measuring the quantities which occurred in ,clausius' expression for the mean free path1 8the phenomena of the internal friction of gases1 the conduction of heat through a gas1 and the diffusion of one gas through another1 seem to indicate the possibility of determining accurately the mean length of path which a particle describes between two collisions4 ,in order1 therefore1 to lay the foundation of such investigations on strict mechanical principles10 he continues1 8,i shall demonstrate the laws of motion of an indefinite number of small1 hard and perfectly elastic spheres acting on one another only during impact40 ,maxwell then proceeds to consider in the first case the impact of two spheres4 ,but a gas consists of an indefinite number of molecules4 ,now it is impossible to deal with each molecule individually1 to trace its history and follow its path4 ,in order1 therefore1 to avoid this difficulty ,maxwell introduced the statistical method of dealing with such problems1 and this introduction is the first great step in molecular theory with which his name is connected4 ,he was led to this method by his investigation into the theory of ,saturn's rings1 which had been completed in #ahef1 and in which he had shown that the conditions of stability required the supposition that the rings are composed of an indefinite number of free particles revolving round the planet1 with velocities depending on their distances from the centre4 ,these particles may either be arranged in separate rings1 or their motion may be such that they are continually coming into collision with each other4 ,as an example of the statistical method1 let us consider a crowd of people moving along a street4 ,taken as a whole the crowd moves steadily forwards4 ,any individual in the crowd1 however1 is jostled backwards and forwards and from side to side2 if a line were drawn across the street we should find people crossing it in both directions4 ,in a considerable interval more people would cross it1 going in the direction in which the crowd is moving1 than in the other1 and the velocity of the crowd might be estimated by counting the number which crossed the line in a given interval4 ,this velocity so found would differ greatly from the velocity of any individual1 which might have any value within limits1 and which is continually changing4 ,if we knew the velocity of each individual and the number of individuals we could calculate the average velocity1 and this would agree with the value found by counting the resultant number of people who cross the line in a given interval4 ,again1 the people in the crowd will naturally fall into groups according to their velocities4 ,at any moment there will be a certain number of people whose velocities are all practically equal1 or1 to be more accurate1 do not differ among themselves by more than some small quantity4 ,the number of people at any moment in each of these groups will be very different4 ,the number in any group1 which has a velocity not differing greatly from the mean velocity of the whole1 will be large2 comparatively few will have either a very large or a very small velocity4 ,again1 at any moment1 individuals are changing from one group to another2 a man is brought to a stop by some obstruction1 and his velocity is considerably altered--he passes from one group to a different one2 but while this is so1 if the mean velocity remains constant1 and the size of the crowd be very great1 the number of people at any moment in a given group remains unchanged4 ,people pass from that group into others1 but during any interval the same number pass back again into that group4 ,it is clear that if this condition is satisfied the distribution is a steady one1 and the crowd will continue to move on with the same uniform mean velocity4 ,now1 ,maxwell applies these considerations to a crowd of perfectly elastic spheres1 moving anyhow in a closed space1 acting upon each other only when in contact4 ,he shows that they may be divided into groups according to their velocities1 and that1 when the steady state is reached1 the number in each group will remain the same1 although the individuals change4 ,moreover1 it is shown that1 if ,a and ,b represent any two groups1 the state will only be steady when the numbers which pass from the group ,a to the group ,b are equal to the numbers which pass back from the group ,b to the group ,a4 ,this condition1 combined with the fact that the total kinetic energy of the motion remains unchanged1 enables him to calculate the number of particles in any group in terms of the whole number of particles1 the mean velocity1 and the actual velocity of the group4 ,from this an accurate expression can be found for the pressure of the gas1 and it is proved that the value found by others1 on the assumption that all the particles were moving with a common velocity1 is correct4 ,previous to this paper of ,maxwell's it had been realised that the velocities could not be uniform throughout4 ,there had been no attempt to determine the distribution of velocity1 or to submit the problem to calculation1 making allowance for the variations in velocity4 ,maxwell's mathematical methods are1 in their generality and elegance1 far in advance of anything previously attempted in the subject4 ,so far it has been assumed that the particles in the vessel are all alike4 ,maxwell next takes the case of a mixture of two kinds of particles1 and inquires what relation must exist between the average velocities of these different particles1 in order that the state may be steady4 ,now1 it can be shown that when two elastic spheres impinge the effect of the impact is always such as to reduce the difference between their kinetic energies4 ,hence1 after a very large number of impacts the kinetic energies of the two balls must be the same2 the steady state1 then1 will be reached when each ball has the same kinetic energy4 ,thus if m1 m be the masses of the particles in the two sets respectively1 v1 v their mean velocities we must have finally-- m v m v ,this is the second of the two great laws enunciated by ,waterston in #ahde and #ahea1 but which1 as we have seen1 had remained unknown until #ahei1 when it was again given by ,maxwell4 ,now1 when gases are mixed their temperatures become equal4 ,hence we conclude1 in ,maxwell's words1 8that the physical condition which determines that the temperature of two gases shall be the same1 is that the mean kinetic energy of agitation of the individual molecules of the two gases are equal40 ,thus1 as the result of ,maxwell's more exact researches on the motion of a system of spherical particles1 we find that we again can obtain the equations-- ,t mv p ,n mv ,,nt ,t_/m ,from these results we obtain as before the laws of ,boyle1 ,charles and ,avrogadro4 ,again if be the specific heat of the gas at constant volume1 the quantity of heat required to raise a single molecule of mass m one degree will be m4 ,thus1 when a molecule is heated1 the kinetic energy must increase by this amount4 ,but the increase of temperature1 which in this case is #a1 is measured by the increase of kinetic energy of the single molecule4 ,hence the amount of heat required to raise the temperature of a single molecule of all gases #a is the same4 ,thus the quantity m is the same for all gases2 or1 in other words1 the specific heat of a gas is inversely proportional to the mass of its individual molecules4 ,the density of a gas--since the number of molecules per unit volume at a given pressure and temperature is the same for all gases--is also proportional to the mass of each individual molecule4 ,thus the specific heats of all gases are inversely proportional to their densities4 ,this is the law discovered experimentally by ,dulong and ,petit to be approximately true for a large number of substances4 99 99 99 99 99 ,in the next part of the paper ,maxwell proceeded to determine the average number of collisions in a given time1 and hence1 knowing the velocities1 to determine1 in terms of the size of the particles and their numbers1 the mean free path of a particle2 the result so found differed somewhat from that already obtained by ,clausius4 ,having done this he showed how1 by means of experiments on the viscosity of gases1 the length of the mean free path could be determined4 ,an illustration due to ,professor ,balfour ,stewart will perhaps make this clear4 ,let us suppose we have two trains running with uniform speed in opposite directions on parallel lines1 and1 further1 that the engines continue to work at the same rate1 developing just sufficient energy to overcome the resistance of the line1 etc41 and to maintain the speed constant4 ,now suppose passengers commence to jump across from one train to the other4 ,each man carries with him his own momentum1 which is in the opposite direction to that of the train into which he jumps2 the result is that the momentum of each train is reduced by the process2 the velocities of the two decrease2 it appears as though a frictional force were acting between the two4 ,maxwell suggests that a similar process will account for the apparent viscosity of gases4 ,consider two streams of gas1 moving in opposite directions one over the other2 it is found that in each case the layers of gas near the separating surface move more slowly than those in the interior of the streams2 there is apparently a frictional force between the two streams along this surface1 tending to reduce their relative velocity4 ,maxwell's explanation of this is that at the common surface particles from the one stream enter the other1 and carry with them their own momentum2 thus near this surface the momentum of each stream is reduced1 just as the momentum of the trains is reduced by the people jumping across4 ,internal friction or viscosity is due to the diffusion of momentum across this common surface4 ,the effect does not penetrate far into the gas1 for the particles soon acquire the velocity of the stream to which they have come4 ,now1 the rate at which the momentum is diffused will measure the frictional force1 and will depend on the mean free path of the particles4 ,if this is considerable1 so that on the average a particle can penetrate a considerable distance into the second gas before a collision takes place and its motion is changed1 the viscosity will be considerable2 if1 on the other hand1 the mean free path is small1 the reverse will be true4 ,thus it is possible to obtain a relation between the mean free path and the coefficient of viscosity1 and from this1 if the coefficient of viscosity be known1 a value for the mean free path can be found4 ,maxwell1 in the paper under discussion1 was the first to do this1 and1 using a value found by ,professor ,stokes for the coefficient of viscosity1 obtained as the length of the mean free path of molecules of air #a_/ddgjjj of an inch1 while the number of collisions per second experienced by each molecule is found to be about #h1jgg1bjj1jjj4 ,moreover1 it appeared from his theory that the coefficient of viscosity should be independent of the number of molecules of gas present1 so that it is not altered by varying the density4 ,this result ,maxwell characterises as startling1 and he instituted an elaborate series of experiments a few years later with a view of testing it4 ,the reason for this result will appear if we remember that1 when the density is decreased1 the mean free path is increased2 relatively1 then1 to the total number of molecules present1 the number which cross the surface in a given time is increased4 ,and it appears from ,maxwell's result that this relative increase is such that the total number crossing remains unchanged4 ,hence the momentum conveyed across each unit area per second remains the same1 in spite of the decrease in density4 ,another consequence of the same investigation is that the coefficient of viscosity is proportional to the mean velocity of the molecules4 ,since the absolute temperature is proportional to the square of the velocity1 it follows that the coefficient of viscosity is proportional to the square root of the absolute temperature4 ,the second part of the paper deals with the process of diffusion of two or more kinds of moving particles among one another4 ,if two different gases are placed in two vessels separated by a porous diaphragm such as a piece of unglazed earthenware1 or connected by means of a narrow tube1 ,graham had shewn that1 after sufficient time has elapsed1 the two are mixed together4 ,the same process takes place when two gases of different density are placed together in the same vessel4 ,at first the denser gas may be at the bottom1 the less dense above1 but after a time the two are found to be uniformly distributed throughout4 ,maxwell attempted to calculate from his theory the rate at which the diffusion takes place in these cases4 ,the conditions of most of ,graham's experiments were too complicated to admit of direct comparison with the theory1 from which it appeared that there is a relation between the mean free path and the rate of diffusion4 ,one experiment1 however1 was found1 the conditions of which could be made the subject of calculation1 and from it ,maxwell obtained as the value of the mean free path in air #a_/chijjj of an inch4 ,the number was close enough to that found from the viscosity to afford some confirmation of his theory4 ,however1 a few years later ,clausius criticised the details of this part of the paper1 and ,maxwell1 in his memoir of #ahff1 admits the calculation to have been erroneous4 ,the main principles remained unaffected1 the molecules pass from one gas to the other1 and this constitutes diffusion4 ,now1 suppose we have two sets of particles in contact of such a nature that the mean kinetic energy of the one set is different from that of the other2 the temperatures of the two will then be different4 ,these two sets will diffuse into each other1 and the diffusing particles will carry with them their kinetic energy1 which will gradually pass from those which have the greater energy to those which have the less1 until the average kinetic energy is equalised throughout4 ,but the kinetic energy of translation is the heat of the particles4 ,this diffusion of kinetic energy is a diffusion of heat by conduction1 and we have here the mechanical theory of the conduction of heat in a gas4 ,maxwell obtained an expression1 which1 however1 he afterwards modified1 for the conductivity of a gas in terms of the mean free path4 ,it followed from this that the conductivity of air was only about #a_/gjjj of that of copper4 ,thus the diffusion of gases1 the viscosity of gases1 and the conduction of heat in gases1 are all connected with the diffusion of the particles carrying with them their momenta and their energy2 while values of the mean free path can be obtained from observations on any one of these properties4 ,in the third part of his paper ,maxwell considers the consequences of supposing the particles not to be spherical4 ,in this case the impacts would tend to set up a motion of rotation in the particles4 ,the direction of the force acting on any particle at impact would not necessarily pass through its centre2 thus by impact the velocity of its centre would be changed1 and in addition the particles would be made to spin4 ,some part1 therefore1 of the energy of the particles will appear in the form of the translational energy of their centres1 while the rest will take the form of rotational energy of each particle about its centre4 ,it follows from ,maxwell's work that for each particle the average value of these two portions of energy would be equal4 ,the total energy will be half translational and half rotational4 ,this theorem1 in a more general form which was afterwards given to it1 has led to much discussion1 and will be again considered later4 ,for the present we will assume it to be true4 ,clausius had already called attention to the fact that some of the energy must be rotational unless the molecules be smooth spheres1 and had given some reasons for supposing that the ratio of the whole energy to the energy of translation is in a steady state a constant4 ,maxwell shows that for rigid bodies this constant is #b4 ,let us denote it for the present by the symbol 4 ,thus1 if the translational energy of a molecule is m v1 its whole energy is m v4 ,the temperature is still measured by the translational energy1 or m v2 the heat depends on the whole energy4 ,hence if ,h represent the amount of heat--measured as energy--contained by a single molecule1 and ,t its temperature1 we have-- ,h ,t ,from this it can be shewn#ej that if represent the ratio of the specific heat of a gas at constant pressure to the specific heat at constant volume1 then-- #a_/7-a7 ,for air and some other gases the value of has been shown to be #adjh4 ,from this it follows that #afcd4 ,now1 ,maxwell's theory required that for smooth hard particles1 approximately spherical in shape1 should be #b1 and hence he concludes 8we have shown that a system of such particles could not possibly satisfy the known relation between the two specific heats of all gases40 ,since this statement was made many more experiments on the value of have been undertaken2 it is not equal to #adjh for all gases4 ,hence the value of is different for various gases4 ,it is of some importance to notice that the value of just found for air is very approximately #aff or #e_/c4 ,for mercury vapour the value of has been shown by ,kundt to be #acc or #a1 and hence is equal to #a4 ,thus all the energy of a particle of mercury vapour is translational1 and its behaviour in this respect is consistent with the assumption that a particle of mercury vapour is a smooth sphere4 ,the two results of this theory which seemed to lend themselves most readily to experimental verification were 7#a7 that the viscosity of a gas is independent of its density1 and 7#b7 that it is proportional to the square root of the absolute temperature4 ,the next piece of work connected with the theory was an attempt to test these consequences1 and a description of the experiments was published in the 8,philosophical ,transactions0 for #ahfe1 in a paper on the 8,viscosity or ,internal ,friction of ,air and other ,gases10 and forms the ,bakerian lecture for that year4 ,the first result was completely proved4 ,it is shewn that the value of the coefficient#ea of viscosity 8is the same for air at #je inch and at #cj inches pressure1 provided that the temperature remains the same40 ,it was clear also that the viscosity depended on the temperature1 and the results of the experiments seemed to show that it was nearly proportional to the absolute temperature4 ,thus for two temperatures1 #ahe ,fah4 and #ea ,fah41 the ratio of the two coefficients found was #abfbd2 the ratio of the two temperatures1 each measured from absolute zero1 is #abfje4 ,this result1 then1 does not agree with the hypothesis that a gas consists of spherical molecules acting only on each other by a kind of impact1 for1 if this were so1 the coefficient would1 as we have seen1 depend on the square root of the absolute temperature4 ,but ,maxwell's result1 connecting viscosity with the first power of the absolute temperature1 has not been confirmed by other investigators4 ,according to it we should have as the relation between 1 the coefficient of viscosity at t and 1 that at zero the equation-- 7#a 4#jjcfe t74 ,the most recent results of ,professor ,holman 7,philosophical ,magazine1 ,vol4 xxi41 p4 #bab7 give-- 7#a 4#jjbge t - 4#jjjjjjcd t74 ,and results similar to this are given by ,o4 ,e4 ,meyer1 ,puluj1 and ,obermeyer4 ,maxwell's coefficient #jjcfe is too large1 but #jjahb1 the coefficient obtained by supposing the viscosity proportional to the square root of the temperature1 would be too small4 ,it still remains true1 therefore1 that the laws of the viscosity of gases cannot be explained by the hypothesis of the impact of hard spheres2 but some deductions drawn by ,maxwell in his next paper from his supposed law of proportionality to the first power of the absolute temperature require modification4 ,it was clear from his experiments just described that the simple hypothesis of the impact of elastic bodies would not account for all the phenomena observed4 ,accordingly1 in #ahff1 ,maxwell took up the problem in a more general form in his paper on the 8,dynamical ,theory of ,gases10 ,phil4 ,trans41 #ahff4 ,in it he considered the molecules of the gas not as elastic spheres of definite radius1 but as small bodies1 or groups of smaller molecules1 repelling one another with a force whose direction always passes very nearly through the centre of gravity of the molecules1 and whose magnitude is represented very nearly by some function of the distance of the centres of gravity4 8,i have made10 he continues1 8this modification of the theory in consequence of the results of my experiments on the viscosity of air at different temperatures1 and ,i have deduced from these experiments that the repulsion is inversely as the fifth power of the distance40 ,since more recent observation has shown that the numerical results of ,maxwell's work connecting viscosity and temperature are erroneous1 this last deduction does not hold2 the inverse fifth power law of force will not give the correct relation between viscosity and temperature4 ,maxwell himself at a later date1 8,on the ,stresses in ,rarefied ,gases10 ,phil4 ,trans41 #ahgi1 realised this2 but even in this last paper he adhered to the fifth power law because it leads to an important simplification in the equations to be dealt with4 ,the paper of #ahff is chiefly important because it contains for the first time the application of general dynamical methods to molecular problems4 ,the law of the distribution of velocities among the molecules is again investigated1 and a result practically identical with that found for the elastic spheres is arrived at4 ,in obtaining this conclusion1 however1 it is assumed that the distribution of velocities is uniform in all directions about any point1 whatever actions may be taking place in the gas4 ,if1 for example1 the temperature is different at different points1 then1 for a given velocity1 all directions are not equally probable4 ,maxwell's expression1 therefore1 for the number of molecules which at any moment have a given velocity only applies to the permanent state in which the distribution of temperature is uniform4 ,when dealing1 for example1 with the conduction of heat1 a modification of the expression is necessary4 ,this was pointed out by ,boltzmann4#eb ,in the paper of #ahff1 ,maxwell applies his generalised results to the final distribution of two gases under the action of gravity1 the equilibrium of temperature between two gases1 and the distribution of temperature in a vertical column4 ,these results are1 as he states1 independent of the law of force between the molecules4 ,the dynamical causes of diffusion viscosity and conduction of heat are dealt with1 and these involve the law of force4 ,it follows also from the investigation that1 on the hypotheses assumed as its basis1 if two kinds of gases be mixed1 the difference between the average kinetic energies of translation of the gases of each kind diminishes rapidly in consequence of the action between the two4 ,the average kinetic energy of translation1 therefore1 tends to become the same for each kind of gas1 and as before1 it is this average energy of translation which measures the temperature4 ,a molecule in the theory is a portion of a gas which moves about as a single body4 ,it may be a mere point1 a centre of force having inertia1 capable of doing work while losing velocity4 ,there may be also in each molecule systems of several such centres of force bound together by their mutual actions4 ,again1 a molecule may be a small solid body of determinate form2 but in this case we must1 as ,maxwell points out1 introduce a new set of forces binding together the parts of each molecule3 we must have a molecular theory of the second order4 ,in any case1 the most general supposition made is that a molecule consists of a series of parts which stick together1 but are capable of relative motion among each other4 ,in this case the kinetic energy of the molecule consists of the energy of its centre of gravity1 together with the energy of its component parts1 relative to its centre of gravity4#ec ,now ,clausius had1 as we have seen1 given reasons for believing that the ratio of the whole energy of a molecule to the energy of translation of its centre of gravity tends to become constant4 ,we have already used to denote this constant4 ,thus1 while the temperature is measured by the average kinetic energy of translation of the centre of gravity of each molecule1 the heat contained in a molecule is its whole energy1 and is times this quantity4 ,thus the conclusions as to specific heat1 etc41 already given on page #acj1 apply in this case1 and in particular we have the result that if be the ratio of the specific heat at constant pressure to that at constant volume1 then-- #a_/7-a7 ,maxwell's theorem of the distribution of kinetic energy among a system of molecules applied1 as he gave it in #ahff1 to the kinetic energy of translation of the centre of gravity of each molecule4 ,two years later ,dr4 ,boltzmann1 in the paper we have already referred to1 extended it 7under certain limitations7 to the parts of which a molecule is composed4 ,according to ,maxwell the average kinetic energy of the centre of gravity of each molecule tends to become the same4 ,according to ,boltzmann the average kinetic energy of each part of the molecule tends to become the same4 ,maxwell1 in the last paper he wrote on the subject 78,on ,boltzmann's ,theorem on the ,average ,distribution of ,energy in a ,system of ,material ,points10 ,camb4 ,phil4 ,trans41 ,,xii471 took up this problem4 ,watson had given a proof of it in #ahgf differing from ,boltzmann's1 but still limited by the stipulation that the time1 during which a particle is encountering other particles1 is very small compared with the time during which there is no sensible action between it and other particles1 and also that the time during which a particle is simultaneously within the distance of more than one other particle may be neglected4 ,maxwell claims that his proof is free from any such limitation4 ,the material points may act on each other at all distances1 and according to any law which is consistent with the conservation of energy2 they may also be acted on by forces external to the system1 provided these are consistent with that law4 ,the only assumption which is necessary for the direct proof is that the system1 if left to itself in its actual state of motion1 will sooner or later pass through every phase which is consistent with the conservation of energy4 ,in this paper ,maxwell finds in a very general manner an expression for the number of molecules which at any time have a given velocity1 and this1 when simplified by the assumptions of the former papers1 reduces to the form already found4 ,he also shows that the average kinetic energy corresponding to any one of the variables which define his system is the same for every one of the variables of his system4 ,thus1 according to this theorem1 if each molecule be a single small solid body1 six variables will be required to determine the position of each1 three variables will give us the position of the centre of gravity of the molecule1 while three others will determine the position of the body relative to its centre of gravity4 ,if the six variables be properly chosen1 the kinetic energy can be expressed as a sum of six squares1 one square corresponding to each variable4 ,according to the theorem the part of the kinetic energy depending on each square is the same4 ,thus1 the whole energy is six times as great as that which arises from any one of the variables4 ,the kinetic energy of translation is three times as great as that arising from each variable1 for it involves the three variables which determine the position of the centre of gravity4 ,hence1 if we denote by ,k the kinetic energy due to one variable1 the whole energy is #f ,k1 and the translational energy is #c ,k2 thus1 for this case-- #f,k_/#c,k #b ,or1 again1 if we suppose that the molecule is such that m variables are required to determine its position relatively to its centre of gravity1 since #c are needed to fix the centre of gravity1 the total number of variables defining the position of the molecule is m #c1 and it is said to have m #c degrees of freedom4 ,hence1 in this case1 its total energy is 7m #c7 ,k and its energy of translation is #c ,k1 thus we find-- 7m #c7_/c ,hence #a #b_/7m #c7 #a #b_/n if n be the number of degrees of freedom of the molecule4 ,thus1 if this ,boltzmann-,maxwell theorem be true1 the specific heat of a gas will depend solely on the number of degrees of freedom of each of its molecules4 ,for hard rigid bodies we should have n equal to #f1 and hence #accc4 ,now the fact that this is not the value of for any of the known gases is a fundamental difficulty in the way of accepting the complete theory4 ,boltzmann has called attention to the fact that if n be equal to five1 then has the value #adj4 ,and this agrees fairly with the value found by experiment for air1 oxygen1 nitrogen1 and various other gases4 ,we will1 however1 return to this point shortly4 ,there is1 perhaps1 no result in the domain of physical science in recent years which has been more discussed than the two fundamental theorems of the molecular theory which we owe to ,maxwell and to ,boltzmann4 ,the two results in question are 7#a7 the expression for the number of molecules which at any moment will have a given velocity1 and 7#b7 the proposition that the kinetic energy is ultimately equally divided among all the variables which determine the system4 ,with regard to 7#a7 ,maxwell showed that his error law was one possible condition of permanence4 ,if at any moment the velocities are distributed according to the error law1 that distribution will be a permanent one4 ,he did not prove that such a distribution is the only one which can satisfy all the conditions of the problem4 ,the proof that this law is a necessary1 as well as a sufficient1 condition of permanence was first given by ,boltzmann1 for a single monatomic gas in #ahgb1 for a mixture of such gases in #ahhf1 and for a polyatomic gas in #ahhg4 ,other proofs have been given since by ,watson and ,burbury4 ,it would be quite beyond the limits of this book to go into the question of the completeness or sufficiency of the proofs4 ,the discussion of the question is still in progress4 ,the ,british ,association ,report for #ahid contains an important contribution to the question1 in the shape of a report by ,mr4 ,g4 ,h4 ,bryan1 and the discussion he started at ,oxford by reading this report has been continued in the pages of ,nature and elsewhere since that time4 ,mr4 ,bryan shows in the first place what may be the nature of the systems of molecules to which the results will apply1 and discusses various points of difficulty in the proof4 ,the theorem in question1 from which the result 7#a7 follows as a simple deduction1 has been thus stated by ,dr4 ,larmor4#ed 8,there exists a positive function belonging to a group of molecules which1 as they settle themselves into a steady state--on the average derived from a great number of configurations--maintains a steady downward trend4 ,the ,maxwell-,boltzmann steady state is the one in which this function has finally attained its minimum value1 and is thus a unique steady state1 it still being borne in mind that this is only a proposition of averages derived from a great number of instances in which nothing is conserved in encounters1 except the energy1 and that exceptional circumstances may exist1 comparatively very few in number1 in which the trend is1 at any rate1 temporarily the other way40 ,this theorem1 when applied to cases of motion1 such as that of a gas at constant temperature enclosed in a rigid envelope impermeable to heat1 appears to be proved4 ,for such a case1 therefore1 the ,maxwell-,boltzmann law is the only one possible4 ,but whether this be so or not1 the law first introduced by ,maxwell is one of those possible1 and the advance in molecular science due to its introduction is enormous4 ,we come now to the second result1 the equal partition of the energy among all the degrees of freedom of each molecule4 ,lord ,kelvin has pointed out a flaw in ,maxwell's proof1 but ,boltzmann showed 7,philosophical ,magazine1 ,march1 #ahic7 how this flaw can easily be corrected1 and it may be said that in all cases in which the ,boltzmann-,maxwell law of the distribution of velocities holds1 ,maxwell's law of the equal partition of energy holds also4 ,three cases are considered by ,mr4 ,bryan1 in which the law of distribution fails for rigid molecules3 the first is when the molecules have all1 in addition to their velocities of agitation1 a common velocity of translation in a fixed direction2 the second is when the gas has a motion of uniform rotation about a fixed axis2 while the third is when each molecule has an axis of symmetry4 ,in this last case the forces acting during a collision necessarily pass through the axis of symmetry1 the angular velocity1 therefore1 of any molecule about this axis remains constant1 the number of molecules having a given angular velocity will remain the same throughout the motion1 and the part of the kinetic energy which depends on this component of the motion will remain fixed1 and will not come into consideration when dealing with the equal partition of the energy among the various degrees of freedom4 ,such a molecule has five1 and not six1 degrees of freedom2 three quantities are needed to determine the position of its centre of gravity1 and two to fix the position of the axis of symmetry4 ,in this case1 then1 as ,boltzmann points out1 in the expression for the ratio of the specific heats1 we must have n equal to #e1 and hence #a #b_/n #a #b_/e #ad agreeing fairly with the value found for air and various other permanent gases4 ,for cases1 then1 in which we consider each atom as a single rigid body1 the ,boltzmann-,maxwell theorem appears to give a unique solution1 and the ,maxwell law of the distribution of the energy to be in fair accordance with the results of observation4#ee ,if we can never go further--and it must be admitted that the difficulties in the way of further advance are enormous--it may1 ,i think1 be claimed for ,maxwell that the progress already made is greatly due to him4 ,both these laws1 for the case of elastic spheres1 are contained in his first paper of #ahfj2 and while it is to the genius of ,boltzmann that we owe their earliest generalisation1 and in particular the proof of the uniqueness of the solution under proper restrictions1 ,maxwell's last paper contributed in no small degree to the security of the position4 ,not merely the foundations1 but much of the superstructure of molecular science is his work4 ,the difficulties in the way of advance are1 as we have said1 enormous4 ,boltzmann1 in one of his papers1 has considered the properties of a complex molecule of a gas1 consisting maybe of a number of atoms and possibly of ether atoms bound with them1 and he concludes that such a molecule will behave in its progressive motion1 and in its collisions with other molecules1 nearly like a rigid body4 ,but to quote from ,mr4 ,bryan3 8,the case of a polyatomic molecule1 whose atoms are capable of vibrating relative to one another1 affords an interesting field for investigation and speculation4 ,is the ,boltzmann distribution still unique1 or do other permanent distributions exist in which the kinetic energy is unequally divided80 ,again1 the spectroscope reveals to us vibrations of the ether1 which are connected in some way with the vibrations of the molecules of gas1 whose spectrum we are observing4 ,it seems clear that the law of equal partition does not apply to these1 and yet1 if we are to suppose that the ether vibrations are due to actual vibrations of the atoms which constitute a molecule1 why does it not apply8 ,where does the condition come in which leads to failure in the proof8 ,or1 again1 is it1 as has been suggested1 the fact that the complex spectrum of a gas represents the terms of a ,fourier ,series1 into which some elaborate vibration of the atoms is resolved by the ether8 or is the spectrum due simply to electro-magnetic vibrations on the surface of the molecules--vibrations whose period is determined chiefly by the size and shape of the molecule1 but in which the atoms of which it is composed take part8 ,there are grave difficulties in the way of either of these explanations1 but we must not let our dread of the task which remains to be done blind our eyes to the greatness of ,maxwell's work4 ,one other important paper1 and a number of shorter articles1 remain to be mentioned4 ,the ,boltzmann-,maxwell law applies only to cases in which the temperature is uniform throughout4 ,in a paper published in the ,philosophical ,transactions for #ahgi1 on 8,stresses in ,rarefied ,gases ,arising from ,inequalities of ,temperature10 ,maxwell deals1 among other matters1 with the theory of the radiometer4 ,he shows that the observed motions will not take place unless gas1 in contact with a solid1 can slide along the surface of the solid with a finite velocity between places where the temperature is different2 and in an appendix he proves that1 on certain assumptions regarding the nature of the contact of the solid and the gas1 there will be1 even when the pressure is constant1 a flow of gas along the surface from the colder to the hotter parts4 ,among his less important papers bearing on molecular theory must be mentioned a lecture on 8,molecules0 to the ,british ,association at its ,bradford meeting2 8,scientific ,papers of ,clerk ,maxwell10 vol4 ii41 p4 #cfa2 and another on 8,the ,molecular ,constitution of ,bodies10 ,scientific ,papers1 vol4 ii41 p4 #dah4 ,in this latter1 and also in a review in ,nature of ,van der ,waals' book on 8,the ,continuity of the ,gaseous and ,liquid ,states10#ef he explains and discusses ,clausius' virial equation1 by means of which the variations of the permanent gases from ,boyle's law are explained4 ,the lecture gives a clear account1 in ,maxwell's own inimitable style1 of the advances made in the kinetic theory up to the date at which it was delivered1 and puts clearly the difficulties it has to meet4 ,maxwell thought that those arising from the known values of the ratio of the specific heats were the most serious4 ,in the articles1 8,atomic ,constitution of ,bodies0 and 8,diffusion10 in the ninth edition of the ,encyclopdia ,britannica1 we have ,maxwell's later views on the fundamental assumptions of the molecular theory4 ,the text-book on 8,heat0 contains some further developments of the theory4 ,in particular he shows how the conclusions of the second law of thermo-dynamics are connected with the fact that the coarseness of our faculties will not allow us to grapple with individual molecules4 ,the work described in the foregoing chapters would have been sufficient to secure to ,maxwell a distinguished place among those who have advanced our knowledge2 it remains still to describe his greatest work1 his theory of ,electricity and ,magnetism4 ,,chapter ,,ix4 ,,scientific ,,work4--,,electrical ,,theories4 ,clerk ,maxwell's first electrical paper--that on ,faraday's 8,lines of ,force0--was read to the ,cambridge ,philosophical ,society on ,december #ajth1 #ahee1 and ,part ,,ii4 on ,february #aath1 #ahef4 ,the author was then a ,bachelor of ,arts1 only twenty-three years in age1 and of less than one year's standing from the time of taking his degree4 ,the opening words of the paper are as follows 7,scientific ,papers1 vol4 i41 p4 #aee73-- 8,the present state of electrical science seems peculiarly unfavourable to speculation4 ,the laws of the distribution of electricity on the surface of conductors have been analytically deduced from experiment2 some parts of the mathematical theory of magnetism are established1 while in other parts the experimental data are wanting2 the theory of the conduction of galvanism1 and that of the mutual attraction of conductors1 have been reduced to mathematical formul1 but have not fallen into relation with the other parts of the science4 ,no electrical theory can now be put forth1 unless it shows the connection1 not only between electricity at rest and current electricity1 but between the attractions and inductive effects of electricity in both states4 ,such a theory must accurately satisfy those laws1 the mathematical form of which is known1 and must afford the means of calculating the effects in the limiting cases where the known formul are inapplicable4 ,in order1 therefore1 to appreciate the requirements of the science1 the student must make himself familiar with a considerable body of most intricate mathematics1 the mere retention of which in the memory materially interferes with further progress4 ,the first process1 therefore1 in the effectual study of the science1 must be one of simplification and reduction of the results of previous investigation to a form in which the mind can grasp them4 ,the results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis4 ,in the first case we entirely lose sight of the phenomena to be explained2 and though we may trace out the consequences of given laws1 we can never obtain more extended views of the connections of the subject4 ,if1 on the other hand1 we adopt a physical hypothesis1 we see the phenomena only through a medium1 and are liable to that blindness to facts and rashness in assumption which a partial explanation encourages4 ,we must therefore discover some method of investigation which allows the mind at every step to lay hold of a clear physical conception1 without being committed to any theory founded on the physical science from which that conception is borrowed1 so that it is neither drawn aside from the subject in pursuit of analytical subtleties1 nor carried beyond the truth by a favourite hypothesis4 8,in order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies4 ,by a physical analogy ,i mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other4 ,thus all the mathematical sciences are founded on relations between physical laws and laws of numbers1 so that the aim of exact science is to reduce the problems of ,nature to the determination of quantities by operations with members4 ,passing from the most universal of all analogies to a very partial one1 we find the same resemblance in mathematical form between two different phenomena giving rise to a physical theory of light4 8,the changes of direction which light undergoes in passing from one medium to another are identical with the deviations of the path of a particle in moving through a narrow space in which intense forces act4 ,this analogy1 which extends only to the direction1 and not to the velocity of motion1 was long believed to be the true explanation of the refraction of light2 and we still find it useful in the solution of certain problems1 in which we employ it without danger as an artificial method4 ,the other analogy1 between light and the vibrations of an elastic medium1 extends much farther1 but1 though its importance and fruitfulness cannot be over-estimated1 we must recollect that it is founded only on a resemblance in form between the laws of light and those of vibrations4 ,by stripping it of its physical dress and reducing it to a theory of #8transverse alternations1' we might obtain a system of truth strictly founded on observation1 but probably deficient both in the vividness of its conceptions and the fertility of its method4 ,i have said thus much on the disputed questions of optics1 as a preparation for the discussion of the almost universally admitted theory of attraction at a distance4 8,we have all acquired the mathematical conception of these attractions4 ,we can reason about them and determine their appropriate forms or formul4 ,these formul have a distinct mathematical significance1 and their results are found to be in accordance with natural phenomena4 ,there is no formula in applied mathematics more consistent with ,nature than the formula of attractions1 and no theory better established in the minds of men than that of the action of bodies on one another at a distance4 ,the laws of the conduction of heat in uniform media appear at first sight among the most different in their physical relations from those relating to attractions4 ,the quantities which enter into them are temperature1 flow of heat1 conductivity4 ,the word force is foreign to the subject4 ,yet we find that the mathematical laws of the uniform motion of heat in homogeneous media are identical in form with those of attractions varying inversely as the square of the distance4 ,we have only to substitute source of heat for centre of attraction1 flow of heat for accelerating effect of attraction at any point1 and temperature for potential1 and the solution of a problem in attractions is transformed into that of a problem in heat4 8,this analogy between the formul of heat and attraction was1 ,i believe1 first pointed out by ,professor ,william ,thomson in the ,cambridge ,mathematical ,journal1 ,vol4 ,,iii4 8,now the conduction of heat is supposed to proceed by an action between contiguous parts of a medium1 while the force of attraction is a relation between distant bodies1 and yet1 if we knew nothing more than is expressed in the mathematical formul1 there would be nothing to distinguish between the one set of phenomena and the other4 8,it is true that1 if we introduce other considerations and observe additional facts1 the two subjects will assume very different aspects1 but the mathematical resemblance of some of their laws will remain1 and may still be made useful in exciting appropriate mathematical ideas4 8,it is by the use of analogies of this kind that ,i have attempted to bring before the mind1 in a convenient and manageable form1 those mathematical ideas which are necessary to the study of the phenomena of electricity4 ,the methods are generally those suggested by the processes of reasoning which are found in the researches of ,faraday1 and which1 though they have been interpreted mathematically by ,professor ,thomson and others1 are very generally supposed to be of an indefinite and unmathematical character1 when compared with those employed by the professed mathematicians4 ,by the method which ,i adopt1 ,i hope to render it evident that ,i am not attempting to establish any physical theory of a science in which ,i have hardly made a single experiment1 and that the limit of my design is to show how1 by a strict application of the ideas and methods of ,faraday1 the connection of the very different orders of phenomena which he has discovered may be clearly placed before the mathematical mind4 ,i shall therefore avoid as much as ,i can the introduction of anything which does not serve as a direct illustration of ,faraday's methods1 or of the mathematical deductions which may be made from them4 ,in treating the simpler parts of the subject ,i shall use ,faraday's mathematical methods as well as his ideas4 ,when the complexity of the subject requires it1 ,i shall use analytical notation1 still confining myself to the development of ideas originated by the same philosopher4 8,i have in the first place to explain and illustrate the idea of #8lines of force4' 8,when a body is electrified in any manner1 a small body charged with positive electricity1 and placed in any given position1 will experience a force urging it in a certain direction4 ,if the small body be now negatively electrified1 it will be urged by an equal force in a direction exactly opposite4 8,the same relations hold between a magnetic body and the north or south poles of a small magnet4 ,if the north pole is urged in one direction1 the south pole is urged in the opposite direction4 8,in this way we might find a line passing through any point of space1 such that it represents the direction of the force acting on a positively electrified particle1 or on an elementary north pole1 and the reverse direction of the force on a negatively electrified particle or an elementary south pole4 ,since at every point of space such a direction may be found1 if we commence at any point and draw a line so that1 as we go along it1 its direction at any point shall always coincide with that of the resultant force at that point1 this curve will indicate the direction of that force for every point through which it passes1 and might be called on that account a line of force4 ,we might in the same way draw other lines of force1 till we had filled all space with curves indicating by their direction that of the force at any assigned point4 8,we should thus obtain a geometrical model of the physical phenomena1 which would tell us the direction of the force1 but we should still require some method of indicating the intensity of the force at any point4 ,if we consider these curves not as mere lines1 but as fine tubes of variable section carrying an incompressible fluid1 then1 since the velocity of the fluid is inversely as the section of the tube1 we may make the velocity vary according to any given law1 by regulating the section of the tube1 and in this way we might represent the intensity of the force as well as its direction by the motion of the fluid in these tubes4 ,this method of representing the intensity of a force by the velocity of an imaginary fluid in a tube is applicable to any conceivable system of forces1 but it is capable of great simplification in the case in which the forces are such as can be explained by the hypothesis of attractions varying inversely as the square of the distance1 such as those observed in electrical and magnetic phenomena4 ,in the case of a perfectly arbitrary system of forces1 there will generally be interstices between the tubes2 but in the case of electric and magnetic forces it is possible to arrange the tubes so as to leave no interstices4 ,the tubes will then be mere surfaces1 directing the motion of a fluid filling up the whole space4 ,it has been usual to commence the investigation of the laws of these forces by at once assuming that the phenomena are due to attractive or repulsive forces acting between certain points4 ,we may1 however1 obtain a different view of the subject1 and one more suited to our more difficult inquiries1 by adopting for the definition of the forces of which we treat1 that they may be represented in magnitude and direction by the uniform motion of an incompressible fluid4 8,i propose1 then1 first to describe a method by which the motion of such a fluid can be clearly conceived2 secondly to trace the consequences of assuming certain conditions of motion1 and to point out the application of the method to some of the less complicated phenomena of electricity1 magnetism1 and galvanism2 and lastly1 to show how by an extension of these methods1 and the introduction of another idea due to ,faraday1 the laws of the attractions and inductive actions of magnets and currents may be clearly conceived1 without making any assumptions as to the physical nature of electricity1 or adding anything to that which has been already proved by experiment4 8,by referring everything to the purely geometrical idea of the motion of an imaginary fluid1 ,i hope to attain generality and precision1 and to avoid the dangers arising from a premature theory professing to explain the cause of the phenomena4 ,if the results of mere speculation which ,i have collected are found to be of any use to experimental philosophers1 in arranging and interpreting their results1 they will have served their purpose1 and a mature theory1 in which physical facts will be physically explained1 will be formed by those who by interrogating ,nature herself can obtain the only true solution of the questions which the mathematical theory suggests40 ,the idea was a bold one3 for a youth of twenty-three to explain1 by means of the motions of an incompressible fluid1 some of the less complicated phenomena of electricity and magnetism1 to show how the laws of the attractions of magnets and currents may be clearly conceived without making any assumption as to the physical nature of electricity1 or adding anything to that which has already been proved by experiment4 ,it may be useful to review in a very few words the position of electrical theory#eg in #ahee4 ,coulomb's experiments had established the fundamental facts of electrostatic attraction and repulsion1 and ,coulomb himself1 about #aghe1 had stated a theory based on these experiments which could 8only be attacked by proving his experimental results to be inaccurate40#eh ,coulomb supposes the existence of two electric fluids1 the theory developed previously by ,franklin1 but says-- 8,je prviens pour mettre la thorie qui va suivre l'abri de toute dispute systmatique1 que dans la supposition de deux fluides lectriques1 je n'ai autre intention que de prsenter avec le moins d'lments possible les rsultats du calcul et de l'exprience1 et non d'indiquer les vritables causes de l'lectricit40 ,cavendish was working in ,england about the same time as ,coulomb1 but he published very little1 and the value and importance of his work was not recognised until the appearance in #ahgi of the 8,electrical ,researches of ,henry ,cavendish10 edited by ,clerk ,maxwell4 ,early in the present century the application of mathematical analysis to electrical problems was begun by ,laplace1 who investigated the distribution of electricity on spheroids1 and about #ahaa ,poisson's great work on the distribution of electricity on two spheres placed at any given distance apart was published4 ,meanwhile the properties of the electric current were being investigated4 ,galvani's discovery of the muscular contraction in a frog's leg1 caused by the contact of dissimilar metals1 was made in #agij4 ,volta invented the voltaic pile in #ahjj1 and ,oersted in #ahbj discovered that an electric current produced magnetic force in its neighbourhood4 ,on this ,ampre laid the foundation of his theory of electro-dynamics1 in which he showed how to calculate the forces between circuits carrying currents from an assumed law of force between each pair of elements of the circuits4 ,his experiments proved that the consequences which follow from this law are consistent with all the observed facts4 ,they do not prove that ,ampre's law alone can explain the facts4 ,maxwell1 writing on this subject in the 8,electricity an ,magnetism10 vol4 ii41 p4 #afb1 says-- 8,the experimental investigation by which ,ampre established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science4 8,the whole1 theory and experiment1 seems as if it had leaped full grown and full armed from the brain of the #8,newton of ,electricity4' ,it is perfect in form and unassailable in accuracy1 and it is summed up in a formula from which all the phenomena may be deduced1 and which must always remain the cardinal formula of electro-dynamics4 8,the method of ,ampre1 however1 though cast into an inductive form1 does not allow us to trace the formation of the ideas which guided it4 ,we can scarcely believe that ,ampre really discovered the law of action by means of the experiments which he describes4 ,we are led to suspect1 what1 indeed1 he tells us himself1 that he discovered the law by some process which he has not shown us1 and that when he had afterwards built up a perfect demonstration1 he removed all traces of the scaffolding by which he had built it40 ,the experimental evidence for ,ampre's theory1 so far1 at least1 as it was possible to obtain it from experiments on closed circuits1 was rendered unimpeachable by ,w4 ,weber about #ahdf1 while in the previous year ,grassman and ,f4 ,e4 ,neumann both published laws for the attraction between two elements of current which differ from that of ,ampre1 but lead to the same result for closed circuits4 ,in a paper published in #ahdf ,weber announced his hypothesis connecting together electrostatic and electro-dynamic action4 ,in this paper he supposed that the force between two particles of electricity depends on the motion of the particles as well as on their distance apart4 ,a somewhat similar theory was proposed by ,gauss and published after his death in his collected works4 ,it has been shown1 however1 that ,gauss' theory is inconsistent with the conservation of energy4 ,weber's theory avoids this inconsistency and leads1 for closed circuits1 to the same results as ,ampre4 ,it has been proved1 however1 by ,von ,helmholtz1 that1 under certain circumstances1 according to it1 a body would behave as though its mass were negative--it would move in a direction opposite to that of the force4#ei ,since #ahdf many other theories have been proposed to explain ,ampre's laws4 ,meanwhile1 in #ahba1 ,faraday observed that under certain circumstances a wire carrying a current could be kept in continuous rotation in a magnetic field by the action between the magnets and the current4 ,in #ahbd ,arago observed the motion of a magnet caused by rotating a copper disc in its neighbourhood1 while in #ahca ,faraday began his experimental researches into electro-magnetic induction4 ,about the same period ,joseph ,henry1 of ,washington1 was making1 independently of ,faraday1 experiments of fundamental importance on electro-magnetic induction1 but sufficient attention was not called to his work until comparatively recent years4 ,in #ahcc ,lenz made some important researches1 which led him to discover the connection between the direction of the induced currents and ,ampre's laws1 summed up in his rule that the direction of the induced current is always such as to oppose by its electro-magnetic action the motion which induces it4 ,in #ahde ,f4 ,e4 ,neumann developed from this law the mathematical theory of electro-magnetic induction1 and about the same time ,w4 ,weber showed how it might be deduced from his elementary law of electrical action4 ,the great name of ,von ,helmholtz first appears in connection with this subject in #ahea1 but of his writings we shall have more to say at a later stage4 ,meanwhile1 during the same period1 various writers1 ,murphy1 ,plana1 ,charles1 ,sturm1 and ,gauss1 extended ,poisson's work on electrostatics1 treating the questions which arose as problems in the distribution of an attracting fluid1 attracting or repelling according to ,newton's law1 though here again the greatest advances were made by a self-taught ,nottingham shoemaker1 ,george ,green by name1 in his paper 8,on the ,application of ,mathematical ,analysis to the ,theories of ,electricity and ,magnetism10 #ahbh4 ,green's researches1 ,lord ,kelvin writes1 8have led to the elementary proposition which must constitute the legitimate foundation of every perfect mathematical structure that is to be made from the materials furnished by the experimental laws of ,coulomb40 ,green1 it may be remarked1 was the inventor of the term ,potential4 ,his essay1 however1 lay neglected from #ahbh1 until ,lord ,kelvin called attention to it in #ahde4 ,meanwhile1 some of its most important results had been re-discovered by ,gauss and ,charles and ,thomson himself4 ,until about #ahde1 the experimental work on which these mathematical researches in electrostatics were based was that of ,coulomb4 ,an electrified body is supposed to have a charge of some imponderable fluid 8electricity40 ,particles of electricity repel each other according to a certain law1 and the fluid distributes itself in equilibrium over the surface of any charged conductor in accordance with this law4 ,there are on this theory two opposite kinds of electric fluid1 positive and negative1 two charges of the same kind repel1 two charges of opposite kinds attract2 the repulsion or attraction is proportional to the product of the charges1 and inversely proportional to the square of the distance between them4 ,the action between two charges is action at a distance taking place across the space which separates the two4 ,faraday1 in #ahcg1 in the eleventh series of his 8,experimental ,researches10 published his first paper on 8,electrostatic ,induction40 ,he showed--as indeed ,cavendish had proved long previously1 though the result remained unpublished--that the force between two charged bodies will depend on the insulating medium which surrounds them1 not merely on their shape and position4 ,induction1 as he expresses it1 takes place along curved lines1 and is an action of contiguous particles2 these curved lines he calls the 8lines of force40 ,discussing these researches in #ahde1 ,lord ,kelvin writes#fj3-- 8,mr4 ,faraday's researches 444 were undertaken with a view to test an idea which he had long possessed that the forces of attraction and repulsion exercised by free electricity are not the resultants of actions exercised at a distance1 but are propagated by means of molecular action among the contiguous particles of the insulating medium surrounding the electrified bodies1 which he therefore calls the dielectric4 ,by this idea he has been led to some very remarkable views upon induction1 or1 in fact1 upon electrical action in general4 ,as it is impossible that the phenomena observed by ,faraday can be incompatible with the results of experiment which constitute ,coulomb's theory1 it is to be expected that the difference of his ideas from those of ,coulomb must arise solely from a different method of stating and interpreting physically the same laws2 and further1 it may1 ,i think1 be shown that either method of viewing this subject1 when carried sufficiently far1 may be made the foundation of a mathematical theory which would lead to the elementary principles of the other as consequences4 ,this theory would1 accordingly1 be the expression of the ultimate law of the phenomena1 independently of any physical hypothesis we might from other circumstances be led to adopt4 ,that there are necessarily two distinct elementary ways of viewing the theory of electricity may be seen from the following considerations44440 ,in the pages which follow1 ,lord ,kelvin develops the consequences of an analogy between the conduction of heat and electrostatic action1 which he had pointed out three years earlier 7#ahdb71 in his paper on 8,the ,uniform ,motion of ,heat in ,homogeneous ,solid ,bodies10 and discusses its connection with the mathematical theory of electricity4 ,the problem of distributing sources of heat in a given homogeneous conductor of heat1 so as to produce a definite steady temperature at each point on the conductor is shewn to be mathematically identical with that of distributing electricity in equilibrium1 so as to produce at each point an electrical potential having the same value as the temperature4 ,thus the fundamental laws of the conduction of heat may be made the basis of the mathematical theory of electricity1 but the physical idea which they suggest is that of the propagation of some effect by means of the mutual action of contiguous particles1 rather than that of material particles attracting or repelling at a distance1 which naturally follows from the statement of ,coulomb's law4 ,lord ,kelvin continues3-- 8,all the views which ,faraday has brought forward and illustrated1 as demonstrated by experiment1 lead to this method of establishing the mathematical theory1 and1 as far as the analysis is concerned1 it would in most general propositions be more simple1 if possible1 than that of ,coulomb4 ,of course the analysis of particular problems would be identical in the two methods4 ,it is thus that ,faraday arrives at a knowledge of some of the most important of the mathematical theorems which from their nature seemed destined never to be perceived except as mathematical truths40 ,lord ,kelvin's papers on 8,the ,mathematical ,theory of ,electricity10 published from #ahdh to #ahej1 his 8,propositions on the ,theory of ,attraction0 7#ahdb71 his 8,theory of ,electrical ,images0 7#ahdg71 and his paper on 8,the ,mathematical ,theory of ,magnetism0 7#ahdi71 contain a statement of the most important results achieved in the mathematical sciences of ,electrostatics and ,magnetism up to the time of ,maxwell's first paper4 ,the opening sentences of that paper have already been quoted4 ,in the preface to the 8,electricity and ,magnetism0 ,maxwell writes thus3-- 8,before ,i began the study of electricity ,i resolved to read no mathematics on the subject till ,i had first read through #8,experimental ,researches on ,electricity4' ,i was aware that there was supposed to be a difference between ,faraday's way of conceiving phenomena and that of the mathematicians1 so that neither he nor they were satisfied with each other's language4 ,i had also the conviction that this discrepancy did not arise from either party being wrong4 ,i was first convinced of this by ,sir ,william ,thomson1 to whose advice and assistance1 as well as to his published papers1 ,i owe most of what ,i have learned on the subject4 8,as ,i proceeded with the study of ,faraday1 ,i perceived that his method of conceiving the phenomena was also a mathematical one1 though not exhibited in the conventional form of mathematical symbols4 ,i also found that these methods were capable of being expressed in the ordinary mathematical forms1 and thus compared with those of the professed mathematicians4 8,for instance1 ,faraday1 in his mind's eye1 saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance4 ,faraday saw a medium where they saw nothing but distance4 ,faraday sought the seat of the phenomena in real actions going on in the medium4 ,they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids40 ,now1 ,maxwell saw an analogy between electrostatics and the steady motion of an incompressible fluid like water1 and it is this analogy which he develops in the first part of his paper4 ,the water flows along definite lines2 a surface which consists wholly of such lines of flow will have the property that no water ever crosses it4 ,in any stream of water we can imagine a number of such surfaces drawn1 dividing it up into a series of tubes2 each of these will be a tube of flow1 each of these tubes remain always filled with water4 ,hence1 the quantity of water which crosses per second any section of a tube of flow perpendicular to its length is always the same4 ,thus1 from the form of the tube1 we can obtain information as to the direction and strength of the flow1 for where the tube is wide the flow will be proportionately small1 and vice vers4 ,again1 we can draw in the fluid a number of surfaces1 over each of which the pressure is the same2 these surfaces will cut the tubes of flow at right angles4 ,let us suppose they are drawn so that the difference of pressure between any two consecutive surfaces is unity1 then the surfaces will be close together at points at which the pressure changes rapidly2 where the variation of pressure is slow1 the distance between two consecutive surfaces will be considerable4 ,if1 then1 in any case of motion1 we can draw the pressure surfaces1 and the tubes of flow1 we can determine the motion of the fluid completely4 ,now1 the same mathematical expressions which appear in the hydro-dynamical theory occur also in the theory of electricity1 the meaning only of the symbols is changed4 ,for velocity of fluid we have to write electrical force4 ,for difference of fluid pressure we substitute work done1 or difference of electrical potential or pressure4 ,the surfaces and tubes1 drawn as the solution of any hydro-dynamical problem1 give us also the solution of an electrical problem2 the tubes of flow are ,faraday's tubes of force1 or tubes of induction1 the surfaces of constant pressure are surfaces of equal electrical potential4 ,induction may take place in curved lines just as the tubes of flow may be bent and curved2 the analogy between the two is a complete one4 ,but1 as ,maxwell shows1 the analogy reaches further still4 ,an electric current flowing along a wire had been recognised as having many properties similar to those of a current of liquid in a tube4 ,when a steady current is passing through any solid conductor1 there are formed in the conductor tubes of electrical flow and surfaces of constant pressure4 ,these tubes and surfaces are the same as those formed by the flow of liquid through a solid whose boundary surface is the same as that of the conductor1 provided the flow of liquid is properly proportioned to the flow of electricity4 ,these analogies refer to steady currents in which1 therefore1 the flow at any point of the conductor does not depend on the time4 ,in ,part ,,ii4 of his paper ,maxwell deals with ,faraday's electro-tonic state4 ,faraday had found that when changes are produced in the magnetic phenomena surrounding a conductor1 an electric current is set up in the conductor1 which continues so long as the magnetic changes are in progress1 but which ceases when the magnetic state becomes steady4 8,considerations of this kind led ,professor ,faraday to connect with his discovery of the induction of electric currents the conception of a state into which all bodies are thrown by the presence of magnets and currents4 ,this state does not manifest itself by any known phenomena as long as it is undisturbed1 but any change in this state is indicated by a current or tendency towards a current4 ,to this state he gave the name of the #8,electro-tonic ,state1' and although he afterwards succeeded in explaining the phenomena which suggested it by means of less hypothetical conceptions1 he has on several occasions hinted at the probability that some phenomena might be discovered which would render the electro-tonic state an object of legitimate induction4 ,these speculations1 into which ,faraday had been led by the study of laws which he has well established1 and which he abandoned only for want of experimental data for the direct proof of the unknown state1 have not1 ,i think1 been made the subject of mathematical investigation4 ,perhaps it may be thought that the quantitative determinations of the various phenomena are not sufficiently rigorous to be made the basis of a mathematical theory4 ,faraday1 however1 has not contented himself with simply stating the numerical results of his experiments and leaving the law to be discovered by calculation4 ,where he has perceived a law he has at once stated it1 in terms as unambiguous as those of pure mathematics1 and if the mathematician1 receiving this as a physical truth1 deduces from it other laws capable of being tested by experiment1 he has merely assisted the physicist in arranging his own ideas1 which is confessedly a necessary step in scientific induction4 8,in the following investigation1 therefore1 the laws established by ,faraday will be assumed as true1 and it will be shown that by following out his speculations other and more general laws can be deduced from them4 ,if it should1 then1 appear that these laws1 originally devised to include one set of phenomena1 may be generalised so as to extend to phenomena of a different class1 these mathematical connections may suggest to physicists the means of establishing physical connections1 and thus mere speculation may be turned to account in experimental science40 ,maxwell shows how to obtain a mathematical expression for ,faraday's electro-tonic state4 ,in his 8,electricity and ,magnetism10 this electro-tonic state receives a new name4 ,it is known as the ,vector ,potential1#fa and the paper under consideration contains1 though in an incomplete form1 his first statement of those equations of the electric field which are so indissolubly bound up with ,maxwell's name4 ,the great advance in theory made in the paper is the distinct recognition of certain mathematical functions as representing ,faraday's electrotonic-state1 and their use in solving electro-magnetic problems4 ,the paper contains no new physical theory of electricity1 but in a few years one appeared4 ,in his later writings ,maxwell adopted a more general view of the electro-magnetic field than that contained in his early papers on 8,physical ,lines of ,force40 ,it must1 therefore1 not be supposed that the somewhat gross conception of cog-wheels and pulleys1 which we are about to describe1 were anything more to their author than a model1 which enabled him to realise how the changes1 which occur when a current of electricity passes through a wire1 might be represented by the motion of actual material particles4 ,the problem before him was to devise a physical theory of electricity1 which would explain the forces exerted on electrified bodies by means of action between the contiguous parts of the medium in the space surrounding these bodies1 rather than by direct action across the distance which separates them4 ,a similar question1 still unanswered1 had arisen in the case of gravitation4 ,astronomers have determined the forces between attracting bodies2 they do not know how those forces arise4 ,maxwell's fondness for models has already been alluded to2 it had led him to construct his top to illustrate the dynamics of a rigid body rotating about a fixed point1 and his model of ,saturn's rings 7now in the ,cavendish ,laboratory7 to illustrate the motion of the satellites in the rings4 ,he had explained many of the gaseous laws by means of the impact of molecules1 and now his fertile ingenuity was to imagine a mechanical model of the state of the electro-magnetic field near a system of conductors carrying currents4 ,faraday1 as we have seen1 looked upon electrostatic and magnetic induction as taking place along curved lines of force4 ,he pictures these lines as ropes of molecules starting from a charged conductor1 or a magnet1 as the case may be1 and acting on other bodies near4 ,these ropes of molecules tend to shorten1 and at the same time to swell outwards laterally4 ,thus the charged conductor tends to draw other bodies to itself1 there is a tension along the lines of force1 while at the same time each tube of molecules pushes its neighbours aside2 a pressure at right angles to the lines of force is combined with this tension4 ,assuming for a moment this pressure and tension to exist1 can we devise a mechanism to account for it8 ,maxwell himself has likened the lines of force to the fibres of a muscle4 ,as the fibres contract1 causing the limb to which they are attached to move1 they swell outwards1 and the muscle thickens4 ,again1 from another point of view1 we might consider a line of force as consisting of a string of small cells of some flexible material each filled with fluid4 ,if we then suppose this series of cells caused to rotate rapidly about the direction of the line of force1 the cells will expand laterally and contract longitudinally2 there will again be tension along the lines of force and pressure at right angles to them4 ,it was this last idea1 as we shall see shortly1 of which ,maxwell made use-- 8,i propose now0 he writes 78,on ,physical ,lines of ,force10 ,phil4 ,mag41 vol4 xxi47 8to examine magnetic phenomena from a mechanical point of view1 and to determine what tensions in1 or motions of1 a medium are capable of producing the mechanical phenomena observed4 ,if by the same hypothesis we can connect the phenomena of magnetic attraction with electro-magnetic phenomena1 and with those of induced currents1 we shall have found a theory which1 if not true1 can only be proved to be erroneous by experiments1 which will greatly enlarge our knowledge of this part of physics40 ,lord ,kelvin had in #ahdg given a mechanical representation of electric1 magnetic and galvanic forces by means of the displacements of an elastic solid in a state of strain4 ,the angular displacement at each point of the solid was taken as proportional to the magnetic force1 and from this the relation between the various other electric quantities and the motion of the solid was developed4 ,but ,lord ,kelvin did not attempt to explain the origin of the observed forces by the effects due to these strains1 but merely made use of the mathematical analogy to assist the imagination in the study of both4 ,maxwell considered magnetic action as existing in the form of pressure or tension1 or more generally1 of some stress in some medium4 ,the existence of a medium capable of exerting force on material bodies and of withstanding considerable stress1 both pressure and tension1 is thus a fundamental hypothesis with him2 this medium is to be capable of motion1 and electro-magnetic forces arise from its motion and its stresses4 ,now1 ,maxwell's fundamental supposition is that1 in a magnetic field1 there is a rotation of the molecules continually in progress about the lines of magnetic force4 ,consider now the case of a uniform magnetic field1 whose direction is perpendicular to the paper2 we are to look upon the lines of force as parallel strings of molecules1 the axes of these strings being perpendicular to the paper4 ,each string is supposed to be rotating in the same direction about its axis1 and the angular velocity of rotation is a measure of the magnetic force4 ,in consequence of this rotation there will be differences of pressure in different directions in the medium2 the pressure along the axes of the strings will be less than it would be if the medium were at rest1 that in the directions at right angles to the axes will be greater1 the medium will behave as though it were under tension along the axes of the molecules under pressure at right angles to them4 ,moreover1 it can be shown that the pressure and the tension are both proportional to the square of the angular velocity--the square1 that is1 of the magnetic force--and this result is in accordance with the consequences of experiment4 ,more elaborate calculation shows that this statement is true generally4 ,if we draw the lines of force in any magnetic field1 and then suppose the molecules of the medium set in rotation about these lines of force as axes1 with velocities which at each point are proportional to the magnetic force1 the distribution of pressure throughout is that which we know actually to exist in the magnetic field4 ,according to this hypothesis1 then1 a permanent bar magnet has the power of setting the medium round it into continuous molecular rotation about the lines of force as axes4 ,the molecules which are set in rotation we may consider as spherical1 or nearly spherical1 cells filled with a fluid1 or an elastic solid substance1 and surrounded by a kind of membrane1 or sack1 holding the contents together4 ,so far the model does not give any account of electrical actions which go on in the magnetic field4 ,the energy is wholly rotational1 and the forces wholly magnetic4 ,consider1 however1 any two contiguous strings of molecules4 ,let them cut the paper as shown in the two circles in ,fig4 #a3-- ,illustration3 ,fig4 #a4 ,fig4 #b4 ,then these cells are both rotating in the same direction1 hence at ,c1 where they touch1 their points of contact will be moving in opposite directions1 as shown by the arrow heads1 and it is difficult to imagine how such motion can continue2 it would require the surfaces of the cells to be perfectly smooth1 and if this were so they would lose the power of transmitting action from one cell to the next4 ,the cells ,a and ,b may be compared to two cog-wheels placed close together1 which we wish to turn in the same direction4 ,if the cogs can interlock1 as in ,fig4 #b1 this is impossible3 consecutive wheels in the train must move in opposite directions4 ,illustration3 ,fig4 #c4 ,but in many machines the desired end is attained by inserting between the two wheels ,a and ,b a third idle wheel ,c1 as shewn in ,fig4 #c4 ,this may be very small1 its only function is to transmit the motion of ,a to ,b in such a way that ,a and ,b may both turn in the same direction4 ,it is not necessary that there should be cogs on the wheels2 if the surfaces be perfectly rough1 so that no slipping can take place1 the same result follows without the cogs4 ,guided by this analogy ,maxwell extended his model by supposing each cell coated with a number of small particles which roll on its surface4 ,these particles play the part of the idle wheels in the machine1 and by their rolling merely enable the adjacent parts of two cells to move in opposite directions4 ,consider now a number of such cells and their idle wheels lying in a plane1 that of the paper1 and suppose each cell is rotating with the same uniform angular velocity about an axis at right angles to that plane1 each idle wheel will be acted on by two equal and opposite forces at the ends of the diameter in which it is touched by the adjacent cells2 it will therefore be set in rotation1 but there will be no force tending to drive it onwards2 it does not matter whether the axis on which it rotates is free to move or fixed1 in either case the idle wheel simply rotates4 ,but suppose now the adjacent cells are not rotating at the same rate4 ,in addition to its rotation the idle wheel will be urged onward with a velocity which depends on the difference between the rotations1 and1 if it can move freely1 it will move on from between the two cells4 ,imagine now that the interstices between the cells are fitted with a string of idle wheels4 ,so long as the adjacent cells move with different velocity there will be a continual stream of rolling particles or idle wheels between them4 ,maxwell in the paper considered these rolling particles to be particles of electricity4 ,their motion constitutes an electric current4 ,in a uniform magnetic field there is no electric current2 if the strength of the field varies1 the idle wheels are set in motion and there may be a current4 ,these particles are very small compared with the magnetic vortices4 ,the mass of all the particles is inappreciable compared with the mass of the vortices1 and a great many vortices with their surrounding particles are contained in a molecule of the medium2 the particles roll on the vortices without touching each other1 so that so long as they remain within the same molecule there is no loss of energy by resistance4 ,when1 however1 there is a current or general transference of particles in one direction they must pass from one molecule to another1 and in doing so may experience resistance and generate heat4 ,maxwell states that the conception of a particle1 having its motion connected with that of a vortex by perfect rolling contact1 may appear somewhat awkward4 8,i do not bring it forward10 he writes1 8as a mode of connection existing in ,nature1 or even as that which ,i would willingly assent to as an electrical hypothesis4 ,it is1 however1 a mode of connection which is mechanically conceivable and easily investigated1 and it serves to bring out the actual mechanical connections between the known electro-magnetic phenomena1 so that ,i venture to say that anyone who understands the provisional and temporary character of this hypothesis will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena40 ,the first part of the paper deals with the theory of magnetism2 in the second part the hypothesis is applied to the phenomena of electric currents1 and it is shown how the known laws of steady currents and of electro-magnetic induction can be deduced from it4 ,in ,part ,,iii41 published ,january and ,february1 #ahfb1 the theory of molecular vortices is applied to statical electricity4 ,the distinction between a conductor and an insulator or dielectric is supposed to be that in the former the particles of electricity can pass with more or less freedom from molecule to molecule4 ,in the latter such transference is impossible1 the particles can only be displaced within the molecule with which they are connected2 the cells or vortices of the medium are supposed to be elastic1 and to resist by their elasticity the displacement of the particles within them4 ,when electrical force acts on the medium this displacement of the particles within each molecule takes place until the stresses due to the elastic reaction of the vortices balance the electrical force2 the medium behaves like an elastic body yielding to pressure until the pressure is balanced by the elastic stress4 ,when the electric force is removed the cells or vortices recover their form1 the electricity returns to its former position4 ,in a medium such as this waves of periodic displacement could be set up1 and would travel with a velocity depending on its electric properties4 ,the value for this velocity can be obtained from electrical observations1 and ,maxwell showed that this velocity1 so found1 was1 within the limits of experimental error1 the same as that of light4 ,moreover1 the electrical oscillations take place1 like those of light1 in the front of the wave4 ,hence1 he concludes1 8the elasticity of the magnetic medium in air is the same as that of the luminiferous medium1 if these two coexistent1 coextensive1 and equally elastic media are not rather one medium40 ,the paper thus contains the first germs of the electro-magnetic theory of light4 ,moreover1 it is shown that the attraction between two small bodies charged with given quantities of electricity depends on the medium in which they are placed1 while the specific inductive capacity is found to be proportional to the square of the refractive index4 ,the fourth and final part of the paper investigates the propagation of light in a magnetic field4 ,faraday had shown that the direction of vibration in a wave of polarised light travelling parallel to the lines of force in a magnetic field is rotated by its passage through the field4 ,the numerical laws of this relation had been investigated by ,verdet1 and ,maxwell showed how his hypothesis of molecular vortices led to laws which agree in the main with those found by ,verdet4 ,he points out that the connection between magnetism and electricity has the same mathematical form as that between certain other pairs of phenomena1 one of which has a linear and the other a rotatory character2 and1 further1 that an analogy may be worked out assuming either the linear character for magnetism and the rotatory character for electricity1 or the reverse4 ,he alludes to ,prof4 ,challis' theory1 according to which magnetism is to consist in currents in a fluid whose directions correspond with the lines of magnetic force1 while electric currents are supposed to be accompanied by1 if not dependent upon1 a rotatory motion of the fluid about the axis of the current2 and to ,von ,helmholtz's theory of a somewhat similar character4 ,he then gives his own reasons--agreeing with those of ,sir ,w4 ,thomson 7,lord ,kelvin7--for supposing that there must be a real rotation going on in a magnetic field in order to account for the rotation of the plane of polarisation1 and1 accepting these reasons as valid1 he develops the consequences of his theory with the results stated above4 ,his own verdict on the theory is given in the 8,electricity and ,magnetism0 7vol4 ii41 #hca1 first edition1 p4 #daf73-- 8,a theory of molecular vortices1 which ,i worked out at considerable length1 was published in the ,phil4 ,mag4 for ,march1 ,april1 and ,may1 #ahfa2 ,jan4 and ,feb41 #ahfb4 8,i think we have good evidence for the opinion that some phenomenon of rotation is going on in the magnetic field1 that this rotation is performed by a great number of very small portions of matter1 each rotating on its own axis1 this axis being parallel to the direction of the magnetic force1 and that the rotations of these different vortices are made to depend on one another by means of some kind of mechanism connecting them4 8,the attempt which ,i then made to imagine a working model of this mechanism must be taken for no more than it really is1 a demonstration that mechanism may be imagined capable of producing a connection mechanically equivalent to the actual connection of the parts of the electro-magnetic field4 ,the problem of determining the mechanism required to establish a given species of connection between the motions of the parts of a system always admits of an infinite number of solutions4 ,of these1 some may be more clumsy or more complex than others1 but all must satisfy the conditions of mechanism in general4 8,the following results of the theory1 however1 are of higher value3-- 87#a7 ,magnetic force is the effect of the centrifugal force of the vortices4 87#b7 ,electro-magnetic induction of currents is the effect of the forces called into play when the velocity of the vortices is changing4 87#c7 ,electromotive force arises from the stress on the connecting mechanism4 87#d7 ,electric displacement arises from the elastic yielding of the connecting mechanism40 ,in studying this part of ,maxwell's work1 it must clearly be remembered that he did not look upon the ether as a series of cog-wheels with idle wheels between1 or anything of the kind4 ,he devised a mechanical model of such cogs and idle wheels1 the properties of which would in some respects closely resemble those of the ether2 from this model he deduced1 among other things1 the important fact that electric waves would travel outwards with the velocity of light4 ,other such models have been devised since his time to illustrate the same laws4 ,prof4 ,fitzgerald has actually constructed one of wheels connected together by elastic bands1 which shows clearly the kind of processes which ,maxwell supposed to go on in a dielectric when under electric force4 ,professor ,lodge1 in his book1 8,modern ,views of ,electricity10 has very fully developed a somewhat different arrangement of cog-wheels to attain the same result4 ,maxwell's predictions as to the propagation of electric waves have in recent days received their full verification in the brilliant experiments of ,hertz and his followers2 it remains for us1 before dealing with these1 to trace their final development in his hands4 ,the papers we have been discussing were perhaps too material to receive the full attention they deserved2 the ether is not a series of cogs1 and electricity is something different from material idle wheels4 ,in his paper on 8,the ,dynamical ,theory of the ,electro-magnetic ,field10 ,phil4 ,trans41 #ahfd1 ,maxwell treats the same questions in a more general manner4 ,on a former occasion he says1 8,i have attempted to describe a particular kind of motion and a particular kind of strain so arranged as to account for the phenomena4 ,in the present paper ,i avoid any hypothesis of this kind2 and in using such words as electric momentum and electric elasticity in reference to the known phenomena of the induction of currents and the polarisation of dielectrics1 ,i wish merely to direct the mind of the reader to mechanical phenomena1 which will assist him in understanding the electrical ones4 ,all such phrases in the present paper are to be considered as illustrative and not as explanatory40 ,he then continues3-- 8,in speaking of the energy of the field1 however1 ,i wish to be understood literally4 ,all energy is the same as mechanical energy1 whether it exists in the form of motion or in that of elasticity1 or in any other form4 8,the energy in electro-magnetic phenomena is mechanical energy4 ,the only question is1 ,where does it reside8 8,on the old theories it resides in the electrified bodies1 conducting circuits1 and magnets1 in the form of an unknown quality called potential energy1 or the power of producing certain effects at a distance4 ,on our theory it resides in the electro-magnetic field1 in the space surrounding the electrified and magnetic bodies1 as well as in those bodies themselves1 and is in two different forms1 which may be described without hypothesis as magnetic polarisation and electric polarisation1 or1 according to a very probable hypothesis1 as the motion and the strain of one and the same medium4 8,the conclusions arrived at in the present paper are independent of this hypothesis1 being deduced from experimental facts of three kinds3-- 87#a7 ,the induction of electric currents by the increase or diminution of neighbouring currents according to the changes in the lines of force passing through the circuit4 87#b7 ,the distribution of magnetic intensity according to the variations of a magnetic potential4 87#c7 ,the induction 7or influence7 of statical electricity through dielectrics4 8,we may now proceed to demonstrate from these principles the existence and laws of the mechanical forces1 which act upon electric currents1 magnets1 and electrified bodies placed in the electro-magnetic field40 ,in his introduction to the paper1 he discusses in a general way the various explanations of electric phenomena which had been given1 and points out that-- 8,it appears1 therefore1 that certain phenomena in electricity and magnetism lead to the same conclusion as those of optics1 namely1 that there is an therial medium pervading all bodies1 and modified only in degree by their presence2 that the parts of this medium are capable of being set in motion by electric currents and magnets2 that this motion is communicated from one part of the medium to another by forces arising from the connection of those parts2 that under the action of these forces there is a certain yielding depending on the elasticity of these connections2 and that1 therefore1 energy in two different forms may exist in the medium1 the one form being the actual energy of motion of its parts1 and the other being the potential energy stored up in the connections in virtue of their elasticity4 8,thus1 then1 we are led to the conception of a complicated mechanism capable of a vast variety of motion1 but at the same time so connected that the motion of one part depends1 according to definite relations1 on the motion of other parts1 these motions being communicated by forces arising from the relative displacement of the connected parts1 in virtue of their elasticity4 ,such a mechanism must be subject to the general laws of dynamics1 and we ought to be able to work out all the consequences of its motion1 provided we know the form of the relation between the motions of the parts40 ,these general laws of dynamics1 applicable to the motion of any connected system1 had been developed by ,lagrange1 and are expressed in his generalised equations of motion4 ,it is one of ,maxwell's chief claims to fame that he saw in the electric field a connected system to which ,lagrange's equations could be applied1 and that he was able to deduce the mechanical and electrical actions which take place by means of fundamental propositions of dynamics4 ,the methods of the paper now under discussion were developed further in the 8,treatise on ,electricity and ,magnetism10 published in #ahgc2 in endeavouring to give some slight account of ,maxwell's work1 we shall describe it in the form it ultimately took4 ,the task which ,maxwell set himself was a double one2 he had first to express in symbols1 in as general a form as possible1 the fundamental laws of electro-magnetism as deduced from experiments1 chiefly the experiments of ,faraday1 and the relations between the various quantities involved2 when this was done he had to show how these laws could be deduced from the general dynamical laws applicable to any system of moving bodies4 ,there are two classes of phenomena1 electric and magnetic1 which have been known from very early times1 and which are connected together4 ,when a piece of sealing-wax is rubbed it is found to attract other bodies1 it is said to exert electric force throughout the space surrounding it2 when two different metals are dipped in slightly acidulated water and connected by a wire1 certain changes take place in the plates1 the water1 the wire1 and the space round the wire1 electric force is again exerted and a current of electricity is said to flow in the wire4 ,again1 certain bodies1 such as the lodestone1 or pieces of iron and steel which have been treated in a certain manner1 exhibit phenomena of action at a distance3 they are said to exert magnetic force1 and it is found that this magnetic force exists in the neighbourhood of an electric current and is connected with the current4 ,again1 when electric force is applied to a body1 the effects may be in part electrical1 in part mechanical2 the electrical state of the body is in general changed1 while in addition1 mechanical forces tending to move the body are set up4 ,experiment must teach us how the electrical state depends on the electric force1 and what is the connection between this electric force and the magnetic forces which may1 under certain circumstances1 be observed4 ,now1 in specifying the electric and magnetic conditions of the system1 various other quantities1 in addition to the electric force1 will have to be introduced2 the first step is to formulate the necessary quantities1 and to determine the relations between them and the electric force4 ,consider now a wire connecting the two poles of an electric battery--in its simplest form1 a piece of zinc and a piece of copper in a vessel of dilute acid--electric force is produced at each point of the wire4 ,let us suppose this force known2 an electric current depending on the material and the size of the wire flows along it1 its value can be determined at each point of the wire in terms of the electric force by ,ohm's law4 ,if we take either this current or the electric force as known1 we can determine by known laws the electric and magnetic conditions elsewhere4 ,if we suppose the wire to be straight and very long1 then1 so long as the current is steady and we neglect the small effect due to the electrostatic charge on the wire1 there is no electric force outside the wire4 ,there is1 however1 magnetic force1 and it is found that the lines of magnetic force are circles round the wire4 ,it is found also that the work done in travelling once completely round the wire against the magnetic force is measured by the current flowing through the wire1 and is obtained in the system of units usually adopted by multiplying the current by #d4 ,this last result then gives us one of the necessary relations1 that between the magnetic force due to a current and the strength of the current4 ,again1 consider a steady current flowing in a conductor of any form or shape1 the total flow of current across any section of the conductor can be measured in various ways1 and it is found that at any time this total flow is the same for each section of the conductor4 ,in this respect the flow of a current resembles that of an incompressible fluid through a pipe2 where the pipe is narrow the velocity of flow is greater than it is where the pipe is broad1 but the total quantity crossing each section at any given instant is the same4 ,consider now two conducting bodies1 two spheres1 or two flat plates placed near together but insulated4 ,let each conductor be connected to one of the poles of the battery by a conducting wire4 ,then1 for a very short interval after the contact is made1 it is found that there is a current in each wire which rapidly dies away to zero4 ,in the neighbourhood of the balls there is electric force2 the balls are said to be charged with electricity1 and the lines of force are curved lines running from one ball to the other4 ,it is found that the balls slightly attract each other1 and the space between them is now in a different condition from what it was before the balls were charged4 ,according to ,maxwell1 ,electric ,displacement has been produced in this space1 and the electric displacement at each point is proportional to the electric force at that point4 ,thus1 7i7 when electric force acts on a conductor1 it produces a current1 the current being by ,ohm's law proportional to the force3 7ii7 when it acts on an insulator it produces electric displacement1 and the displacement is proportional to the force2 while 7iii7 there is magnetic force in the neighbourhood of the current1 and the work done in carrying a magnetic pole round any complete circuit linked with the current is proportional to the current4 ,the first two of these principles give us two sets of equations connecting together the electric force and the current in a conductor or the displacement in a dielectric respectively2 the third connects the magnetic force and the current4 ,now let us go back to the variable period when the current is flowing in the wires2 and to make ideas precise1 let the two conductors be two equal large flat plates placed with their faces parallel1 and at some small distance apart4 ,in this case1 when the plates are charged1 and the current has ceased1 the electric displacement and the force are confined almost entirely to the space between the plates4 ,during the variable period the total flow at any instant across each section of the wire is the same1 but in the ordinary sense of the word there is no flow of electricity across the insulating medium between the plates4 ,in this space1 however1 the electric displacement is continuously changing1 rising from zero initially to its final steady value when the current ceases4 ,it is a fundamental part of ,maxwell's theory that this variation of electric displacement is equivalent in all respects to a current4 ,the current at any point in a dielectric is measured by the rate of change of displacement at that point4 ,moreover1 it is also an essential point that if we consider any section of the dielectric between the two plates1 the rate of change of the total displacement across this section is at each moment equal to the total flow of current across each section of the conducting wire4 ,currents of electricity1 therefore1 including displacement currents1 always flow in closed circuits1 and obey the laws of an incompressible fluid in that the total flow across each section of the circuit--conducting or dielectric--is at any moment the same4 ,it should be clearly remembered that this fundamental hypothesis of ,maxwell's theory is an assumption only to be justified by experiment4 ,von ,helmholtz1 in his paper on 8,the ,equations of ,motion of ,electricity for ,bodies at ,rest10 formed his equations in an entirely different manner from ,maxwell1 and arrived at results of a more general character1 which do not require us to suppose that currents flow always in closed circuits1 but permit of the condensation of electricity at points in the circuit where the conductors end and the non-conducting part of the circuit begins4 ,we leave for the present the question which of the two theories1 if either1 represents the facts4 ,we have obtained above three fundamental relations--7i7 that between electric force and electric current in a conductor2 7ii7 that between electric force and electric displacement in a dielectric2 7iii7 that between magnetic force and the current which gives rise to it4 ,and we have seen that an electric current--i4e4 in a dielectric the variation of the strength of an electric field of force--gives rise to magnetic force4 ,now1 magnetic force acting on a medium produces 8magnetic displacement10 or magnetic induction1 as it is called4 ,in all media except iron1 nickel1 cobalt1 and a few other substances1 the magnetic induction is proportional to the magnetic force1 and the ratio between the magnetic induction produced by a given force and the force is found to be very nearly the same for all such media4 ,this ratio is known as the permeability1 and is generally denoted by the symbol 4 ,a relation reciprocal to that given in 7iii7 above might be anticipated1 and was1 in fact1 discovered by ,faraday4 ,changes in a field of magnetic induction give rise to electric force1 and hence to displacement currents in a dielectric or to conduction currents in a conductor4 ,in considering the relation between these changes and the electric force1 it is simplest at first not to deal with magnetic matter such as iron1 nickel1 or cobalt2 and then we may say that 7iv7 the work which at any instant would be done in carrying a unit quantity of electricity round a closed circuit in a magnetic field against the electric forces due to the field is equal to the rate at which the total magnetic induction which threads the circuit is being decreased4 ,this law1 summing up ,faraday's experiments on electro-magnetic induction1 gives a fourth principle1 leading to a fourth series of equations connecting together the electric and magnetic quantities involved4 ,the equations deduced from the above four principles1 together with the condition implied in the continuity of an electric current1 constitute ,maxwell's equations of the electro-magnetic field4 ,if we are dealing only with a dielectric medium1 the reciprocal relation between the third and fourth principle may be made more clear by the following statement3-- 7,a7 ,the work done at any moment in carrying a unit quantity of magnetism round a closed circuit in a field in which electric displacement is varying1 is equal to the rate of change of the total electric displacement through the circuit multiplied by #d 4#fb 7,b7 ,the work done at any moment in carrying a unit quantity of electricity round a circuit in a field in which the magnetic induction is varying1 is equal to the rate of change of the total magnetic induction through the circuit4 ,from these two principles1 combined with the laws connecting electric force and displacement1 magnetic force and induction1 and with the condition of continuity1 ,maxwell obtained his equations of the field4 ,faraday's experiments on electro-magnetic induction afford the proof of the truth of the fourth principle4 ,it follows from those experiments that when the number of lines of magnetic induction which are linked with any closed circuit are made to vary1 an induced electromotive force is brought into play round that circuit4 ,this electromotive force is1 according to ,faraday's results1 measured by the rate of decrease in the number of lines of magnetic induction which thread the circuit4 ,maxwell applies this principle to all circuits1 whether conducting or not4 ,in obtaining equations to express in symbols the results of the fourth principle just enunciated1 ,maxwell introduces a new quantity1 to which he gives the name of the 8vector potential40 ,this quantity appears in his analysis1 and its physical meaning is not at first quite clear4 ,professor ,poynting has1 however1 put ,maxwell's principles in a slightly different form1 which enables us to see definitely the meaning of the vector potential1 and to deduce ,maxwell's equations more readily from the fundamental statements4 ,we are dealing with a circuit with which lines of magnetic induction are linked1 while the number of such lines linked with the circuit is varying4 ,now1 let us suppose the variation to take place in consequence of the lines of induction moving outwards or inwards1 as the case may be1 so as to cut the circuit4 ,originally there are none linked with the circuit4 ,as the magnetic field has grown to its present strength lines of magnetic induction have moved inwards4 ,each little element of the circuit has been cut by some1 and the total number linked with the circuit can be found by adding together those cut by each element4 ,now1 ,professor ,poynting's statement of ,maxwell's fourth principle is that the electrical force in the direction of any element of the circuit is found by dividing by the length of the element the number of lines of magnetic induction which are cut in one second by it4 ,moreover1 the total number of lines of magnetic induction which have been cut by an element of unit length is defined as the component of the vector potential in the direction of the element2 hence the electrical force in any direction is the rate of decrease of the component of the vector potential in that direction4 ,we have thus a physical meaning for the vector potential1 and shall find that in the dynamical theory this quantity is of great importance4 ,professor ,poynting has modified ,maxwell's third principle in a similar manner2 he looks upon the variation in the electric displacement as due to the motion of tubes of electric induction1#fc and the magnetic force along any circuit is equal to the number of tubes of electric induction cutting or cut by unit length of the circuit per second1 multiplied by #d4 ,from the equations of the field1 as found by ,maxwell1 it is possible to derive two sets of symmetrical equations4 ,the one set connects the rate of change of the electric force with quantities depending on the magnetic force2 the other set connects in a similar manner the rate of change of the magnetic force with quantities depending on the electric force4 ,several writers in recent years adopt these equations as the fundamental relations of the field1 establishing them by the argument that they lead to consequences which are found to be in accordance with experiment4 ,we have endeavoured to give some account of ,maxwell's historical method1 according to which the equations are deduced from the laws of electric currents and of electro-magnetic induction derived directly from experiment4 ,while the manner in which ,maxwell obtained his equations is all his own1 he was not alone in stating and discussing general equations of the electro-magnetic field4 ,the next steps which we are about to consider are1 however1 in a special manner due to him4 ,an electrical or magnetic system is the seat of energy2 this energy is partly electrical1 partly magnetic1 and various expressions can be found for it4 ,in ,maxwell's theory it is a fundamental assumption that energy has position4 8,the electric and magnetic energies of any electro-magnetic system10 says ,professor ,poynting1 8reside1 therefore1 somewhere in the field40 ,it follows from this that they are present wherever electric and magnetic force can be shown to exist4 ,maxwell showed that all the electric energy is accounted for by supposing that in the neighbourhood of a point at which the electric force is ,r there is an amount of energy per unit of volume equal to ,,kr_/#h1 ,k being the inductive capacity of the medium1 while in the neighbourhood of a point at which the magnetic force is ,h1 the magnetic energy per unit of volume is ,h_/#h1 being the permeability4 ,he supposes1 then1 that at each point of an electro-magnetic system energy is stored according to these laws4 ,it follows1 then1 that the electro-magnetic field resembles a dynamical system in which energy is stored4 ,can we discover more of the mechanism by which the actions in the field are maintained8 ,now the motion of any point of a connected system depends on that of other points of the system2 there are generally1 in any machine1 a certain number of points called driving-points1 the motion of which controls the motion of all other parts of the machine2 if the motion of the driving-points be known1 that of any other point can be determined4 ,thus in a steam engine the motion of a point on the fly-wheel can be found if the motion of the piston and the connections between the piston and the wheel be known4 ,in order to determine the force which is acting on any part of the machine we must find its momentum1 and then calculate the rate at which this momentum is being changed4 ,this rate of change will give us the force4 ,the method of calculation which it is necessary to employ was first given by ,lagrange1 and afterwards developed1 with some modifications1 by ,hamilton4 ,it is usually referred to as ,hamilton's principle2 when the equations in the original form are used they are known as ,lagrange's equations4 ,now ,maxwell showed how these methods of calculation could be applied to the electro-magnetic field4 ,the energy of a dynamical system is partly kinetic1 partly potential4 ,maxwell supposes that the magnetic energy of the field is kinetic energy1 the electric energy potential4 ,when the kinetic energy of a system is known1 the momentum of any part of the system can be calculated by recognised processes4 ,thus if we consider a circuit in an electro-magnetic field we can calculate the energy of the field1 and hence obtain the momentum corresponding to this circuit4 ,if we deal with a simple case in which the conducting circuits are fixed in position1 and only the current in each circuit is allowed to vary1 the rate of change of momentum corresponding to any circuit will give the force in that circuit4 ,the momentum in question is electric momentum1 and the force is electric force4 ,now we have already seen that the electric force at any point of a conducting circuit is given by the rate of change of the vector potential in the direction considered4 ,hence we are led to identify the vector potential with the electric momentum of our dynamical system2 and1 referring to the original definition of vector potential1 we see that the electric momentum of a circuit is measured by the number of lines of magnetic induction which are interlinked with it4 ,again1 the kinetic energy of a dynamical system can be expressed in terms of the squares and products of the velocities of its several parts4 ,it can also be expressed by multiplying the velocity of each driving-point by the momentum corresponding to that driving-point1 and taking half the sum of the products4 ,suppose1 now1 we are dealing with a system consisting of a number of wire circuits in which currents are running1 and let us suppose that we may represent the current in each wire as the velocity of a driving-point in our dynamical system4 ,we can also express in terms of these currents the electric momentum of each wire circuit2 let this be done1 and let half the sum of the products of the corresponding velocities and momenta be formed4 ,in maintaining the currents in the wires energy is needed to supply the heat which is produced in each wire2 but in starting the currents it is found that more energy is needed than is requisite for the supply of this heat4 ,this excess of energy can be calculated1 and when the calculation is made it is found that the excess is equal to half the sum of the products of the currents and corresponding momenta4 ,moreover1 if this sum be expressed in terms of the magnetic force1 it is found to be equal to ,h_/#h 1 which is the magnetic energy of the field4 ,now1 when a dynamical system is set in motion against known forces1 more energy is supplied than is needed to do the work against the forces2 this excess of energy measures the kinetic energy acquired by the system4 ,hence1 ,maxwell was justified in taking the magnetic energy of the field as the kinetic energy of the mechanical system1 and if the strengths of the currents in the wires be taken to represent the velocities of the driving-points1 this energy is measured in terms of the electrical velocities and momenta in exactly the same way as the energy of a mechanical system is measured in terms of the velocities and momenta of its driving-points4 ,the mechanical system in which1 according to ,maxwell1 the energy is stored is the ether4 ,a state of motion or of strain is set up in the ether of the field4 ,the electric forces which drive the currents1 and also the mechanical forces acting on the conductors carrying the currents1 are due to this state of motion1 or it may be of strain1 in the ether4 ,it must not be supposed that the term electric displacement in ,maxwell's mind meant an actual bodily displacement of the particles of the ether2 it is in some way connected with such a material displacement4 ,in his view1 without motion of the ether particles there would be no electric action1 but he does not identify electric displacement and the displacement of an ether particle4 ,his mechanical theory1 however1 does account for the electro-magnetic forces between conductors carrying currents4 ,the energy of the system depends on the relative positions of the currents which form part of it4 ,now1 any conservative mechanical system tends to set itself in such a position that its potential energy is least1 its kinetic energy greatest4 ,the circuits of the system1 then1 will tend to set themselves so that the electro-kinetic energy of the system may be as large as possible2 forces will be needed to hold them in any position in which this condition is not satisfied4 ,we have another proof of the correctness of the value found for the energy of the field in that the forces calculated from this value agree with those which are determined by direct experiment4 ,again1 the forces applied at the various driving-points are transmitted to other points by the connections of the machine2 the connections are thrown into a state of strain2 stress exists throughout their substance4 ,when we see the piston-rod and the shaft of an engine connected by the crank and the connecting-rod1 we recognise that the work done on the piston is transmitted thus to the shaft4 ,so1 too1 in the electro-magnetic field1 the ether forms the connection between the various circuits in the field2 the forces with which those circuits act on each other are transmitted from one circuit to another by the stresses set up in the ether4 ,to take another instance1 consider the electrostatic attraction between two charged bodies4 ,let us suppose the bodies charged by connecting each to the opposite pole of a battery2 a current flows from the battery setting up electric displacement in the space between the bodies1 and throwing the ether into a state of strain4 ,as the strain increases the current gets less2 the reaction resulting from the strain tends to stop it1 until at last this reaction is so great that the current is stopped4 ,when this is the case the wires to the battery may be removed1 provided this is done without destroying the insulation of the bodies2 the state of strain will remain and shows itself in the attraction between the balls4 ,looking at the problem in this manner1 we are face to face with two great questions--the one1 ,what is the state of strain in the ether which will enable it to produce the observed electrostatic attractions and repulsions between charged bodies8 and the other1 ,what is the mechanical structure of the ether which would give rise to such a state of strain as will account for the observed forces8 ,maxwell gives one answer to the first question2 it is not the only answer which could be given1 but it does account for the facts4 ,he failed to answer the second4 ,he says 78,electricity and ,magnetism10 vol4 i4 p4 #acb73-- 8,it must be carefully borne in mind that we have made only one step in the theory of the action of the medium4 ,we have supposed it to be in a state of stress1 but have not in any way accounted for this stress1 or explained how it is maintained4444 ,i have not been able to make the next step1 namely1 to account by mechanical considerations for these stresses in the dielectric40 ,faraday had pointed out that the inductive action between two bodies takes place along the lines of force1 which tend to shorten along their length and to spread outwards in other directions4 ,maxwell compares them to the fibres of a muscle1 which contracts and at the same time thickens when exerting force4 ,in the electric field there is1 on ,maxwell's theory1 a tension along the lines of electric force and a pressure at right angles to those lines4 ,maxwell proved that a tension ,k ,r_/#h along the lines of force1 combined with an equal pressure in perpendicular directions1 would maintain the equilibrium of the field1 and would give rise to the observed attractions or repulsions between electrified bodies4 ,other distributions of stress might be found which would lead to the same result4 ,the one just stated will always be connected with ,maxwell's name4 ,it will be noticed that the tension along the lines of force and the pressure at right angles to them are each numerically equal to the potential energy stored per unit of volume in the field4 ,the value of each of the three quantities is ,k ,r_/#h 4 ,in the same way1 in a magnetic field1 there is a state of stress1 and on ,maxwell's theory this1 too1 consists of a tension along the lines of force and an equal pressure at right angles to them1 the values of the tension and the pressure being each equal to that of the magnetic energy per unit of volume1 or ,h_/#h4 ,in a case in which both electric and magnetic force exists1 these two states of stress are superposed4 ,the total energy per unit of volume is ,,kr_/#h ,h_/#h2 the total stress is made up of tensions ,,kr_/#h and ,h_/#h along the lines of electric and magnetic force respectively1 and equal pressures at right angles to these lines4 ,we see1 then1 from ,maxwell's theory1 that electric force produced at any given point in space is transmitted from that point by the action of the ether4 ,the question suggests itself1 ,does the transmission take time1 and if so1 does it proceed with a definite velocity depending on the nature of the medium through which the change is proceeding8 ,according to the molecular-vortex theory1 we have seen that waves of electric force are transmitted with a definite velocity4 ,the more general theory developed in the 8,electricity and ,magnetism0 leads to the same result4 ,electric force produced at any point travels outwards from that point with a velocity given by #a_/7,k74 ,at a distant point the force is zero1 until the disturbance reaches it4 ,if the disturbance last only for a limited interval1 its effects will at any future time be confined to the space within a spherical shell of constant thickness depending on the interval2 the radii of this shell increase with uniform speed #a_/7,k74 ,if the initial disturbance be periodic1 periodic waves of electric force will travel out from the centre1 just as waves of sound travel out from a bell1 or waves of light from a candle flame4 ,a wire carrying an alternating current may be such a source of periodic disturbance1 and from the wire waves travel outwards into space4 ,now1 it is known that in a sound wave the displacements of the air particles take place in the direction in which the wave is travelling2 they lie at right angles to the wave front1 and are spoken of as longitudinal4 ,in light waves1 on the other hand1 the displacements are1 as ,fresnel proved1 in the wave front1 at right angles1 that is1 to the direction of propagation2 they are transverse4 ,theory shows that in general both these waves may exist in an elastic solid body1 and that they travel with different velocities4 ,of which nature are the waves of electric displacement in a dielectric8 ,it can be shewn to follow as a necessary consequence of ,maxwell's views as to the closed character of all electric currents1 that waves of electric displacement are transverse4 ,electric vibrations1 like those of light1 are in the wave front and at right angles to the direction of propagation2 they depend on the rigidity or quasi-rigidity of the medium through which they travel1 not on its resistance to compression4 ,again1 an electric current1 whether due to variation of displacement in a dielectric or to conduction in a conductor1 is accompanied by magnetic force4 ,a wave of periodic electric displacement1 then1 will be also a wave of periodic magnetic force travelling at the same rate2 and ,maxwell shewed that the direction of this magnetic force also lies in the wave front1 and is always at right angles to the electric displacement4 ,in the ordinary theory of light the wave of linear displacement is accompanied by a wave of periodic angular twist about a direction lying in the wave front and perpendicular to the linear displacement4 ,in many respects1 then1 waves of electric displacement resemble waves of light1 and1 indeed1 as we proceed we shall find closer connections still4 ,hence comes ,maxwell's electro-magnetic theory of light4 ,it is only in dielectric media that electric force is propagated by wave motion4 ,in conductors1 although the third and fourth of ,maxwell's principles given on page #ahe still are true1 the relation between the electric force and the electric current differs from that which holds in a dielectric4 ,hence the equations satisfied by the force are different4 ,the laws of its propagation resemble those of the conduction of heat rather than those of the transmission of light4 ,again1 light travels with different velocities in different transparent media4 ,the velocity of electric waves1 as has been stated1 is equal to #a_/7,k72 but in making this statement it is assumed that the simple laws which hold where there is no gross matter--or1 rather1 where air is the only dielectric with which we are concerned--hold also in solid or liquid dielectrics4 ,in a solid or a liquid1 as in vacuo1 the waves are propagated by the ether4 ,we assume1 as a first step towards a complete theory1 that so far as the electric waves are concerned the sole effect produced by the matter shews itself in a change of inductive capacity or of permeability4 ,it is not likely that such a supposition should be the whole truth1 and we may1 therefore1 expect results deduced from it to be only approximation to the true result4 ,now1 electro-magnetic experiments show that1 excluding magnetic substances1 the permeability of all bodies is very nearly the same1 and differs very slightly from that of air4 ,the inductive capacity1 however1 of different bodies is different1 and hence the velocity with which electro-magnetic waves travel differs in different bodies4 ,but the refraction of waves of light depends on the fact that light travels with different velocities in different media2 hence we should expect to have waves of electric displacement reflected and refracted when they pass from one dielectric1 such as air1 to another1 such as glass or gutta-percha2 moreover1 for light the refractive index of a medium such as glass is the ratio of the velocity in air to the velocity in the glass4 ,thus the electrical refractive index of glass is the ratio of the velocity of electric waves in air to their velocity in glass4 ,now let ,k be the inductive capacity of air1 ,k that of glass1 taking the permeability of air and glass to be the same1 we have the result that-- ,electrical refractive index 7,k_/,k74 ,but the ratio of the inductive capacity of glass to that of air is known as the specific inductive capacity of glass4 ,hence1 the specific inductive capacity of any medium is equal to the square of the electrical refractive index of that medium4 ,since ,maxwell's time the mathematical laws of the reflexion and refraction of electric waves have been investigated by various writers1 and it has been shewn that they agree exactly with those enunciated by ,fresnel for light4 ,hitherto we have been discussing the propagation of electric waves in an isotropic medium1 one which has identical properties in all directions about a point4 ,let us now consider how these laws are modified if the dielectric be crystalline in structure4 ,maxwell assumes that the crystalline character of the dielectric can be sufficiently represented by supposing the inductive capacity to be different in different directions2 experiments have since shewn that this is true for crystals such as ,iceland ,spar and ,aragonite2 he assumes also1 and this1 too1 is justified by experiment1 that the magnetic permeability does not depend on the direction4 ,it follows from these assumptions that a crystal will produce double refraction and polarisation of electric waves which fall upon it1 and1 further1 that the laws of double refraction will be those given by ,fresnel for light waves in a doubly refracting medium4 ,there will be two waves in the crystal4 ,the disturbance in each of these will be plane polarised2 their velocity and the position of their plane of polarisation can be found from the direction in which they are travelling by ,fresnel's construction exactly4 ,maxwell's theory1 then1 would appear to indicate some close connection between electric waves and those of light4 ,faraday's experiments on the rotation of the plane of polarisation by magnetic force shew one phenomenon in which the two are connected1 and ,maxwell endeavoured to apply his theory to explain this4 ,here1 however1 it became necessary to introduce an additional hypothesis--there must be some connection between the motion of the ether to which magnetic force is due and that which constitutes light4 ,it is impossible to give a mechanical account of the rotation of the plane of polarisation without some assumption as to the relation between these two kinds of motion4 ,maxwell1 therefore1 supposes the linear displacements of a point in the ether to be those which give rise to light1 while the components of the magnetic force are connected with these in the same way as the components of a vortex in a liquid in vortex motion are connected with the displacements of the liquid4 ,he further assumes the existence of a term of special form in the expression for the kinetic energy1 and from these assumptions he deduces the laws of the propagation of polarised light in a magnetic field4 ,these laws agree in the main with the results of ,verdet's experiments4 ,,chapter ,x4 ,,development ,,of ,,maxwell',s ,,theory4 ,we have endeavoured in the preceding pages to give some account of ,maxwell's contributions to electrical theory and the physics of the ether4 ,we must now consider very briefly what evidence there is to support these views4 ,at ,maxwell's death such evidence1 though strong1 was indirect4 ,his supporters were limited to some few ,english-speaking pupils1 young and enthusiastic1 who were convinced1 it may be1 in no small measure1 by the affection and reverence with which they regarded their master4 ,abroad his views had made very little way4 ,in the last words of his book he writes1 speaking of various distinguished workers-- 8,there appears to be in the minds of these eminent men some prejudice1 or priori objection1 against the hypothesis of a medium in which the phenomena of radiation of light and heat1 and the electric actions at a distance1 take place4 ,it is true that1 at one time1 those who speculated as to the causes of physical phenomena were in the habit of accounting for each kind of action at a distance by means of a special therial fluid1 whose function and property it was to produce these actions4 ,they filled all space three and four times over with thers of different kinds1 the properties of which were invented merely to #8save appearances1' so that more rational enquirers were willing rather to accept not only ,newton's definite law of attraction at a distance1 but even the dogma of ,cotes1#fd that action at a distance is one of the primary properties of matter1 and that no explanation can be more intelligible than this fact4 ,hence the undulatory theory of light has met with much opposition1 directed not against its failure to explain the phenomena1 but against its assumption of the existence of a medium in which light is propagated4 8,we have seen that the mathematical expression for electro-dynamic action led1 in the mind of ,gauss1 to the conviction that a theory of the propagation of electric action in time would be found to be the very key-stone of electro-dynamics4 ,now we are unable to conceive of propagation in time1 except either as the flight of a material substance through space1 or as the propagation of a condition of motion1 or stress1 in a medium already existing in space4 8,in the theory of ,neumann1 the mathematical conception called potential1 which we are unable to conceive as a material substance1 is supposed to be projected from one particle to another in a manner which is quite independent of a medium1 and which1 as ,neumann has himself pointed out1 is extremely different from that of the propagation of light4 8,in the theories of ,riemann and ,betti it would appear that the action is supposed to be propagated in a manner somewhat more similar to that of light4 8,but in all of these theories the question naturally occurs3--,if something is transmitted from one particle to another at a distance1 what is its condition after it has left one particle and before it has reached the other8 ,if this something is the potential energy of the two particles1 as in ,neumann's theory1 how are we to conceive this energy as existing in a point of space1 coinciding neither with the one particle nor with the other8 ,in fact1 whenever energy is transmitted from one body to another in time1 there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other1 for energy1 as ,torricelli#fe remarked1 #8is a quintessence of so subtle a nature that it cannot be contained in any vessel except the inmost substance of material things4' ,hence all these theories lead to a conception of a medium in which the propagation takes place1 and if we admit this medium as an hypothesis1 ,i think it ought to occupy a prominent place in our investigations1 and that we ought to endeavour to construct a mental representation of all the details of its action1 and this has been my constant aim in this treatise40 ,let us see1 then1 what were the experimental grounds in ,maxwell's day for accepting as true his views on electrical action1 and how since then1 by the genius of ,heinrich ,hertz and the labours of his followers1 those grounds have been rendered so sure that nearly the whole progress of electrical science during the last twenty years has consisted in the development of ideas which are to be found in the 8,treatise on ,electricity and ,magnetism40 ,the purely electrical consequences of ,maxwell's theory were of course in accord with all known electrical observations4 ,the equations of the field accounted for the electro-magnetic forces observed in various experiments1 and from them the laws of electro-magnetic induction could be correctly deduced2 but there was nothing very special in this4 ,similar equations had been obtained from the theory of action at a distance by various writers2 in fact1 ,helmholtz's theory1 based on the most general form of expression for the force between two elements of current consistent with certain experiments of ,ampre's1 was more general in its character than ,maxwell's4 ,the destructive features of ,maxwell's theory were3 7#a7 ,the assumption that all currents flow in closed circuits4 7#b7 ,the idea of energy residing throughout the electro-magnetic field in consequence of the strains and stresses set up in the electro-magnetic medium by the actions to which it was subject4 7#c7 ,the identification of this electro-magnetic medium with the luminiferous ether1 and the consequent view that light is an electro-magnetic phenomena4 7#d7 ,the view that electro-magnetic forces arise entirely from strains and stresses set up in the ether2 the electrostatic charge of an insulated conductor being one of the forms in which the ether strain is manifested to us4 7#e7 ,a dielectric under the action of electric force is said to become polarised1 and1 according to ,maxwell 7vol4 i4 p4 #acc71 all electrification is the residual effect of the polarisation of the dielectric4 ,now it must1 ,i think1 be admitted that in ,maxwell's day there was direct proof of very few of these propositions4 ,no one has even yet so measured the displacement currents in a dielectric as to show that the total flow across every section of a circuit is at any given moment the same1 though there are other experiments of an indirect character which have now completely justified ,maxwell's hypothesis4 ,experiments by ,schiller and ,von ,helmholtz prove it is true that some action in the dielectric must be taken into consideration in any satisfactory theory2 they therefore upset various theories based on direct action at a distance1 8but they tell us nothing as to whether any special form of the dielectric theory1 such as ,maxwell's or ,helmholtz's1 is true or not40 7,j4 ,j4 ,thomson1 8,report on ,electrical ,theories10 ,b4,a4 ,report1 #ahhe1 p4 #adi47 ,when ,maxwell died there had been little if any experimental evidence as to the stresses set up in a body by electric force4 ,fontana1 ,govi1 and ,duter had all observed that changes take place in the volume of the dielectric of a condenser when it is charged4 ,quincke had taken up the work1 and the first of his classic papers on this subject was published in #ahhj1 the year following ,maxwell's death4 ,maxwell himself was fond of shewing an experiment in which a charged insulated sphere was brought near to the surface of paraffin2 the stress on the surface causes a heaping up of the paraffin under the sphere4 ,kerr had shewn in #ahge that many substances become doubly refracting under electric stress2 his complete determination of the laws of this action was published at a later date4 ,as to direct measurements on electric waves1 there were none2 the value of the velocity with which1 if ,maxwell's theory were true1 they must travel had been determined from electrical observations of quite a different character4 ,weber and ,kohlrausch had measured the value of ,k for air1 for which is unity1 and from their observations it follows that the value of the wave velocity for electro-magnetic waves is about #ca #aj centimetres per second4 ,the velocity of light was known1 from the experiments of ,fizeau and ,foucault1 to have about this value1 and it was the near coincidence of these two values which led ,maxwell to write in #ahfd3-- 8,the agreement of the results seems to show that light and magnetism are affections of the same substance1 and that light is an electro-magnetic disturbance propagated through the field according to electro-magnetic laws40 ,by the time the first edition of the 8,electricity and ,magnetism0 was published1 ,maxwell and ,thomson 7,lord ,kelvin7 had both made determinations of ,k1 and had shewn that for air at least the resulting value for the velocity of electro-magnetic waves was very nearly that of light4 ,for other substances at that date the observations were fewer still4 ,gibson and ,barclay had determined the specific inductive capacity of paraffin1 and found that its square root was #adje1 while its refractive index for long waves is #adbb4 ,maxwell himself thought that if a similar agreement could be shewn to hold for a number of substances1 we should be warranted in concluding that 8the square root of ,k1 though it may not be the complete expression for the index of refraction1 is at least the most important term in it40 ,between this time and ,maxwell's death enough had been done to more than justify this statement4 ,it was clear from the observations of ,boltzmann1 ,silow1 ,hopkinson1 and others that there were many substances for which the square root of the specific inductive capacity was very nearly indeed equal to the refractive index1 and good reason had been given why in some cases there should be a considerable difference between the two4 ,hopkinson found that in the case of glass the differences were very large1 and they have since been found to be considerable for most solids examined1 with the exception of paraffin and sulphur4 ,for petroleum oil1 benzine1 toluene1 carbon-bisulphide1 and some other liquids the agreement between ,maxwell's theory and experiment is close4 ,for the fatty oils1 such as castor oil1 olive oil1 sperm oil1 neatsfoot oil1 and also for ether1 the differences are considerable4 ,it seems probable that the reason for this difference lies in the fact that1 in the light waves1 we are dealing with the wave velocity of a disturbance of an extremely short period4 ,now1 we know that the substances mentioned shew optical dispersion1 and we have at present no completely satisfactory theory from which we can calculate1 from experiments on very short waves1 what the velocity for very long waves will be4 ,in most cases ,cauchy's formula has been used to obtain the numbers given4 ,the value of ,k1 however1 as found by experiment1 corresponds to these infinitely long waves1 and to quote ,professor ,j4 ,j4 ,thomson's words1 8the marvel is not that there should not be substances for which the relation ,k does not hold1 but that there should be any for which it does40#ff ,it has been shewn1 moreover1 both by ,professor ,j4 ,j4 ,thomson himself and by ,blondlot1 that when the value of ,k is measured under very rapidly varying electrifications1 changing at the rate of about #be1jjj1jjj to the second1 the value of the inductive capacity for glass is reduced from about #fh or #g to about #bg2 the square root of this is #af1 which does not differ much from its refractive index4 ,the values of the inductive capacity of paraffin and sulphur1 which it will be remembered agree fairly with ,maxwell's theory1 were found to be not greatly different in the steady and in the rapidly varying field4 ,on the other hand1 some experiments of ,arons and ,rubens in rapidly varying fields lead to values which do not differ greatly from those given by other methods4 ,the theory1 however1 of these experiments seems open to criticism4 ,to attempt anything like a complete account of modern verifications of ,maxwell's views and modern developments of his theory is a task beyond our limits1 but an account of ,maxwell written in #ahie would be incomplete without a reference to the work of ,heinrich ,hertz4 ,maxwell told us what the properties of electro-magnetic waves in air must be4 ,hertz#fg in #ahhg enabled us to measure those properties1 and the measurements have verified completely ,maxwell's views4 ,the method of producing electrical oscillations in a conductor had long been known4 ,thomson and ,von ,helmholtz had both pointed it out4 ,schiller had examined such oscillations in #ahgd1 and had determined the inductive capacity of glass by their means1 using oscillations whose period varied from #jjjjef to #jjjab of a second4 ,these oscillations were produced by discharging a condenser through a coil of wire having self-induction4 ,if the electrical resistance of the coil be not too great1 the charge oscillates backwards and forwards between the plates of the condenser until its energy is dissipated in the heat produced in the wire1 and in the electro-magnetic radiations which leave it4 ,the period of these oscillations under proper conditions is given by the formula ,t #b7;,,cl7 where ,l1 the coefficient of self induction1 and ,c the capacity of the condenser4 ,these quantities can be calculated1 and hence the time of an oscillation is known4 ,from such an arrangement waves radiate out into space4 ,if we could measure by any method the length of such a wave we could determine its velocity by dividing the wave length by the period4 ,but it is clear that since the velocity is comparable with that of light the wave length will be enormous1 unless the period is very short4 ,thus1 a wave1 travelling with the velocity of light1 whose period was #jjja second1 such as the waves ,schiller worked with1 would have a length of #jjja #cj1jjj1jjj1jjj or #c1jjj1jjj centimetres1 and would be quite unmeasurable4 ,before measurements on electric waves could be made it was necessary 7#a7 to produce waves of sufficiently rapid period1 7#b7 to devise means to detect them4 ,this is what ,hertz did4 ,the wave length of the electrical oscillations can be reduced by reducing either the electrical capacity of the system1 or the coefficient of self-induction of the wire4 ,hertz adopted both these expedients4 ,his vibrator1 in some of his more important experiments1 consisted of two square brass plates #dj cm4 in the side4 ,to each of these is attached a piece of copper wire about #cj cm4 in length1 and each wire ends in a small highly-polished brass ball4 ,the plates are placed so that the wires lie in the same straight line1 the brass balls being separated by a very small air gap4 ,the two plates are then charged1 the one positively the other negatively1 until the insulation resistance of the air gap breaks down and a discharge passes across4 ,under these conditions the discharge is oscillatory4 ,it does not consist of a single spark1 but of a series of sparks1 which pass and repass in opposite directions1 until the energy of the original charge is radiated into space or dissipated as heat2 the plates are then recharged and the process repeated4 ,in ,hertz's experiments the oscillator was charged by being connected to the secondary terminals of an induction coil4 ,in #ahhc ,professor ,fitzgerald had called attention to this method of producing electric waves in air1 and had given two metres as the minimum wave length which might be attained4 ,in #ahgj ,herr von ,bezold had actually made observations on the propagation and reflection of electrical oscillations1 but his work1 published as a preliminary communication1 had attracted little notice4 ,hertz was the first to undertake in #ahhg in a systematic manner the investigation of the electric waves in air which proceed from such an oscillator with a view to testing various theories of electro-magnetic action4 ,it remained1 however1 necessary to devise an apparatus for detecting the waves4 ,when the waves are incident on a conductor1 electric surgings are set up in the conductor1 and may1 under proper conditions1 be observed as tiny sparks4 ,hertz used as his detector a loop of wire1 the ends of which terminated in two small brass balls4 ,the wire was bent so that the balls were very close together1 and the sparks could be seen passing across the tiny air gap which separated them4 ,such a wire will have a definite period of its own for oscillations of electricity with which it may be charged1 and if the frequency of the electric waves which fall on it agrees with that of the waves which it can itself emit1 the oscillations which are set up in the wire will be stronger than under other conditions1 the sparks seen will be more brilliant4#fh ,hertz's resonator was a circle of wire thirty-five centimetres in radius1 the period for such a resonator would1 he calculated1 be the same as that of his vibrator4 ,there is1 however1 very considerable difficulty in determining the period of an electric oscillator from its dimensions1 and the value obtained from calculation for that of ,hertz's radiator is not very trustworthy4 ,the complete period is1 however1 comparable with two one hundredth millionths of a second2 in his original papers1 ,hertz1 through an error1 gave a value greater than this4 ,with these arrangements ,hertz was able to detect the presence of electrical radiation at considerable distances from the radiator2 he was also able to measure its wave length4 ,in the case of sound waves the existence of nodes and loops formed under proper conditions is well known4 ,when waves are directly reflected from a flat surface1 interference takes place between the incident and reflected waves1 stationary vibrations are set up1 and nodes and loops--places1 that is1 of minimum and of maximum motion respectively--are formed4 ,the position of these nodes and loops can be determined by the aid of suitable apparatus1 and it can be shewn that the distance between two consecutive nodes is half the wave length4 ,similarly when electrical vibrations fall on a reflector1 a large flat surface of metal1 for example1 stationary vibrations due to the interference between the incident and reflected waves are produced1 and these give rise to electrical nodes and loops4 ,the position of such nodes and loops can be found by the use of ,hertz's apparatus1 or in other ways1 and hence the length of the electrical waves can be found4 ,the existence of the nodes and loops shews that the electric effects are propagated by wave motion4 ,the length of the waves is found to be definite1 since the nodes and loops recur at equal intervals apart4 ,if it be assumed that the frequency is known1 the velocity of wave propagation can be determined4 ,hertz found from his experiments that in air the waves travelled with the velocity of light4 ,it appears1 however1 that there were two errors in the calculation which happened to correct each other1 so that neither the value of the frequency given in ,hertz's paper nor the wave length observed is correct4 ,by modifying the apparatus it was possible to measure the wave length of the waves transmitted along a copper wire1 and hence1 again assuming the period of oscillation1 to calculate the velocity of wave propagation along the wire4 ,hertz made the experiment1 and found from his first observations that the waves were propagated along the wire with a finite velocity1 but that the velocity differed from that in air4 ,the half-wave length in the wire was only about #bh metres2 that in air was about #de metres4 ,now1 this experiment afforded a crucial test between the theories of ,maxwell and ,von ,helmholtz4 ,according to the former1 the waves do not travel in the wire at all2 they travel through the air alongside the wire1 and the wave length observed by ,hertz ought to have been the same as in air4 ,according to ,von ,helmholtz1 the two velocities observed by ,hertz should have been different1 as1 indeed1 they were1 and the experiment appeared to prove that ,maxwell's theory was insufficient and that a more general one1 such as that of ,von ,helmholtz1 was necessary4 ,but other experiments have not led to the same result4 ,hertz himself1 using more rapid oscillations in some later measurements1 found that the wave length of the electric waves from a given oscillator was the same whether they were transmitted through free space or conducted along a wire4#fi ,lecher and ,j4 ,j4 ,thomson have arrived at the same result2 but the most complete experiments on this point are those of ,sarasin and ,de la ,rive4 ,it may be taken1 then1 as established that ,maxwell's theory is sufficient1 and that the greater generality of ,von ,helmholtz is unnecessary4 ,in a later paper ,hertz showed that electric waves could be reflected and refracted1 polarised and analysed1 just like light waves4 ,in his introduction to his 8,collected ,papers0 he writes 7p4 #ai73-- 8,casting now a glance backwards1 we see that by the experiments above sketched the propagation in time of a supposed action at a distance is for the first time proved4 ,this fact forms the philosophic result of the experiments1 and indeed1 in a certain sense1 the most important result4 ,the proof includes a recognition of the fact that the electric forces can disentangle themselves from material bodies1 and can continue to subsist as conditions or changes in the state of space4 ,the details of the experiments further prove that the particular manner in which the electric force is propagated exhibits the closest analogy#gj with the propagation of light2 indeed1 that it corresponds almost completely to it4 ,the hypothesis that light is an electrical phenomenon is thus made highly probable4 ,to give a strict proof of this hypothesis would logically require experiments upon light itself4 8,what we here indicate as having been accomplished by the experiments is accomplished independently of the correctness of particular theories4 ,nevertheless1 there is an obvious connection between the experiments and the theory in connection with which they were really undertaken4 ,since the year #ahfa science has been in possession of a theory which ,maxwell constructed upon ,faraday's views1 and which we therefore call the ,faraday-,maxwell theory4 ,this theory affirms the possibility of the class of phenomena here discovered just as positively as the remaining electrical theories are compelled to deny it4 ,from the outset ,maxwell's theory excelled all others in elegance and in the abundance of the relations between the various phenomena which it included4 8,the probability of this theory1 and therefore the number of its adherents1 increased from year to year4 ,but as long as ,maxwell's theory depended solely upon the probability of its results1 and not on the certainty of its hypotheses1 it could not completely displace the theories which were opposed to it4 8,the fundamental hypotheses of ,maxwell's theory contradicted the usual views1 and did not rest upon the evidence of decisive experiments4 ,in this connection we can best characterise the object and the result of our experiments by saying3 ,the object of these experiments was to test the fundamental hypotheses of the ,faraday-,maxwell theory1 and the result of the experiments is to confirm the fundamental hypotheses of the theory40 ,since ,maxwell's death volumes have been written on electrical questions1 which have all been inspired by his work4 ,the standpoint from which electrical theory is regarded has been entirely changed4 ,the greatest masters of mathematical physics have found1 in the development of ,maxwell's views1 a task that called for all their powers1 and the harvest of new truths which has been garnered has proved most rich4 ,but while this is so1 the question is still often asked1 ,what is ,maxwell's theory8 ,hertz himself concludes the introduction just referred to with his most interesting answer to this question4 ,prof4 ,boltzmann has made the theory the subject of an important course of lectures4 ,poincar1 in the introduction to his 8,lectures on ,maxwell's ,theories and the ,electro-magnetic ,theory of ,light10 expresses the difficulty1 which many feel1 in understanding what the theory is4 8,the first time10 he says1 8that a ,french reader opens ,maxwell's book a feeling of uneasiness1 often even of distrust1 is mingled with his admiration4 ,it is only after prolonged study1 and at the cost of many efforts1 that this feeling is dissipated4 ,some great minds retain it always40 ,and again he writes3 8,a ,french savant1 one of those who have most completely fathomed ,maxwell's meaning1 said to me once1 #8,i understand everything in the book except what is meant by a body charged with electricity4'0 ,in considering this question1 ,poincar's own remark--8,maxwell does not give a mechanical explanation of electricity and magnetism1 he is only concerned to show that such an explanation is possible0--is most important4 ,we cannot find in the 8,electricity0 an answer to the question--,what is an electric charge8 ,maxwell did not pretend to know1 and the attempt to give too great definiteness to his views on this point is apt to lead to a misconception of what those views were4 ,on the old theories of action at a distance and of electric and magnetic fluids attracting according to known laws1 it was easy to be mechanical4 ,it was only necessary to investigate the manner in which such fluids could distribute themselves so as to be in equilibrium1 and to calculate the forces arising from the distribution4 ,the problem of assigning such a mechanical structure to the ether as will permit of its exerting the action which occurs in an electro-magnetic field is a harder one to solve1 and till it is solved the question--,what is an electric charge8--must remain unanswered4 ,still1 in order to grasp ,maxwell's theory this knowledge is not necessary4 ,the properties of ether in dielectrics and in conductors must be quite different4 ,in a dielectric the ether has the power of storing energy by some change in its configuration or its structure2 in a conductor this power is absent1 owing probably to the action of the matter of which the conductor is composed4 ,when we are said to charge an insulated conductor we really act on the ether in the neighbourhood of the body so as to store it with energy2 if there be another conductor in the field we cannot store energy in the ether it contains4 ,as1 then1 we pass from the outside of this conductor to its interior there is a sudden change in some mechanical quantity connected with the ether1 and this change shows itself as a force of attraction between the two conductors4 ,maxwell called the change in structure1 or in property1 which occurs when a dielectric is thus stored with electrostatic energy1 ,electric ,displacement2 if we denote it by ,d1 then the electric force ,r is equal to #d;,d_/,k1 and hence the energy in a unit of volume is #b;,d_/,k1 where ,k is a quantity depending on the insulator4 ,now1 ,d1 the electric displacement1 is a quantity which has direction as well as magnitude4 ,its value1 therefore1 at any point can be represented by a straight line in the usual way2 inside a conductor it is zero4 ,the total change in ,d1 which takes place all over the surface of a conductor as we enter it from the outside measures1 according to ,maxwell1 the total charge on the conductor4 ,at points at which the lines representing ,d enter the conductor the charge is negative2 at points at which they leave it the charge is positive2 along the lines of the displacement there exists throughout the ether a tension measured by #b;,d_/,k2 at right angles to these lines there is a pressure of the same amount4 ,in addition to the above the components of the displacement ,d must satisfy certain relations which can only be expressed in mathematical form1 the physical meaning of which it is difficult to state in non-mathematical language4 ,when these relations are so expressed the problem of finding the value of the displacement at all points of space becomes determinate1 and the forces acting on the conductors can be obtained4 ,moreover1 the total change of displacement on entering or leaving a conductor can be calculated1 and this gives the quantity which is known as the total electrical charge on the conductor4 ,the forces obtained by the above method are exactly the same as those which would exist if we supposed each conductor to be charged in the ordinary sense with the quantities just found1 and to attract or repel according to the ordinary laws4 ,if1 then1 we define electric displacement as that change which takes place in a dielectric when it becomes the seat of electrostatic energy1 and if1 further1 we suppose that the change1 whatever it be mechanically1 satisfies certain well-known laws1 and that in consequence certain pressures and tensions exist in the dielectric1 electrostatic problems can be solved without reference to a charge of electricity residing on the conductors4 ,something such as this1 it appears to me1 is ,maxwell's theory of electricity as applied to electrostatics4 ,it is not necessary1 in order to understand it1 to know what change in the ether constitutes electric displacement1 or what is an electric charge1 though1 of course1 such knowledge would render our views more definite1 and would make the theory a mechanical one4 ,when we turn to magnetism and electro-magnetism1 ,maxwell's theory develops itself naturally4 ,experiment proves that magnetic induction is connected with the rate of change of electric displacement1 according to the laws already given4 ,if1 then1 we knew the nature of the change to which the name 8electric displacement0 has been given1 the nature of magnetic induction would be known4 ,the difficulties in the way of any mechanical explanation are1 it is true1 very great2 assuming1 however1 that some mechanical conception of 8electric displacement0 is possible1 ,maxwell's theory gives a consistent account of the other phenomena of electro-magnetism4 ,again1 we have1 it is true1 an electro-magnetic theory of light1 but we do not know the nature of the change in the ether which affects our eyes with the sensation of light4 ,is it the same as electric displacement1 or as magnetic induction1 or since1 when electric displacement is varying1 magnetic induction always accompanies it1 is the sensation of light due to the combined effect of the two8 ,these questions remain unanswered4 ,it may be that light is neither electric displacement nor magnetic induction1 but some quite different periodic change of structure of the ether1 which travels through the ether at the same rate as these quantities1 and obeys many of the same laws4 ,in this respect there is a material difference between the ordinary theory of light and the electro-magnetic theory4 ,the former is a mechanical theory2 it starts from the assumption that the periodic change which constitutes light is the ordinary linear displacement of a medium--the ether--having certain mechanical properties1 and from those properties it deduces the laws of optics with more or less success4 ,lord ,kelvin1 in his labile ether1 has devised a medium which could exist and which has the necessary mechanical properties4 ,the periodic linear displacements of the labile ether would obey the laws of light1 and from the fundamental hypotheses of the theory1 a mechanical explanation1 reasonably satisfactory in its main features1 can be given of most purely optical phenomena4 ,the relations between light and electricity1 or light and magnetism1 are not1 however1 touched by this theory2 indeed1 they cannot be touched without making some assumption as to what electric displacement is4 ,in recent years various suggestions have been made as to the nature of the change which constitutes electric displacement4 ,one theory1 due to ,von ,helmholtz1 supposes that the electro-kinetic momentum1 or vector potential of ,maxwell1 is actually the momentum of the moving ether2 according to another1 suggested1 it would appear originally in a crude form by ,challis1 and developed within the last few months in very satisfactory detail by ,larmor1 the velocity of the ether is magnetic force2 others have been devised1 but we are still waiting for a second ,newton to give us a theory of the ether which shall include the facts of electricity and magnetism1 luminous radiation1 and it may be gravitation4#ga ,meanwhile we believe that ,maxwell has taken the first steps towards this discovery1 and has pointed out the lines along which the future discoverer must direct his search1 and hence we claim for him a foremost place among the leaders of this century of science4 ,,footnotes #a ,a full biographical account of the ,clerk and ,maxwell families is given in a note by ,miss ,isabella ,clerk in the 8,life of ,james ,clerk ,maxwell10 and from this the above brief statement has been taken4 #b 8,life of ,j4 ,c4 ,maxwell10 p4 #bf4 #c 8,life of ,j4 ,c4 ,maxwell10 p4 #bg4 #d 8,life of ,j4 ,c4 ,maxwell10 p4 #di4 #e 8,life of ,j4 ,c4 ,maxwell10 p4 #eb4 #f 8,life of ,j4 ,c4 ,maxwell10 p4 #ef4 #g 8,life of ,j4 ,c4 ,maxwell10 p4 #fg4 #h 8,life of ,j4 ,c4 ,maxwell10 p4 #ge4 #i ,professor ,garnett in ,nature1 ,november #acth1 #ahgi4 #aj 8,life of ,j4 ,c4 ,maxwell10 p4 #aje4 #aa 8,life of ,j4 ,c4 ,maxwell10 p4 #aaf4 #ab 8,life of ,j4 ,c4 ,maxwell10 pp4 #abc-abi4 #ac 8,life of ,j4 ,c4 ,maxwell10 p4 #aij4 #ad ,dean of ,canterbury4 #ae ,master of ,trinity4 #af 8,life of ,j4 ,c4 ,maxwell10 p4 #agd4 #ag 8,life of ,j4 ,c4 ,maxwell10 p4 #aie4 #ah 8,life of ,j4 ,c4 ,maxwell10 p4 #bjg4 #ai 8,life of ,j4 ,c4 ,maxwell10 p4 #bjh4 #bj 8,life of ,j4 ,c4 ,maxwell10 p4 #baj4 #ba 8,life of ,j4 ,c4 ,maxwell10 p4 #baa4 #bb 8,life of ,j4 ,c4 ,maxwell10 p4 #baf4 #bc 8,life of ,j4 ,c4 ,maxwell10 p4 #bef4 #bd 8,life of ,j4 ,c4 ,maxwell10 p4 #bfg4 #be 8,life of ,j4 ,c4 ,maxwell10 p4 #bfi4 #bf 8,life of ,j4 ,c4 ,maxwell10 p4 #bgh4 #bg 8,life of ,j4 ,c4 ,maxwell10 p4 #bib4 #bh 8,life of ,j4 ,c4 ,maxwell10 p4 #cjc4 #bi 8,life of ,j4 ,c4 ,maxwell10 p4 #bei4 #cj ,b4,a4 ,report1 ,newcastle1 #ahfc4 #ca 8,life of ,j4 ,c4 ,maxwell10 p4 #cdj4 #cb 8,life of ,j4 ,c4 ,maxwell10 p4 #ccb4 #cc 8,life of ,j4 ,c4 ,maxwell10 p4 #ccf4 #cd ,the ,professors who were consulted were ,challis1 ,willis1 ,stokes1 ,cayley1 ,adams1 and ,liveing4 #ce 8,life of ,j4 ,c4 ,maxwell10 p4 #cdi4 #cf 8,life of ,j4 ,c4 ,maxwell10 p4 #cha4 #cg 8,life of ,j4 ,c4 ,maxwell10 p4 #cgi4 #ch ,an account of the laboratory is given in ,nature1 vol4 x41 p4 #aci4 #ci ,the ,chancellor continued to take to the end of his life a warm interest in the work at the laboratory4 ,in #ahhg1 the ,jubilee year1 as ,proctor--at the same time ,i held the office of ,demonstrator--it was my duty to accompany the ,chancellor and other officers to ,windsor to present an address from the ,university to ,her ,majesty4 ,i was introduced to the ,chancellor at ,paddington1 and he at once began to question me closely about the progress of the laboratory1 the number of students1 and the work being done there1 showing himself fully acquainted with recent progress4 #dj ,in #ahid the list contained1 in ,part ,,ii41 sixteen names1 and in ,part ,i41 one hundred and three names4 #da ,under the new regulations ,physics was removed from the first part of the ,tripos and formed1 with the more advanced parts of ,astronomy and ,pure ,mathematics1 a part by itself1 to which only the ,wranglers were admitted4 ,thus the number of men encouraged to read ,physics was very limited4 ,this pernicious system was altered in the regulations at present in force1 which came into action in #ahib4 ,part ,i4 of the ,mathematical ,tripos now contains ,heat1 ,elementary ,hydrodynamics and ,sound1 and the simpler parts of ,electricity and ,magnetism1 and candidates for this examination do come to the laboratory1 though not in very large numbers4 ,the more advanced parts both of ,mathematics and ,physics are included in ,part ,,ii4 #db 8,life of ,j4 ,c4 ,maxwell10 p4 #chc4 #dc 8,statique ,exprimentale et ,thorique des ,liquides soumis aux seules ,forces ,molculaires40 ,par ,j4 ,plateau1 ,professeur l',universit de ,gaud4 #dd ,the 8,red ,lions0 are a club formed by ,members of the ,british ,association to meet for relaxation after the graver labours of the day4 #de 8,leonum arida nutrix40--,horace4 #df v4r41 endless4 #dg 8,life of ,j4 ,c4 ,maxwell10 p4 #cid4 #dh 8,life of ,j4 ,c4 ,maxwell10 p4 #djd4 #di ,in his 8,hydrodynamics10 published in #agch1 ,daniel ,bernouilli had discussed the constitution of a gas1 and had proved from general considerations that the pressure1 if it arose from the impact of a number of moving particles1 must be proportional to the square of their velocity4 7,see 8,pogg4 ,ann410 ,bd4 #ajg1 #ahei1 p4 #dij47 #ej ,the proof is as follows3-- ,if be the specific heat at constant volume1 at constant pressure1 and consider a unit of mass of gas at pressure p and volume v1 let the volume increase by an amount dv1 while the temperature dy4 ,thus d,t d,t pdv ,but pv ,t_/m ,hence p being constant1 pdv d,t_/m ,therefore #a_/m ,now suppose an amount of heat1 d,h1 is given to a single molecule and that its temperature is ,t4 ,its specific heat is 1 and d,h md,t ,but d,h d,t ,therefore m ,hence #a_/m _/ ,thus 7#a #b_/7c77 ,and _/ ,therefore #a #b_/7c7 ,or #b_/7c7-a77 #ea ,owing to an error of calculation the actual value obtained by ,maxwell from these observations for the coefficient of viscosity is too great4 ,more recent observers have found lower values than those given by him2 the difference is thus explained4 #eb ,studien ber das ,gleichgewicht der lebendigen ,kraft zwischen bewegten materiellen ,punkten ,sitz d4 k4 ,akad ,wien1 ,band ,,lviii41 #ahfh4 #ec ,another supposition which might be made1 and which is necessary in order to explain various actions observed in a compound gas under electric force1 is that the parts of which a molecule is composed are continually changing4 ,thus a molecule of steam consists of two parts of hydrogen1 one of oxygen1 but a given molecule of oxygen is not always combined with the same two molecules of hydrogen2 the particles are continually changed4 ,in ,maxwell's paper an hypothesis of this kind is not dealt with4 #ed ,nature1 vol4 #a41 p4 #aeb 7,december #acth1 #ahid74 #ee ,see papers by ,mr4 ,capstick1 ,phil4 ,trans41 vols4 #ahe-ahf4 #ef ,nature1 vol4 x4 #eg ,an historical account of the development of the science of electricity will be found in the article 8,electricity0 in the ,encyclopdia ,britannica1 ninth edition1 by ,professor ,chrystal4 #eh ,thomson 7,lord ,kelvin71 8,papers on ,electrostatics and ,magnetism10 p4 #ae4 #ei ,j4 ,j4 ,thomson1 ,b4,a41 ,report1 #ahhe1 pp4 #aji1 #aac1 ,report on ,electrical ,theories4 #fj ,papers on 8,electrostatics10 etc41 p4 #bf4 #fa ,it is difficult to explain without analysis exactly what is measured by ,maxwell's ,vector ,potential4 ,its rate of change at any point of space measures the electromotive force at that point1 so far as it is due to variations of the electric current in neighbouring conductors2 the magnetic induction depends on the first differential coefficients of the components of the electro-tonic state2 the electric current is related to their second differential coefficients in the same manner as the density of attracting matter is related to the potential it produces4 ,in language which is now frequently used in mathematical physics1 the electromotive force at a point due to magnetic induction is proportioned to the rate of change of the ,vector ,potential1 the magnetic induction depends on the 8curl0 of the ,vector ,potential1 while the electric current is measured by the 8concentration0 of the ,vector ,potential4 ,from a knowledge of the ,vector ,potential these other quantities can be obtained by processes of differentiation4 #fb ,the #d is introduced because of the system of units usually employed to measure electrical quantities4 ,if we adopted ,mr4 ,oliver ,heaviside's 8rational units10 it would disappear1 as it does in 7,b74 #fc ,for an exact statement as to the relation between the directions of the lines of electric displacement and of the magnetic force1 reference must be made to ,professor ,poynting's paper1 ,phil4 ,trans41 #ahhe1 ,part ,,ii41 pp4 #bhj1 #bha4 ,the ideas are further developed in a series of articles in the ,electrician1 ,september1 #ahie4 ,reference should also be made to ,j4 ,j4 ,thomson's 8,recent ,researches in ,electricity and ,magnetism40 #fd ,preface to ,newton's 8,principia10 #bnd edition4 #fe 8,lezioni ,accademiche0 7,firenze1 #agae71 p4 #be4 #ff ,in his sentence stands for the refractive index4 #fg ,hertz's papers have been translated into ,english by ,d4 ,e4 ,jones1 and are published under the title of ,electric ,waves4 #fh ,some of the consequences of this electrical resonance have been very strikingly shown by ,professor ,oliver ,lodge4 ,see ,nature1 ,february #bjth1 #ahij4 #fi ,hertz's original results were no doubt affected by waves reflected from the walls and floor of the room in which he worked4 ,an iron stove also1 which was near his apparatus1 may have had a disturbing influence2 but for all this1 it is to his genius and his brilliant achievements that the complete establishment of ,maxwell's theory is due4 #gj ,the analogy does not consist only in the agreement between the more or less accurately measured velocities4 ,the approximately equal velocity is only one element among many others4 #ga ,for a very suggestive account of some possible theories1 reference should be made to the presidential address of ,professor ,w4 ,m4 ,hicks to ,section ,a of the ,british ,association at ,ipswich in #ahie4 ,,index4 ,aberdeen1 ,maxwell elected ,professor at1 #de2 formation of ,university of1 #ea ,adams1 ,w4 ,g41 succeeds ,maxwell as ,professor at ,king's ,college1 ,london1 #eh ,adams ,prize1 ,the1 #dh2 gained by ,maxwell1 #ej ,ampre1 #aee1 #bjd ,ampre's ,law1 #aee1 #aef ,annals of ,philosophy1 ,thomson's1 #aab1 #aac 8,apostles10 club so called1 #cj1 #hi ,arago1 #aeg ,aragonite1 #bjj ,atom1 article by ,maxwell in ,encyclopdia ,britannica1 #ajh ,avogadros' ,law1 #aag1 #abd ,bakerian ,lecture1 delivered by ,maxwell1 #eh ,berkeley on the ,theory of ,vision1 #ch ,bernouilli1 ,d41 #aac ,blackburne1 ,professor1 #af ,blore1 ,rev4 ,e4 ,w41 #fg ,boehm1 ,bust of ,maxwell by1 #ij ,boltzmann1 ,dr41 #ace1 #acg1 #ach1 #add1 #baf ,boltzmann-,maxwell ,theory1 ,the1 #adj1 #ade ,boscovitch on ,atoms1 #ajh1 #aji ,boyle's ,law1 #aad1 #aag1 #abd ,brewster1 ,sir ,david1 on ,colour ,sensation1 #ii ,british ,association1 ,maxwell and1 #db1ed2 ,lecture before1 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#da2 ,helmholtz on1 #ii ,conductors and ,insulators1 ,distinction between1 #agc ,cookson1 ,dr41 #fa ,corsock1 ,maxwell buried at1 #ij ,cotes1 #bjb ,coulomb1 #aed ,curves1 investigated by ,maxwell1 #ai ,daniell's cells1 #gg ,democritus1 #ajh ,demonstrator of ,physics1 ,w4 ,garnett appointed1 #ge ,description of ,oval ,curves1 first paper by ,maxwell1 #ai ,devonshire1 ,duke of1 ,cavendish ,laboratory built by1 #gc1 #gd2 ,letter of ,thanks from ,university of ,cambridge1 #gd ,dewar1 ,miss ,k4 ,m41 her marriage to ,maxwell1 #ea ,dickinson1 ,lowes2 ,portrait of ,maxwell by1 #ij ,diffusion of gases1 #abh ,discs for colour experiments1 #ii-aja ,droop1 ,h4 ,r41 #eg ,dynamical ,theory of the ,electro-magnetic ,field1 ,maxwell on1 #eg1 #agg ,dynamical ,theory of ,gases1 ,maxwell on1 #eh1 #acd ,edinburgh ,academy1 ,maxwell's school-life at1 #ac-ah ,edinburgh1 ,royal ,society of1 ,maxwell at meetings of1 #ah ,edinburgh1 ,university of1 ,maxwell at1 #bb ,elastic ,spheres1 #add ,electric 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,professor1 #agg1 #baa ,forbes1 ,professor ,j4 ,d41 #ah1 #dd1 #ed2 friendship with ,maxwell1 #ai2 paper on ,theory of ,glaciers1 #ai2 resigns ,professorship at ,edinburgh1 #ed ,galvani1 #aee ,garnett1 ,w41 appointed ,demonstrator of ,physics at ,cambridge1 #ge2 ,life of ,maxwell by1 #id ,gases1 ,molecular theory of1 #eg1 #ajh2 ,waterston on general theory of1 #aah2 ,clausius on1 #aai2 diffusion of1 #abh ,gauss' ,theory1 #aef ,gay ,lussac's ,law1 #aag ,general ,theory of ,gases1 ,waterston on1 #aah2 ,clausius on1 #aai ,glenlair1 home of ,maxwell1 #aa1 #bc2 laboratory at1 #bd2 ,maxwell's life at1 #eh1 #ei2 8,electricity and ,magnetism0 written at1 #gi ,gordon1 ,j4 ,e4 ,h41 #gg1 #gh ,green1 ,g41 of ,nottingham1 paper on electricity and magnetism1 #aeh2 inventor of term 8,potential10 #aeh ,hamilton1 ,sir ,w4 ,r41 #bb ,hamilton's ,principle1 #aij ,heat1 ,text-book on1 by ,maxwell1 #gi ,helmholtz1 #ii1 #aef1 #aeg1 #age1 #bba ,henry1 ,j41 of ,washington1 on electro-magnetic induction1 #aeg ,herapath on molecules1 #aab-aaf ,hertz1 ,heinrich1 #bjd1 #bji-bac ,hicks1 ,w4 ,m41 #bba ,hockin1 ,c41 #ef ,holman1 ,professor1 #acc ,iceland ,spar1 #bjj ,insulators and ,conductors1 ,distinction between1 #agc ,jenkin1 ,fleeming1 #ee1 #ef ,kelland1 ,professor1 #bb ,kelvin1 ,lord1 #af1 #adb1 #aeh1 #aei1 #afj1 #afh2 on the ,uniform ,motion of ,heat1 #afj2 papers on ,electricity and ,magnetism1 #afa1 #afb ,kinetic energy1 #abd1 #abi1 #acf1 #aci1 #aia ,king's ,college1 ,london1 ,maxwell elected ,professor at1 #ed ,kohlrausch1 #bjf ,kundt1 #acb ,labile ,ether1 #bbj ,laboratory at ,glenlair1 #bd ,lagrange1 #agi ,lagrange's ,equations1 #agi1 #aij ,laplace1 #aee ,larmor1 ,j41 #ada1 #adb ,lecher1 #bad ,lenz1 #aeg ,litchfield1 ,r4 ,b41 #df ,light1 ,electro-magnetic ,theory of1 #agd2 ,waves of1 #aih1 #aii ,lodge1 ,professor1 book on ,modern ,views of ,electricity1 #agg ,lucretius1 #ajh ,luminous ,radiation1 #bba ,mathematical ,tripos at ,cambridge1 subjects1 #fj2 ,maxwell an examiner for1 #fj1 #hj2 experimental work in1 #gf ,matter and ,motion1 ,maxwell on1 #gi ,maxwell1 ,james ,clerk1 parentage and birthplace1 #aj1 #aa2 childhood and school-days1 #ab-ah2 his mother's death1 #ac2 first lessons in geometry1 #ag2 attends meetings of ,royal ,society of ,edinburgh1 #ah2 his first published paper1 #ai2 friendship with ,professor ,forbes1 #ai2 his polariscope1 #bj2 enters the ,university of ,edinburgh1 #bb2 papers on ,rolling ,curves and ,elastic ,solids1 #bc2 vacations at ,glenlair1 #bc2 laboratory at ,glenlair1 #bd2 undergraduate life at ,cambridge1 #bh-cf2 elected scholar of ,trinity1 #bi2 illness at ,lowestoft1 #bi2 his friends at ,cambridge1 #cj2 ,tripos and degree1 #ce-cg2 early researches1 #ch-dd2 paper on ,colours1 #dj1 #da2 elected ,fellow of ,trinity1 #dc2 ,lecturer at ,trinity1 #dc2 ,professor at ,aberdeen1 #de2 his father's death1 #de2 gains the ,adams ,prize1 #ej2 marriage1 #ea2 powers as teacher and lecturer1 #eb1 #ec2 ,professor at ,king's ,college1 ,london1 #ed2 gains the ,rumford ,medal1 #ee2 delivers ,bakerian lecture1 #eh2 resigns ,professorship at ,king's ,college1 ,london1 #eh2 life at ,glenlair1 #eh1 #ei2 visit to ,italy1 #ei2 ,examiner for ,mathematical ,tripos1 #fj1 #hj2 elected ,professor of ,experimental ,physics at ,cambridge1 #fh2 ,introductory ,lecture1 #fh-gb2 ,examiner for ,natural ,sciences ,tripos1 #gi2 articles in ,encyclopdia ,britannica1 #hj1 #aah1 #adf2 papers in ,nature1 #hj2 lectures before ,british ,association and ,chemical ,society1 #hj-hb2 humorous poems1 #hc-hg2 delivers ,rede ,lecture on the ,telephone1 #hi2 last illness and death1 #hi1 #ij2 buried at ,corsock1 #ij2 bust and portrait1 #ij2 religious views1 #ia1 #ib ,maxwell1 ,john ,clerk1 #aj1 #aa ,meyer1 ,o4 ,e41 #acc ,mill's ,logic1 #ch ,molecular ,evolution1 ,lines on1 #he ---- ,physics1 #id ---- ,constitution of ,bodies1 ,maxwell on1 #adf ---- ,theory of ,gases1 #eg1 #ajh ,molecules1 #aji1 #aaj2 ,herapath on1 #aab-aaf2 lecture by ,maxwell on1 #adf ,motion of 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,thomson's ,annals of ,philosophy1 #aab1 #aac ,uniform ,motion of ,heat in ,homogeneous ,solid ,bodies1 paper by ,lord ,kelvin1 #afj1 #afa ,university ,commission1 #dg1 #dh1 #fb ,urr1 ,vale of1 #aa ,vector ,potential1 ,the1 #afe1 #bba ,viscosity of ,gases1 ,experiments on1 #eh1 #abe1 #acb ,volta1 ,inventor of voltaic pile1 #aee ,waterston1 ,j4 ,j41 on molecular theory of gases1 #aad1 #aae2 on general theory of gases1 #aah ,waves of ,light1 #aih1 #aii ,weber1 ,w41 #aef1 #bjf ,wedderburn1 ,mrs41 #ad ,wheatstone's ,bridge1 #gg ,williams1 ,j41 ,archdeacon of ,cardigan1 #af ,willis1 ,professor1 #dd ,wilson1 ,e41 lines in memory of1 #hf1 #hg ,young1 ,t41 on colour sensation1 #ig1 #ih ,,printed ,,by ,,cassell ,,company1 ,,limited1 ,,la ,,belle ,,sauvage1 ,,london1 ,e4,c4 99 99 99 99 99 99 ,transcriber's note3 ,punctuation1 hyphenation1 and spelling were made consistent when a predominant preference was found in the original book2 otherwise they were not changed4 ,simple typographical errors were corrected2 unpaired quotation marks were remedied when the change was obvious1 and otherwise left unpaired4 ,illustrations in this e,book have been positioned between paragraphs and outside quotations4 ,footnotes1 originally at the bottoms of pages1 have been collected1 renumbered1 and placed just before the ,index4 ,the ,index was not checked for proper alphabetization or correct page references4 ,some values in the original book are known today to be incorrect1 but have not been changed here4 ,page #acc3 ,the last equation on the page1 7#a 4#jjbge t - 4#jjjjjjcd t7 was misprinted as #a 4#jjbge t 4#jjjjjjcd t4 ,it is shown here with corrections based on its cited source3 https3_/_/archive4org_/details_/s#jephil osophicalmag#balonduoft_/page_/#bab ,page #add3 8possibly of ether atoms bound with them0 was printed that way1 but 8ether0 may be a misprint for 8other04 ,page #agj3 8hence at ,c1 where they touch0 was printed as 8,a01 but ,figure #a at that point is labelled 8,c04