REESE LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 Class No. 
 
OEIGINAL PAPERS 
 
 BY 
 
 JOHN HOPKINSON 
 
itonUon: 0. J. CLAY AND SONS, 
 CAMBRIDGE UNIVERSITY PRESS WAKEHOUSE, 
 
 AVE MARIA LANE. 
 laggoto: 50, WELLINGTON STREET. 
 
 ILetpjtfl: F. A. BROCKHAUS. 
 gorfe: THE MACMILLAN COMPANY. 
 E. SEYMOUR HALE. 
 
 [All Rights reserved] 
 
ORIGINAL PAPERS 
 
 BY THE LATE 
 
 JOHN HOPKINSON, D.So., F.R.S. 
 
 VOL. I. 
 TECHNICAL PAPERS 
 
 EDITED 
 
 WITH A MEMOIR 
 
 BY 
 
 B. HOPKINSON, B.Sc. 
 
 CAMBRIDGE: 
 
 AT THE UNIVERSITY PRESS. 
 1901 
 
It 
 
 'Nl 
 
 Cambridge: 
 
 PRINTED BY J. AND C. F. CLAY, 
 AT THE UNIVERSITY PRESS. 
 
CONTENTS OF VOL. I. 
 
 PAGE 
 
 Memoir . . .. . ........ i 
 
 Memorandum on Engineering Education . . . . . . Ixiii 
 
 (Written for a Cambridge University Syndicate in 1890.) 
 
 1. Group-Flashing Lights 1 
 
 (Pamphlet first published in October 1874.) 
 
 2. The Electric Lighthouses of Macquarie and of Tino . . 7 
 
 (From the Proceedings of the Institution of Civil Engineers, Vol. 
 LXXXVII. Session 188687, Part I.) 
 
 3. On Electric Lighting . . . , . . . . . 32 
 
 (From the Proceedings of the Institution of Mechanical Engineers, 
 April 25th, 1879.) (First Paper.) 
 
 4. On Electric Lighting 47 
 
 (From the Proceedings of the Institution of Mechanical Engineers, 
 pp. 266274. April 23rd, 1880.) (Second Paper.) 
 
 5. Some points in Electric Lighting . . . . . . 57 
 
 (A Lecture delivered at the Institution of Civil Engineers, April 5th, 
 
 1883.) 
 
 6. Dynamo-Electric Machinery 84 
 
 (From the Philosophical Transactions of the Royal Society, Part I., 
 1886.) 
 
 7. Dynamo-Electric Machinery 122 
 
 (From the Proceedings of the Royal Society, VoL LI., 1892.) 
 
 8. On the Theory of Alternating Currents, particularly in reference 
 
 to Two Alternate-Current Machines connected to the same 
 
 Circuit 133 
 
 (From the Proceedings of the Institution of Electrical Engineers, 
 pp. 321, November 13th, 1884.) 
 
 b2 
 
 95827 
 
vi CONTENTS. 
 
 PAGE 
 
 9. Note on the Theory of the Alternate Current Dynamo . . 152 
 (From the Proceedings of the Royal Society, Vol. XLII., pp. 167 170.) 
 
 10. Alternate Current Dynamo-electric Machines .... 156 
 
 (From the Philosophical Transactions of the Royal Society, 1896, 
 pp. 229252.) 
 
 11. An Unnoticed Danger in certain Apparatus for Distribution of 
 
 Electricity 184 
 
 (From the Philosophical Magazine, September, 1885.) 
 
 12. Induction Coils or Transformers . . . . . . .188 
 
 (From the Proceedings of the Royal Society, February, 1887.) 
 
 13. Report to the Westinghouse Company of the test of two 
 
 6,500-watt Westinghouse Transformers. May 31st, 1892 . 192 
 
 14. Presidential Address to the Institution of Electrical Engineers, 
 
 January 9th, 1890 212 
 
 (Magnetism.) 
 
 15. Inaugural Address, Institution of Electrical Engineers, January 
 
 16th, 1896 236 
 
 16. Presidential Address to the Junior Engineering Society*, Novem- 
 
 ber 4th, 1892, On the Cost of Electric Supply . . . 254 
 (From the Transactions of the Junior Engineering Society, Vol. in., 
 Part I., pp. 114.) 
 
 17. Relation of Mathematics to Engineering 269 
 
 (From the Proceedings of the Institution of Civil Engineers, Vol. 
 cxvm., Session 1893 1894, Part IV. " James Forrest " Lec- 
 ture.) 
 
 * Now the Institution of Junior Engineers. 
 
 PORTRAITS. 
 
 Dr Hopkinson at the age of forty-eight .... Frontispiece 
 
 Dr Hopkinson at the age of about twenty-three . . To face page xxx 
 
EDITOR'S NOTE. 
 
 WITH the exception of the Memorandum on Engineering 
 Education, the whole of the papers here reprinted have been 
 published in various periodicals and books, and I have to thank 
 the owners of the copyrights for permission to republish them. 
 Dr Hopkinson issued a reprint of certain of his papers in 1893*, 
 and intended to publish a complete collection. I have endeavoured 
 in this reprint to carry out bis intentions as to editing so far as 
 they could be ascertained. In a few cases I have copies on which 
 he noted certain omissions as desirable ; in others I have had to 
 use my own judgement as to what he would have done. The 
 omissions on the whole, however, are few ; and the papers for 
 the most part are reprinted just as they appeared with obvious 
 corrections. Vol. I., roughly speaking, contains the papers on 
 technical subjects, and Vol. n. those of a more scientific character. 
 The papers fall naturally into groups based on their subjects, and 
 have been so arranged. 
 
 I have to thank Mr G. T. Walker, Fellow of Trinity College, 
 Cambridge, for kindly reading the Mathematical papers at the 
 end of Vol. n. for me. 
 
 * " Original Papers on Dynamo-Machinery and allied Subjects." Whittaker & Co. 
 
MEMOIK. 
 
 THESE volumes contain all that John Hopkinson wrote of an 
 original character on Engineering or Scientific subjects. They 
 form a record of his career to which little can be added. His 
 practical inventions, and certain parts of his constructive en- 
 gineering, however, are not directly illustrated in them, and 
 a short account of these may perhaps enhance the value of the 
 book as a memorial. It is also desirable from this point of 
 view, as well as interesting as a matter of history, to trace the 
 influence of his work on the development of the Arts and 
 Sciences with which it dealt. There have been few men in 
 whose minds the spirit of scientific research has been so 
 closely associated with the power of practical application as 
 in Hopkinson's. His scientific work was always informed with 
 a desire to satisfy practical needs, without being unduly cramped 
 thereby. Thus, while in many cases it resulted in rapid Engi- 
 neering advance, it also exercised a great influence on methods 
 of research. It was conceived in sympathy with practical aims 
 and practical men's ideas and yet it did not cease to be pure 
 and disinterested seeking after knowledge. To those who know 
 his work in only one of these aspects, a connected account of it 
 showing something of the other may be acceptable ; and finally, 
 a little should be said of his education, which was in many ways 
 remarkable. 
 
 To give much more than this in the way of biography is 
 hardly possible. John Hopkinson's life had few features of in- 
 terest for the general public: this is, perhaps, inevitable of 
 one whose work dealt with natural and not with human forces. 
 
X MEMOIR. 
 
 In the relations with the world of a statesman or a soldier 
 personality is all-important and feeling may be a very powerful 
 factor. It is therefore of interest, after his death, to know the 
 emotional as well as the rational side of his nature, and there 
 is justification for revealing it by a detailed account of his 
 private life. With an engineer it is different. If a man would 
 command Nature, emotion is out of place ; and the more he 
 can efface himself and become a thinking machine, the more 
 likely he is to succeed. Hopkinson had this power in an un- 
 common degree ; once in his office, his reasoning faculty asserted 
 itself to the exclusion of all others. It is true that he could com- 
 mand not only the respect, but the love, of those who served 
 him, so that they worked for him as they would for few. But 
 this power was accompanied by no feeling on his part, and, though 
 it was doubtless due to a subtle influence which could not have 
 been exercised by one of less perfect character, it may be said 
 broadly that a very great part of his personality found no ex- 
 pression in his work and therefore does not concern the public. 
 There seems, in his case, to be no excuse for revealing in its 
 entirety after his death, what in life he did not reveal. He was 
 the most reserved of men, and only his family knew him inti- 
 mately. 
 
 Another cause would make it difficult if it were desirable 
 to write an interesting life of John Hopkinson. It sometimes 
 happens in a great man's career that the whole force of his 
 nature is pitted in a struggle with adverse circumstances. Such 
 occasions form the most valuable items in biography. But they 
 depend for their interest on the sternness of the struggle no 
 less than on the might of the combatants. It is something 
 for the biographer to be able to say that his subject overcame 
 such and such things: it is far more if it can be said that he 
 only just overcame them. Of strife of this evenly-balanced 
 kind there was none in John Hopkinson's life. He had his 
 battles to fight like other men, and against odds that lesser 
 minds could not have faced. But the issue never seemed in 
 doubt ; he always won with an unknown reserve in hand. From 
 contemplation of what he did, one can infer no limitation to 
 
MEMOIR. xi 
 
 his powers. And in such limitation centres no little of the 
 interest of biography, for upon it depends in large measure the 
 sympathy which the reader may feel for the subject. In con- 
 sequence, too, of his freedom from disappointment, Hopkinson 
 changed remarkably little after early manhood. In most lives 
 adversity comes in plenty and leaves its mark good or bad 
 upon character: none came to John Hopkinson. For twenty- 
 five years the only change in him was a gradual and unresisted 
 expansion. As he came to feel his strength his power of expres- 
 sion grew, and with happy family life his sympathies widened : in 
 other ways he altered little. Reading the letters which he wrote 
 long ago from Cambridge and Birmingham, on the threshold of his 
 career, one seems to see the same man in all essentials whom 
 one knew quite recently. I feel, therefore, that it will suffice 
 for the non-technical part of this introduction if I can give 
 a short account of him as he was then, and of how he came 
 to be so. This course is possible because biographical material 
 is fairly plentiful during the first thirty years of his life. His 
 letters reveal far more of himself then than later, when they 
 came to be mere records of passing events, given without com- 
 ment and affording but little clue to the state of mind of the 
 writer. 
 
 John Hopkinson was by birth and breeding a North-country- 
 man. His mother born Alice Dewhurst of Skipton was of 
 a family which has occupied a leading position in that town 
 for several generations. Her father was the founder, and her 
 brothers for long the heads, of the successful cotton-spinning 
 factory which bears their name. Mr Dewhurst, John's grand- 
 father, was in many ways an ancestor to be proud of. In early 
 life he suffered much trouble in the death of his wife and all 
 his family ; but he married again, and had many children. One 
 can infer that he possessed much of the immense vitality and 
 energy which distinguished his grandson. As John knew him, 
 he was a fine old Yorkshireman, impetuous, even fiery, but 
 possessed of the kindest of hearts. He was much troubled 
 with rheumatism, but he fought his malady with the most 
 indomitable courage and tenacity. His grandson had a vivid 
 
Xli MEMOIR. 
 
 recollection of his hobbling round his garden, determined not 
 to give in to his infirmity. He had strong religious views, and 
 brought up his children on nonconformist principles which they 
 taught with undiminished vigour in their own families. The 
 spirit, if not the form, of his fine puritanical creed lives in 
 many of his descendants to-day, and in none is it more ap- 
 parent than it was in John Hopkinson. It was the expression 
 of a sturdy independence of character, and it taught an almost 
 stern devotion to truth and duty. These were the qualities 
 which Alice Hopkinson learnt from her father and passed on 
 to her son. Of the narrowness which sometimes marred the 
 nonconformist faith in those days there was none in her 
 teaching. Thus it was, that though John Hopkinson in part 
 rejected the form of her creed, he was able to keep its essence, 
 and this slight divergence never affected the sympathy between 
 him and his mother. To the end of his life it remained, a 
 perpetual joy to both of them. 
 
 John Hopkinson's father, now Alderman Hopkinson of 
 Manchester, was born in Lancashire and began life as an 
 apprentice in the firm of Wren and Bennett, manufacturing 
 engineers. In this concern he became a partner, held that 
 position until 1881, and then devoted himself exclusively to 
 consulting work. He was interested in several coal and iron 
 enterprises and has been for many years Chairman of the 
 Carnforth Iron Works. He has made himself an honoured 
 name in connection with the affairs of his native city ; his 
 membership of the Council dates from 1861 and he was Mayor 
 in 1882. As an engineer, he was brought up in a school in 
 which practical experience was regarded as the one essential to 
 success : but though in the first place practical, he had a re- 
 markable sympathy with scientific development. His training 
 made him attach much importance to precedent ; but if con- 
 servative, he was by no means conventional in his ideas. He 
 had much of the independence which so distinguished his eldest 
 son. Especially was this the case in matters relating to the 
 education of his children. In sending John to Cambridge while 
 intending him to be an engineer, he went contrary to all 
 
MEMOIR. xiii 
 
 the traditions as to technical training in which he had been 
 brought up. 
 
 It is inevitable that in the first few years of childhood the 
 mother's influence should be the more potent; and this was 
 doubtless the case with John Hopkinson, though less so than 
 usual : Mr Hopkinson, more than most fathers, made companions 
 of his children, and John, the eldest, was constantly with him 
 from a very early age. He was a teacher of exceptional ability, 
 and during the long rambles in the Lake District and Wales 
 and the visits to the Works when he accompanied his father, 
 John must have learnt something of his powers of observation 
 and have acquired some of his bent towards engineering and 
 scientific pursuits. A singularly complete education rather ef- 
 faced the surface effects of these early years, and it is perhaps 
 difficult to find indications of their importance for those who 
 have only known John Hopkinson as a man and have never 
 known his parents. Others more fortunate, who have seen 
 Mr Hopkinson with children even in his old age, will be able 
 to form some idea of his relations with John at a time when 
 the father was full of youthful vigour and the son a bright 
 and healthy boy, eager for information on all going on around 
 him. Though the first-born was naturally the most favoured 
 one, all the family shared in the advantage of having such 
 a father. Of the five sons, three, including John, became en- 
 gineers of distinction. A fourth, Albert, is a doctor of medicine 
 in large practice in Manchester. Alfred, who was second in 
 order of age, became Principal of Owens College in 1898 after 
 a successful career at the Bar and in Parliament. Such diverse 
 successes in one family must be largely due to home influences ; 
 to the father is to be ascribed the aptitude for scientific and 
 practical pursuits which has been so apparent in four of his 
 sons and most of all in the eldest. 
 
 After a short time at a day-school near his home, John was 
 sent to Lindow Grove in Cheshire. This school was then in 
 the hands of a Mr Satterthwaite ; but, in the summer of 1861, 
 it passed into those of Charles Willmore, who, for some years 
 after this, had charge of John's education and undoubtedly 
 
XIV MEMOIR. 
 
 exercised great influence upon him. His views on the training 
 of boys were remarkable and are worth quoting here, as they 
 furnish the key to much in John Hopkinson's early training. 
 In a letter written to him in December 1866, Willmore says : 
 "I greatly object to long hours of study for boys. I have 
 a great belief in the physical development being the main 
 thing till the time a boy leaves school ; that is for what I have 
 just said might be misinterpreted that any intellectual advance 
 at the expense of health is very dearly bought." These doc- 
 trines he practised consistently without much regard for what 
 the world thought of them. The school was situated in fine 
 country and the boys were encouraged to spend much of their 
 time out of doors. Thus the taste for open-air pursuits which 
 Mr Hopkinson had given to John was further strengthened by 
 his school-life, and this was beyond question the most important 
 feature of that part of his education : its effects never left 
 him. Throughout his life he rejoiced in exercise and fresh air 
 beyond all things. As he himself put it, Willmore taught him 
 the "self-regarding virtues." and that, in his case, put all the 
 other teaching in the shade, good though it was. But for his 
 healthy tastes, his rather delicate body could hardly have carried 
 " that most fiery spirit." Of course he might have acquired them 
 at one of the Public Schools though there were not so many of 
 them in country districts then as there are now. But it must 
 be remembered that John Hopkinson did not belong to the class 
 from which Public School boys are drawn. His father intended 
 him to be an engineer ; he had neither the inclination nor the 
 means to let his son spend five years in enjoying himself and 
 learning Latin verse at Harrow or Rugby. It was necessary 
 that he should get as much knowledge of a useful kind as 
 possible in the short time available before taking to business. 
 Willmore was almost alone among schoolmasters in seeing that, 
 even for boys of such a class, health and healthy tastes were 
 more necessary still ; and in acting on his belief. Unfortunately, 
 parents did not all show such wisdom as Mr Hopkinson did, 
 and realise the soundness of these views. Willmore's firm 
 stand against all manner of cramming and excessive study for 
 
MEMOIR. XV 
 
 examinations, perhaps cost him many pupils ; but he never 
 wavered from it and it has set an honourable and distinctive 
 stamp upon his work. 
 
 So it happened that John Hopkinson had a thoroughly good 
 time at school. Without being precocious, he had more than 
 common intelligence and was able, without great difficulty, to 
 hold his own with his schoolfellows at their lessons. The atmo- 
 sphere of his home gave him a tendency to hard work; but he 
 was by no means a book-worm, and had much time and energy 
 to spare for enjoying life. One letter, written from Lindow 
 Grove, may perhaps be quoted here: it gives an idea of what 
 he was like shows that he already had a sturdy, independent 
 character: "There was a row yesterday about jumping over 
 the farmer's bank ; after all, though, we have paid very cheap 
 for the fun. The farmer, when he caught them, used all sorts 
 of imprecations at them ; he said if he ever caught them again 
 he would take them to Macclesfield. I was not in the party 
 that he met. I do not believe that he would have told if it 
 had not been that when he shouted most of the boys of our 
 party ran. I did not. I think if we had walked away quietly, 
 he would have been satisfied, but as they ran he thought that 
 we meant it to annoy him. We had a very great deal of fun, 
 and we only got stopped going walks." 
 
 In 1864 Mr Willmore left Lindow Grove and became head- 
 master of Queenwood in Hampshire. John and some other boys 
 accompanied him thither. The school was situated in wild and 
 beautiful country on the confines of the New Forest. No better 
 place could be found for carrying out Willmore's ideas of education. 
 Unfortunately, discipline had been rather slack under his pre- 
 decessor, and he had at first to be rather strict. John's letters 
 were mournful for the first few weeks because he could not 
 go for long walks in the surrounding country ; he evidently felt 
 this restriction deeply; but it was soon relaxed and then for a year 
 his life was more enjoyable even than at Lindow Grove. Mr 
 Willmore says that he developed greatly at this time both in body 
 and in mind. He was great at bird-nesting and would go about 
 it with much energy and daring, climbing the highest forest trees 
 
XVI MEMOIR. 
 
 in search of eggs. Then in summer there were hornets' nests to 
 be taken and butterflies to be caught. He used to tell a story of 
 how he once caught some hornets for one of the masters. The 
 insects were duly presented, shut up in a bottle : the master 
 expressed a hope that " the cat's paw wasn't burnt." " No," said 
 John, "and I hope the monkey's mouth won't be"; a retort of which 
 he was always very proud. Similar touches of humour abound in 
 his letters. He seems to have shown a decided bent for mathe- 
 matics while at Queenwood. He was, in fact, rather beyond the 
 teaching provided in this subject ; though it was probably much 
 better than could be found in most schools of the same class. He 
 also received a fair grounding in Chemistry. In its teaching of 
 Science, though it was rudimentary compared with what one finds 
 now, Queenwood was almost unique at that time. Among its 
 masters, it had counted Tyndall, Frankland, and Debus. 
 
 One may fittingly close this sketch of John's time with 
 Willmore by giving his own views of it. They are recorded in a 
 speech delivered at a dinner given by old Queenwood boys in honour 
 of their schoolmaster. He says, referring in half-serious spirit 
 to the virtues which they owed to Mr Willmore : " I will confine 
 myself to one virtue, yielding in importance to none, one which 
 I suppose moralists would class as a self-regarding one, one which 
 has not received a place in systems of ethics I mean that of 
 obtaining through life such enjoyment as it is capable of affording. 
 As far as I can remember, Mr Willmore did not inculcate this 
 virtue upon us, but I am bound to say that he gave us every 
 opportunity of practising it, and he was never better pleased than 
 when he saw us practising it with reasonable discretion.... I am 
 sure that if it were possible for one of us to do a thing that was 
 mean or shabby, one of the greatest deterrents to his being guilty 
 of it would be to remember the burning scorn with which Mr 
 Willmore would have regarded anything of the kind when he was 
 at school." 
 
 Early in 1865, when he was 15| years of age, John Hopkinson 
 began his student days at Owens College. At that time the 
 education furnished by Owens was the nearest approach there was 
 to what is now considered the proper training for an Engineer. 
 
MEMOJR. xvii 
 
 Cambridge had not yet awakened to her responsibilities in this 
 respect and the more old-fashioned engineers thought that their 
 sons should go into the shops at fourteen. Owens aimed at re- 
 placing the first three years of an engineer's " time " with a more 
 liberal and wider education than could be found in the workshops. 
 The spirit of the place was much the same as it is now, though 
 the appliances for teaching were far less elaborate. If the great 
 laboratories which are now the pride of the College were not yet 
 made there was plenty of experimenting for lecture purposes 
 within its walls. There (and at that time only there) the best of 
 teaching in experimental science and in engineering subjects was 
 combined with pure mathematics and other studies of an academic 
 character. Sandeman, the purest of pure mathematicians, of whom 
 it is said that Hopkinson was the only man who ever understood 
 his lectures, Barker, more practical but still a typical senior 
 wrangler, taught under the same roof with Roscoe and Schor- 
 lemmer the chemists and Clifton the physicist. These were the 
 men who were Hopkinson's teachers just at the time when his 
 studies were becoming important. He soon began to impress 
 them with his ability. He showed up ahead of his fellow students 
 in the College competitions from the first ; even in German he 
 got a certificate evidence of general power, but not, I fear, of 
 lasting proficiency. It was his mathematics which won his 
 successes ; he did not care for and could not remember the long 
 string of facts, which then formed so large a part of chemistry ; 
 but he could do sums a power rare among chemistry students, 
 and therefore liberally rewarded with marks. 
 
 Hopkinson's examinations and his success therein were a 
 somewhat remarkable feature of his life. They began with the 
 Dalton scholarships in 1867, in which year also he matriculated 
 at London University (coming out ninth in the Honours Division), 
 and continued almost without intermission until he took his 
 fellowship at Trinity in 1871. His first attempt was for a small 
 exhibition at Owens in 1865 and it failed because he worked too 
 hard in preparing for it. This little disaster, taken very seriously 
 at the time, gave him a horror of cramming which never left him. 
 In certain subjects, such as Botany, which were out of his line, but 
 
XV111 MEMOIR. 
 
 of which regulations required that he should show some knowledge, 
 he would occasionally condescend to it, but in Mathematics and 
 Physics he regarded it as quite useless even for the immediate 
 purpose of impressing an examiner. Thus his academic successes 
 were a real index of his remarkable quickness of mind and not, as 
 is so often the case, merely evidence of a good memory and of 
 great industry. He hardly ever missed being first in a competition 
 in which he was seriously interested. Few men have made so 
 large a sum as he did in this way : none have repaid it more 
 fully to the world. 
 
 While at Owens, Hopkinson lived at home. His brothers were 
 then, as they always remained, his principal companions ; and he 
 had few other intimate friends. John Hopkinson took a high 
 view of his responsibilities as eldest son and at quite an early 
 age he began to assist in teaching the younger members of the 
 family. When they grew older they followed in his footsteps. 
 Everything that he did, and especially new departures, such as 
 going to Cambridge, had far-reaching effects as an example to his 
 brothers. His brilliant success in all that he undertook gave them 
 confidence in following him. Later still, when he came to occupy 
 an influential position, he helped them in every possible way. He 
 had very strong clan feeling, based no doubt partly on sentiment, 
 but largely also upon knowledge of the power of a united and able 
 family. In recent years this appeared even more in his relations 
 with his own children. That which made him an ideal elder 
 brother made him also a perfect father. 
 
 This is perhaps the place to say something of Hopkinson's life 
 in the mountains, for it was there that his friendship with his 
 brothers, and later with his children, found its most perfect 
 expression. Reference has already been made to his tree- 
 climbing proclivities while at school. During the vacations at 
 Owens he began to find more magnificent game in the hills. The 
 expeditions in North Wales and the Lake District were probably 
 not so sensational as they afterwards became, but in the course of 
 their long tramps the brothers must have come across many 
 pieces of scrambling which would test steadiness of head and 
 sureness of foot. Rock-climbing is probably the finest of all 
 
MEMOIR. xix 
 
 exercises in the variety of its demands upon bodily activity ; and 
 his apprenticeship in the art did much to consolidate Hopkinson's 
 frame. He was of a very spare and wiry build with a long reach. 
 When at the height of his powers few men were his equal upon 
 difficult rock. It was not till comparatively late in life that he 
 took to mountaineering as a sport, but when once he had tasted 
 its joys he cared for no other recreation. His first visit to the 
 Alps was in the Autumn of 1871 just after he left Cambridge, but 
 the fascination of the snows apparently did not seize upon him 
 then, and it was not until some years later that he began to 
 spend his summer vacation there regularly. He reached the 
 zenith of his strength and activity when he was about forty years 
 of age. At that time he was a truly magnificent sight upon a 
 mountain. I have seen him ploughing through soft snow up to 
 his waist on the slopes of the Aletschhorn and tiring out men ten 
 years his junior who had but to follow in his tracks. On other 
 occasions he would lead, carrying the day's provisions, over rocks 
 where his companions could scarcely follow him unloaded. He 
 seemed to need no sleep, he would do two long ascents in con- 
 secutive days, and enjoy both thoroughly. He and his brothers 
 soon got beyond the powers of the average Swiss guide. I 
 remember several occasions in which we took one to make up our 
 party, but it was always a failure ; the poor man was too slow 
 and generally had reason to regret his job, for my father was 
 exceedingly impatient of being kept back. He took pleasure, but 
 to no inordinate degree, in making new ascents; his sentiment 
 in the matter was much the same as in scientific discovery. In 
 the one case as in the other, he cared quite as much for his 
 own feeling that he stood where no man had been before, as for 
 public knowledge of that fact, and despised all squabbling for 
 priority. The fascination of the sport for him perhaps needs no 
 explanation; nothing else within his reach could seize his attention 
 and require the exercise of all his bodily and mental faculties. 
 If he rode on horseback, his active mind was always occupied 
 with some point in his work. Golf, shooting, fishing had no 
 attractions for him. Nothing seemed to serve him as a holiday 
 and set him up for the next year's labours except a month in the 
 
 H. I. 
 
XX MEMOIR. 
 
 Alps. Though it was the immediate cause of his death I cannot 
 regret that he was a mountaineer, for it was in the Alps that one 
 came to know him best. There alone the enthusiasm and poetry 
 in his nature would blaze forth unrestrained. 
 
 Mr Hopkinson intended that his eldest son should join him 
 in his own works and to that end would probably have put him 
 to practical work in the shops on his leaving Owens : he certainly 
 had no thought of sending him to Cambridge. In those days a 
 Cambridge education was considered to be waste of time for an 
 engineer. The successful members of the profession had had no 
 such education themselves ; many of them had started as common 
 workmen. The consequence was that most engineers, including 
 John Hopkinson J s father, did not even number College men among 
 their acquaintance, much less thought of sending their sons to a 
 University. The initiative in Hopkinson's case came from the boy 
 himself. Young though he was, he had remarked that the engineers 
 of the time suffered from the narrowness of their training. They 
 began with practical experience, and if they kept pace at all with 
 the developments in their Art following in the wake of science, 
 they had to learn that science late in life. John determined that 
 he would reverse the process and devote some time to the study 
 of science before beginning to practise. Mr Willmore seems to 
 have been the first to hint to him and to his father that he might 
 score academic successes in a wider field than Owens. It was, 
 however, principally due to Professor Barker that the idea of 
 seeking at Cambridge his engineering education took definite 
 shape in his mind. Ifc was Barker's advice and encouragement 
 which led him in the spring of 1867 to enter for a Mathematical 
 Scholarship at Trinity College. He was first among some thirty 
 competitors. His success settled any doubts which his father 
 might have felt and in October of the same year he began his 
 University life. 
 
 The Trinity Scholarship examination was the first in which 
 Hopkinson met men other than his fellow-students at Owens. 
 Among his competitors were of course some of the best of his 
 year at Cambridge. His success in it therefore established his 
 reputation for ability in a wider circle than Owens College, 
 
MEMOIR. XXI 
 
 and he added to it by his performance in the First B.Sc. Exami- 
 nation, at London University. Then as now, this competition, 
 owing to its high standard and the emoluments associated with 
 it, attracted the best Cambridge mathematicians in their first 
 and second years. Among those who were in the honours 
 division about this time were Moulton and Harding senior 
 wranglers and W. K. Clifford, who was second in the Tripos. 
 Hopkinson was beaten for the Mathematical Exhibition by 
 Pendlebury, who was a year senior to him at Cambridge and 
 was subsequently senior wrangler, but he obtained sufficient marks 
 to qualify for it and won the exhibition for Natural Philosophy 
 and Chemistry. It is therefore not surprising that when he went 
 to Cambridge he was already regarded as the probable senior 
 wrangler of his year. For private tuition, he went to Routh, who 
 had for some years held the first place as mathematical coach. 
 His academic career was much like that of other men destined to 
 be senior wrangler, though it was more than usually free from 
 failures. He took in succession the Sheepshanks Exhibition, the 
 Scholarship in Mathematics at London, and all the other honours 
 and emoluments which fall to the lot of the first mathematician 
 of his year at Cambridge. It is unnecessary to catalogue them 
 here ; they can be found in the University Calendars of the time. 
 Perhaps, however, the Whitworth Scholarship deserves more 
 particular mention. These scholarships were founded with a view 
 " to the promotion of engineering and mechanical industry in this 
 country." The examination was largely of a practical character 
 and Hopkinson's success in it is a reminder that in his academic 
 surroundings he did not forget what he had learnt in his father's 
 works. Indeed he was in the habit of spending a large part of 
 his vacations there, an excellent corrective to the Cambridge of 
 those days with its horror of all things technical. 
 
 To one who is not specially interested in his Engineering 
 work, Hopkinson's time at Cambridge and a few years after is 
 probably the most interesting part of his life. At school and at 
 Owens he was but a clever boy with few distinctive features except 
 such as appear in his class-lists. Having regard to what lie 
 became, the process of his education is of interest ; but his 
 
 o 2 
 
XX11 MEMOIR. 
 
 personality is undefined. On the other hand, from a few years after 
 leaving Cambridge the uniformity of his success and the freedom 
 from strife make his life of little interest to any but his intimates. 
 But at Cambridge it is different : there is constant development, 
 there is sometimes trouble and difficulty, which, if it appears slight 
 to older men, was of vast importance to the youth who suffered it 
 and no doubt had as great an effect upon him as the sharpest 
 struggle with adverse fate on one more hardened. His letters 
 from Cambridge, too, reveal far more of his inner self than at any 
 other time of his life, and with their aid it is possible to form a 
 fairly vivid picture of what he was like. 
 
 His work filled the largest place in his life. It has been stated 
 that he came up to Cambridge with a considerable reputation. One 
 of his contemporaries (Rev. Arnold Thomas) remembers his being 
 pointed out in October of 1867 as the prospective senior wrangler, 
 "a keen, strong face, without however any of the peculiarities of 
 expression which are usually supposed to characterise the child of 
 genius." To some extent he shared the popular belief in himself. 
 In his first term he writes to his father : " As for competition, 
 there is plenty in my own year; though I am probably the best 
 man now, I don't think I shall be able to hold that position long, 
 much less three years and a half." A rare faculty of his, and one 
 very apparent even in these days, was an unbiassed judgment 
 as to his own powers. Not only did he know what he could 
 do, but he did not affect ignorance. It is interesting to read 
 his letters from Cambridge and to see how, as data accumulate, 
 showing him to be the best man of his year, he coldly draws his 
 conclusions and frankly avows them. It was then the custom, 
 as it is now, for the coach to set his pupils a weekly paper 
 of problems to be done at leisure. For this marks were given, 
 and all the best undergraduate mathematicians of the year 
 met in these competitions. Hopkinson faithfully recorded the 
 results ; during his first year he was often second and even third 
 among his contemporaries. But it troubled him not at all; he 
 still went steadily on his way with a single eye to the greater 
 competitions to come. The fierce excitement of the Tripos 
 perhaps affected him a little in the usual way. In the midst of it 
 
MEMOIR. XXlll 
 
 he writes: "There is no doubt how the matter stands, viz.: that 
 if I had done up to my usual form, my place would have been safe, 
 but as it is it is very likely I have lost it, and if one man beats 
 me, two or three may." However, if he felt fear in that supreme 
 moment he took no panic measures. " On the Monday evening," 
 he writes, " for some reason certainly not funk, for I have been 
 cool as a cucumber the whole time I did not get to sleep till 
 about five in the morning, and as I was without chloral or spirits, 
 I had no means of forcing it. However, I did not feel it on 
 Tuesday. Last night I got some chloral and secured immediate 
 sleep ; having had one's brain in vigorous activity, it is rather 
 hard to get the blood out of it." Even in such a crisis, he could 
 regard himself as a physiological problem. 
 
 The result, in spite of his gloomy forebodings, was of course 
 never in doubt. He turned out to have been first in fourteen 
 out of sixteen papers. In the Smith's Prize he was again first. 
 This examination was contrived to test originality of thought 
 rather than the great speed which led to success in the 
 Tripos. The papers were hard and the time for doing them 
 was unlimited. Hopkinson's success in it therefore established 
 his position beyond doubt as the first mathematician of his 
 year. The year was thought by the examiners to be a fairly good 
 one and judging from the subsequent careers of the men it was 
 well up to the average, if not in the very first rank. That so 
 eminent a mathematician as Dr Glaisher was second seems to 
 imply that Hopkinson was much above the average of senior 
 wranglers. His strong point of course lay in the physical appli- 
 cation of mathematics. But the testimony of so high an authority 
 as Professor Cayley, who was greatly impressed by Hopkinson's 
 work in the Smith's Prize examination, shows that he was little 
 inferior in pure mathematics. Hopkinson himself took little 
 interest in that branch of the science ; he used to compare it 
 irreverently to chess-problems, the elegance of whose solution 
 depends chiefly on the smallness of the number of moves. He 
 had no appreciation of any originality or beauty in the problem 
 itself. Still he looked upon the whole thing from a business-like 
 point of view, and was not deterred from thorough study of a 
 
XXIV MEMOIR. 
 
 subject by any doubts as to its ultimate value. His principal 
 aim at Cambridge was to come out top. His subsequent career is 
 a triumphant vindication of competitive examination, for surely 
 few men have been so completely under its influence as he was 
 for five years of his life. 
 
 This concentration of his energies on the one aim was one 
 of several causes which prevented him from making many friends 
 at Cambridge. He was one of a large family, with brothers near 
 his own age, and there was therefore no great inducement to 
 him to seek society away from home : his inclination was quite 
 the other way. Probably too, on their side, his fellow-men did 
 not fully understand him. They admired the tremendous energy 
 with which he would row a hard race on the river and then, 
 on the same day, go in and win a scholarship ; but it was 
 wonder, rather than sympathy, that they felt. One can well 
 imagine too that in those days he would be at no pains to 
 conceal his impatience when he came into contact with less 
 vigorous minds. It was in no sense "side" the greatest of all 
 sins in undergraduate eyes it was that he was driven forward 
 faster than others could follow and it was positive pain to him 
 to hold back. He writes in 1869: "The meeting of the Ray 
 Club I went to was awfully slow. I had some talk with Prof. 
 Babington at the beginning of the evening which was inte- 
 resting. I then did nothing but gaze about me for half-au- 
 hour, and finished up by sitting down to a book till it was 
 time to go...." His was not the easy-going temperament which 
 is the right medium for College friendships. Later in the same 
 letter he remarks : " I have lots of work on now and plenty 
 to think of, what with Mathematics, boating and other engage- 
 ments; I like a certain amount of pressure," and he frequently 
 says that the place would be intolerable without plenty to do. 
 It is easy to understand that such a character would provoke 
 the respect of undergraduates, but not their love. 
 
 That he stood somewhat apart from the majority of his fellows 
 did not affect him greatly. Once in a moment of trouble he 
 alludes to it and in a rare fit of introspection seeks for its cause 
 in himself. But that one allusion shows that he felt the need of 
 
MEMOIR. XXV 
 
 sympathy in those around him, and though he cared nothing for 
 general popularity he was by no means a recluse. Nor was the 
 pursuit of his primary purpose at all inconsistent with the fullest 
 enjoyment of every side of life at Cambridge. He made several 
 intimate friends among the mathematicians, notably J. W. L. 
 Glaisher, and Carver, who was fourth in the Tripos. Towards the 
 end of his time, when his great powers commanded attention, 
 he came to know such men as James Stuart, J. F. Moulton, 
 W. K. Clifford, and he was made a member of the famous 
 Apostles' Club. He was a good oarsman, and became captain 
 of the Second Trinity Boat Club in 1869. On the running-path 
 he won several races, he was especially proud of a mile won 
 shortly before his Tripos. His description of a walking race, in 
 which he owed his success to his tactics as much as to his speed, 
 is worth quoting: "At the end of the first round each round is 
 one-third of a mile Marriott led by about 10 yards. I did not 
 see the fun of that, so I caught him and passed him as rapidly as 
 I could, then he kept sprinting to catch me, to encourage 
 which, I slackened at each corner and let him try to pass me. 
 So for about eight corners he tried to pass me and walked 
 on the outside in consequence. I found this manoeuvre very 
 useful: for the last two rounds he was content to walk just 
 behind. About 150 yards from the end I put on the spurt and 
 left him some 10 or 15 yards behind." 
 
 He had his full share of the high spirits which are supposed 
 to be the glory of healthy British youth ; and many were the 
 escapades into which they led him. In one of them perhaps re- 
 membered by his companion, who is now one of the great ones 
 of the College, " sulphuretted hydrogen, a horribly bad-smelling 
 gas," was generated in the next man's rooms, wherefore porters 
 and plumbers came to take up the drains, and the University 
 Professor of Latin was driven from his quarters. His conflicts 
 with the authorities were many and various; though, as a rule, 
 they were wisely condoned. Against compulsory chapels, which 
 were then more of an incubus than they are now, he waged 
 unceasing war. To the end of his days he carefully preserved 
 his correspondence with the Dean ; who appears, however, to have 
 
XXVI MEMOIR. 
 
 been a person of great discretion, and not much disposed to 
 exact the letter of the law from a prospective Senior Wrangler. 
 Hopkinson's attitude in such matters was no doubt largely that 
 of the healthy undergraduate : but it was also based on a mental 
 characteristic, which outlasted youth. To the end of his life he 
 had a hatred of all conventions, unless one must so name the 
 moral principles which were part of himself and of which he 
 was hardly conscious. Any law or custom whose breach would 
 not be inconsistent with these must be justified to his reason, 
 or he would thrust it aside not only without compunction, but 
 with keen pleasure. He took a simple delight in mildly shocking 
 people, as all who have seen him in his lighter moments will 
 remember. At Cambridge he greatly relished his position as 
 a Nonconformist and Radical among the Tory Churchmen, and 
 seized every opportunity of playing the Philistine. The same 
 spirit often appears in a more serious form in his manner of 
 dealing with scientific questions. It was not only that he was 
 original; he took a positive pleasure in working away from 
 traditional lines, because they were traditional. There is no 
 doubt, for example, that he found additional zest in his mag- 
 netic researches, because they showed the elaborate mathematical 
 hypotheses of the subject to be without any basis of fact. If he 
 could ever be said to be affected by prejudice in such matters it 
 was against accepted theories. 
 
 Hopkinson soon made up his mind that it would not suit 
 him to spend his days as a Cambridge don; and in his last 
 year he began to look about for a profession. He had some 
 thoughts of taking a Mathematical Lectureship at Owens 
 College, which was vacant about this time. The letter which 
 he wrote to Principal Greenwood asking for information about 
 the place, and stating his qualifications for it, is of much in- 
 terest : " My qualifications for the post are a thorough know- 
 ledge of pure and applied mathematics so far as examination 
 can test such a knowledge; together with a better knowledge 
 of science generally, especially general Physics and Chemistry, 
 than is possessed by most men of equal Mathematical attain- 
 ments. On the other hand I am not accustomed to the use 
 
MEMOIR. XXVll 
 
 of instruments of physical research, have had no experience 
 of teaching, and am much younger than is usually thought 
 suitable for such positions. But all these objections are less 
 serious when the head of the department is a man of such 
 high standing as Professor Balfour Stewart, and the last is 
 thus far an advantage that I shall have had no time to learn 
 to be idle. Unless it is intended immediately to very greatly 
 extend this department of the College, I imagine there will not 
 be enough work completely to occupy the time of the second 
 professor. This would give me two advantages in my candi- 
 dature : first, if another man had the post it would probably 
 be necessary to bring him to Manchester to do work which 
 would not sufficiently occupy him ; second, what surplus time 
 I may have on leaving Cambridge, I intend to devote to 
 acquiring such knowledge of engineering as will give a more 
 practical turn to the studies I have been engaged in here, the 
 being partially engaged in such work would, it seems to me, be 
 valuable to a professor in Owens College." His principal motive 
 in applying for the post was probably a desire for independence 
 of means ; he certainly thought that his career was to be found 
 in engineering and did not regard this professorship as more 
 than a temporary expedient. His father, however, with rare 
 breadth of view, saw that even so it would unduly cramp his 
 energies and advised him to give it up. As Dr Routh was of 
 the same opinion he withdrew his application. His election to 
 a Fellowship at Trinity in the autumn of 1871 gave him the 
 independence he wanted ; though the condition of celibacy, which 
 was then attached to it, was destined to limit his tenure to some 
 eighteen months only. It is interesting to note that the fellow- 
 ships of 1871 were the first awarded without the imposition of 
 a religious test. 
 
 On leaving Cambridge Hopkinson at once proceeded to carry 
 out his own and his father's intention by starting work in 
 Wren and Hopkinson's factory. It was not long, however, before 
 another and better opening appeared. Many years before, the 
 firm had made glass-grinding machinery for Messrs Chance 
 Brothers and Co., Light-house Engineers, of Birmingham, to 
 
XXV111 MEMOIR. 
 
 Mr Hopkinson's design. Mr James Chance, the head of the 
 firm, was himself a mathematician of much ability and had 
 a distinguished academic career. From time to time he heard 
 with interest of John's successes at Cambridge and when, in 
 1871, he wished to be relieved of the active superintendence 
 of the Lighthouse Department, his thoughts turned to young 
 Hopkinson as a likely man to take his place. He commis- 
 sioned Mr Hopkinson to make an arrangement with John 
 under which the latter was to become Engineer and Manager 
 of the Optical Works for a year. It was arranged that he 
 should spend a few months at his father's works in order to 
 acquire some practical experience ; and at the end of that time, 
 in March 1872, he began his professional life in a position of 
 much responsibility. It was no light undertaking that con- 
 fronted him. He was not yet 23 years old and had had little 
 engineering experience. He was put at the head of men many 
 of whom had spent a much longer life than his at the work in 
 which he was to supervise and command them. Yet within 
 three years of his appointment he was not only acknowledged 
 master, but he had largely increased the profits of his depart- 
 ment by various changes in the methods of management. The 
 rapidity with which he gained both the respect of his subordi- 
 nates from whom, as he said, he had everything to learn 
 and the confidence of his employers, was extraordinary. It was 
 doubtless due in part to the fact that his position was one pecu- 
 liarly fitted to his powers in no other branch of engineering 
 could one so favourable have been found. If, for example, he 
 had begun in railway engineering, he would have had to spend 
 much time in learning the accumulated experience on which 
 the art is principally founded, and without which no man, what- 
 ever his genius, can attempt to practise it. Though his ability 
 and energy must have brought ultimate success, it could hardly 
 have come so quickly as it did. But the design of lighthouse 
 apparatus rests, in the first place, upon mathematical deductions 
 from experiment on the optical properties of glass. Experience, 
 if useful, is not so essential for its accomplishment. To a man of 
 Hopkinson's attainments the mathematics were a simple matter ; 
 
MEMOIR. XXIX 
 
 his training at Owens directly fitted him for the experiment. 
 Thus in one important part of his work he had little to learn. 
 It was of course by no means all, but his preeminence in it at 
 once gave him a status with those above and below him and 
 more than atoned for his lack of experience in other depart- 
 ments. Nor was the latter want by any means an unmixed 
 evil. To one of his vigour of mind and character six months 
 sufficed to supply it to a great extent; and then he was none 
 the worse for having come to his work fresh and unhampered 
 by tradition. 
 
 During the year 1872 he lived alone at an inn a few miles 
 from the Glass-works. There is, in his correspondence for that 
 year, an almost daily record of his doings. He was at first put 
 in charge of the Lighthouse and Optical Glass Departments: 
 the Coloured Glass Department was subsequently added. In 
 addition to designing the lighthouse apparatus, he had to 
 superintend its manufacture from beginning to end. Glass- 
 making, the grinding and polishing of lenses, the design of 
 iron towers all these matters came under his management. 
 In no one of them had he previous experience ; but by the 
 end of that first year not only did he know them soundly, 
 but he had left his mark on each. As early as July 1872 he 
 began experiments with the intention of improving the quality 
 of the optical glass, which, as then manufactured, was of poor 
 colour. Six months later he writes that their leading customer 
 in this line is in high good humour with the glass they are 
 supplying. So it was throughout his work. Even in this first 
 year, when most men would have been content with learning 
 the job and keeping the place going, he introduced change and 
 improvement in every direction. 
 
 There is something very attractive in the picture of a young 
 man in a position of great responsibility, presented in that series 
 of letters. The responsibility one has to infer it sits so lightly 
 on him that it is rarely mentioned. But the youthfulness is 
 very evident. Every new problem is hailed with delight and 
 attacked without a trace of fear or anxiety. One sees, so to 
 speak, only the overflow, and is left to imagine the further 
 
XXX MEMOIR. 
 
 depths of energy and power necessary for the routine work. 
 The technical questions which came before him interested him 
 most. The management of the men was less to his taste, and 
 he found the settlement of wages rather a worry. Yet even 
 here he inaugurated a new order of things, introducing a system 
 of premiums on the work turned out in less than a specified 
 time ; and in due course he got piece-work in operation through- 
 out his department. This was in some ways his most remark- 
 able achievement in this year, as it was certainly the most 
 valuable in its results both to the men and their employers. 
 In many parts of his work he found his father's ripe experience 
 of great assistance. During this year he constantly asked for 
 Mr Hopkinson's advice, both on technical points and on his 
 relations with his employers. He always had great confidence 
 in his father's judgment in such matters, and to the end of his 
 life would often refer to him for help. 
 
 The lonely year at Birmingham ended in March, 1873, when 
 Hopkinson married Evelyn Oldenbourg, to whom he had become 
 engaged a year previously. He had now a wife and home, a 
 considerable income and an established position ; and this at a 
 time of life when most young men are occupied in struggling 
 for one or more of these desiderata. He was free from all anxiety 
 for the future. He had satisfied sufficient of his ambitions to give 
 him confidence that the others would be in due course satisfied 
 also ; and meanwhile he had the joy which attends striving when 
 success is almost certain. Such a frame of mind was the best 
 possible for his work, and to it in no small measure must be 
 ascribed his early productiveness. How far that extraordinary 
 power of concentration which was the secret of his rapidity of 
 work would have been proof against constant personal worries, 
 how far it was due to their absence it is difficult to say. It would 
 seem that freedom from anxiety was essential to his scientific 
 work at any rate : at the time when he was contemplating 
 removing to London for instance, he remarks in a letter : " At 
 present being unsettled I am doing nothing in science," arid 
 similar expressions occur on other occasions. 
 
 Hopkinson remained with Chance Bros, until the end of 1877. 
 
MEMOIR. XXXI 
 
 During that time he designed and manufactured the optical parts 
 of many lighthouses which are now working in various parts of 
 the world*. If one had to point to concrete objects as evidence of 
 his power one would choose these lights. They do not perhaps 
 appeal to the imagination as does a great bridge, but there is 
 about them a certain finality and completeness which makes 
 them no mean monument. The chief feature which Hopkinson 
 originated in lighthouse practice was the group-flash system This 
 invention like many others of great practical value was perhaps 
 less remarkable for its ingenuity than for the exact apprecia- 
 tion of what was wanted which prompted it. The various crude 
 methods of identifying lights which preceded it are described in 
 Hopkinson's pamphlet on the subject f . In 1872 Sir W. Thomson 
 read a paper at the British Association in which he proposed as 
 an improvement the use of long and short flashes according to the 
 Morse code. In the discussion which followed Hopkinson vigor- 
 ously criticised this proposal. It does not appear from his account 
 of the incident whether he then advocated the group flashing, but 
 it must have come into his mind about this time. Whether the 
 idea was wholly original is not quite certain; there is no doubt 
 that some experiments were tried in Belfast, in which a gas-light 
 was turned up and down rapidly during the revolution of an 
 ordinary revolving apparatus, thus producing a group-flash of 
 somewhat uncertain character. These were published in 1872 as 
 evidence of the value of gas in lighthouses and did not lead to 
 any result except, perhaps, to give Hopkinson an idea. The 
 merit of his achievement is untouched by them; it lay in his 
 appreciation of the value of the idea, and the neat modification 
 of the optical apparatus by which he put it into practice with- 
 out great expense or loss of efficiency. 
 
 Many other points of detail in lighthouse construction such 
 as friction rollers, clock governors and the like received substan- 
 tial improvement in Hopkinson's hands. Some of them appear 
 incidentally in his papers and it does not seem necessary to refer 
 to them further here. His lighthouse work was remarkable 
 
 * Among the more important ones in the British Isles were those on the Cas- 
 quets, Longships, St Catherine's Point (Isle of Wight) and Bull Point (Devonshire), 
 t Vol. i. p. 1. 
 
XXX11 MEMOIR. 
 
 relatively rather than absolutely. Very striking as coming from 
 one so young and with so little experience, it would have been 
 less so in a man of forty of equal mathematical attainments and 
 brought up to works management and mechanical design. Good 
 though it was, it had not the original value of the pure scientific 
 work done at the same time to which we will now turn. 
 
 While at Cambridge and in the first year at Birmingham 
 Hopkinson had published several pieces of original Mathematics. 
 They are interesting now because they were his work rather 
 than from any great intrinsic value. It is from this point 
 of view that some of them are reproduced here. They exhibit a 
 decided tendency to make the mathematics fit the facts, and 
 therein they contain the germ of what became Hopkinson's most 
 marked characteristic as a scientific man*. His mind had been 
 influenced by two schools of thought. On the one hand there 
 were the engineers, who distrusted theory and did not appreciate 
 its value even as a means to practical ends : on the other was 
 Cambridge, where the theory was considered the thing, while 
 the facts to which it was to be applied were of minor import- 
 ance. Until the application of electricity there was little sym- 
 pathy between the two. A few great Cambridge men Stokes, 
 Thomson, Maxwell had gone so far as to make mathematics a 
 real instrument in physical research. But Hopkinson was the 
 first to go further and to give both mathematics and experiment 
 their true places in Engineering. A third school Owens College 
 professed to combine the best features in the teaching of the 
 other two and undoubtedly had much effect on him. But it 
 needed the object-lesson furnished by his work at Birmingham 
 to complete the union. That the elements of his education were 
 still slightly discordant when he went to Birmingham is shown by 
 his remark that he used to feel a sort of pleased surprise when he 
 found that his calculations came out right and that his lenses 
 really distributed the light as theory said they would. This 
 feeling soon gave place to a most complete confidence in the 
 power of mathematics and of laboratory experiment as engineering 
 tools. At the same time he learnt their limitations ; his contact 
 
 * See especially those on the breaking of an iron wire, vol. n. pp. 316 and 321. 
 
MEMOIR. XXX111 
 
 with hard facts eradicated any lingering regard for hypothesis for 
 its own sake which Cambridge may have planted in him. If his 
 science strongly influenced his practical work, the practical work 
 reacted no less strongly on the science. The long train of pure 
 research on electrostatic capacity took its rise in experiments on 
 the glass which he made at the Works; and similarly in later 
 years his work on magnetism was preceded and prompted l?y 
 enquiries into the properties of iron with a view to the construction 
 of dynamo machines. 
 
 It was Sir George Stokes who inspired Hopkinson's first 
 experiments on glass. They had a practical object that of 
 making glasses which should achromatise with one another 
 without producing a secondary spectrum. It had been found 
 that the dispersion of a phosphatic glass could be corrected in 
 the required way that is, the blue end of the spectrum could 
 be extended without a proportionate increase in the total dis- 
 persion between blue and red by an admixture of titanic acid. 
 A perfectly achromatic telescope had in fact been constructed 
 of glass prepared in this way ; but its softness was a bar to its 
 general use. Sir G. Stokes thought that similar effects might 
 follow the addition of titanic acid to ordinary silicic glass ; and 
 made the suggestion to Hopkinson. The glass was duly made 
 at Birmingham but the expectations were not realised*. For 
 Hopkinson the most valuable result of the research was perhaps 
 the long correspondence which it occasioned with one of the first 
 scientific men of the age. 
 
 This work went on during the year 1874 and part of 1875. At 
 this time Hopkinson saw much of Sir William Thomson, who 
 more than any other man was to influence the direction of his 
 thought. The occasion of their first meeting has been mentioned 
 above when the young man stood up and attacked Sir William's 
 view on lighthouse illumination. Sir William was keenly in- 
 terested in the subject ; he had himself done much for mariners in 
 other directions and was an enthusiastic yachtsman. Thus there 
 was from the first a bond of sympathy between the two men, 
 which widened rapidly as they became more intimate. Of Sir 
 
 * See Vol. ii. pp. 341, 342. 
 
XXXIV MEMOIR. 
 
 William's kindness in these days and of the interest he took in 
 his work Hopkinson always spoke with the warmest appreciation. 
 He felt and expressed the greatest admiration for him. In one of 
 his letters written after a visit to Glasgow he says : " It does one 
 t much good to come in contact with such a man ; with most 
 scientific men I meet I feel as though I had as clear a view 
 into Natural Philosophy as they, but very far from it with Sir 
 William Thomson." The force of such words from John Hopkinson 
 can only be adequately appreciated by one who has read through 
 his correspondence. Of the other men he met he said but little, 
 but it is quite clear that Thomson was one of the few two or 
 three at most whom he felt to be his equal in mental calibre. 
 
 Another potent influence in Hopkinson ? s intellectual life at 
 this time was Maxwell's Electricity and Magnetism. The first 
 edition of this work appeared in 1872. For a long time his 
 evenings were regularly occupied with intense study of the book, 
 and to it and to Sir William Thomson's personal influence is 
 directly traceable his early work on Electrostatics. It is probable 
 that from the first two leading ideas were present to him directing 
 the course of his experiment on this subject. One is to some 
 extent foreshadowed in one of the suggestive hints in which 
 Maxwell's book abounds. Speaking of residual charge, "it may 
 indicate a new kind of electric polarisation of which a homogeneous 
 substance may be capable, and this in some cases may perhaps 
 resemble electrochemical polarisation much more than dielectric 
 polarisation*." Hopkinson went further and said that dielectric 
 polarisation with its attendant residual charge, and electrolytic 
 conduction, were perfectly continuous phenomena so closely 
 related that it was impossible to say where one began and the 
 other left off. The other point which, though connected with the 
 first, appears to have been entirely the creation of Hopkinson's 
 own brain is that to residual charge is to be ascribed the 
 difference between the capacity of a dielectric as ordinarily known 
 and measured and its capacity as inferred from its refractive index 
 according to the Electromagnetic Theory of Light. Knowing as 
 we do that the capacity of glass varies with the time of electrifi- 
 
 * "Treatise on Electricity and Magnetism," Art. 331. 
 
MEMOIR. XXXV 
 
 cation it is in no way remarkable, but rather just what we 
 should expect, that glass should "deviate from Maxwell's law." 
 Hopkinson's great generalisation, to which half his scientific work 
 was directed, is that bodies in which such deviation occurs also 
 exhibit residual charge and (under proper conditions) electrolytic 
 conduction. He began by investigating the slower changes of 
 capacity with time, he then carefully determined the effect of the 
 more rapid changes in making the specific inductive capacity as 
 ordinarily measured greater than the square of the refractive 
 index, and finally, but a year before his death, he found a 
 substance in which the whole process could be traced from 
 beginning to end. He discovered that the capacity of ice which, 
 after electrification for y^ of a second, is of the order of 80, falls 
 to about 3 if the time be y^J^- of a second. In other words, the 
 great deviation from Maxwell's law observed in this case is almost 
 wholly due to Residual Charge coming out in the times dealt with 
 in ordinary electrical experiment. 
 
 The first paper on Residual Charge * described some qualitative 
 experiments and formulated a working hypothesis as to the nature 
 of the phenomenon. Sir William Thomson had long previously 
 suggested that a dielectric under electric force might be regarded 
 as in a polarised state similar to that of a magnet and so explained 
 specific inductive capacity. Hopkinson supposed that a portion of 
 this polarisation took time to develope, or to decay after removal 
 of the electric force. The remanent polarisation he regarded as 
 analogous to the coercive force of a magnet and this analogy 
 led him to try the effect of mechanical agitation which in a 
 magnet destroys the coercive force. He found that tapping a 
 Leyden jar which has been charged, discharged, and then insulated, 
 has the effect of accelerating the appearance of the residual charge 
 undoubtedly the most notable point in the paper. In the second 
 paper f, published nine months later, the polarisation theory gave 
 place to a much more comprehensive way of looking at the facts. 
 In his book Maxwell treated conduction in dielectrics as made up 
 of the displacement currents due to capacity and the conduction 
 
 * VoL ii. p. l. 
 t Vol. ii. p. 10. 
 
 H. i. d 
 
XXXVI MEMOIR. 
 
 currents which are observed after long application of electric force. 
 This way of regarding it was inadequate, as it gave no account of 
 residual charge except by making use of the artificial hypothesis 
 of a stratified dielectric. Maxwell himself looked upon the latter 
 as nothing more than a model and personally suggested to Hop- 
 kinson the mode of expression which he adopted in the second 
 paper. Suppose a dielectric to have been continuously under the 
 action of dielectric force, and that X was the magnitude of the 
 
 force t seconds ago. Then the resulting electric displacement is 
 - 
 
 properly expressed as X . $ (t) . dt, where </> (t) is a function of t 
 
 Jo 
 
 only, whose form depends on the nature of the dielectric. The 
 most valuable part of the second paper is the experimental proof 
 in the case of glass of the assumptions involved in this expression 
 that residual charge is proportional to the electric forces which 
 produced it, and that the effects of these forces may be added if 
 they were applied at different times. 
 
 This one expression includes capacity as ordinarily known, 
 residual charge, and dielectric conductivity as ordinarily known. 
 It constitutes therefore a statement of the first generalisation 
 mentioned above that these three things are really parts of one 
 continuous phenomenon. That Hopkinson should adopt it is 
 eminently characteristic of his scientific methods. He cared only 
 to express observed facts and their relations ; any hypothesis that 
 went further than this appeared to him useless and often mis- 
 chievous. Though consistent with what was known it might 
 well turn out to be at variance with the unknown when that came 
 to be discovered. Analogy and hypothesis he would use as a means 
 of suggestion, but in so doing he took care never to lose sight of 
 the foundation of his work a mode of expression of the known, 
 sufficiently wide to be consistent with the unknown, whatever it 
 might turn out to be. He did not like the old way of looking at 
 conduction because it admitted only two constants, capacity and 
 conductivity, and had to invent stratification in order to explain 
 Residual Charge. He preferred rather to express the latter 
 phenomenon by the introduction of fresh dielectric constants ; 
 it seemed quite arbitrary to regard it as less fundamental than 
 
MEMOIR. XXX Vll 
 
 the capacity and conductivity on which it was sought to base it. 
 That he was right is shown by the reductio ad absurdum in 
 which resulted the attempts at applying the old theory to the 
 facts of metallic reflection. Hopkinson's way of looking at the 
 matter leads to results which are quite consistent with observation. 
 In the same way, though he was convinced of the truth of the 
 Electromagnetic Theory of Light, it was in his mind shorn of all 
 reference to a medium. To him electric and magnetic forces were 
 simply directed quantities in space, and light an electromagnetic 
 phenomenon. It was as wrong to " explain " the electric forces as 
 due to displacement and pressures in a material medium as it 
 would be to explain the pressure between bodies as due to 
 electricity. The two classes of phenomena were to his mind 
 equally fundamental. 
 
 In the year 1876 Hopkinson published some very careful 
 determinations of the refractive indices of various glasses*; and 
 this was closely followed by an account of his first experiments 
 on its Specific Inductive Capacity f. The latter paper opens with 
 a statement of the relation between the two quantities predicted 
 by the Electromagnetic Theory of Light and then proceeds to the 
 description of observations, showing that in the case of glass ^ 
 and K are very far from being equal. There is no comment on 
 this result except a warning against the inference that Maxwell's 
 Theory is (in its more general characters) disproved thereby. 
 Hopkinson's work on Residual Charge and Capacity led to his 
 election as a Fellow of the Royal Society in 1877. 
 
 In 1877 Hopkinson decided to remove to London. He did not 
 sever his connection with Chance Bros., but made an arrangement 
 with them compatible with residence away from Birmingham. 
 This helped him considerably in what was otherwise a very bold 
 step, for his family responsibilities had increased greatly in the 
 five previous years, and he had little to depend upon except his 
 brains and growing reputation. Work came very slowly at first in 
 the new field, but when it once began it increased rapidly, and in 
 the first six months of 1880 he did better than in the previous 
 
 * Vol. ii. p. 44. 
 t Vol. n. p. 54. 
 
 d2 
 
XXXV111 MEMOIR. 
 
 two years. The most lucrative part of his practice was, as it 
 always remained, expert evidence in patent suits. Hopkinson's 
 powers were of a kind to ensure his success in this profession. In 
 concentration and rapidity of thought he was of course pre- 
 eminent. The fighting instinct in him made him delight in the 
 exercise of these faculties when under cross-examination by a 
 clever counsel. But perhaps his capacity of drawing the line 
 between fact and argument was that which most distinguished 
 him. Expert evidence is a curious mixture of these two elements, 
 and the best experts are those who can separate them. Some men 
 cannot avoid usurping the position of the advocate and take a side 
 about what the facts are, thus discrediting themselves with the 
 judge. Others fail to make the most of trhe controversial points 
 as to the interpretation of the facts, which though supposed to be 
 matters of fact, and of law for the judge, are really questions of 
 argument in which the expert witness takes a large share. 
 Hopkinson, alike in the witness-box and in the laboratory, knew 
 exactly how far he was bound by the facts and where difference 
 of opinion could come in. 
 
 The telephone cases were the first important ones in which he 
 was engaged ; the case of Attorney-General v. The National 
 Telephone Co., in which it was decided that telephone messages 
 were part of the Postmaster-General's monopoly had more than a 
 passing interest. A portion of Hopkinson's evidence in that suit 
 is worth quoting as a fairly representative example of his style. 
 " If the telephone exchange is not used otherwise than is described 
 in the affidavits, and as I am informed and believe, no message 
 telephonic or other is transmitted by its agency or along the wires 
 occupied by ^ts subscribers. When A and B are conversing by the 
 telephonic exchange they speak directly with each other. A 
 message implies an agent who conveys the message. If A, having 
 no speaking trumpet, asks C who has one to say something to B 
 at a distance from him the communication may be called a 
 message ; but if A pays C a shilling for the loan of the instrument 
 and speaks himself, it is no message. Replace the trumpet by the 
 telephone and wires, and the same distinction holds. I therefore 
 say that it is untrue that messages are transmitted by the tele- 
 
MEMOIR. XXXIX 
 
 phonic exchange." Another case which will be remembered was 
 Easterbrook v. Great Western Railway Co. The patent in question 
 was for a system of interlocking railway signals. Hopkinson, who 
 acted for the Defendants, discovered that it was possible by certain 
 movements of the levers to put the signals at variance with the 
 points. The Plaintiffs, wholly unsuspecting, had closed their case ; 
 and their consternation may be imagined when Sir Frederick 
 Bramwell expounded on their own model how their system would 
 lead to a collision. The patent was of course upset. Other 
 achievements less dramatic but as useful to clients soon gave 
 Hopkinson a wide reputation, and for many years he was employed 
 in every case of importance. 
 
 Some may be inclined to regret that Hopkinson was so much 
 employed as a patent expert. This is not the place to discuss the 
 usefulness or otherwise of that kind of work; but it is at all 
 events desirable that it should be done well, and Hopkinson set a 
 standard of well-doing that will not soon be forgotten. Apart 
 altogether, however, from the possible intrinsic worth of expert 
 work done as he did it, it had through him an indirect value 
 which fully justified his adoption of it as part of his profession. 
 He did it with extraordinary ease and rapidity, and if it had 
 no lasting results its comparative freedom from responsibility and 
 the substantial income derived from it enabled him to attack 
 his engineering and scientific problems in peace of mind, un- 
 disturbed alike by professional worries and family responsibility. 
 I think that this absence of anxiety was of great importance 
 to him. Had he depended for his living upon constructive work 
 of a more wearing character its results might have been more 
 useful than what he did in the Courts, but it is doubtful 
 whether he would have risen to such heights in other directions. 
 His patent work was of considerable ,use too in keeping him in 
 touch with a great variety of engineering and manufacturing 
 practice. Experience so acquired is of course of a very superficial 
 character and of little value to one who has not commanding 
 originality, but to Hopkinson it was frequently a means of 
 suggesting new advances, and it was a strong connecting-link 
 between his scientific thought and the world of practice. 
 
Xl MEMOIR. 
 
 When Hopkinson came up to London in 1878 Electric 
 Lighting was just emerging from the laboratory and a very 
 limited sphere of application and had hardly become a com- 
 mercial question. Its practice had advanced little since 1851, 
 when it was applied to Lighthouse illumination ; its theory rested 
 almost where Faraday had left it. The discoveries of Wilde, 
 Siemens and Wheatstone as to the excitation of dynamo machines, 
 important as they afterwards became, had as yet little practical 
 significance. Furthermore these discoveries and indeed almost all 
 that was known to engineers about electrical machinery were of a 
 qualitative character, the quantities concerned were not under- 
 stood and had only been measured in the roughest way. Still 
 there was a vague impression among engineers that Electric 
 Lighting had a great future which led them to give no little 
 attention to it and to look eagerly for some means of applying 
 it more generally. The invention of the incandescent lamp in 
 the early eighties supplied that means and at once gave im- 
 portance to everything concerning Electric Lighting. There 
 naturally followed a demand for the accurate measurement and 
 scientific treatment of the phenomena thus suddenly brought 
 into prominence, and it fell to John Hopkinson to supply this 
 want. One is struck by the fact that he, the man fitted above 
 all others for the task by genius and education, came at exactly 
 the right moment for its fulfilment. He had two or three years 
 before the excitement of the electric lighting "boom" in which to 
 quietly study the problems involved. When the "boom" came, 
 bringing with it the stimulus of universal public interest and the 
 rapid development due to the application of capital, he had done 
 much of his work. He was perfectly prepared to attack the new 
 questions which were constantly arising, and he was already 
 recognised as one of the first authorities on the subject, so that 
 everything he said and did took effect. 
 
 It is difficult at the present day to imagine the chaos which he 
 reduced to order. The only quantities recognised or understood 
 by the majority of engineers in connection with electrical machinery 
 were the candle-power it could produce and the horse-power 
 required to drive it. Early in 1878 a paper was read before the 
 
MEMOIR. xli 
 
 Institution of Civil Engineers on dynamo machines*. In that 
 paper reference is hardly ever made to an electrical quantity; 
 where made it is vague and inaccurate. Current and potential 
 were confused; it was gravely asserted and Hopkinson was the 
 only man in the discussion who contested the assertion that the 
 maximum theoretical efficiency of electric power transmission was 
 50 per cent. That paper gave rise to what was probably the first 
 public discussion on Electric Lighting, and also I believe the first 
 before the Institution in which Hopkinson took part. He had 
 then no practical acquaintance with the subject, and he contented 
 himself with formulating the questions which arose in his mind. 
 What were the resistances of the armature and field coils of the 
 dynamos tested ? What was the power actually expended in the 
 electric arc, and of the balance how much was wasted in the 
 various parts of the machinery ? These and such as these were 
 the points, ignored by his fellow engineers, whose future import- 
 ance he foresaw. To him belongs the distinction of pointing out 
 what were the questions which must be answered no less than 
 that of answering them. 
 
 It has been stated that one of the chief applications of the 
 electric light in 1878 was to Lighthouse illumination. It was in 
 that connection that Hopkinson made his first acquaintance with 
 the art. Early in the year he began to enquire into the various 
 forms of dynamo machines, and in the autumn he bought a 
 medium sized Siemens dynamo for Chance Bros. Experiments on 
 that machine were the subject of the first paper on " Electric 
 Lighting," before the Mechanical Engineers f. There for the first 
 time, logical expression was given to the properties of dynamo 
 machines by means of the characteristic curve. The efficiency 
 was roughly measured ; it was shown how the capacity of a 
 dynamo could properly be specified. A second paper, read before 
 the same Institution twelve months laterj, was* directed more 
 particularly to measurements on the electric arc % On this point 
 also there had been great confusion, and it will be found that 
 
 * "Some Recent Improvements in Dynamo-Electric Apparatus." Higgs and 
 Brittle, Proc. Inst. C. E., vol. LH. p. 36. 
 
 t Vol. i. p. 32. I Vol. i. p. 47. 
 
xlii MEMOIR. 
 
 both in the paper above referred to on Dynamo Machines and in 
 a later one by Sir James Douglass on Lighthouse Illumination*, 
 the brightness of the arc is almost always stated in terms of 
 standard candles without reference to colour or direction. Hop- 
 kinson indicated the influence of these two factors. He also 
 showed that the resistance of the arc was not constant, and 
 pointed out several properties of dynamo machines which could 
 be inferred from the characteristic curve. It may be said that in 
 these two papers and in that on Alternating Currents read in 
 1884f, engineers were told how to find out all that it was useful 
 to know about existing electrical machinery. The next step was 
 to tell them how that machinery could be improved, and applied 
 to new purposes. 
 
 In the early part of 1882 the newly formed English Edison 
 Company appointed him to be one of their consulting engineers. 
 The Company had been started by Americans with the object of 
 working Mr Edison's and other inventions in this country. Prior 
 to Hopkinson's appointment they had put down a small central 
 station at Holborn Viaduct which was fitted with American plant. 
 In those days the aims of the Company included the supply of all 
 kinds of continuous current machinery as well as incandescent 
 lamps; and they also took out several of the first Provisional 
 Orders with the intention of starting supply stations, which how- 
 ever was never fulfilled. In his capacity as consulting engineer, 
 therefore, Hopkinson had to deal with a great variety of electrical 
 problems, and there is no doubt that his advice to the Directors 
 of the Edison Company had a great effect in shaping the course 
 of the electric lighting industry, though many of his prophecies 
 were forgotten before they were actually realised. From time to 
 time he wrote a report to the Directors on such scientific matters 
 as concerned the business of the Company. These letters are very 
 interesting reading ; in them are set out the fundamental ideas 
 underlying almost every point in the art of supplying electricity. 
 It was long before many of his suggestions were appreciated, but 
 they are now accepted as common-places. As early as June, 1882, 
 
 * Proc. Inst. C. E., vol. LVII. 
 t Vol. i. p. 133. 
 
MEMOIR. xliii 
 
 Hopkinson stated the principles which should guide the undertaker 
 in charging for current. In a report of that date to the Edison 
 Company on the policy which they should adopt in relation to the 
 Electric Lighting Bill he points out the great importance of the 
 dead charges in central stations and urges the use of a double 
 system of charge, viz. a fixed payment per annum dependent upon 
 the maximum amount of current demanded by the consumer 
 together with so much for every unit registered by the meter. 
 This point he continually impressed upon his clients, and he 
 secured powers to charge in this way in their early provisional 
 orders. It was not, however, till some years later in the first stations 
 which he himself designed, that it was actually put into practice. 
 Now Hopkinson's method of charging with slight variations in 
 detail is in use in half the stations in the country. Again, he clearly 
 foresaw the impetus which the continuous current would receive 
 on the introduction of a good storage battery, and he constantly 
 urged the Edison Company to push the transmission of power, a 
 great field open to them and at that time denied to their alter- 
 nating current rivals. 
 
 The machinery first introduced by the Edison Company was of 
 course manufactured in America. Hopkinson quickly perceived 
 the defects in the early Edison machines and set to work to remedy 
 them. Probably he had not then arrived at the idea of the com- 
 posite magnetic circuit, but he had a strong opinion that length 
 in the magnets beyond that required for getting on the windings 
 was a disadvantage and that the machine should be designed so 
 that the armature and magnets were magnetically saturated 
 together. This idea must have been present to him when he 
 wrote to the Company in September 1882 : " It is necessary to 
 make a critical study of the (Edison) machines with a view not 
 only of improving them but of placing ourselves in a position to 
 say beforehand how we should modify a machine to meet varying 
 
 conditions I am not without hope that we may succeed in 
 
 largely increasing the output of the machines by alterations of the 
 magnets." The matter was put to the test in his laboratory a few 
 weeks later. Small models of the Edison machine were made to 
 scale and also of the modified magnets and armature which 
 
xliv MEMOIR. 
 
 Hopkinson proposed. The inductions in the armature windings 
 in the various forms were then compared by jerking the armature 
 out of the magnet field and observing the kick on a ballistic 
 galvanometer connected to its winding. It was found that in 
 some of the Edison machines the armature and magnets were not 
 saturated together, while much of the effective area of the armature 
 was lost by bolt holes and the like, and that shorter magnets 
 of the same cross section would give as large an induction with a 
 smaller magnetising current. Hopkinson lost no time in urging 
 the Edison Company to have a machine made with shorter 
 magnets and an armature of the same weight but greater effective 
 cross-section. This, the first dynamo constructed on scientific 
 principles, was made by Messrs Mather and Platt, and the results 
 completely justified Hopkinson's anticipations, for the out-put was 
 more than double that of the Edison machine of equal weight and 
 cost from which it had been evolved. In Hopkinson's report to 
 the Edison Company of the tests upon it (May 17, 1883) one 
 detects a note of triumph which he rarely permitted himself in 
 such a communication: "The new dynamo machine was last 
 week tested at Messrs Mather and Platt's at full speed. It was 
 found to be capable of supplying 200 ordinary 'A' lamps with 
 ease when running at 1170 revolutions* and with an economy of 
 power superior to any machine that has ever yet been made." 
 
 The Edison-Hopkinson dynamo and the statement of the 
 principles which it embodied constituted a very notable advance ; 
 its greatest interest however lies in its origin : it sprang in full 
 perfection from laboratory experiment ; and it is a remarkable 
 instance of the absolute confidence which John Hopkinson had 
 come to have in such methods. Apart from the way it was arrived 
 at it was of less importance ; for it constituted but a small step 
 towards the complete art of dynamo design. It stands in the same 
 relation to the dynamo as did the discovery of condensing to the 
 steam-engine but if one may continue the analogy there was as 
 yet no application of thermodynamics that was made in the great 
 paper on dynamos two years later. Men soon began to cry out 
 
 * The Edison machine of the same weight and speed could only supply about 
 half the number. 
 
MEMOIR. xv 
 
 for more light. Their requirements were clearly formulated in the 
 preface to the best known work of the time on dynamo machines*. 
 " The true mathematical theory of the dynamo can indeed only be 
 written when the true basis for writing it shall have been dis- 
 covered. That basis, the exact law of induction in the electro- 
 magnet, does not yet exist Of the laws of induction of 
 
 magnetism in circuits consisting partly of iron, partly of strata of 
 air or copper wire, we know, in spite of the researches of Rowland, 
 
 Stoletow, Strouhal, Ewing and Hughes very little indeed 
 
 We want some new philosopher to do for the magnetic circuit 
 what Dr Ohm did for the voltaic circuit fifty years ago." That is 
 a clear statement of the difficulty which John Hopkinson and his 
 brother Edward removed in 1886 ; Ohm's discovery is fairly 
 analagous to their achievement. 
 
 It is probable that the law governing the induction in dynamo 
 machines was in a general way appreciated by Hopkinson as early 
 as 1882. In the notes of the experiments on the Edison machines 
 above referred to there is a remark that a discrepancy between 
 the behaviour of the model and the full sized machine is probably 
 due to an error in the air-space of the former, which would of 
 course be very likely to occur. It would appear therefore that 
 Hopkinson then recognised the importance of the air-space term 
 though he had not at the time any definite data as to its magni- 
 tude. Further notes at the end of 1883 and beginning of 1884 
 disclose all the essentials of the theory of the composite magnetic 
 circuit, though the want of knowledge of the magnetisation curve 
 of iron made accurate application of the theory impossible. The 
 missing data were supplied by Hopk in son's experiments on the 
 "Magnetisation of Iron," published in the Royal Society Transac- 
 tions in 1885f. In that paper the fundamental equations of the 
 composite magnetic circuit are given. The circuit used in the 
 experiments contained two parts of different area and permea- 
 bility, the specimen under examination and the wrought-iron 
 block in which its ends were bedded. Given these equations 
 it seems but a simple matter to proceed to the calculation of the 
 
 * " Dynamo-Electric Machinery," by Silvanus P. Thompson, 1st Edition, 1884. 
 f Vol. n. p. 154, and Appendix to Vol. I. 
 
xlvi MEMOIR. 
 
 induction in a circuit containing air and iron instead of two kinds 
 of iron. Perhaps, however, owing to the fact that the equations 
 referred to form but a subsidiary part of the 1885 paper, and are 
 only used for the purpose of investigatiug the correction due to 
 the magnetic force in the wrought- iron yoke (a correction subse- 
 quently neglected), the solution of the further problem the 
 synthesis of the characteristic curve of a dynamo machine came 
 as a revelation to those interested in the subject. This was the 
 ground-work of the joint paper in 1886*. Greater knowledge of 
 the magnitudes of the various terms involved, however, revealed 
 many discrepancies between the facts, and the inferences from the 
 theory in its crude form. The careful investigation of these 
 forms the greater part of the paper and involved much patient 
 research. The spreading of the lines of force beyond the pole- 
 pieces, waste field, and armature reaction were all exhaustively 
 dealt with. Finally the amount and distribution of the losses in 
 the machine were determined by the beautiful method of coupling 
 two similar dynamos mechanically and electrically and measuring 
 the power required to drive the combination. Not only did the 
 Hopkinsons give the world a brilliant idea, but they instanced 
 its application to every point of importance in dynamo design. 
 Their paper is the complete and unassailable foundation on which 
 that art has been built up. Almost everything that has been 
 done on the dynamo since is in the nature of a rider on the 
 propositions enunciated and proved by them. 
 
 It is a legal maxim that a principle cannot be patented, and 
 the attitude of the world towards those who give it new ideas is 
 much that of the law. It seldom happens that they reap so much 
 material reward from their discoveries as those to whom they 
 have taught them and who are thereby enabled to make new 
 things. John Hopkinson however was to some extent an excep- 
 tion to the rule. He was able to take advantage of his own 
 teaching and in his own person to turn it to practical use. His 
 position was a favourable one, for his work on electric lighting 
 and dynamo machines was the answer to riddles already existing 
 for engineers and in some cases formulated by them. Having 
 
 * Vol. i. p. 84. 
 
MEMOIR. xlvii 
 
 found the answer he could and did use it just as his fellow- 
 engineers did after he had taught it to them. It was during the 
 years 1880 1886 that he produced his most important electrical 
 inventions. Though some of them became of great practical value, 
 to his biographer they seem insignificant compared with the more 
 general ideas produced at the same time to which they were mere 
 corollaries. The most successful of all, the three-wire-system of 
 distribution, was a happy thought which might have occurred to 
 anyone who had Hopkinson's clear knowledge of electric lighting. 
 The interesting point about it is the evidence it furnishes that he 
 alone possessed that knowledge, not that possessing it he made 
 the invention. The same remarks apply to the closed-circuit 
 transformer and the series-parallel system of motor-control, either 
 of which could hardly have cost him an hour's labour when once 
 he had grasped the principles involved ; though nowadays no 
 transformer is made without using the one and no electric loco- 
 motive without the other. These discoveries however were not a 
 pecuniary success, the transformer patent was of doubtful validity 
 owing to a chance anticipation of ancient date, and the series 
 parallel system was invented ten years before there were any 
 electric locomotives. On the other hand the first electricity 
 meter*, on which he spent a very large amount of time and 
 labour, and which required far more ingenuity and power than 
 the other three, was not a practical success. So it was with several 
 other inventions into which he put a great deal of brains. He 
 was in a sense too great a man to make a very successful inventor. 
 Not only did he see too far ahead and so bring out things before 
 the time was ripe for them, but he had not the sort of business 
 instinct which correctly assesses the value of an invention, and 
 makes the fortune of its possessor far more certainly than any 
 amount of ingenuity. In his case this want resulted in a great 
 expenditure of thought on things which yielded no return ; while 
 he reaped rich harvests where he least expected them. In the 
 light of after events it seems remarkable to find the three-wire 
 system patented along with an electricity meter, a means of 
 
 * Patents No. 49 of 1882, 3576 of 1882, and 3475 of 1883. 
 
xlviii MEMOIR. 
 
 measuring potential and an automatic switch*; and the series 
 parallel system of control a subsidiary claim in a patent primarily 
 devoted to an electric hoist j". Neither of these epoch-making 
 inventions was considered worthy of a patent to itself! Hopkinson 
 used to say that on the whole he had been fairly paid for the time 
 he spent on inventing ; but the things which paid best were those 
 which cost him least trouble. 
 
 Hopkinson's early association with the Edison Company, and 
 his conviction that the continuous current was destined to fill a 
 bigger place than alternating currents in future electrical distri- 
 bution, made it inevitable that most of his practical work and 
 inventing in the years 1880 1886 should be on direct current 
 machinery. The theory of the magnetic circuit however, as well 
 as other ideas which he originated or first brought to the notice of 
 engineers in connection with their art, had no such limitations. 
 Though he illustrated them at first by their application to direct 
 current problems, they were equally applicable, and he applied 
 them, to the rival system. Thus he was as much a pioneer in the 
 theory of that system, if not in its practice, as he was in the 
 domain of continuous currents. He was the first to show theoreti- 
 cally that two alternating current machines if run in multiple, 
 would tend to keep in synchronism ; thus bringing to light a fact 
 discovered long previously by Wilde, but forgotten before it 
 became practically important. This and many other properties of 
 alternating currents were enunciated or proved in a paper read 
 before the Institution of Civil Engineers, in April 1883J. On 
 that occasion as on many others, Hopkinson acted as interpreter 
 between Faraday and Maxwell on the one hand, and electric 
 lighting engineers on the other. It was a part for which his 
 sympathy with both sides peculiarly fitted him. That sympathy 
 constantly found expression. In a communication to the Royal 
 Society, he would use analogies drawn from engineering as when 
 he suggested that the practice of telegraph cables should be 
 followed in measuring the capacity of a fiint-glass flask, the time 
 
 * Patent No. 3576 of 1882. 
 t Patent No. 2989 of 1881. 
 Vol. i. p. 57. 
 
MEMOIR. xlix 
 
 of electrification however being one hundred millionth of a second 
 instead of one minute*. On the other hand in the 1883 paper 
 just referred to, which is addressed to Engineers, he begins with 
 a statement of the laws of electric induction discovered by Faraday, 
 which are beautifully illustrated by mechanical models, he goes 
 on to apply them to practical questions, and the paper concludes 
 with a comparison of the cost of lighting by electricity and gas. 
 A further paper read before the Electrical Engineers in Nov. 1884, 
 dealt with the mathematical treatment of alternating current 
 circuits f. The problems solved were simple applications of the 
 laws of induction, the machine being regarded as a circuit of 
 constant self-induction moving in a simple harmonic field; but 
 they were introduced to Engineers for the first time, and it was 
 long before the solutions were improved upon. The more im- 
 portant and original work of deducing the properties of alternating 
 current dynamos and transformers from their dimensions and the 
 properties of the iron was done in 1887, a year after the same 
 problem had been solved for continuous current machines. Like 
 the improved dynamo, Hopkinson invented the closed circuit 
 transformer some years before he fully investigated its properties 
 in fact it was not until 1892 that he finished with it. In that 
 year he made the first accurate determination of the amount 
 and distribution of the losses in a transformer; using a method 
 similar to that which he had devised in 1886 for the dynamo J. 
 His experimental work on the alternating current dynamo, too, 
 came at a comparatively late period. The first good measure- 
 ments of efficiency on such machines were some tests of his in 
 Newcastle in 1895. Similar tests were made on a pair of Siemens 
 machines in 1896, and at the same time he investigated the effect 
 of the currents in the magnet poles induced by the armature 
 currents. 
 
 We must now return to John Hopkinson's purely scientific 
 research, which never ceased during the years of which we have 
 
 * "On the Capacity and Residual Charge of Dielectrics as affected by tempera- 
 ture and time." Vol. n. p. 122. 
 t Vol. i. p. 133. 
 I Vol. i. p. 192. 
 Vol. i. p. 156. 
 
1 MEMOIR. 
 
 been speaking. Down to 1885 his experimental work dealt mainly 
 with electrostatic capacity. Further determinations of the capacity 
 of glass, confirming his earlier measurements, were published in 
 1880*; together with the results of experiments on various liquids. 
 As regards the latter he reached the general conclusion that the 
 hydrocarbons agreed with Maxwell's law, while oils containing 
 oxygen exhibited considerable deviation from it. He found in 
 this result a confirmation of his theory that the deviation was 
 due to something which might be indifferently described as 
 residual charge or incipient electrolysis; for one would expect 
 bodies like castor oil to behave like electrolytes, while paraffin 
 would exhibit no such properties. A very interesting piece of 
 work on electrostatics was a paper written for the Royal Society 
 Proceedings in 1886*. Professor Quiucke had made some 
 determinations of the capacity of liquids by measuring the change 
 of pressure of an air-bubble in a fluid under electrostatic 
 force, and by weighing the attraction between the plates of 
 a fluid condenser. He found a considerable difference between 
 the values of the capacity determined by these two methods. 
 Hopkinson examined this result, and showed that it could be 
 explained either by assuming that capacity depended, like the 
 permeability of iron, on the force, or by supposing that the 
 capacity of a condenser did not vary inversely as the distance 
 between the plates. The first assumption was negatived by some 
 experiments of his own, the second was "subversive of all accepted 
 ideas of electrostatics." He concluded by suggesting that the 
 discrepancy was perhaps due to neglecting the capacity of the 
 wires and key used in the experiments, a source of error which he 
 had himself experienced. Correspondence with Quincke ensued, 
 and that gentleman ascertained the capacity of his connections 
 and found it to be responsible for the supposed discrepancy. 
 Hopkinson was always very proud of this achievement, and indeed 
 it was a remarkable piece of scientific criticism. One other paper 
 should be noticed before we return to his work on magnetism, 
 because it was so characteristic of his mode of thought. A con- 
 troversy had long raged indeed it is not yet set at rest as to 
 * Vol. ii. p. 65. f Vol. ii. p. 104. 
 
MEMOIR. 11 
 
 the true nature of contact electricity and the seat of the electro- 
 motive force in a Voltaic cell. One party maintained that the 
 difference of potential between different metals in contact should 
 be measured by the Peltier effect in a thermoelectric couple. 
 The other, led by Sir W. Thomson, held that it must be deduced 
 from electrostatic experiments. John Hopkinson took neither 
 side, saying that the question was " one of the relative simplicity 
 of certain hypotheses, and definitions used to represent admitted 
 facts*." One feels, in reading his development of this thesis, how 
 utterly unbiassed he was in his scientific judgment. It was 
 almost like the strife in the last century over the proper method 
 of measuring the force of bodies in motion. " Shortly all Europe 
 was divided between the rival theories. Germany took part with 
 Leibnitz and Bernoulli ; while England, true to the old measure, 
 combated their arguments with great success. France was 
 divided, an illustrious lady, the Marquise du Chatelet being first 
 a warm supporter and then an opponent of Leibnitzian opinions. 
 
 But what was most strange in this great dispute was that the 
 
 same problem, solved by geometers of opposite opinions, had the 
 same solution. However the force was measured, whether by the 
 first or second power of the velocity, the result was the samef." 
 Like d'Alembert in that historic controversy, Hopkinson showed 
 that the whole dispute was a mere question of words. 
 
 Hopkinson 's work on Magnetism began with the Royal Society 
 paper in 1885 referred to above J. The experiments described 
 were intended primarily for practical ends, and found their first 
 application in the theory of the dynamo machine. There were 
 however one or two points of much scientific interest, notably the 
 absence of the magnetic property in steel containing 12 per cent, 
 of manganese. The fact was known to several people, among 
 them Mr Groves of Bolsover Street, the instrument-maker, who 
 brought it to Hopkinson's notice. Hopkinson made accurate 
 determinations of the properties of the steel, and showed that 
 the want of magnetism could not be ascribed to a mere admixture 
 
 * Vol. u. p. 375. 
 
 t "Elementary Rigid Dynamics," by E. J. Kouth, 5th Edition, p. 277. 
 
 J Vol. n. p. 154. 
 
 H. I. e 
 
lii MEMOIR. 
 
 of a non-magnetic material with the iron, even if the two sub- 
 stances were arranged in the manner most favourable to that 
 hypothesis. The rest of the paper consists of determinations in 
 absolute measure of the magnetisation of various samples of 
 iron. The full value of this work will only be appreciated when 
 some general law is found covering the isolated phenomena of 
 the magnetisation of iron. In the present state of knowledge the 
 determinations are of practical rather than scientific value, though 
 their accuracy and the completeness with which the mechanical 
 state and chemical composition of each sample is known, as well 
 as the fact that they are in absolute measure, distinguish them 
 from most other results of the kind. 
 
 Hopkinson's next experiments on magnetism, however, consti- 
 tute a step, albeit a small one, towards the generalisation, the 
 search for which seems likely to baffle men for a long time to 
 come. It was known that the magnetic property of iron dis- 
 appeared suddenly at about red heat. It was also known that if 
 iron be heated to redness and allowed to cool, there is at a certain 
 temperature a considerable liberation of heat not unlike, and 
 comparable in amount with, that which occurs when water freezes. 
 Hopkinson carefully examined these two phenomena and fuund 
 that the magnetism disappeared with great suddenness at the 
 temperature of " recalescence " as the liberation of heat is called*. 
 Farther experiments showed that both changes were accompanied 
 by a sudden decrease in the temperature rate of variation of the 
 specific resistance of the iron-f-. The true significance of this 
 discovery cannot be better put than in Hopkinson's own words. 
 " When iron passes from the magnetic to the non -magnetic state 
 it experiences a change of state of comparable importance with 
 the change from the solid to the liquid state, and a large quantity 
 of heat is absorbed in the change. There is then no need to 
 suppose chemical change, the great physical fact accompanying 
 the absorption of heat, is the disappearance of the capacity for 
 magnetisation J." 
 
 In the course of these experiments on the influence of tempe- 
 
 * Vol. ii. p. 217. t Vol. ii. p. 214. 
 
 $ Address to the Institution of Electrical Engineers, Vol. i. p. 233. 
 
MEMOIR. liii 
 
 rat ure on magnetisation, Hopkinson hit upon that extraordinary 
 body, steel containing 25 per cent, of nickel. He found that this- 
 substance, which is substantially non-magnetic as it comes from 
 the manufacturer, becomes magnetic if it be cooled below 20 C. T 
 and remains so if after cooling it be allowed to return to the 
 ordinary temperature. Its magnetic property cannot now be 
 destroyed unless it be heated above 580 C. If that be done and 
 it be allowed to cool again, it will be found to have returned to its 
 original and non-magnetic state. Further investigation showed 
 that many other properties of this steel were different according 
 as it was in one or other of these two states. Its density, its 
 elastic properties, and its electrical resistance could all be sub- 
 stantially changed by heating it to 580 0., and could then be 
 restored by cooling to 20 C. or vice versa. In fact almost the 
 only property common to the two states was that of containing 
 75 per cent, of iron and 25 per cent, of nickel. 
 
 This discovery of a substance, non-magnetic as ordinarily 
 known, which could be rendered magnetic by cooling seemed 
 to open up an endless vista of possibilities. Why should not 
 other metals exhibit the same property if treated in a similar 
 way ? John Hopkinson's imagination was kindled by that thought 
 in a manner rare with him. I well remember the time when he 
 put it to the test of experiment. Rings of chromium, non- 
 magnetic manganese steel, and other metals, which from their 
 chemical similarity to iron or other causes seemed worth trying, 
 were put into solid carbonic acid and tested magnetically by the 
 ballistic galvanometer. The results obtained were wholly negative ; 
 no one of the metals tried exhibited any sign of magnetisation. 
 I think that on that occasion even Hopkinson came near to feel- 
 ing disappointed with the course of Nature. The nickel steel with 
 its twofold character, like iron with its magnetisation, remained 
 in a state of inscrutable isolation. 
 
 Hopkinson's work as an inventor was practically confined to 
 the decade 1879 to 1889. During those ten years his name 
 appears in the patent records some five and twenty times, whereas 
 he only took out six patents during the remainder of his life. His 
 scientific work in the latter period shows that this was not due to 
 
liv MEMOIR. 
 
 any decay of original power. It was part of a general change in 
 his professional position following necessarily upon the develop- 
 ment of the electrical industry. In the early eighties Hopkinson 
 was almost alone in his grasp of the correct principles underlying 
 the new applications of electricity. That period was marked not 
 only by much invention, but by papers to the Engineering 
 Societies of a general character in which he gave to the world 
 the principles which had guided him in inventing. As the field 
 of electrical engineering widened, there was a corresponding 
 increase in the number of qualified workers in it. They owed 
 much of what they knew to Hopkinson ; and knowing it they 
 stood in much the same position as he had occupied some years 
 before. The power of making electrical inventions, which Hop- 
 kinson had shared with very few others, came to belong to a 
 much larger class owing its existence in large measure to him. 
 The Edison-Hopkinson dynamo was of unique value because it 
 was the first concrete expression of the correct principles of 
 dynamo design. But it was a simple deduction from those 
 principles, and after they were published in 1886 it was in the 
 power of many to apply them in similar manner to the new needs 
 which were constantly arising. So it was with the closed circuit 
 transformer, and others of his inventions. It was for John 
 Hopkinson to create the art of designing electrical machinery. 
 The simpler matter of practising that art he soon left to others, 
 and turned to work worthier of his powers. 
 
 Such work naturally followed the great extension of knowledge 
 about electrical matters of which we have just been speaking. 
 Hopkinson's advice to the Edison Company and other clients in 
 early days had dealt with questions of general policy in electric 
 lighting, without reference to particular circumstances with 
 model provisional orders, methods of charge and systems of supply. 
 But with the spread of these and other ideas, there came into 
 being numbers of actual commercial undertakings in electric 
 lighting and power transmission, and as a necessary corollary 
 the profession of consulting electrical engineer was established. 
 Hopkinson took his place as leader of that profession. He came 
 to be regarded as one whom anyone with an electrical project in 
 
MEMOIR. IV 
 
 hand must consult. Henceforward his professional work consists 
 largely of advice on particular schemes. 
 
 In this way he influenced the course of most of the important 
 electrical enterprises which were undertaken in this country 
 during his lifetime, and was responsible for the execution of 
 many. In London he was consulting engineer to the Metropolitan 
 Electric Supply Company from its commencement, and he advised 
 several other electrical corporations at critical stages in their 
 careers. In the provinces he designed the Manchester Electric 
 Lighting Works, and that undertaking was the first thing of the 
 kind on a large scale which he carried out in detail. The works 
 were designed in 1891 and were completed two years later. In 
 Manchester Hopkinson had the satisfaction of putting into a 
 concrete form several ideas which he had advocated for a long 
 time. Chief among these was the maximum demand system of 
 charging for electrical supply, which was here adopted for the 
 first time. Another novel feature was the "five-wire" an 
 extension of the "three-wire" method of distribution, the use 
 of which was prompted by Board of Trade rules as to pressure of 
 supply. Hopkinson foresaw the relaxation of these rules, and this 
 led him to prefer the use of continuous current in many places 
 where others with less foresight would have advocated the rival 
 system a prejudice (as some have thought it) which has been 
 amply justified by experience. The success of the Manchester 
 Station brought a good deal more work of the same kind in its 
 train. Its details are of no great interest. Hopkinson himself 
 grew tired of making electric lighting stations as their design 
 became stereotyped, though he spared no pains in doing it. He 
 took little pleasure in working on established lines; still less 
 when they had been laid down by himself. 
 
 It is often said that England has been behind other countries 
 in adopting improved means of transport. It must not be for- 
 gotten however that the City and South London Railway was 
 constructed ten years ago by English engineers at a time when 
 nearly every other capital in the world had only horse trams. 
 In the making of this railway John Hopkinson took an important 
 part, acting as consulting engineer to Messrs Mather and Platt 
 
Ivi MEMOIR. 
 
 who were contractors for the generating machinery and rolling 
 stock. In more recent developments of electric traction in this 
 country he also had a large share. He was the engineer of all 
 the more important city tramways on which electric haulage was 
 adopted in his time. That from Kirkstall to Roundhay in Leeds, 
 and the first electric lines in Liverpool, were constructed under his 
 supervision. It is certain that had he lived he would have taken 
 an even more prominent position in work of this class than in 
 electric lighting construction. It must be admitted however that, 
 in the particular case of electric surface tramways, the Americans 
 had several years' start of us, and it may be doubted whether 
 Hopkinson would have found much interest in problems which 
 had already been pretty fully worked out by others. In con- 
 structive engineering he liked to do one big job of a kind, but 
 did not care about the work of the same sort which would neces- 
 sarily follow its successful accomplishment. A large practice in 
 traction or lighting engineering had no attractions for him. He 
 had one great desire, and that was to carry out a long-distance 
 transmission of power. It would, he used to say, turn his hair 
 white, but in doing it he would "fulfil the end of his being." 
 It was a dream the realisation of which was probably only 
 prevented by his death. He had been consulted on many 
 occasions by people having such schemes in their minds. One 
 of them a big project for taking power from the Victoria Falls 
 on the Zambesi came near taking him to South Africa but 
 was frustrated by the Matabele war. I well remember his joy 
 at the prospect of doing this work ; he would have thrown up 
 everything for it. A year later a proposal for taking a large 
 amount of power from Niagara to Toronto was brought to him. 
 He did a great deal of work on it, and it was under consideration 
 when he died. 
 
 The inspiration to purely scientific research which Hopkinson 
 was wont to find in his professional work has been several times 
 alluded to. With the change in the character of his business 
 which has been mentioned above as having taken place about 
 the year 1890 this stimulus disappeared to a great extent. The 
 increasing calls on his time also left him less leisure for ex- 
 
MEMOIR. Ivii 
 
 periment, and these causes largely account for his lessened 
 productiveness in this line during the last ten years of his life. 
 The effects of both were mitigated to a great extent by his 
 appointment in 1892 to the chair of Electrical Engineering which 
 had just been founded by Lady Siemens at King's College, 
 London. The experiments requiring the time which he could 
 no longer devote to them personally could now be done under 
 his direction by assistants, and the constant need to keep his 
 students occupied with subjects of research was a new and 
 powerful stimulus to producing ideas. A great deal of work 
 which has already been noticed was done at the King's College 
 Laboratory. The first experiments there were directed to the 
 verification of the theory of commutation which John and 
 Edward Hopkinson had enunciated in the 1886 paper on Dynamo 
 Machines*. They were followed by the work on the alternating 
 current dynamo in which a rotating contact maker was employed 
 fixed to the armature, and making contact once in a revolution. 
 By means of a quadrant electrometer the potential, whether of the 
 machine itself or across a non-inductive resistance in series with 
 it, could be measured at any given epoch. In this manner the 
 potential of the machine, and the current passing in it, were plotted 
 in terms of the time. The results disclosed the large effects of 
 the currents induced in the solid cores by the varying action 
 of the armature current -f-. Similar methods were applied to the 
 determination of the change in the cyclic curve of magnetisation 
 of iron which occurs if the cycle be effected 100 times per 
 second or more, instead of quite slowly J. There was also an in- 
 vestigation of electrolysis with alternating currents, which led 
 to a remarkable estimate of the size of atoms . The last piece 
 of work done at King's College was that on " Residual Charge 
 and Capacity as affected by Temperature and Time." I think 
 that this was in many ways my father's crowning achievement 
 in pure research. Its place in his work has already been men- 
 tioned in speaking of the experiments done long before on 
 Residual Charge, to which it was the fitting sequel. His con- 
 
 * Vol. i. p. 122. t Vol. i. p. 156. 
 
 t Vol. n. p. 272. Vol. n. p. 383. 
 
Iviii MEMOIR. 
 
 ception of " deviation from Maxwell's law " as only another name 
 for residual charge found justification in these experiments twenty 
 years after it was formed. I cannot give a better account of this 
 paper than that contained in the abstract which was sent to the 
 Royal Society Proceedings : 
 
 " The major portion of the experiments described in the paper 
 have been made on window glass and ice. It is shown that for 
 long times residual charge diminishes with rise of temperature 
 in the case of glass ; but for short times it increases both for 
 glass and ice. The capacity of glass when measured for ordinary 
 durations of time, such as 1/1 00th to I/ 10th second, increases 
 much with rise of temperature, but when measured for short 
 periods, such as 1/10 6 second, it does not sensibly increase. The 
 difference is shown to be due to the residual charge which comes 
 out between l/50,000th second and l/100th second. The capacity 
 of ice when measured for periods of l/100th to l/10th second 
 increase both with rise of temperature and with increase of time ; 
 its value is of the order of 80, but when measured for periods 
 such as 1/10 6 second its value is less than 3. The difference 
 again is due to residual charge coming out during short times. 
 In the case of glass conductivity has been observed at fairly high 
 temperatures and after short times of electrification ; it is found 
 that the conductivity after l/50,000th second electrification is 
 much greater than after l/10,000th, but for longer times is 
 sensibly constant. Thus a continuity is shown between the con- 
 duction in dielectrics which exhibit residual charge and deviation 
 from Maxwell's law, and (that in) ordinary electrolytes." 
 
 It is unnecessary to give here a catalogue of the honours 
 and distinctions which were the natural results of Hopkinson's 
 achievements. He cared little for such things and took no pains 
 to get them. One or two however may be mentioned which 
 did give him peculiar pleasure. Such were the Royal Society 
 medal awarded to him in 1890 for his magnetic researches, and 
 his election in 1886 and again in 1893 to the Council of the 
 Society. That he should be President of the Institution of 
 Electrical Engineers at an exceptionally early age was the natural 
 consequence of his position, but his election to that post a second 
 
MEMOIR. lix 
 
 time in 1895 was a tribute to his personal character which he 
 greatly appreciated, though the duties of President were little 
 to his taste. It was at a critical period in the history of the 
 Institution, and his fellow-engineers came to him not only as their 
 acknowledged leader, but as one above all petty jealousy or desire 
 for advertisement. Another honour which implied something 
 more than mere scientific distinction was his election to the 
 Athenaeum Club in 1887 as one of the nine annually chosen 
 for eminence in " literature, art or science." Such things pleased 
 him more than he admitted, though less than they would please 
 most men. 
 
 This Memoir has dealt chiefly, as was fitting, with Hopkinson's 
 professional and scientific work. It remains to say something 
 of his activity in other directions. He had strong and original 
 political views which he would advocate vigorously in conver- 
 sation, though he had little ambition to impress them on a wider 
 circle. He was however strangely moved by the events at the 
 end of 1895 and beginning of 1896 ; indeed there is an entry 
 in his diary at that time that he is unable to do much effective 
 work in the present state of politics the more significant as 
 it is almost the only remark of a subjective kind which occurs 
 anywhere either in his diary or in his later correspondence. His 
 feelings in that crisis led him to the formation of the Electrical 
 Engineers Volunteers Corps, of which he was the first Com- 
 manding Officer. He had the satisfaction of seeing the utility 
 of the Corps proved, and its success assured, though it had hardly 
 been long enough formed when he died to get the full benefit 
 of his powers of organisation. 
 
 Of what is called " general reading " such as novels, poetry, 
 and philosophy he did little in his later years. His favourite 
 novelist was Thackeray; Esmond was a work he especially ad- 
 mired. He would also read Fielding on occasion. But George 
 Eliot and Dickens did not attract him, still less any novelists of 
 later date. Of poets he liked Tennyson better than any, doubt- 
 less because of his sympathy with modern scientific conceptions. 
 I do not remember ever seeing him read a purely philosophical 
 work though he had read many in early days and always liked 
 
Ix MEMOIR. 
 
 to discuss philosophical cr ethical questions. He regarded them 
 as mental exercises, very pleasant, and no doubt healthful, but 
 of no real importance. He had certain deep-seated moral con- 
 victions which argument could no more explain than it could 
 destroy. A dishonourable action excited disgust ; it was profit- 
 less, though amusing, to discuss why. 
 
 The most important part of Hopkinson's work outside his 
 own profession lay, however, in education. From the early days 
 when he instructed his brothers he was always a great teacher 
 of those he loved. His method was to leave as much as he 
 possibly could to the unaided intelligence of the pupil. It de- 
 lighted him to watch a keen but untutored mind struggling with 
 a difficulty, and he took care never to spoil the sport by too 
 much assistance. From time to time he would give a hint or 
 a suggestion just sufficient to put his pupil on the track again; 
 only after long and painful floundering would he give a complete 
 and consecutive demonstration. It was also "suppose you try 
 so and so " ; never " do you follow me ? " I well remember my 
 first introduction to the Calculus in this way. I was told to 
 find the area of some curve, and for two hours or more I suffered 
 all the troubles of the circle-squarers. Then, when I was pretty 
 well beaten, a ray of light was admitted in the shape of a 
 suggestion to try " cutting it up into little bits." More wrestling 
 followed, then another hint, and so on till the problem was solved. 
 On a small scale that was my father's theory of education in 
 relation to the individual. He had a great belief in allowing 
 young people, sound in body and mind, to go their own ways 
 without let or hindrance. No obstacles should be put in the 
 path, and guidance or help should only be given when it was 
 really needed and when its value would be appreciated. 
 
 It was in his own family of course that John Hopkinson's 
 influence as a teacher was deepest ; but in his later years it was 
 felt in a much wider circle. In addition to the great effects of 
 his personality on the young men with whom he came in contact 
 at King's College and in the course of his business, a large 
 proportion of the electrical profession were latterly in the position 
 of his disciples. It will be found that nearly all his later addresses 
 
MEMOIR. Ixi 
 
 to Engineering Societies were if one may use the word without 
 offence of a didactic character: that is to say the subject-matter 
 was not original, though put in a new way, and it was regarded 
 by most of the audience as non-controversial. Twice in his life 
 he came near to taking a University professorship ; but he would 
 not have been so powerful a teacher had teaching been his pro- 
 fession. No professor pure and simple, however eminent, could 
 have spoken to electrical engineers with half the authority which 
 he possessed. His utterances on points of pure science or mathe- 
 matics might have been accepted -just as Hopkinson's were 
 without question ; but his auditors would have felt doubts as to 
 his sympathy with their aims. Someone would have been sure to 
 say, directly or indirectly, that he was not a "practical man," 
 with the implication that practical men must discount what he 
 said. That cry was never raised against John Hopkinson, and 
 therein lay the secret of his power as a teacher among engineers 
 generally. In his classes at King's College, where he came per- 
 sonally into contact with individuals, the effect of his dual 
 position in the world of theory and in that of practice was even 
 more marked. He spent but little time there on the average 
 perhaps one hour a day but he came there each time fresh 
 from the execution of big engineering works. Sometimes he 
 would turn at once to a question such as the capacity of glass 
 purely scientific and so far as could be seen utterly without 
 promise of practical utility. On other occasions he would bring 
 an electricity meter or a storage battery to be tested. There 
 were two cardinal points in his teacher's creed. One was that 
 the educational value of a piece of work was in nowise impaired 
 if it happened to be practically useful. " From an educational 
 point of view it is just as useful to learn to thoroughly test a 
 steam-engine as to determine accurately the value of V or of 
 the ohm." The other, that it is worth a student's while even 
 at a technical college to do pieces of purely scientific research. 
 Both were constantly put into practice at King's. But the 
 greatest lesson of all more than any precepts which he could 
 impart in the short half-hour at his disposal was to see him at 
 work, to see revealed the sources of his power. 
 
Ixii MEMOIR. 
 
 Hopkinson took a very active interest in the more general 
 aspects of education. As a member of the Senate of London 
 University he was able to give expression to strong views on 
 that necessary adjunct of teaching, examination. He had had 
 as examiner and candidate an almost unique experience of it. 
 One point on which he felt very strongly was that the number 
 of examinations of much the same standard should not be mul- 
 tiplied. On this ground he had a great belief in the high 
 function of the University of London, and I do not think he liked 
 the idea of its forsaking its exclusively examining character, and 
 becoming in part a teaching body. It was not a point on which 
 he was disposed to insist very much but he certainly felt that 
 London University was doing work which no other body ever 
 would or could do, and doing it very well ; work, moreover, which 
 concerned the whole country and not London alone. That work 
 could not continue if the University were at all controlled by 
 the teaching staff of London Colleges; whether the advantages 
 of such control would at all make up for what it destroyed was 
 a point on which he felt considerable doubt. His opinion was 
 of great weight, for he knew the education of engineers, who 
 formed a large proportion of London University candidates and 
 will form a larger proportion of its students, in every aspect 
 most thoroughly ; and though himself a London professor he 
 was free from all suspicion of personal bias. Besides the ex- 
 perience of his own remarkable training he was closely concerned 
 with engineering education as a member of the Council of the 
 Institution of Civil Engineers. Then he advised the Syndicate 
 whose labours resulted in the formation of the Engineering 
 Laboratory at Cambridge. He took a very warm interest in 
 that school from its commencement. It was the University of 
 Cambridge in no small degree that made him what he was, and 
 his opinions on her place in engineering education are the most 
 fitting preface to this reprint of his papers. They were expressed 
 in a Memorandum written for the Syndicate and were apropos 
 of a proposal to add a properly equipped Laboratory to the old 
 Workshops. 
 
MEMORANDUM ON ENGINEERING EDUCATION. 
 
 [Written for a Cambridge University Syndicate in 1890.] 
 
 AN Engineering School in the University has two uses; 
 first for men other than those intending to be Engineers, and 
 second for those purposing to follow that profession. It is one 
 of the greatest possible advantages to members of the Bar to 
 have some knowledge of mechanics and mechanical operations. 
 Many cases in the courts turn on mechanical points, and though 
 it is wholly unnecessary for a barrister to be in any sense an 
 Engineer it is almost a necessity if he is to do his work properly 
 that he should have so far to come in contact with engineering 
 appliances as readily to apprehend what they are, to understand 
 the point of view of the practical men with whom he may have 
 to deal in the case in hand, and to be able to understand the 
 conventions which are used in mechanical drawing. Such a 
 training as is required can be given in a variety of ways. A 
 little time spent in a drawing office and in a workshop would 
 almost answer the purpose by the mere presence of the student 
 amongst mechanical appliances even if he acquire no skill as 
 a handicraftsman. Work in an engineering laboratory would 
 answer the same purpose though possibly less effectually. To 
 the same class will belong men whose career in life will lie in 
 managing one or other of the manufacturing industries of the 
 country. Here it is unnecessary that a man should be capable of 
 designing machinery, but it is most desirable that he should be 
 competent to form an independent opinion upon the facts con- 
 cerning machinery which may be laid before him. In the case 
 
Ixiv MEMORANDUM 
 
 of clergymen again it is desirable that they should be able to 
 enter into the point of view of those with whom they have to 
 deal, the more real the everyday duties of his parishioners can 
 be to a clergyman the better will he be able to work amongst 
 them. For this no profound knowledge is required but such 
 knowledge as may be acquired by working for a few hours from 
 time to time in a mechanical workshop. 
 
 For this large class then of those who have no intention of 
 practising the engineering profession, workshops such as those at 
 present established are in my judgment invaluable ; properly 
 managed they are calculated just to give that reality to knowledge 
 which cannot be obtained from books and which opens up quite a 
 different point of view from anything which the student is likely 
 to obtain outside of the Engineering School or the School of 
 Practical Physics. Whether or not the University should add a 
 school for producing Engineers I think it should provide for 
 imparting the education which I have indicated and which if not 
 imparted at the University will not be given at all to those who 
 should receive it. 
 
 For the second class of students, those who intend to become 
 Engineers, different considerations apply; I do not think it probable 
 that Cambridge will ever become a large school for Engineers. 
 The majority of Engineers in the country must be practical men 
 who can deal effectually with the actual execution of a limited 
 class of work, and for these it is probably best that their workshop 
 education should begin earlier than the usual time of leaving the 
 University. But there is also room in the profession for others 
 who have a wider education addressed to enabling them to deal 
 with circumstances for which there is no direct precedent. For 
 this I believe that the mathematical education of the University 
 would be of great value ; but with it should be coupled con- 
 stant contact with the physical phenomena in some shape or 
 other so that the men may realise that every bit of their mathe- 
 matical knowledge has its counterpart in objective facts. Of 
 course for such men the more nearly their physical work bears 
 upon practical engineering the better. From an educational point 
 of view it is just as useful to learn to thoroughly test a steam- 
 
ON ENGINEERING EDUCATION. Ixv 
 
 engine as to determine accurately the value of V or of the ohm, 
 but in learning to test a steam-engine the student learns a great 
 deal that will be of value to him when he comes to practise his 
 profession. In my opinion it is not necessary that the class of 
 Engineers which the University is calculated to produce should be 
 handicraftsmen, but they must at some time or other come in 
 contact with the actual execution of work and will learn to know 
 when work is properly done and when it is not. Probably this 
 would be less effectually accomplished in a workshop such as the 
 University at present possesses than in any reasonably good 
 mechanical engineering workshop engaged in trade. If I were 
 sending a son to the University who was afterwards to practise 
 the profession of an Engineer I should not send him to the 
 mechanical workshop as at present arranged but let him work at 
 mathematics and in the physical laboratory. What I take it is 
 really wanted is that in addition to the workshops there should be 
 a physical laboratory addressed to dealing with those matters 
 which have a particular interest to Engineers, such for example 
 as the investigation of the mechanical properties of materials, the 
 thorough testing of steam and gas engines, hydraulic experiments, 
 the testing from every point of view of dynamo machines, but 
 not their manufacture. 
 
 There is another reason why the University should be possessed 
 of a properly equipped engineering school. Many men no doubt 
 go to the University with talent for Engineering as yet undeveloped 
 and who, if they were provided with an opportunity at the Uni- 
 versity, would probably go into that profession for which they were 
 best suited, and who otherwise might be diverted into other 
 professions. There are also probably many students who intend 
 to pursue Engineering as a means of livelihood, but who desire to 
 enjoy the general advantages afforded by the University in other 
 ways than in their professional training. For both it is of great 
 importance, and of great importance to the country as well, that 
 they should have an opportunity to pursue at the University that 
 line best adapted to their subsequent work. 
 
 If an Engineering Laboratory were provided for the University 
 a workshop of some sort would be a necessity ; for the laboratory 
 
Ixvi MEMORANDUM, ETC. 
 
 alone the workshop might possibly be on a smaller scale than 
 that which at present exists but in that case the workshop would 
 be insufficient to deal with the class of students who did not 
 contemplate becoming Engineers. 
 
 It seems to me then that in any case the University workshop 
 should be retained as a most desirable part of the education of 
 most of the men who have afterwards to deal with practical life. 
 I think also that if funds are found, an Engineering Laboratory 
 for the benefit of those who think of Engineering as a profession 
 should be established under the same management as the work- 
 
 It has been suggested that a great deal of Engineering testing 
 can be done with very simple appliances and at a small expense. 
 This is perfectly true, but to do it at all you have to depend on 
 the ingenuity and resource of your Professor, and in any case the 
 appliances possessed by the University for teaching Engineering 
 would compare most favourably with the appliances possessed by 
 many colleges in the large towns. 
 
 It was suggested by Professor Reynolds that the University 
 might raise subscriptions for the purpose of founding a proper 
 Engineering Laboratory from outside of the University. I see no 
 reason whatever why this should not be done, but if done I think 
 the appeal should be made on the ground that in founding a 
 professional school which might not attain to very large dimensions 
 the University was also providing a very valuable element of 
 education to many other students. There are but few Engineers 
 who are members of the University of Cambridge, but there are 
 hosts of men who must feel that a measure of mechanical training 
 would have been of value to them in the career which they have 
 selected. 
 
OF THE 
 
 UNIVERSITY 
 
 *LIFOg^ 
 1. 
 
 GROUP-FLASHING LIGHTS. 
 
 [Pamphlet first published in October, 1874.] 
 
 EXTENSION of trade, and the consequent increase in the 
 number of Lighthouses upon frequented coasts, continually causes 
 a demand for greater variety in the appearance of Lights, in 
 order to avoid confusion from the nearness of Lights of the same 
 character. This is apparent in the fact that the scheme proposed 
 by the first French Lighthouse Commission, and intended to be 
 complete, has subsequently required extension. The first French 
 scheme admitted but three distinctions, the fixed Light, and re- 
 volving Lights with flashes every minute and every thirty seconds. 
 Now, the French system comprises quick-flashing Lights, revolving 
 Lights with red flashes alternating with white, and fixed Lights 
 varied by flashes ; of the last there are no less than twenty-three 
 on the French coast. Indeed the use of red at all in revolving 
 Lights, involving as it does a serious tax on the luminous power 
 of the flashes, or increased expense for the same power, sufficiently 
 indicates that new combinations are, and will continue to be 
 required. Our present purpose is to offer in a complete shape 
 two new forms of Lighthouse apparatus, and to point out the 
 advantages they possess over some very useful forms now in use. 
 Before doing so it will be well to examine what are the qualities 
 of a good Light. That for any given cost the intensity of the 
 light should be as great as possible, or conversely, that when a 
 given intensity of light is required it should be attained at a 
 minimum expense, is obvious. Most distinctions of beacons 
 depend on the succession of intervals of light and darkness. 
 
 H. I. 1 
 
 .. 
 
2 GROUP-FLASHING LIGHTS. 
 
 The following are suggested as rules of comparison of the efficiency 
 of such distinctions : 
 
 1. The Light must not be too long obscured or an accident 
 might occur in the interval, which a sight of the Light would 
 have prevented. What period of darkness is admissible is a 
 nautical question, and will depend on the position the Lighthouse 
 occupies and the nature of the traffic which it has to guide. 
 Flashes at intervals of as much as three minutes have been in 
 use, but the tendency is to prefer shorter periods, as in the case 
 of South Stack, which is to be altered from flashes every two 
 minutes to flashes every minute. We may therefore assert that, 
 other things being the same, the efficiency is increased as the 
 time of eclipse is shortened. 
 
 2. Unless the eclipse is very short it is necessary that the 
 duration of the flash should be sufficient to take the bearing of 
 the Light. It is this among other reasons which necessitates 
 a special form of revolving dioptric apparatus for condensing the 
 electric light; with the usual form for oil flames, the flash of a 
 half-minute electric light would last but the fraction of a second. 
 What time is sufficient for taking a bearing, is again a purely 
 nautical question, but we may safely say that a flash of con- 
 siderable duration is more useful than one which gives bare time 
 for observation. 
 
 3. The character of the Light must not be too long in 
 declaring itself, in other words the Light must pass through its 
 phases in a reasonable period of time, indeed the shorter this 
 period the better. The fixed and flashing Lights of the French 
 system are usually characterised by a bright flash, preceded and 
 followed by a very brief eclipse, occurring every three or four 
 minutes ; not less than that period of watching is needed to 
 identify the Light. It is a question for those whose experience 
 justifies an expression of opinion, whether in some circumstances 
 such a length of time is not too much. In this respect the 
 revolving Lights with red and white flashes combined, are less 
 favourable than the ordinary revolving Lights of the same period ; 
 for example, to distinguish a half-minute revolving Light showing 
 red and white flashes alternately, from one in which there is a red 
 followed by two whites, requires a minute and a half. Suppose 
 the navigator first sees a white flash, then a red and again a 
 
GROUP-FLASHING LIGHTS. 3 
 
 white, a minute has passed and he must still wait thirty seconds 
 to see if the next flash will be white or red. It should, however, 
 be observed that this remark only applies to the hypothetical 
 case in which two such Lights are placed near each other. 
 
 4. One point insisted upon by Authorities who have them- 
 selves had nautical experience is, that the distinctions should be 
 as simple and easy to apprehend as possible. It is mainly on this 
 account that the scheme proposed by Mr Babbage never received 
 any practical recognition. For the same reason it is unwise to 
 trust too much to any but very marked differences in the period 
 of ordinary revolving Lights. A forty-five second should not be 
 considered safely distinguishable from a minute flash. 
 
 5. The characteristic appearance of the Light must be main- 
 tained at all distances and in all states of the weather in which 
 the Light can be seen at all. If red and white flashes are com- 
 bined, the portion of light devoted to each flash must be such 
 that they shall have equal penetrating power. It would appear 
 that the fixed and flashing Lights so popular on the French 
 coast, would lead to mistakes at times when the feeble fixed 
 Light is obscured, if the intervals of the flashes were not so long 
 as to distinguish them from the ordinary revolving Lights. 
 
 The additional source of variation which I now propose is, 
 that revolving apparatus should be constructed to exhibit two or 
 three white flashes in rapid succession, in place of one at stated 
 intervals of time. This would increase the capacity for variation 
 of the revolving Lights three-fold, we should have single, double 
 and triple flashes at whatever intervals are now considered suitable 
 for revolving Lights. The optical apparatus for producing such 
 combinations would be simple and cost little more than an 
 ordinary revolving Light. For the double flash of the first order 
 we should require a twelve-sided Light, the axes of the panels 
 being placed at unequal intervals, alternately 15 and 45 (Fig. A.); 
 the effect of this would be, that, with an apparatus completing a 
 revolution in three minutes, and using as source of light the usual 
 four-wick flame, there would be a flash of about 2" duration 
 followed by about 5" dark, again a flash of 2", this double flash 
 being separated from the next by about 20J seconds of darkness. 
 The ordinary eight-sided revolving Light condenses 45 of the 
 light of the flame into about 4 in azimuth, thus producing a flash 
 
 12 
 
4 GROUP-FLASHING LIGHTS. 
 
 of intensity 11J, if the continuous light of the fixed apparatus be 
 taken as unity. In the double flashing Light each panel has 30 
 in azimuth, and would therefore give to each flash an intensity 
 represented by 7. Let us see how far this form of Light fulfils 
 the requirements of a good Light. With periods of half a minute 
 the longest eclipse would be 20J seconds, giving a slight ad- 
 vantage over a half-minute Light with eight sides, which is 
 eclipsed for about 27 seconds. The two flashes near to each 
 other would be almost as convenient for taking a bearing as a 
 continuous flash lasting from the beginning of the first flash to 
 the end of the second ; we may therefore consider that we have 
 9J seconds available to take a bearing. It would only be neces- 
 sary to see the two flashes in succession to identify the character 
 of the Light, 9^ seconds would suffice without any counting to 
 
 FIG. A. 
 
 recognise what the Light might be. The peculiarity of such 
 a Light would lie, not in the precise periods between the flashes, 
 but in the flash being a double one. No timing or counting is 
 
GROUP-FLASHING LIGHTS. O 
 
 requisite, for the double and triple flash would be distinguished 
 without any conscious process of counting. The two flashes of the 
 pair being exactly of the same power, the general appearance of 
 the Light must be always the same. 
 
 The triple flash would be conveniently obtained by a revolving 
 apparatus of fifteen sides covering 24 each, the axes of the panels 
 being placed at intervals of 48 and 12. From such an appa- 
 ratus, if a group of three flashes is to be exhibited every half- 
 minute, each flash would last nearly two seconds, and the three 
 would be separated by dark periods of three seconds. We should 
 thus have a longest period of darkness of eighteen seconds, and 
 twelve seconds in which to take a bearing. An apparatus giving 
 four flashes in a group could be readily and economically formed 
 of sixteen sides, there would not be the slightest difficulty in 
 construction, and the flash would be of the same power as that of 
 an ordinary sixteen-sided revolving Light. But it is doubtful if 
 the need for counting so many as four flashes would not be found 
 an unnecessary complication. All I would say here is that such a 
 Light can easily be made. 
 
 The electric spark lends itself more readily than an oil flame 
 to the production of any desired arrangement of the flashes of a 
 revolving Light. Perhaps as unmistakable a form as any that 
 could be suggested, would be a number of very quick flashes 
 and eclipses, constituting a group which should recur at stated 
 intervals. 
 
 It is worthy of notice that if a coast were lit on a system 
 based on the use of group flashes, the appearance of the Light 
 could be made to correspond to the blasts of the fog-horn or the 
 strokes of the fog-bell; a group of three flashes, at intervals 
 of thirty seconds, would naturally be used in conjunction with 
 a fog-signal, sounded three times in succession at the same 
 interval. 
 
 The following Table is intended to show the comparative 
 advantages and disadvantages of group flashes, and the best forms 
 of revolving Lights now in use. In this table the flashes or 
 groups of flashes are supposed to have a half- minute period, the 
 apparatus to be of the first order, and the divergence due to 
 magnitude of flame to be 4. The first column gives the power of 
 the flash, the fixed Light being taken as unity. 
 
GROUP-FLASHING LIGHTS. 
 
 
 Power. 
 
 Time available 
 for taking a 
 bearing. 
 
 Time which 
 may be required 
 to identify 
 the character 
 of Light. 
 
 Greatest 
 duration of 
 darkness. 
 
 Percentage 
 of whole Light 
 wasted by 
 use of colour. 
 
 Eight-sided revolving Light, ) 
 of the usual form \ 
 
 Sixteen-sided ditto 
 
 114 
 
 54 
 
 2f Seconds. 
 
 5-a 
 
 30 Seconds. 
 30 
 
 27 
 24 
 
 
 
 Twelve-sided Light, giving a) 
 double flash ( 
 
 7* 
 
 9* ,, 
 
 10 
 
 20 
 
 
 Fifteen-sided Light, giving) 
 a triple flash ) 
 
 6 
 
 12 
 
 12 
 
 18 
 
 _ 
 
 Nine-sided Light, giving a) 
 red flash, followed by two > 
 white ) 
 
 6 
 
 3 
 
 90 
 
 27 
 
 36-84 
 
 Sixteen-sided Light, giving) 
 white and red alternate ... j 
 
 3 
 
 5i 
 
 90 
 
 24i 
 
 46-66 
 
 Eight-sided Light, red only... 
 
 4 T V 
 
 2 
 
 30 
 
 27i 
 
 63-66 
 
 Sixteen-sided Light, red only 
 
 2* 
 
 5i 
 
 30 
 
 24 
 
 63-66 
 
 It will be observed that in power, the double flash ranks 
 second ; in duration the group flashes are best, as also in respect 
 to time required for identification. 
 
 Group-Flashing Lights can readily be obtained on the 
 Catoptric system, or by using a number of small Holophotes, 
 but such Lights would be subject to all the objections to which 
 revolving Lights with single flashes produced by many lamps are 
 obnoxious. 
 
 NOTE. The Hopkinson Group-Flashing system was for the 
 first time applied, in 1875, to the Catoptric Floating Light on the 
 Royal Sovereign Shoals, near Beachy Head, and has since been 
 applied to several Lightships of the Trinity Corporation. 
 
 The first Land Light on this system was for Tampico Light- 
 house, Gulf of Mexico, Second Order triple-flashing, in 1875. 
 Eighteen Sea Lights in all, and two Harbour Lights, have been 
 constructed by Messrs Chance Brothers and Co., Limited, since 
 1875. 
 
 The Group-Flashing system has also been adopted by the 
 French makers, who have, since 1876, supplied many lights to 
 foreign Governments. 
 December, 1890. 
 
2. 
 
 THE ELECTRIC LIGHTHOUSES OF MACQUARIE AND 
 
 OF TINO. 
 
 [From the Proceedings of The Institution of Civil Engineers, 
 Vol. LXXXVII. Session 1886-87. Part i.] 
 
 THE subject of the use of the electric light in lighthouses was 
 fully discussed at the Institution in 1879, when Papers by Sir 
 James Douglass, M. Inst. C.E., and by Mr James T. Chance, Assoc. 
 Inst. C.E., were read*. 
 
 The subject has been further elaborately examined by Mr 
 E. Allardf, and more recently in practical experiments, made at 
 the South Foreland, exhaustively reported on by a Committee of 
 the Trinity House t. The justification of the present communica- 
 tion is that, at the lighthouses of Macquarie and of Tino, the 
 optical apparatus is on a larger scale than has hitherto been used 
 for the electric arc in lighthouses, and presents certain novel 
 features in the details of construction. Further, as regards the 
 electrical apparatus, tests were made upon the machinery for 
 Macquarie when it was in the hands of Messrs Chance Brothers 
 and Company, which still possess some value, although five years 
 old ; and, in the case of Tino, the machines are practically worked 
 together in a manner not previously used otherwise than by way 
 of experiment. 
 
 * Minutes of Proceedings Inst. C.E. vol. Ivii. pp. 77 and 168. 
 t Memoire sur les Phares Electriques, 1881. 
 
 Keport into the relative merits of Electricity, Gas, and Oil as Lighthouse 
 Illuminants. Parts 1 and 2. PP. 1885. 
 
8 ELECTRIC LIGHTHOUSES. 
 
 In the case of both lighthouses, Messrs Chance Brothers and 
 Company, of Birmingham, entered into a contract for the supply 
 of all the apparatus required, including engines, machines, con- 
 ductors, lamps, optical apparatus, and lanterns ; and Sir James 
 Douglass, Engineer-in-Chief of the Trinity House, acted as 
 Inspecting Engineer to the respective Colonial and Foreign 
 Governments. 
 
 As these two lighthouses present many features in common, it 
 may be most convenient to give a full description of the earlier 
 lighthouse, and then limit the description of Tino to those points 
 in which it differs from Macquarie. 
 
 MACQUARIE. 
 
 This lighthouse is situated on South Head, near Sydney, the 
 precise position being shown in a copy from the chart, Fig. 1. A 
 lighthouse was first placed at this important landfall in 1817. 
 The focal plane is 346 feet above the sea, and the distance 
 of the sea-horizon is therefore 21*6 nautical miles, and the 
 range about 27 nautical miles for an observer 15 feet above 
 the sea. 
 
 Optical Apparatus. The light is a revolving one, giving a 
 single flash of eight seconds duration every minute. On account 
 of the considerable altitude of the lighthouse, it was necessary to 
 secure that a substantial quantity of light should be directed to 
 the nearer sea ; but it was also essential, on account of the 
 exceptional power of the apparatus, that this dipping light should 
 only be a small fraction of that sent to the horizon, otherwise its 
 effect would be excessively dazzling. Many years ago, Mr James 
 T. Chance urged that it was not wise to make use of very small 
 apparatus for the electric arc, because a larger apparatus renders 
 it possible for the optical engineer to effect with greater precision 
 the distribution of light which is most desirable, and because any 
 trifling error which may occur in the position of the electric arc 
 has, with the larger apparatus, a less marked effect on the light as 
 seen from the sea. In the lighthouses of Souter Point, the South 
 Foreland, and the Lizard, the third-order apparatus of 500-milli- 
 metre focal length was adopted. Optically, the larger the appa- 
 
ELECTRIC LIGHTHOUSES. 
 
 9 
 
 ratus used the better, but there might be some question whether, 
 on purely optical grounds, the advantage of going beyond the 
 third order is sufficient to justify the additional expense, but in 
 the case of a revolving apparatus, the third order is a very 
 inconvenient size for the service of the lamp; it is too large 
 to be conveniently served from the outside, and too small to admit 
 the attendant within it with comfort. With the large currents, 
 which are now easily obtained and are likely to be used in 
 lighthouses, a first or second order apparatus has the further 
 
 Scale, 32 Miles 1 inch 
 
 FIG. 1. 
 
 advantage that it is less liable to injury from particles thrown 
 off from the heated carbons. In the case of Macquarie, it was 
 
10 ELECTRIC LIGHTHOUSES. 
 
 decided to adopt an apparatus of the first order, 920-millimetre 
 focal length ; it was further decided that the optical apparatus 
 should produce its condensing effect by means of a single agent ; 
 that is to say, the vertical straight prisms which were used in 
 Souter Point and other revolving electric lighthouses should be 
 dispensed with. The condensation and distribution of light 
 necessary may be obtained by means of a single agent, with 
 apparatus such as has been proposed by Mr Alan Brebner, jun., 
 Assoc. M. Inst. C.E.* ; but this construction is open to the 
 objections that it is somewhat costly, and that it increases the 
 length of the path of the rays through the glass, and consequent 
 absorption. A practically better plan is to adopt forms not 
 differing very greatly from those introduced by Fresnel ; to 
 specially arrange them for the purpose in hand, and to accept 
 certain consequent minute deviations from a mathematically 
 accurate solution for the sake of advantages of greater importance, 
 when all the actual conditions are taken into account. Fig. 2 
 shows the optical apparatus in vertical section; the upper and 
 the lower totally-reflecting prisms are, as is usual in revolving 
 lights, forms of revolutions about a horizontal axis ; they direct 
 the light incident upon them to the horizon and the distant sea 
 from 10' above the horizon to 30' below; they are specially 
 adjusted to distribute the light in azimuth over the arc of 3 
 necessary for a proper duration of flash. 
 
 The refracting portion of the apparatus has the profile so 
 calculated that the central Jens, and the three rings next to the 
 lens above and below, direct their light to the horizon without 
 vertical divergence, except what is due to the size of the arc ; 
 the light for the nearer sea is obtained from the remaining ten 
 lens-segments, Nos. 5 to 9 inclusive, above and below the centre, 
 counting the centre as No. 1, the distribution being according 
 to the following Table, in which the first column gives the 
 denomination of the elements of the lens in accordance with 
 the numbers marked upon the section ; the second, the angle 
 between the direction of the sea-horizon and the ray emerging 
 from the upper limit of the element ; the third, the angle between 
 the direction of the sea-horizon and the ray from the lower limit 
 of the element, the negative sign denoting that the emerging ray 
 
 * Minutes of Proceedings Inst. C.E. vol. Ixx. p. 386. 
 
ELECTRIC LIGHTHOUSES. 
 
 11 
 
 is above the horizon. This practice, of appropriating certain 
 elements of the apparatus to different distances on the sea, was 
 
 I. 
 
 II. 
 
 III. 
 
 9 top 
 
 / // 
 
 -10 
 
 O ' // 
 
 2 30 59 
 
 8 
 
 2 30 59 
 
 5 8 52 
 
 7 
 
 -10 
 
 2 37 30 
 
 6 
 
 -10 
 
 1 30 
 
 5 
 
 -10 
 
 100 
 
 5 bottom 
 
 -10 
 
 100 
 
 6 , 
 
 -10 
 
 1 30 
 
 7 
 
 1 30 
 
 3 44 27 
 
 8 .... 
 
 3 44 27 
 
 5 50 41 
 
 9 
 
 5 50 41 
 
 7 46 57 
 
 
 
 
 first introduced by Mr James T. Chance, in the lights of the 
 South Foreland exhibited in January 1872. 
 
 The ray, dipping at an angle of 7 46' 57" below the horizon, 
 will strike the sea at J mile, while 5 8' 52" corresponds to mile, 
 2 37' 30" to 1J mile, 1 30' to 2 miles, 1 to 2 miles, and 30' to 
 about 4 miles. Thus the direct light begins at about J mile from 
 the lighthouse. From ^ mile to f mile the sea receives light from 
 one element of the apparatus, from J to 1 J mile from two elements, 
 from 1J mile to 2 miles from three elements, from 2 to 2 miles 
 from four elements, and beyond 2 miles from six elements ; the 
 upper and lower totally reflecting prisms come in aid at about 
 5 miles. The main power of the apparatus is hardly attained till 
 a distance of 8 or 10 miles. Fig. 3 is a sectional plan of the 
 apparatus by a horizontal plane through the focus. It will be 
 seen that a dioptric mirror is placed on the landward side of the 
 arc. This mirror is arranged to form the image of the arc at one 
 side of the carbons, so avoiding the interception of light which 
 would result if the mirror were used in the ordinary way, and 
 contributing to the horizontal divergence necessary. Further 
 horizontal divergence is given by the form of the lens. In the 
 ordinary revolving light the inner face of the lens is plane ; here 
 it is cylindrical, the axis of the cylinder being vertical. This 
 method of obtaining horizontal divergence is a modification of a 
 proposal of Mr Thomas Stevenson*, M. Inst. C.E. ; it is not mathe- 
 matically accurate, inasmuch as the cylindrical form of the inner 
 
 * Lighthouse Construction and Illumination, p. 186. 
 
12 
 
 ELECTRIC LIGHTHOUSES. 
 
 face of the lens not only displaces the emergent ray horizontally, 
 but also in the case of rays not in the vertical nor horizontal plane 
 
 FIG. 2. 
 
 FIG. 4. 
 
 FIG. 5. 
 
 through the focus, to a small extent vertically, but the error is 
 easily calculable, and is unimportant, provided the lens is narrow, 
 
ELECTRIC LIGHTHOUSES. 
 
 13 
 
 and the horizontal divergence of the beam moderate. Plate 9, 
 Fig. 4, shows a complete panel in elevation with revolving carriage. 
 Fig. 5 shows the plan of the service-table of the pedestal and 
 lamp-table. A new construction was adopted for the gun-metal 
 framework of the optical apparatus to reduce the interception of 
 light by the frame to a minimum. The metal segment A, Fig. 6, 
 forms part of the lower prism -frame, B part of the upper frame, 
 whilst C and D are parts of the frame for the refracting portion of 
 the apparatus ; uprights E support the upper prism-frames without 
 throwing weight on the lens-frames. With the ordinary construc- 
 tions of frame, Figs. 7 and 8, the equivalent of these ring segments 
 A and B would intercept about double as much light as in this 
 new construction. 
 
 FIG. 6. 
 
 FIG. 7. 
 
 FIG. 8. 
 
 Mechanism for Rotation. The pedestal is similar to those 
 designed by Sir James Douglass to permit the light-keeper to 
 obtain access from below to the interior of the apparatus without 
 in any way interfering with its rotation. The clock-work is fitted 
 with the governor, and maintaining power used by Messrs Chance 
 Brothers and Company for the last twelve years. The roller-ring 
 may be mentioned as of an improved type, for although it has 
 been used for some years in all Messrs Chance's lights, it has not 
 been described before. The rollers and roller-paths which carry 
 the whole weight of the optical apparatus have long been made 
 conical, so that the surfaces roll upon each other without twisting. 
 There is consequently a very considerable radial force on each 
 
ELECTRIC LIGHTHOUSES. 
 
 roller tending to force it outwards, the reaction against this force 
 causes a very important part of the total frictional resistance. 
 Fig. 9 shows a portion of the roller-ring and one of the 
 conical rollers, according to the old construction; Figs. 10, 11, 
 according to the improved construction ; in the former it will be 
 observed that the thrust of the roller is received on a collar ; in 
 
 n 
 
 FIG. 9. 
 
 FIG. 10. 
 
 FIG. 11. 
 
 the latter, on the end of a pin. The reduction of friction is 
 practically very considerable, and although of small importance in 
 a slow -moving apparatus like Macquarie, is of great importance in 
 heavier and quicker apparatus; for example, the triple-flashing 
 light at Bull Point, in Devonshire. 
 
 Lamps. These are of the Serrin type, and were supplied by 
 Baron De Meritens. 
 
 Lamp-Table. The arrangements for rapidly changing electric 
 lamps, and for substituting gas or oil when desired, are shown in 
 Figs. 12, 13, 14, 15. 
 
 The intention was to use a gas-lamp in clear weather, and 
 half-power or full-power electric light in thick weather, according 
 to the opacity of the atmosphere ; but the Author understands 
 that in practice the electric arc is always used. The paraffin 
 oil-lamp is intended as a resource in case of failure of the supply 
 of gas. 
 
 Focussing the Arc. Two approximately rectangular prisms are 
 fixed upon the mirror frame at about 90 from each other, the 
 longer face of each is plane, the other two faces convex, of such 
 curvature as to form a good image of the arc upon the service- 
 table, as shown in Fig. 16. During daylight, a pointed sight or 
 focimeter is placed at the position of the image formed by the 
 
ELECTRIC LIGHTHOUSES. 
 
 15 
 
 lens of an object on the horizon ; this then is the position which 
 the arc should occupy. A sight is next taken over the focimeter 
 into one of the adjusting prisms, and a bright object such as a 
 threepenny piece placed on the service-table, is moved about 
 until its centre is seen in the prism, exactly upon the point of 
 the focimeter; a mark is made in the then position of the object. 
 
 FIG. 12. 
 
 Fm. 13. 
 
 FIG. 14. 
 Arrangement for Oil Lamp. 
 
 FIG. 15. 
 Arrangement for Gas-burner. 
 
 When the arc is correctly adjusted, its image on the service-table 
 will be at the point where the mark is made. Two prisms are 
 used in order to secure that the arc shall be in the centre of the 
 apparatus as well as at the correct level. 
 
 Lantern. The lantern is of the well known Douglass type*. 
 
 * Minutes of Proceedings Inst. C.E. vol. Ivi. p. 77. 
 
16 
 
 ELECTRIC LIGHTHOUSES. 
 
 Dynamo-electric Machines. Two alternate-current machines, 
 with permanent magnets manufactured by De Meritens, were 
 supplied. Each machine has five rings in its armature, and in 
 each ring there are sixteen segments. In supplying one arc for a 
 lighthouse the machine runs about 830 revolutions per minute, 
 and gives a current of 55 amperes when half the coils are used, 
 
 FIG. 16. 
 
 and of 110 when the whole of the machine is in action, the 
 internal resistance in the two cases being 0*062 and 0*031 ohm. 
 It is unnecessary to give a description of the machine as its 
 general construction and dimensions are well known, but some 
 numerical details are given below. 
 
 Engines. Each machine is driven by an 8 H.P. Crossley gas- 
 engine through a belt without countershafting. 
 
 Tests. Whilst the dynamo machines were at the works of 
 Messrs Chance Brothers and Company, a series of experiments 
 was made in March 1881 to determine their properties. The 
 time is long passed when it would be profitable to give the 
 details of these experiments, but the general conclusions drawn 
 at the time are still interesting. When the external resistance 
 was a metallic conductor with small self-induction, it was found 
 that with varying resistance and speed the currents observed 
 agreed fairly well with calculation from the formula 
 
 * Lectures on the "Practical Application of Electricity." Session 1882-83. 
 Some points in Electric Lighting. By Dr John Hopkinson, p. 88. 
 
ELECTRIC LIGHTHOUSES. 17 
 
 in which R is the total resistance of the circuit, y the self-induc- 
 tion, and T the periodic time. When the machine was running 
 
 830 revolutions per minute -4 = 67 volts and (-^r) =0'197 in 
 
 ohm squared, hence y = 6 "4 x 10 5 centimetres. The eighty sections 
 of the machine are arranged four in series, twenty parallel. For 
 a single section the value of y would be 32 x 10 5 centimetres. 
 The maximum induction in the core, which has an area of 5 square 
 centimetres, is 24,600 or 4,920 per square centimetre. The loss 
 of power was greater when the machine was doing little or no 
 external work than when that work was great. This is clearly 
 seen in the following table : 
 
 Current amperes 7'70 73-60 
 
 Electrical work H.P 0-69 5-66 
 
 Mechanical work applied . . . 3-09 6-55 
 
 Loss 2-40 0-89 
 
 Photometric experiments were made upon the arc, and simul- 
 taneous measurements of effective power applied and of current 
 passing. The red light was measured through bright copper ruby 
 glass, and the blue through a solution of sulphate of copper and 
 ammonia. The H.P. was measured by a transmission dynamo- 
 meter ; but the results must be accepted with some reserve, on 
 account of the difficulty of ascertaining the mean tension in a 
 strap which is constantly varying. The oscillations of the dyna- 
 mometer were damped by a dashpot containing tar. 
 
 Half Power. Pull Power. 
 
 Red candles 1,988 4,708 
 
 Blue 4,079 11,382 
 
 Current (amperes) 54-5 105 
 
 Mechanical power applied (H.P.) 4-5 6*9 
 
 Power expended in heating conducting wires (H.P.) . 0'24 0-95 
 
 The results illustrate the fact that, as the current increases, 
 the total light increases in a higher ratio, red light in a slightly 
 higher ratio, and blue in a considerably higher. 
 
 The machinery for this lighthouse was sent out to New South 
 Wales in November 1881, and was put up and started under the 
 superintendence of Mr J. Barnett, the Architect of the Colony, to 
 whom is mainly due the success of the whole from the first start. 
 The glare of the light upon the sky is said to have been seen at a 
 distance of over 60 miles, far beyond the distance at which it 
 would cease to be directly visible. The only criticism from 
 H. i. 2 
 
18 
 
 ELECTRIC LIGHTHOUSES. 
 
 mariners has been that when somewhat near the lighthouse the 
 flashes are so bright as to dazzle the eye. This is an excellent 
 proof of the power of the light, as a much smaller proportion of 
 the light is directed upon the nearer sea than in any previous 
 lighthouse. The lesson is that with powerful electric lighthouses 
 almost all the light should, in ordinary weather at least, be 
 directed to the horizon, and that the quantity thrown upon the 
 nearer sea must be strictly limited. This is only possible when 
 the focal length of the apparatus is large. 
 
 TINO. 
 
 This station is on a small island at the mouth of the Gulf of 
 Spezia. Fig. 17 is copied from the chart of the neighbour- 
 hood. The focus is 386 feet above sea-level. The distance of 
 the sea-horizon is 22'7 nautical miles, and the range practically 
 28 miles. The conditions, therefore, were very similar to those of 
 Macquarie, with the exception that it was required to throw some 
 light down into the channel between Palmaria and Tino. The 
 
 Voltri 
 
 Scale, 16fi Miles *=1 inch 
 
 FIG. 17. 
 
 lighthouse itself presents some interesting historical features. The 
 buildings were originally a place of defence against the pirates who 
 occasionally made descents upon the coast. Subsequently a coal- 
 fire lighthouse was established, and in the spring of 1885 part of 
 
ELECTRIC LIGHTHOUSES. 
 
 19 
 
 the stock of lignite was still found to be in some of the buildings, 
 where it had been lying for fifty years. In 1839 a dioptric light 
 was established, one of the earliest of Fresnel's types, the lens-ring 
 being replaced by short straight prisms, which formed by no 
 means a bad approximation, and could be ground without special 
 machinery. The present electric lighthouse has been in contem- 
 plation for several years. 
 
 FIG. 20. 
 
 FIG. 19. 
 
 Optical apparatus. The distinctive character of the light is a 
 triple flash every half-minute. The apparatus for producing this 
 effect is of the general form introduced by the author in 1874. 
 In October of that year he issued a pamphlet pointing out the 
 several advantages of group-flashing lights, showing for the first 
 time a simple dioptric apparatus suitable to their production, and 
 
 22 
 
20 
 
 ELECTRIC LIGHTHOUSES. 
 
 also pointing oat how easy it is to give the group-flashing effect 
 with catoptric apparatus. Since that time a large number of 
 dioptric group-flashing lights have been made by Messrs Chance 
 Brothers and Company, and some also in France, and Mr Allard 
 has incorporated group-flashing lights in the system of distinctions 
 he recommends ; also a considerable proportion of the light- vessels 
 on the English coasts have been converted into group-flashing 
 lights of the catoptric system. On the ground of economy the 
 second-order apparatus of TOO-millimetre focus was adopted in 
 the case of Tino. It is just large enough for tolerably convenient 
 service of the lamp by an attendant entering within the apparatus. 
 The apparatus, shown in vertical section in Fig. 18, and in hori- 
 zontal section through the focus in Fig. 19, has twenty- four sides, 
 eight groups of three ; one group of three is shown in elevation in 
 Fig. 20. The horizontal divergence is obtained in exactly the 
 same way as at Macquarie, excepting that no mirror is used. The 
 metal framework, however, approximates to the ordinary type, as 
 the type used at Macquarie would have been costly when applied 
 to a triple-flash light. The distribution of light vertically is as 
 follows : upper and lower prisms, and the central lens, with the 
 two lens-rings next adjoining it, all to the horizon and most 
 distant sea. The lens and lens-rings direct their rays according 
 to the following Table, which is arranged in exactly the same way 
 as the Table already given for Macquarie 
 
 I. 
 
 II. 
 
 III. 
 
 7 top 
 
 31 35 
 all to the 
 
 ' I' 
 
 3 16 
 200 
 1 30 
 100 
 45 
 30 
 30 
 horizon. 
 
 6 , 
 
 
 4 , 
 
 4 bottom 
 
 5 
 
 6 
 
 7 
 
 No. 7 bottom was directed wholly to the horizon, in order to 
 avoid the horizontal bar of the lantern. It will be observed that 
 the quantity of light thrown upon the nearer sea is much less 
 in the case of Tino than in that of Macquarie, and that greater 
 reliance is placed upon the accuracy with which the arc can be 
 
ELECTRIC LIGHTHOUSES. 
 
 21 
 
 kept in focus ; experience has justified these changes, as improve- 
 ments of a perfectly safe nature. 
 
 A small part of each flash is bent downwards and distributed 
 over the channel between Tino and Palmaria, by means of sub- 
 sidiary prisms fixed upon the lantern, shown at X, Fig. 18. These 
 subsidiary prisms are really superfluous, as the scattered light 
 from the beams overhead is found to be as effective at this short 
 distance. Fig. 21 shows the plan of lamp shunting-table and 
 service -table. 
 
 FIG. 21. 
 
 Engines. As there is no water upon the island, the practice of 
 the Trinity House was followed, and two of the Brown hot-air 
 engines were supplied, each driving through a countershaft one of 
 the machines. The countershafts could be connected by means of 
 a Mather and Platt friction-coupling, so that the two machines 
 could be driven together, or either machine from either engine. 
 Drawings of the Brown engines are given in Sir James Douglass's 
 Paper*. The accompanying indicator-diagrams were taken from 
 the compressing- and working-cylinders. Whilst these diagrams 
 were taken the effective power developed was measured by a 
 friction- brake on the driving-pulley, and was found to be 9'1 H.P. 
 Thus of 33-1 H.P. indicated in the working-cylinder, 177 H.P. is 
 employed in compressing the air, 6*3 H.P. is wasted in friction in 
 various parts of the machine, and only 9*1 H.P. is effective upon 
 the brake. The engines consume about 4 Ibs. of coke per effective 
 H.P. per hour. In future lighthouses, when a steam-engine can- 
 not be employed, it would be preferable on every ground to use 
 
 * Minutes of Proceedings of the Inst., vol. LVII. Plate 6. 
 
22 
 
 ELECTRIC LIGHTHOUSES. 
 
 gas-engines, and manufacture on the spot either Dowson gas or 
 ordinary gas, according to the character of the fuel available. 
 
 Dynamo Machines. There are two machines of exactly the 
 same type as those supplied for Macquarie, the only novelty lying 
 in the method of using them. In 1868 Mr Wilde discovered, by 
 experiment, that two alternate-current dynamos, independently 
 driven at the same speed, would, if electrically connected, so con- 
 trol each other's motions that they would add their currents. The 
 
 FIG. 22. Compressor-pump cylinder, 24 inches in diameter. 
 Indicated H.P., 17.7. 
 
 Stroke, 22 inches. 
 
 FIG. 23. Working cylinder, 32 inches in diameter. Stroke, 20 inches. Indicated 
 H.P., 33.1. Revolutions per minute, 64. Power on brake of fly-wheel, 9.12 H.P. 
 Pressure in reservoir, 19 to 24 Ibs. 
 
 author subsequently arrived at the same conclusion independently, 
 on theoretical grounds, and gave a thorough explanation of the 
 fact*. The result has been put to a practical application at Tino. 
 
 * Lectures on the "Practical Application of Electricity." Session 1882-83. 
 Paper on "Some Points in Electric Lighting," reprinted in this volume. By 
 Dr John Hopkinsou. And Journal of the Society of Telegraph Engineers and 
 Electricians, vol. xin. p. 496. 
 
ELECTRIC LIGHTHOUSES. 23 
 
 The machines are connected to a single switchboard, so that each 
 half of the two machines can at pleasure be connected to, or dis- 
 connected from, the main conductors. Thus a current can be 
 supplied from either machine at half power, 55 amperes, or full 
 power, 110 amperes, or from the two machines of double power, or 
 about 200 amperes. Further, a change can be made without 
 extinction of the light from one dynamo and engine to the other. 
 Thus, suppose one machine is working full power, clutch the 
 countershafts gradually together, so starting the second engine; 
 throw on the band of the second machine, cut out half the first 
 machine, and connect half the second machine at the switchboard ; 
 the two machines at once synchronize, without affecting the light. 
 Disconnect the remaining half of the first machine, and connect 
 the remaining half of the second, unclutch the countershafts, and 
 stop the first engine. One man can effect the change, with no 
 more disturbance of the light than a change from full to half 
 power for about one second. A further conclusion, deduced from 
 theoretical considerations, was that of two alternate current 
 machines of equal potential, one could be used as a generator 
 of electricity, the other as a motor converting the current gene- 
 rated back into mechanical power. It was found impossible to 
 verify this conclusion with such intermittent driving as that of 
 a hot-air engine. But Professor W. G. Adams effected the verifi- 
 cation without difficulty at the South Foreland, the motive power 
 being steam. 
 
 Lamps. These are the improved Serrin of M. Berjot. One of 
 the three lamps supplied is of larger size, for the double power 
 current from the two machines. This lamp was said to be 
 suitable for a still greater current, but with about 200 amperes 
 it soon became dangerously heated; a simple modification 
 rendered the lamp equal to the actual work it had to do. It 
 is, however, probable that for the occasional circumstances when 
 it is necessary to use so great a current as 200 amperes in a 
 lighthouse, a lamp worked partly by hand would be preferable to 
 a regulator entirely automatic. 
 
 The apparatus was delivered in November, 1884, and was put 
 up by workmen from Messrs Chance's workshops, under the super- 
 vision of Mr L. Luiggi, of Genoa, to whose ability and energy the 
 complete success of the lighthouse is largely due. A complete 
 
24 ELECTRIC LIGHTHOUSES. 
 
 test of the performance of the light, as seen from the sea in 
 all grades of its power, was made in April, 1885, by a commission, 
 consisting of Professor Garibaldi, of Genoa ; Mr Giaccone, engineer- 
 in-chief for Italian lighthouses ; Captain Sartoris, and Mr Luiggi, 
 the author attending on behalf of Messrs Chance. The light was 
 well observed through rain, when distant 32 nautical miles, and 
 although below the horizon, the position was precisely localized, 
 and the triple flash distinction unmistakeable. At 18 miles 
 distant the illumination of the flash upon white paper was 
 sufficient to make out letters marked in pencil 1J inch high, 
 and when 14 miles distant it was easy to ascertain the time from 
 a watch. The light is frequently seen at a distance of 50 miles 
 near to Genoa. 
 
 A review of work which has been carried out naturally suggests 
 many questions as to what conclusions experience has established, 
 and what indications it gives of the probable direction for future 
 developments. In the use of electric light in lighthouses there 
 are many questions upon which there is wide difference of opinion, 
 questions both as to when and where electric light should be 
 adopted, and questions as to the best way of employing it. It 
 may not be unprofitable to allude to some of them. Although 
 English engineers are now well agreed that a large optical 
 apparatus should be used for the electric light, this opinion is 
 not universally accepted. The advantages of a large apparatus 
 have already been mentioned. To balance them, there is nothing 
 on the other side but the less prime cost of the smaller apparatus. 
 Although the difference of cost appears considerable when atten- 
 tion is confined to the optical apparatus, it is unimportant when 
 the whole outlay on the lighthouse is brought into account. 
 Cases are, however, conceivable in which a small optical apparatus 
 such as a fourth order, having a focal distance of 250 millimetres, 
 would be properly preferred ; such, for example, as a harbour light 
 which could be supplied with current from machinery also used 
 for other purposes, but such cases are likely to be exceptional. 
 
 When a flame from oil or gas is the source of light, there is of 
 necessity a considerable divergence vertically; and the distribution 
 of the light through the angle of vertical divergence is not at 
 disposal, except to a very limited extent in some cases, but is 
 
ELECTRIC LIGHTHOUSES. 25 
 
 determined by the size and character of the flame. With the 
 electric arc and a large optical apparatus it can be determined in 
 considerable measure how the light shall be distributed how 
 much shall be sent to the distant sea, how much to the various 
 distances between the foot of the tower and a distance of some 
 miles. It becomes then a question what use is to be made of this 
 facility. The experience at Macquarie and at Tino is emphatic, 
 that it is in every way advantageous to direct much the greater 
 part of the light to the horizon with a very small divergence, and 
 to distribute the comparatively small remainder over the nearer 
 sea with intensity increasing with the distance. 
 
 A question allied to the last is this : Whether it be desirable 
 to provide means of directing the strongest light downwards on to 
 the nearer sea in time of fog? The answer must depend upon 
 the circumstances of the particular locality. Take the case of a 
 lighthouse on an isolated rock, the purpose of which is primarily 
 to be a beacon to keep ships off that rock; a lighthouse which 
 would not exist were it not more practical or cheaper to build and 
 maintain the lighthouse rather than remove the rock. Here 
 surely it is of the greatest use to provide means whereby, if the 
 light cannot penetrate 2 miles, it shall if possible be visible at 
 1 mile. But other cases occur in which the lighthouse has to 
 cover a long length of coast, and has almost as much to do with 
 points of the coast 10 miles distant as with the point upon which 
 it is placed, cases in which the lighthouse is far more useful in 
 guiding the regular traffic passing within a radius of 20 miles or 
 more than in preventing vessels running ashore within a mile of 
 the tower. Such a light fails of its purpose if it can only be seen 
 at a distance of a mile, covering less than -^ part of its normal 
 area of illumination ; it becomes comparatively useless unless it 
 penetrates to something like its normal range, and its efficiency 
 must be measured by the fewness of the occasions when it fails 
 to do this. It is a grave question whether it be prudent in such 
 cases to place upon the light-keeper the responsibility of judging 
 when the light should be dipped on to the nearer sea, the fact 
 being that, if his judgment errs, he may actually diminish the 
 range of the light, and cause unnecessarily the lighthouse to fail 
 of fulfilling its most important function. It is easy for him to be 
 misled if the fog is local and does not extend to any great distance 
 from the lighthouse. Another element enters into the considera- 
 
26 ELECTRIC LIGHTHOUSES. 
 
 tion the height above the sea. If the focus be 100 feet above 
 the sea-level, the dip of the sea-horizon is 9' 45", and a ray dipping 
 9' 45" below the sea-horizon will meet the sea at a distance of 3*1 
 nautical miles from the tower. Even with a first-order apparatus, 
 if the arc be a powerful one, it is very difficult to render the 
 light directed to the horizon from an elevation of 100 feet more 
 powerful than that directed to a point distant 4 miles from the 
 tower. Unavoidable divergence will render the two intensities 
 practically equal. 
 
 Passing to questions of another class, what are the relative 
 advantages in an electric lighthouse of continuous and alternating 
 currents ? Present practice tends altogether in favour of alternate 
 currents, but this practice largely results from unfavourable ex- 
 perience of the older continuous-current machines. These machines 
 have in many respects been greatly improved in the last two or 
 three years. The continuous current presents the advantage of 
 greater economy of power in producing the current, less floor- 
 space required by the machine, and a smaller prime cost. The 
 alternate-current magneto machine, on the other hand, has the 
 advantage that it may be driven with a defectively governed 
 prime mover, with an indifferent lamp, and may suffer neglect 
 with impunity; whereas the more compact and efficient con- 
 tinuous-current machine would be in serious peril of destruction. 
 Optical apparatus can be constructed suitable to make the most 
 of either form of arc. Hot-air engines have found favour for 
 electric lighthouses, because in many cases there is no available 
 supply of fresh water. The engines of which the author has 
 experience are open to the objection that they take a great deal 
 of room, are not economical of fuel, and do not govern so quickly 
 as is desirable ; the wear and tear also, when they are worked to 
 anything like their full power, is very serious. A gas-engine, with 
 Dowson or other gas made on the spot, could be used with greater 
 advantage. 
 
 Antecedent to all considerations as to the best apparatus, and 
 machinery to be used, is the question, under what circumstances, 
 if at all, should electric light be used in a lighthouse ? The 
 Trinity House experiments at the South Foreland showed to 
 demonstration that, where the issue to be decided was how to 
 produce a light which should be capable of penetrating the 
 furthest in all weathers, electric light could do that which could 
 
ELECTRIC LIGHTHOUSES. 27 
 
 be done in no other way, and that it was the cheapest light of all 
 when the price is estimated per unit of light. But the conclusion 
 was also reached that an electric light must inevitably cost a 
 large sum, both in first outlay and in maintenance ; therefore that 
 electric light is extravagant unless very extraordinary power is 
 a necessity. This conclusion is doubtless a fair consequence of 
 experience, but it is not an inherent property of electric light. 
 Both the capital outlay and the cost of maintenance are greatly 
 increased by the practice of so arranging the machinery as to 
 provide, at all times, a light of very great power : whence follows 
 that the machinery must be placed at some distance from the 
 lantern, and two men must always be on duty ; one man in the 
 lantern, and another with the machinery. 
 
 The essentials for a cheap electric lighthouse are, that for 
 ordinary states of the atmosphere there shall be provided a plant 
 under the easy control of the light-keeper himself, which shall be 
 precisely adapted to produce that amount of light which is wanted 
 in ordinaiy states of the atmosphere ; but for thick weather there 
 shall be provided a much more powerful engine and dynamo, 
 available also as a reserve in case the smaller machinery from any 
 cause breaks down. The occasional machinery may be more 
 remote from the lantern, as it is a small matter to require a 
 second man to work on the comparatively rare occasions when 
 the maximum power is needed. A small gas-engine and a dynamo 
 machine can be placed without any crowding in the room im- 
 mediately below the lantern, and arrangements can be made 
 whereby the light-keeper, whether he is in the lantern or in 
 the engine-room, can ascertain at a glance whether the arc is 
 in its proper position, with an error of less than 1 millimetre. 
 The attendance on the lamp, rotating apparatus of the lens (if a 
 revolving light), engine and dynamo, would be easy when the 
 whole is brought together, so as to be under observation at once ; 
 in fact the gas-engine, dynamo, and lamp constitute together a 
 gas-burner which, though consisting of many parts, is automatic 
 throughout, and requires nothing but the constant presence of a 
 custodian, exactly as the gas-lamp in a lighthouse requires a 
 custodian, as a guarantee against failure. The same end, viz., 
 the concentration of the whole mechanical and electrical apparatus 
 under one pair of eyes, could be attained, of course, in other ways. 
 Accumulators could be used, or a petroleum-engine. 
 
28 ELECTRIC LIGHTHOUSES. 
 
 In order to give definiteness and afford facilities for criticism, 
 the better course will be to describe a suitable machinery ; state 
 what it will do, what attendance it will require, and what it will 
 cost. The author proposes, then, for an electric lighthouse where 
 small outlay is essential, the following : A Dowson gas-producing 
 apparatus and gas-holder, the generator and superheater being in 
 duplicate, each capable of making 1,200 feet of gas per hour, the 
 gas-holder having a capacity of 3,000 cubic feet. 
 
 An 8-H.P. nominal Otto gas-engine and series-wound dynamo- 
 machine, placed in a room near the base of the tower, and copper 
 conductors to the lantern, the dynamo having magnet coils, 
 divided into sections so as to supply a small current when 
 required. 
 
 A 1-H.P. nominal Otto gas-engine and dynamo-machine, placed 
 in the room immediately beneath the lantern floor, with gas-pipe 
 from the gas-holder ; three electric lamps, to receive either carbons 
 25 millimetres in diameter or any lesser size, with complete adjust- 
 ments for accurate focussing; one paraffin lamp as a substitute; 
 an optical apparatus of the second order of 70-centimetre focal 
 distance. The cost of this apparatus would depend upon the 
 character of the light it was intended to exhibit. To fix ideas, 
 let it be assumed that the light is to be a half-minute revolving 
 light, showing all round the lighthouse. There could then be 
 supplied a sixteen-sided apparatus with pedestal and revolving 
 machinery. Provision would be made in the optical apparatus for 
 giving the horizontal and vertical divergence desired by the same 
 methods successfully used in the lighthouses of Macquarie and of 
 Tino. 
 
 Two focussing prisms would be fixed to form magnified images 
 of the arc, on pieces of obscured glass let into the pedestal floor, so 
 that the keeper, whether in the lantern or in the engine-room, 
 could see at a glance the state of the arc, and observe whether it 
 is of proper length- with the carbons in line, whether it is exactly 
 at the right height and in the centre of the apparatus. An error 
 of 1 millimetre would be glaringly apparent, and call for immediate 
 adjustment, although its effect would be only a displacement of 
 the beam 5' of angle. 
 
 The lantern would be 10 feet diameter, with bent plate-glass. 
 
ELECTRIC LIGHTHOUSES. 29 
 
 The cost of the whole above described would be materially less 
 than the cost of a first-order light and lantern with oil-lamp and 
 large burners. 
 
 Now what result would be obtained? In fine weather the 
 small engine would be used. Its effective power on the brake is 
 fully 1 H.P. ; from this 1 J H.P. the dynamo-machine produces 
 considerably over 800 watts, say 800 watts in the arc itself, or 20 
 amperes through a fairly long arc of 40 volts. Of course the value 
 of this in candles depends upon the colour in which it is measured, 
 and the direction in relation to the axis of the carbons. In red 
 light the mean over the sphere would certainly exceed 1,200 
 candles. In clear weather or in slight haze or rain, the beam of 
 this light through the lenses would be much more powerful at 
 the horizon and on the more distant sea than any single-focus 
 light with oil or gas as the illuminant, and would at least be fairly 
 comparable with anything yet exhibited with oil or gas, whether 
 triform or quadriform. But on the nearer sea the illumination 
 would be reduced, so that no annoyance would be caused by 
 dazzling flashes. In thick weather or indeed in any weather 
 when there was a doubt as to the visibility at the horizon of 
 the lower power, the large engine would be used under the 
 superintendence of the second keeper. This engine will give 
 10 H.P. on the brake, and there is no difficulty in obtaining 85 
 per cent, of this as useful electrical energy outside the machine, 
 that is, 6,340 watts. From this deduct 10 per cent, for the leads 
 and the lamp and for steadying the arc, leaving 5,710 watts in the 
 arc itself, or 114 amperes, with a difference of potential of 50 
 volts. Having regard to the fact that the optical apparatus here 
 proposed acts upon a larger portion of the sphere than that used 
 in the South Foreland experiments, that the vertical divergence is 
 less, and that the potential difference is greater and the current 
 continuous, although less in quantity, it may safely be assumed 
 that the power of the resulting beam would not be inferior. It 
 hence follows, from the South Foreland experiments, that in any 
 fog the flashes would penetrate farther than those of any existing 
 gas or oil light. The increased size of crater, compared with that 
 produced by the current of 20 amperes, will give increased vertical 
 divergence, and so cause the maximum illumination to be attained 
 at a less distance from the lighthouse. The attendance of two 
 men would suffice for all the duties of the lighthouse, because 
 
30 ELECTRIC LIGHTHOUSES. 
 
 under ordinary circumstances one man only need be on duty 
 excepting for two to three hours whilst gas is being made. The 
 consumption of coal would be 4 Ibs. per hour of lighting, of water 
 about gallon, of carbons about 4 inches. The whole cost of 
 maintaining the light would differ little from that of an ordinary 
 oil light of the first order. 
 
 Though it be the fact, that it is possible to exhibit an electric 
 light at moderate cost, it does not follow that it is suitable for all 
 ocean-lights. There is no room in a rock lighthouse tower for a 
 gas-plant, and few would at present be prepared to recommend a 
 petroleum-engine burning oil of a low flashing point. The light- 
 keeper again must understand a gas-producer, a gas-engine, a 
 dynamo, and an arc lamp, instead of only a paraffin lamp and 
 burner, and arrangements must exist for repairing the more 
 extensive machinery. Such considerations will justly weigh 
 against the use of the electric light in remote stations and 
 in countries where the labour available is not capable of much 
 training. 
 
 It may possibly be said that in this Paper no definite conclu- 
 sions are reached as to whether electricity or some other agent 
 is the best source of light in lighthouses generally, nor yet, if 
 electricity be adopted, what is the best way of producing the light 
 and optically dealing with it. The answer is that it is impossible 
 on many points to arrive at general conclusions. Each case must 
 be judged according to its special circumstances. 
 
 Extract from Dr Hopkinson's Reply to the discussion on the 
 Paper : 
 
 Professor Adams had touched upon one suggestion of interest, 
 that in order to obtain, with the exceedingly small centre of light 
 afforded by the electric arc, that necessary divergence ordinarily 
 given by the magnitude of the flame, the arc should be placed 
 somewhat out of focus, that the lens should be approximated 
 somewhat towards the centre of light. No doubt if engineers 
 were under the obligation to make use of precisely the same 
 apparatus for electric light as for oil light, the suggestion would 
 be a desirable one to adopt ; but it was far better, in the case of 
 
ELECTRIC LIGHTHOUSES. 31 
 
 electric light, to make the optical apparatus suit that light, and 
 not to suit something else. Even although the apparatus were 
 already in existence for which it was proposed to use the electric 
 arc instead of the oil flame, it would be better economy to remove 
 that apparatus and employ it in some other situation, and to 
 design a special apparatus for the electric light. 
 
 Mr Kapp had dealt with the question of coupling alternate- 
 current machines parallel without mechanical connection. In the 
 arrangement at Tino two machines were driven from one counter- 
 shaft. In the first instance, when it was attempted to drive the 
 machines together, there was a difference in the size of the pulleys 
 of about 1 millimetre in 300 millimetres. Notwithstanding that, 
 they synchronized perfectly, and the effect was sufficient to control 
 the natural difference in the time of rotation of the machines. He 
 was not prepared off-hand to say how far it was possible to go in 
 that direction. 
 
3. 
 
 ON ELECTRIC LIGHTING. 
 
 [From the Proceedings of the Institution of Mechanical Engineers, 
 April 25, 1879.] 
 
 (First Paper.) 
 
 DURING the last year much has been written and much 
 information communicated concerning the production of light 
 from mechanical power by means of .an electric current. The 
 major portion of what has appeared has been either descriptive 
 of particular machines for producing the current, and of lamps for 
 manifesting a portion of its energy as light ; or a statement of 
 practical results connecting the light obtained with the power 
 applied and the money expended in producing it. 
 
 Whilst fully appreciating the present value of such informa- 
 tion, the author has felt that it did not tell all that was inte- 
 resting or practically useful to know. It is desirable to know 
 what the various machines can do with varied and known re- 
 sistances in the circuit, and with varied speeds of rotation : and 
 what amount of power is absorbed in each case. It is a question 
 of interest, whether a machine intended for one light can or 
 cannot produce two in the same circuit, and if not, why not; 
 whether a machine, such as the Wallace-Farmer, intended as it 
 is for many lights, will give economical results when used for one ; 
 and so on. It is clear that the attempt to examine all separate 
 combinations of so many variables would be hopeless, and that the 
 work must be systematised. 
 
ON ELECTRIC LIGHTING. 33 
 
 The mechanical energy communicated by the steam-engine or 
 other motor is not immediately converted into the energy of heat, 
 but is first converted into the energy of an electric current in a 
 conducting circuit; of this a portion only becomes localised as 
 heat between the carbons of the electric arc ; and of this again a 
 part only becomes sensible to the eye as light. The whole of 
 what we need to know may be more easily ascertained and more 
 shortly expressed if the enquiry is divided into two parts: 
 (a) what current will a machine produce under various con- 
 ditions of circuit, and at what expenditure of mechanical power ; 
 (6) having given the electric conditions under which the arc is 
 placed, no matter how these conditions are produced, what light 
 will be obtained therefrom. Parts of the subject have been 
 treated more or less in this sense by Edlund (Pogg. Annal., 1867 
 and 1868), Houston and Thomson in America, Mascart (Journal 
 de Physique, March 1878), Abney (Proceedings Royal Society, 1878), 
 Trowbridge (Philosophical Magazine, March 1879), Schwendler 
 (Report on Electric Light Experiments), &c. but not so completely 
 that nothing remains to be done ; nor does the author doubt that 
 a great deal of information is in the hands of makers of machines, 
 which they have not thought it necessary to make known. The 
 present communication is limited to an account of some experi- 
 ments on the production of currents by a Siemens medium-sized 
 machine; that is, the machine which is advertised to produce a 
 light of 6000 candles by an expenditure of 3 J horse-power. 
 
 All the machines for converting mechanical power into an 
 electric current consist ultimately of a conducting wire moving in 
 a magnetic field ; and approximately the electromotive force of 
 the machine will be proportional to the velocity with which the 
 circuit moves through the field, and to the intensity of the field. 
 In general the intensity of the field is not constant; and in such 
 machines as the Siemens and the ordinary Gramme machine it 
 may be regarded as a function of the current passing. We must 
 learn what this function is for the machine in question ; or 
 which comes to exactly the same thing, and is better so long 
 as the facts are merely the result of experiment we must con- 
 struct a curve in which the abscissae represent the intensities of 
 currents passing, and the ordinates the corresponding electro- 
 motive forces for a given speed of rotation. But the power of 
 a current, that is its energy per second, is the product of the 
 H. i. 3 
 
34 ON ELECTRIC LIGHTING. 
 
 electromotive force and the intensity, or, in the case of the curve, 
 the product of the ordinate and the abscissa ; this is in all cases 
 less than the power required to drive the machine, and the ratio 
 between the two may fairly be called the efficiency of the 
 machine. 
 
 The object of the enquiry may perhaps be made clearer by an 
 illustration. Consider the case of a pump forcing water through 
 a pipe against friction; then the electric current corresponds 
 to the volume of water passing per second, and the electromotive 
 force to the difference of pressure on the two sides of the pump ; 
 and just as the product of pressure and volume per second is 
 power, so the product of electromotive force and current is power, 
 which is directly comparable with the power expended in driving 
 the machine or the pump, as the case may be. The peculiarity 
 of the so-called dynamo-electric machine lies in this, that what 
 corresponds to the difference of pressure (the electromotive force) 
 depends directly on what corresponds to the volume passing (the 
 current). 
 
 Each experiment requires the determination of the speed, the 
 driving power, the resistances in circuit, and the current passing : 
 or of the difference of potential between the two ends of a known 
 resistance of the circuit. 
 
 The apparatus employed by the author was arranged, not 
 alone with an aim to accuracy, but in part to make use of such 
 instruments as he happened to possess or could easily construct, 
 and in part with a view to ready erection and transport. Much 
 more accurate results may be obtained by anyone who will 
 arrange apparatus with a single aim to attain the greatest 
 accuracy possible. The author's apparatus will however be briefly 
 described, that others may form their own opinion of the im- 
 portance of the various sources of error. 
 
 The speed-counter was that supplied with the electric machine. 
 
 Concerning the steam-engine nothing need be said, save that 
 its speed was maintained very constant by means of a governor, 
 shown in Fig. 1, specially arranged for great sensibility. By 
 placing the joint A above the joint B, instead of below it as in 
 Porter's governor, any degree of sensibility up to instability may 
 be obtained. The speed was varied by means of a weight and 
 a spring, attached to a lever on the throttle-valve spindle. The 
 
ON ELECTRIC LIGHTING. 
 
 35 
 
 ungainly appearance of this governor could easily be remedied by 
 anyone proposing to manufacture it. 
 
 Governor. 
 
 FIG. 1. 
 
 The power is transmitted from the engine to a countershaft by 
 means of a strap, and by a second strap from the countershaft to 
 the pulley of the electric machine. On this second strap is the 
 dynamometer shown in Fig. 2. 
 
 This dynamometer has for some time been used by Messrs 
 Siemens, and was also used by Mr Schwendler; its invention is 
 due to Herr von Hefner- Alteneck. A is the driving pulley; 
 B the pulley of the electric machine ; CG are a pair of loose 
 pulleys between which the strap passes; these are carried in a 
 double triangular frame, which can turn about a bar D. This bar 
 might form part of a permanent structure ; but in order to place 
 the dynamometer readily on any strap, the bar was in this case 
 provided with eyes at either end, and secured in position by six or 
 eight ropes. This plan answers well, as there is very little stress 
 on the bar. Immediately above the pulleys CG a cord leads 
 from the frame through a Salter spring-balance over snatch-blocks 
 to a back balance-weight ; the tension of this cord is read on the 
 spring balance. At first the spring balance was omitted, and the 
 weight at the end of the cord was observed; but the friction 
 of the snatch-block pulleys was found objectionable. The pulley 
 frame carries a pointer, which is adjusted so as to coincide with a 
 datum mark when the line AB bisects the distance between the 
 loose pulleys. Let W be the tension of the cord required to bring 
 the pulley frame to its standard position when no work is being 
 
 32 
 
36 
 
 ON ELECTRIC LIGHTING. 
 
ON ELECTRIC LIGHTING. 37 
 
 transmitted; W" the tension which is required to bring the 
 pointer back to the datum mark, when an observation is made ; 
 and let TF= W - W". Let T', T" be the tensions on the tight 
 and slack halves of the strap; R l , R^ } r the radii of the pulleys 
 A, B, and C, plus half the thickness of the strap ; d, C 2 the 
 distances AJ, JB\ 2d the distance apart of the centres CG\ 
 2j , a 2 the inclinations of the two parts of the strap, on either side 
 of CO, to the line AB. Then 
 
 (T - T") (sin a t + sin a 2 ) = F; 
 -d d 
 
 d 
 
 very nearly. 
 
 The value of T f - T" and the velocity of rotation of the electric 
 machine being known, the power received by it is readily ob- 
 tained, expressed in gram-centimetres per second. Multiplying 
 by 981, the value of gravity in centimetres and seconds, the 
 power is then expressed in ergs* per second, and is ready for 
 comparison with the results of the electrical experiments. 
 
 As already stated, the dynamo-electric machine in the present 
 case was a Siemens medium size ; the armature coil has fifty-six 
 divisions ; and the brushes are single, not divided, that is, each 
 brush is in connection with one segment of the commutator at any 
 instant. 
 
 The leading wire is 100 yards of Siemens No. 90, consisting of 
 seven copper wires, insulated with tape and india-rubber, and 
 having a diameter of about 9| mm. 
 
 The method of determining the current is shown in the diagram, 
 Fig. 3, Plate 27. The current is conveyed from the machine A, 
 through a set of coils of brass wire c, and in some cases through a 
 resistance coil placed in a calorimeter B, and so back to the 
 machine, the connections being made through cups of mercury 
 
 * The dyne is the force which will in one second impart to one gram a velocity of 
 one centimetre per second, and an erg is the work done by a dyne working through a 
 centimetre; a horse-power may be taken as three-quarters of an erg- ten per second, 
 an erg-ten being 10 10 ergs. See Report of Brit. Assoc., 1873 ; and Everett " On the 
 C.G.S. System of Units," published by the Physical Society. 
 
38 
 
 ON ELECTRIC LIGHTING. 
 
 Diagram of Apparatus 
 
 (Calorimeter) 
 
 (Standard Resistance Coils) 
 
 J 
 
 H ; 
 
 K^BBBi 
 
 ~ery) 
 
 b 
 ( K 
 
 (Galvanometer) 
 
 (Pencil Lines) 
 
 FIG. 3. 
 
ON ELECTRIC LIGHTING. 39 
 
 excavated in a piece of wood D. The current passing may be 
 ascertained by the heating of the calorimeter, or by measuring 
 the difference of potential at the extremities of the resistance c, 
 all the resistances of the circuit being supposed known. This 
 difference of potential could of course be very easily measured by 
 means of a quadrant electrometer; but, as the instrument had 
 to be frequently removed, a galvanometer appeared more con- 
 venient. The two points to be measured are connected to the 
 ends of two series of resistance coils a, 6. The galvanometer G 
 is placed in a second derived current, passing from a junction 
 in ab through a battery H, then through a set of high resistances 
 J for adjusting sensibility, a reversing key K, the galvanometer G, 
 the reversing key K again, and so to the other extremity of b. 
 The electromotive force is ascertained by adjusting the resistance b 
 so that the deflection of the galvanometer is nil. 
 
 The resistance coils c comprise ten coils of common brass wire, 
 each wound round a couple of wooden uprights driven into a 
 baseboard common to the set ; each wire is about 60 metres long, 
 and of No. 17 Birmingham wire-gauge (*06 inch or l mm. 
 diameter), weighing about 14'6 grams per metre. Each terminal 
 is connected to a cup of mercury excavated in the baseboard, 
 so that the coils can be placed in series or in parallel circuit 
 at pleasure. The resistance of each coil being about 3 ohms, 
 this set may be arranged to give resistances varying from 0'3 to 
 30 ohms. 
 
 The calorimeter B is a Siemens pyrometer with the top scale 
 removed ; a resistance coil of uncovered German-silver wire nearly 
 2 m. long, 1^ mm. in diameter, and having a resistance of about 
 0'2 ohm, is suspended within it from an ebonite cover, which also 
 carries a little brass stirrer; and the calorimeter is filled with 
 water to a level determined by the mark of a scriber. It was of 
 course necessary to know the capacity of the calorimeter for heat. 
 It was filled with warm water up to the mark, and the coil placed 
 in position ; 120 grams of water were then withdrawn, and the 
 temperature of the calorimeter was observed to be 58*8 C. ; after 
 the lapse of one minute it was 58'3 C. ; after a second minute 
 57*9 C.; 120 grams of cold water, temperature 13'3 C., were then 
 suddenly introduced through a hole in the ebonite cover, and it 
 was found that, two minutes after the reading of 57 "9 C., the 
 
40 ON ELECTRIC LIGHTING. 
 
 temperature was 50'0 C. ; hence we may infer that the capacity 
 of the calorimeter is equal to that of 740 grams of water. Two 
 similar experiments at lower temperatures gave respectively the 
 numbers 749 and 750. Estimating the capacity from the weight 
 of the copper cylinder supplied with the pyrometer, it should be 
 747, to which must be added the capacity of the German-silver 
 wire and stirrer. Taking everything into consideration, 750 grams 
 may be assumed as the most probable result. 
 
 The resistance coils a, b are of German-silver, made by Messrs 
 Elliott Brothers ; they are on the binary scale from ohm to 
 1024 ohms. Separate coils were used, instead of a regular 
 resistance box, because they were more readily applicable to any 
 other purpose for which they might be required ; and the binary 
 scale was adopted, because the coils could at once be used as 
 conductivity coils in parallel circuit, also on the binary scale. 
 Each coil as supplied terminated in two stout copper legs ; these 
 were fitted with cups of india-rubber tubing for mercury, whereby 
 any connections whatever could readily be made. This arrange- 
 ment though rude was very convenient, and perhaps even safer 
 from error than a box with brass plugs to make the connections. 
 By a slight alteration of the connections the whole was instantly 
 available as a Wheatstone's bridge to determine resistances. 
 
 The battery H is a single element of Daniell's battery, in 
 which the sulphate of zinc solution floats on the sulphate of 
 copper; its electromotive force is assumed to be volt. 
 
 The resistances J added in the battery circuit are pencil lines 
 on glass, such as are described in the Philosophical Magazine of 
 February 1879. Three were used, giving a range of sensibility 
 approximately in the proportions 1, 25, 170, 700 the last figure 
 being when all were short-circuited; they are very useful in 
 adjusting the resistance b so as to give no deflection of the 
 galvanometer. 
 
 The reversing key K belongs to Sir W. Thomson's electro- 
 meter, and is quite suitable when high resistances and nil methods 
 are used. 
 
 The galvanometer G is far more sensitive than necessary, and 
 has a resistance of 7000 ohms. 
 
 Preliminary to experiments on the current, determinations of 
 resistances were made. The resistance of each brass coil c was 
 
ON ELECTRIC LIGHTING. 41 
 
 first determined, to afford the means of calculating the value of 
 this resistance in any subsequent experiment. When the ten 
 coils are coupled in parallel circuit, the calculated resistance was 
 0*29 ohm, whilst 0'292 was obtained by direct measurement. 
 The leading wire was then examined; the further ends being 
 disconnected, the insulation resistance was found to be over 
 60,000 ohms ; how much over, it was immaterial to learn. When 
 the ends of the wire were connected, the resistance was found to 
 be 0*129 ohm. The resistances in the dynamo-electric machine A 
 were found to be as follows when cold : magnet coils 0*156 and 
 0*152 respectively, armature coil 0*324 ; total 0*632 ohm. Direct 
 examination was made of the whole machine in eight positions of 
 the commutator, giving 0'643 ohm, with a maximum variation of 
 0*6 per cent, from the mean. After running the machine for 
 some time the resistance was found to be 0*683, an increase which 
 would be accounted for by a rise of temperature of 12 C. or there- 
 abouts. The resistance of the calorimeter B is 0'20 ohm, without 
 its leading wire, which may be taken as 0*01. We have then in 
 circuit three resistances which must be considered: (1) the re- 
 sistance of the machine A and leading wire, assumed throughout 
 as together 0*81 ohm and denoted by c x ; (2) the resistance of the 
 brass coils c, calculated from the several determinations, with the 
 addition of 0'02 ohm, the resistance of the leading wire, and 
 denoted by c 2 ; (3) when present, the resistance of the calorimeter 
 B and leading wire, denoted by c 3 . 
 
 Two approximate corrections were employed, and should be 
 detailed. The first is the correction for the considerable heating 
 of the resistance coils c. These were arranged in two sets of five 
 each, five being in parallel circuit, and the two sets in series. 
 The current from the machine, being about 7*4 webers in each 
 wire, was passed for three or four minutes ; the circuit was then 
 broken, and the resistance c s was determined within one second 
 of breaking circuit, when it was found to be about 5 per cent, 
 greater than when cold. As the resistance was falling, the 
 following was adopted as a rule of correction : square the current 
 in a single wire, and increase the resistance c 2 by -^th per cent, 
 for every unit in the square. The second correction is due to the 
 fact that the calorimeter was losing heat all the time it was 
 being used. It was assumed that it loses 0*01 C. per minute for 
 every 1 C. by which the temperature of the calorimeter exceeds 
 
42 ON ELECTRIC LIGHTING. 
 
 that of the air ; this correction is of course based on the experi- 
 
 ment already mentioned. 
 
 The method of calculation may now be explained : 
 
 R is the total resistance of the circuit in ohms, equal to 
 
 Q is the current passing in webers; 
 
 E is the electromotive force round the circuit in volts; 
 
 Wi is the work per second converted into heat in the circuit, 
 as determined by the galvanometer, measured in erg- tens per 
 second ; 
 
 W z is the work per second as determined by the calorimeter ; 
 
 W 3 is the work per second as determined by the dynamometer, 
 less the power required to drive the machine when the circuit is 
 open; 
 
 HP is the equivalent of W 3 in horse-power; 
 
 n is the number of revolutions per minute of the armature. 
 
 As already mentioned, the standard resistance coils a, b are 
 adjusted in each experiment so that the galvanometer gives no 
 deflection, and the value of b is then noted. The values of c l5 c 2 , c s 
 are known from previous observations. Then 
 
 = QxR, 
 
 w _ R j mechanical equivalent of heat ) 
 2 "~ 0*2 (generated per second in calorimeter.) 
 
 The results of the experiments are given in the accompanying 
 Table. 
 
 A power of 0'21 erg-ten, or 0*28 horse-power, was required to 
 drive the machine at 720 revolutions on open circuit. An ex- 
 amination of the Table shows that the efficiency of the machine is 
 about 90 per cent., exclusive of friction. Comparing experiments 
 11 and 13, and also the last four experiments, it is seen that the 
 electromotive force is proportional to the speed of rotation within 
 the errors of observation. Experiments 14, 15, and 16 were 
 
ON ELECTRIC LIGHTING. 
 
 43 
 
 
 ft 
 
 .2 j 
 
 f si 
 Sis 
 
 D S 
 
 .*a 
 
 ^H 
 
 
 
 CQ CO 
 
 J 
 
 It 
 
 
 PH : : 
 
 a" : ! 
 
 H 
 
 s: 
 
 - 
 
 ^5 00 
 
 * ^ i io 
 
 P I M J 
 
 ll^ 1 ^ 2 
 
 OOOI>0<MCOOOO(M 
 CO CD C** C5 U^ CO CO i^ ^H C"* 
 
 J 
 
 ' 
 
 111 o 
 
 H SEm J> 
 
 .2 gl 
 
 ooooooc^ooaooiaot- 
 
 
 
 So 
 
 j8 
 
 ^C*' 
 
 co co 
 
 ^S5S 
 
 <NCOOD 
 COTJ<(M 
 
44 ON ELECTRIC LIGHTING. 
 
 intended to ascertain the effect of displacing the commutator 
 brushes. 
 
 The principal object of the experiments was to ascertain how 
 the electromotive force depended on the current. This relation 
 is represented by the curve shown in Fig. 4, in which the 
 abscissae represent the currents flowing, or the values of Q in the 
 
 VOLTS 
 10Oi 
 
 CURRENT 
 
 t ' TQ ' 3"o ' To ' 55 
 
 FIG. 4. Curve of Force and Current. 
 
 table, and the ordinates the electromotive forces, or the values 
 of E reduced to a speed of 720 revolutions per minute. The 
 curve may also be taken to represent the intensity of the mag- 
 netic field. It will be remarked that there is a point of inflexion 
 in the curve somewhere near the origin. The experiments 1 to 5 
 indicate that this is the true form of the curve, and it is confirmed 
 in a remarkable manner by a special experiment. A resistance 
 intermediate between 5 and 4 (experiments 3 and 4) was used in 
 circuit, and E and Q were determined in two different ways: 
 first, by starting with an open circuit, which was then closed ; 
 secondly, by starting with a portion of the resistance short- 
 circuited, and a very powerful current passing, and then breaking 
 the short circuit. It was found that E and Q were four times as 
 great in the latter case as in the former. Unfortunately the 
 numbers are not sufficiently accurate to be given, as the solutions 
 of the standard battery had become mixed. 
 
 The curve really gives a great deal more information than 
 appears at first sight. It will determine what current will flow 
 at any given speed of rotation of the machine, and under any 
 conditions of the circuit, whether of resistances or of opposed 
 
ON ELECTRIC LIGHTING. 45 
 
 electromotive forces. It will also give very approximate indica- 
 tions of the corresponding curve for other machines of the same 
 configuration, but in which the number of times the wire passes 
 round the electromagnet or the armature is different. 
 
 It will be well to compare these results with those obtained 
 by others. M. Mascart worked on a Gramme machine with com- 
 paratively low currents: he represents his results approximately 
 by the formula 
 
 where a and b are constants. This corresponds to the rapidly 
 rising part of the curve in Fig. 4. Mr Trowbridge with a Siemens 
 machine obtained a maximum efficiency of 76 per cent., and states 
 that the machine was running below its normal velocity. Mr 
 Schwendler's results, when fully published, will probably be found 
 to be the most complete and most accurate existing. In the 
 precis he states that the loss of power with a Siemens machine in 
 producing currents of over 20 webers is 12 per cent. Now taking 
 the author's experiments 4 to 19, the mean value of W l is 3'027 
 erg-tens and of W 3 3'304: adding to the latter 0'21, the power 
 required to drive the machine when no current passes, it appears 
 that 13*8 per cent, of the power applied is wasted. Again, taking 
 experiments 4, 6, 8, 10, and 12, the mean value of TF 2 is 2'888 
 erg-tens and of W 3 3'076, indicating a waste of power amounting 
 to 12 per cent. Of this, as already stated, 0'21 erg- ten or 0'2& 
 horse-power is accounted for by friction of the journals and com- 
 mutator brush; the remainder is expended in local currents, or 
 by loss of kinetic energy of current when sparks occur at the 
 commutator. 
 
 According to Weber's theory of induced magnetism, as set 
 forth in Maxwell's Electricity, vol. II., if X be the magnetising 
 force and I the intensity of magnetisation, 
 
 X 
 
 I = | , until X rises to the value 6, 
 
 where a and 6 are constants. We should naturally expect that a 
 similar formula would be approximately applicable to dynamo- 
 electric machines. 
 
46 ON ELECTRIC LIGHTING. 
 
 In the present experiments, let / be the electromotive force, 
 X the current passing, and assume a to be 60 and b to be 1 5 ; 
 we then obtain results not far from those of experiment. The 
 capacity of any continuous-current machine may thus be shortly 
 stated by giving the values of a and b ; or, which comes to the 
 same thing, by stating the electromotive force at a given speed 
 when the current is as great as possible, and also the total 
 resistance through which the machine will exert an electromotive 
 force two-thirds of this greatest electromotive force. To this 
 should be added a statement of the resistance of the machine, and 
 of the power it absorbs, with known conditions of the circuit. 
 
 The author has not yet tried any quantitative experiments 
 with the electric light, but hopes shortly to do so. In the 
 meantime he would remark that, as the lamp is usually adjusted, 
 only half the energy of the current appears in the arc, or 44 per 
 cent, of the energy transmitted to the machine by the strap. 
 
 In conclusion the author would express the obligation he is 
 under to Messrs Chance Brothers and Co., on account of the 
 facilities he has enjoyed for making these experiments at their 
 works. It may be mentioned that one principal object of the 
 research of which this is a beginning is to obtain a minute know- 
 ledge of the electric light, with a view to lighthouse illumination. 
 
 Dr J. HOPKINSON said that since the curve, Fig. 4, Plate 29, 
 was drawn out, it had occurred to him that the curious circum- 
 stance of the curve starting in the manner indicated and then 
 bending upwards from the point of inflection might be accounted 
 for in another way. It might be supposed that the magnetisation 
 of the iron in the machine lagged a little behind the current, so 
 that, if the current were decreasing, the magnetisation for the 
 same current would be greater than if it were increasing. If that 
 were so, the curve would be different as the current was rising or 
 falling; and thus, instead of a single curve with a point of 
 inflection, there would be two curves at a little distance from 
 each other. He also thought a sufficiently accurate formula for 
 the curve in question might probably be based upon Weber's 
 theory of induced magnetism in iron, as he had suggested at the 
 end of the paper. It would be a formula with only two constants 
 in it, so that a full description could be given briefly of all the 
 curve had to tell. 
 
ON ELECTRIC LIGHTING. 
 
 [From the Proceedings of the Institution of Mechanical Engineers, 
 pp. 266274. April 23, 1880.] 
 
 (Second Paper.) 
 
 Dynanw-electric Machines. Since the date of the author's 
 former paper in April 1879, other observers have published the 
 results of experiments similar to those described by him. It may 
 be well to exhibit some of these results reduced to the form he has 
 adopted, namely, a curve, such as that previously shown, and now 
 
 VOLTS 
 100 
 
 Siemens Medium size machine. 
 
 380 
 
 cc 
 
 P70 
 
 "J6C 
 
 5: 
 
 540 
 
 m 
 
 CURRENT 
 
 20 
 
 3D 
 
 50 
 
 12. 
 
 60 
 
 720 REV. 
 
 660 REV. 
 
 70WEBERS 
 
 FIG. 1. 
 
 reproduced, with slight alterations, in Fig. 1. Here any abscissa 
 represents a current passing through the dynamo-electric machine, 
 
48 ON ELECTRIC LIGHTING. 
 
 and the corresponding ordinate represents the electromotive force of 
 the machine for a certain speed of revolution, when that current 
 is passing through it. It will be found, (1) that with varying 
 speed the ordinate, or electromotive force, corresponding to any 
 abscissa or current, is proportional to the speed ; (2) that the 
 electromotive force does not increase indefinitely with increasing 
 current, but that the curve approaches an asymptote ; (3) that the 
 earlier part of the curve is, roughly speaking, a straight line, until 
 the current attains a certain value, and that at that point the 
 electromotive force has reached about two-thirds of its maximum 
 value. When the current is such that the electromotive force is 
 not more than two-thirds of its maximum, a very small change in 
 the resistance with speed of engine constant, or in the speed of 
 the engine with resistance constant, causes a great change in the 
 current. For this reason the greatest of these currents, which is 
 that corresponding to the point where the curve breaks away from 
 a straight line, and which is the same for all speeds of revolution, 
 since the curves for different speeds differ only in the scale of 
 ordinates, may be called the " critical current " of the machine. 
 The effect of a change of speed is exhibited in Fig. 1, where 
 the lower dotted line represents the curve for a speed of 660 
 revolutions per minute, instead of 720. The resistance, varying as 
 
 electromotive force . . , , , f , , ,. ~ n 
 
 - , is given by the slope of the line OP. But 
 current 
 
 since the resistance is constant, the slope of this line must be 
 constant ; and it will be seen that it cuts the upper curve at a 
 point corresponding to a current of 15 webers, and the lower at a 
 point corresponding to a current of 5 webers only. 
 
 In Germany, Auerbach and Meyer (Wiedemanris Annalen, 
 Nov. 1879) have experimented fully on a Gramme machine at 
 various speeds, and with various external resistances. The resist- 
 ance of the machine was 0*97 ohm. Their results are summarised 
 in a Table at the end of their paper, which gives the current 
 passing, with resistances in circuit from 1*75 to 200 Siemens units, 
 and at speeds from 20 to 800 revolutions per minute. In the 
 accompanying diagram, Fig. 2, Plate 30, the curve G expresses 
 the relation between electromotive force and current, as deduced 
 from some of their observations; the points marked are plotted 
 from their Table, making allowance, where necessary, for difference 
 in speed. The curve, as actually constructed, is for a speed of 800 
 
OX ELECTRIC LIGHTING. 
 
 49 
 
 revolutions: at this speed it will be seen that the maximum 
 electromotive force is about 76 volts; and the critical current, 
 corresponding to a force of about 51 volts, is 6 '5 webers, with a 
 total resistance of 7 '8 ohms. Up to this point there will be great 
 instability, exactly as was the case in the Siemens machine 
 examined by the author, where the resistance was 4 ohms, and 
 the speed 720 revolutions. 
 
 VOLTS 
 100n 
 
 90- 
 
 Grarnme machine, curve GL 
 Siemens Medium, curve SM. 
 Siemens Smallest, curve Ss. 
 
 10 
 FIG. 2. 
 
 20 30 40 50 60 
 
 Curves of Electromotive Force and Current. 
 
 70WEBERS 
 
 The results of an elaborate series of experiments on certain 
 dynamo-electric machines have recently been presented to the 
 Royal Society by Dr Siemens. One of the machines examined 
 was an ordinary medium-sized machine, substantially similar to 
 that tried by the author in 1879. It is described as having 24 
 divisions of the commutator; 336 coils on the armature, with a 
 resistance of 0'4014 Siemens units ; and 512 coils on the magnets, 
 with a resistance of 0'3065 ; making a total resistance of 0*7079 
 Siemens units = 0*6654 ohms. The curve Sm, Fig. 2, gives the 
 relation of electromotive force and current, reduced to a speed of 
 700 rev. per minute, the actual speeds ranging from 450 to 
 800 rev. The maximum electromotive force appears to be probably 
 76 volts, and the critical current 15 webers : which is the same as 
 in the author's first experiments on a similar machine. 
 
 In the summer of 1879 the author examined a Siemens 
 machine of the smallest size. This machine is generally sold as 
 an exciter for their alternate-current machine. It has an internal 
 resistance of 0'74 ohms, of which 0'395 is in the armature or 
 helix. The machine is marked to run at 1130 rev. per min. The 
 H. i. 4 
 
50 
 
 ON ELECTRIC LIGHTING. 
 
 following Table II. gives, for a speed of 1000 rev., the total resist- 
 ance, current, electromotive force, and horse-power developed as 
 current. The horse-power expended was not determined. 
 
 TABLE II. EXPERIMENTS ON SMALLEST-SIZED SIEMENS 
 DYNAMO-ELECTRIC MACHINE. 
 
 Resistance. 
 
 Electric 
 Current. 
 
 Electro- 
 motive 
 Force. 
 
 Horse-power 
 developed 
 as current. 
 
 Ohms. 
 
 Webers. 
 
 Volts. 
 
 H. P. 
 
 2-634 
 
 5-10 
 
 13-2 
 
 0-09 
 
 2-221 
 
 12-15 
 
 27-0 
 
 0-44 
 
 1-967 
 
 17-0 
 
 33-6 
 
 0-76 
 
 1-784 
 
 20-4 
 
 36-4 
 
 0-99 
 
 1-668 
 
 22-3 
 
 37-2 
 
 I'll 
 
 1-579 
 
 23-2 
 
 36-6 
 
 1-14 
 
 1-503 
 
 25-6 
 
 39-3 
 
 1-34 
 
 1-440 
 
 27-8 
 
 40-0 
 
 1-49 
 
 1-145 
 
 36-2 
 
 41-5 
 
 2-00 
 
 The curve Ss, Fig. 2, gives as usual the relations of electromotive 
 force and current. From this curve it will be seen that the 
 critical current is 11*2 webers, and the maximum electromotive 
 force, at the speed of 1000 rev., is about 42 volts. The determi- 
 nations for this machine were made in exactly the same manner 
 as in the experiments on the medium-sized machine, using the 
 galvanometer, but omitting the experiment with the calorimeter 
 (compare Table I., Proceedings Inst- Mech. Engineers, page 249, 
 1879). 
 
 The time required to develop the current in a Gramme machine 
 has been examined by Herwig (Wiedemann, June 1879). He 
 established the following facts for the machine he examined. A 
 reversed current, having an electromotive force of 0*9 Grove cells, 
 sufficed to destroy the residual magnetism of the electro-magnets. 
 If the residual magnetism was as far as possible reduced, it took a 
 much longer time to get up the current than when the machine 
 was in its usual state. A longer time was required to get up the 
 current when the external resistance was great than when it 
 was small. With ordinary resistance the current required from 
 | second to 1 second to attain its maximum. 
 
 Brightness of the Electric Arc. The measurement of the light 
 emitted by an electric arc presents certain peculiar difficulties. 
 
ON ELECTRIC LIGHTING. 51 
 
 The light itself is of a different colour from that of a standard 
 candle, in terms of which it is usual to express luminous intensi- 
 ties. The statement, without qualification, that a certain electric 
 lamp and machine give a light of a specified number of candles, is 
 therefore wanting in definite meaning. A red light cannot with 
 propriety be said to be any particular multiple of a green light ; 
 nor can one light, which is a mixture of colours, be said with 
 strictness to be a multiple of another, unless the proportions of 
 the colours in the two cases are the same. Captain Abney (Pro- 
 ceedings of the Royal Society, 7 March 1878, p. 157) has given the 
 results of measurements of the red, blue, and actinic light of 
 electric arcs, in terms of the red, blue, and actinic light of a 
 standard candle. The fact that the electric light is a very 
 different mixture of rays from the light of gas or of a candle, has 
 long been known, but has been ignored in statements intended for 
 practical purposes. 
 
 Again, the emission of rays from the heated carbons and arc is 
 by no means the same in all directions. Determinations have been 
 made in Paris of the intensity in different directions, in particular 
 cases. If the measurement is made in a horizontal direction, a 
 very small obliquity in the crater of the positive carbon will throw 
 the light much more on one side than on the other, causing great 
 discordance in the results obtained. 
 
 If the electric light be compared directly with a standard 
 candle, a dark chamber of great length is needed a convenience 
 not always attainable. In the experiments made at the South 
 Foreland by Dr Tyndall and Mr Douglass, an intermediate standard 
 was employed ; the electric light was measured in terms of a large 
 oil lamp, and this latter was frequently compared with a standard 
 candle. 
 
 CARBONS Longitudinal Section 
 
 E 
 
 JE,., , E , , ,*f 
 
 Scale : V34'- h 
 
 i 
 
 STANDAR 
 LIGHT 
 
 FIG. 3. Photometer for Powerful Lights. 
 
 Other engagements have prevented the author from fairly 
 attacking these difficulties; but since May 1879 he has had in 
 occasional use a photometer with which powerful lights can be 
 
 42 
 
ON ELECTRIC LIGHTING. 
 
 measured in moderate space. This photometer is shown in 
 Figs. 3 and 4, and an enlargement of the field-piece in Fig. 5. 
 A convex lens A, of short focus, forms an image at B of the 
 powerful source of light which it is desired to examine. The 
 intensity of the light from this image will be less than that of the 
 actual source by a calculable amount ; and when the distance of 
 
 Transverse Section 
 
 Fm. 4. 
 
 the lens from the light is suitable, the reduction is such that the 
 reduced light becomes comparable with a candle or a carcel lamp. 
 Diaphragms CC are arranged in the cell which contains the lens, 
 to cut off stray light. One of these is placed at the focus of the 
 lens, and has a small aperture. It is easy to see that this 
 diaphragm will cut off all light entering from a direction other 
 
 I 
 
 FIG. 5. Field Piece. 
 
 than that of the source ; so effectually does it do so, that observa- 
 tions may be made in broad daylight on any source of light, if a 
 
ON ELECTRIC LIGHTING. 53 
 
 dark screen be placed behind it. The long box EE, Fig. 3, of 
 about 7 ft. length, is lined with black velvet, the old-fashioned 
 dull velvet, not that now sold with a finish, which reflects a great 
 deal of the light incident at a certain angle. This box serves as a 
 dark chamber, in which the intensity of the image formed by the 
 lens is compared with a standard light, by means of an ordinary 
 Bunsen's photometer F, sliding on a graduated bar. 
 
 Mr Dallmeyer kindly had the lens made for the author: he 
 can therefore rely upon the accuracy of its curvature and thick- 
 ness ; it is plano-convex, the convex side being towards the source 
 of light. The curvature is exactly 1 in. radius and the thickness 
 is 0'04 in. ; it is made of Chance's hard crown-glass, of which the 
 refractive index for the D line in the spectrum is T517. The 
 focal length /is therefore 1*933 inch. 
 
 Let u denote the distance of the source of light from the 
 curved surface of the lens, and v the distance of the image B of 
 the source from the posterior focal plane. Neglecting for the 
 moment loss by reflection at the surface of the glass, the intensity 
 
 of the source is reduced by the factor [ ] . But -+- = --, or 
 
 \u) v u f 
 
 uf / f \ 2 
 
 v = , ; hence the factor of reduction is ( J ~ } . The effect 
 u-f \u-fJ 
 
 of absorption in so small a thickness of very pure glass may be 
 neglected ; but the reflection at the surfaces will cause a loss of 
 8*3 per cent., which must be allowed for. This percentage is 
 calculated from Fresnel's formulae, which are certainly accurate 
 for glasses of moderate refrangibility, and for moderate angles of 
 incidence. 
 
 Suppose, for example, it is required to measure a light of 
 8000 candles ; if it be placed at a distance of 40 in., it will be 
 reduced in the ratio 467 to 1, and becomes a conveniently measur- 
 able quantity. By transmitting through coloured glasses both the 
 light from an electric lamp and that from the standard, a rough 
 comparison may be made of the red or green in the electric light 
 with the red or green in the standard. 
 
 A dispersive photometer, in which a lens is used in a somewhat 
 similar manner, is described in Stevenson's Lighthouse Illumina- 
 tion ; but in that case the lens is not used in combination with a 
 Bunsen's photometer, nor with any standard light. Messrs Ayrton 
 
54 ON ELECTKIC LIGHTING. 
 
 and Perry described a dispersive photometer with a concave lens 
 at the meeting of the Physical Society on 13th December 1879 
 (Proceedings Physical Society, Vol. ill. p. 184). The convex lens 
 possesses however an obvious advantage in having a real focus, at 
 which a diaphragm to cut off stray light may be placed. 
 
 Efficiency of the Electric Arc. To define the electrical condi- 
 tion of an electric arc, two quantities must be stated the current 
 passing, and the difference of electric potential at the ends of the 
 two carbons. Instead of either one of these, we may, if we please, 
 
 , , . difference of potential , ,, . , . r 
 
 state the ratio , and call it the resistance of 
 
 current 
 
 the arc, that is to say, the resistance which would replace the arc 
 without changing the current. But such a use of the term electric 
 resistance is unscientific ; for Ohm's law, on which the definition 
 of electric resistance rests, is quite untrue of the electric arc ; 
 while on the other hand, for a given material of the electrodes, a 
 given distance between them, and a given atmospheric pressure, 
 the difference of potential on the two sides of the arc is approxi- 
 mately constant. The product of the difference of potential and 
 the current is of course equal to the work developed in the arc ; 
 and this, divided by the work expended in driving the machine, 
 may be considered as the efficiency of the whole combination. It 
 is a very easy matter to measure these quantities. The difference 
 of potential on the two sides of the arc may be measured by the 
 method given by the author in his previous paper, or by an 
 electrometer, or in other ways. The current may be measured by 
 an Obach's galvanometer, or by a suitable electro-dynamometer, 
 or best of all, in the author's opinion, by passing the whole current, 
 on its way to the arc, through a very small known resistance, 
 which may be regarded as a shunt for a galvanometer of very 
 high resistance, or to the circuit of which a very high resistance 
 has been added. 
 
 It appears that with the ordinary carbons, and at ordinary 
 atmospheric pressure, no arc can exist with a less difference of 
 potential than about 20 volts ; and that in ordinary work, with an 
 arc about J in. long, the difference of potential is from 30 to 
 50 volts. Assuming the former result, about 20 volts, for the 
 difference of potential, the use of the curve of electromotive forces 
 may be illustrated by determining the lowest speed at which a 
 
ON ELECTRIC LIGHTING. 
 
 55 
 
 given machine can run, and yet be capable of producing a short 
 arc. Taking as the origin of co-ordinates, Fig. 6, set off 
 upon the axis of ordinates the distance OA equal to 20 volts; 
 
 FIG. 6. 
 
 draw AB to intersect at B the negative prolongation of the axis 
 
 OA 
 of abscissae, so that the ratio -^- may represent the necessary 
 
 metallic resistance of the circuit. Through the point B, thus 
 obtained, draw a tangent to the curve, touching it at G, and 
 cutting OA in D. Then the speed of the machine, corresponding 
 to the particular curve employed, must be diminished in the ratio 
 
 ^y-j- , in order that an exceedingly small arc may be just possible. 
 
 The curve may also be employed to put into a somewhat 
 different form the explanation given by Dr Siemens at the Royal 
 Society, respecting the occasional instability of the electric light, 
 as produced by ordinary dynamo-electric machines. The operation 
 of all ordinary regulators is to part the carbons when the current 
 is greater than a certain amount, and to close them when it is 
 less; initially the carbons are in contact. Through the origin 
 0, Fig. 7, draw the straight line OA, inclined at the angle 
 
 FIG. 7. 
 
 representing the resistances of the circuit other than the arc, and 
 meeting the curve at A. The abscissa of the point A represents 
 the current which will pass if the lamp be prevented from 
 operating. Let ON represent the current to which the lamp is 
 adjusted; then if the abscissa of A be greater than ON, the 
 
56 ON ELECTRIC LIGHTING. 
 
 carbons will part. Through N draw the ordinate BN, meeting 
 the curve in the point B ; and parallel to OA draw a tangent CD, 
 touching the curve at D. If the point B is to the right of D, or 
 further from the origin, the arc will persist ; but if B is to the left 
 of D, or nearer to the origin, the carbons will go on parting, till 
 the current suddenly fails and the light goes out. If B, although 
 to the right of D, is very near to it, a very small reduction in the 
 speed of the machine will suffice to extinguish the light. Dr 
 Siemens gives greater stability to the light by exciting the electro- 
 magnets of the machine by a shunt circuit, instead of by the 
 whole current. 
 
 The success of burning more than one regulating lamp in 
 series depends on the use in the regulator of an electro-magnet, 
 excited by a high-resistance wire connecting the two opposed 
 carbons. The force of this magnet will depend upon the difference 
 of potential in the arc, instead of depending, as in the ordinary 
 lamp, upon the current passing. Such a shunt magnet has been 
 employed in a variety of ways. The author has arranged it as an 
 attachment to an ordinary regulator ; the shunt magnet actuates 
 a key, which short-circuits the magnet of the lamp when the 
 carbons are too far parted, and so causes them to close. 
 
 In conclusion the author ventures to remind engineers of the 
 following rule for determining the efficiency of any system of 
 electric lighting in which the electric arc is used, the arc being 
 neither exceptionally long nor exceptionally short. Measure the 
 difference of potential of the arc, and also the current passing 
 through it, in volts and webers respectively ; then the product of 
 these quantities, divided by 746, is the horse-power developed in 
 that arc. It is then known that the difference between the horse- 
 power developed in the arc and the horse-power expended to 
 drive the machine must be absolutely wasted, and has been 
 expended in heating either the iron of the machine or the copper 
 conducting wires. 
 
5. 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 [A Lecture delivered at the Institution of Civil Engineers, 
 5 April, 1883.] 
 
 ARTIFICIAL light is generally produced by raising some body 
 to a high temperature. If the temperature of a body be greater 
 than that of surrounding bodies it parts with some of its energy 
 in the form of radiation. Whilst the temperature is low these 
 radiations are not of a kind to which the eye is sensitive ; they are 
 exclusively radiations less refrangible and of greater wave-length 
 than red light, and may be called infra red. As the temperature 
 is increased the infra red radiations increase, but presently there 
 are added radiations which the eye perceives as red light. As 
 the temperature is further increased, the red light increases and 
 yellow, green and blue rays are successively thrown off in addition. 
 On pushing the temperature to a still higher point, radiations of 
 a wave-length, shorter even than violet light, are produced, to 
 which the eye is insensitive, but which act strongly on certain 
 chemical substances ; these may be called ultra violet rays. It is 
 thus seen that a very hot body in general throws out rays of 
 various wave-lengths, our eyes, it so happens, being only sensitive 
 to certain of these, viz., those not very long and not very short, 
 and that the hotter the body the more of every kind of radiation 
 will it throw out; but the proportion of short waves to long 
 waves becomes vastly greater as the temperature is increased. 
 The problem of the artificial production of light with economy 
 of energy is the same as that of raising some body to such a 
 
58 SOME POINTS IN ELECTRIC LIGHTING. 
 
 temperature that it shall give as large a proportion as possible of 
 those rays which the eye happens to be capable of feeling. For 
 practical purposes this temperature is the highest temperature we 
 can produce. Owing to the high temperature at which it remains 
 solid, and to its great emissive power the radiant body used for 
 artificial illumination is nearly always some form of carbon. In 
 the electric current we have an agent whereby we can convert 
 more energy of other forms into heat in a small space than in any 
 other way ; and fortunately carbon is a conductor of electricity as 
 well as a very refractory substance. 
 
 The science of lighting by electricity very naturally divides 
 itself into two principal parts the methods of production of 
 electric currents, and of conversion of the energy of those cur- 
 rents into heat at such a temperature as to be given off in 
 radiations to which our eyes are sensible. There are other 
 subordinate branches of the subject, such as the considera- 
 tion of the conductors through which the electric energy is 
 transmitted, and the measurement of the quantity of electricity 
 passing and its potential or electric pressure. Although I shall 
 have a word or two to say on the other branches of the subject, I 
 propose to occupy most of the time at my disposal this evening 
 with certain points concerning the conversion of mechanical 
 energy into electrical energy. We know nothing as to what elec- 
 tricity is, and its appeals to our senses are in general less direct 
 than those of the mechanical phenomena of matter. The laws, 
 however, which we know to connect together those phenomena 
 which we call electrical, are essentially mechanical in form, are 
 closely correlated with mechanical laws, and may be most aptly 
 illustrated by mechanical analogues. For example, the terms 
 "potential," "current," and "resistance," with which we are be- 
 coming familiar in electricity have close analogues respectively 
 in " head," " rate of flow," and " coefficient of friction " in the 
 hydraulic transmission of power. Exactly as in hydraulics head 
 multiplied by velocity of flow is power measured in foot-pounds 
 per second or in horse-power, so potential multiplied by current is 
 power and is measurable in the same units. The horse-power not 
 being a convenient electrical unit Dr Siemens has suggested that 
 the electrical unit of power or volt-ampere should be called a watt : 
 746 watts are equal to one horse-power. Again, just as water 
 flowing in a pipe has inertia and requires an expenditure of 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 59 
 
 work to set it in motion, and is capable of producing disruptive 
 effects if its motion is too suddenly arrested as, for example, 
 when a plug-tap is suddenly closed in a pipe through which 
 water is flowing rapidly, so a current of electricity in a wire has 
 inertia ; to set it moving electromotive force must work for a finite 
 time, and if we attempt to arrest it suddenly by breaking the 
 circuit the electricity forces its way across the interval as a spark. 
 Corresponding to mass and moments of inertia in mechanics we 
 have in electricity coefficients of self-induction. We will now 
 show that an electric circuit behaves as though it had inertia. 
 The apparatus we shall use is shown diagrammatically in Fig. 1. 
 
 FIG. 1. 
 
 FIG. 2. 
 
 A current from a Sellon battery A circulates round an electro- 
 magnet E\ it can be made and broken at pleasure at C. Con- 
 nected to the two extremities of the wire on the magnet is 
 a small incandescent lamp D, lent to me by Mr Crompton, of 
 many times the resistance of the coil. On breaking the circuit, 
 the current in the coil, in virtue of its momentum, forces its way 
 through the lamp, and renders it momentarily incandescent, 
 although all connection with the battery, which in any case would 
 be too feeble to send sufficient current through the lamp, 
 has ceased. Let us try the experiment, make contact, break 
 contact. You observe the lamp lights up. Compare with the 
 
60 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 diagram Fig. 2 of the hydraulic analogue the hydraulic ram. 
 There a current of water suddenly arrested forces a way for a 
 portion of its quantity to a greater height than that from which 
 it fell. AB corresponds to the electro-magnet, the valve C to 
 the contact-breaker, and DE to the lamp. There is, however, 
 
 this difference between the inertia 
 of water in a pipe and the inertia 
 of an electric current the inertia 
 of the water is confined to the water, 
 whereas the inertia of the electric 
 current resides in the surrounding 
 medium. Hence arise the pheno- 
 mena of induction of currents upon 
 currents, and of magnets upon 
 moving conductors phenomena 
 which have no immediate ana- 
 logues in hydraulics. There is 
 thus little difficulty to anyone ac- 
 customed to the laws of rational 
 mechanics in adapting the expres- 
 sion of those laws to fit electrical 
 phenomena ; indeed we may go so 
 far as to say that the part of elec- 
 trical science with which we have 
 to deal this evening is essentially 
 a branch of mechanics, and as such 
 I shall endeavour to treat it. 
 
 This is neither the time nor the 
 place for setting forth the funda- 
 mental laws of electricity, but I 
 cannot forbear from showing you 
 a mechanical illustration, or set of 
 mechanical illustrations, of the laws 
 of electrical induction, first dis- 
 covered by Faraday. I have here 
 a model, Fig. 3, which was made 
 to the instructions of the late Pro- 
 fessor Clerk Maxwell, to illustrate the laws of induction. It con- 
 sists of a pulley P, which I now turn with my hand, and which 
 represents one electric circuit, its motion the current therein. 
 

 SOME POINTS IN ELECTRIC LIGHTING. 61 
 
 Here is a second pulley S, representing a second electric circuit. 
 These two pulleys are geared together by a simple differential 
 train, such as is sometimes used for a dynamometer. The inter- 
 mediate wheel of the train, however, is attached to a balanced 
 fly-wheel, the moment of inertia of which can be varied by moving 
 inwards or outwards these four brass weights. The resistances of 
 the two electric circuits are represented by the friction on the pulleys 
 of two strings, the tension of which can be varied by tightening 
 these elastic bands. The differential train, with its fly-wheel, repre- 
 sents the medium, whatever it may be, between the two electric 
 conductors. The mechanical properties of this model are of course 
 obvious enough. Although the mathematical equations which 
 represent the relation between one electric conductor and another 
 in its neighbourhood are the same in form as the mathematical 
 equations which represent the mechanical connection between 
 these two pulleys, it must not be assumed that the magnetic 
 mechanism is completely represented by the model. We shall 
 now see how the model illustrates the action of one electric 
 circuit upon another. You know that Faraday discovered that if 
 you have two closed conductors arranged near to and parallel 
 to each other, and if you cause a current of electricity to begin 
 to flow in the first, there will arise a temporary current in the 
 opposite direction in the second. This pulley, marked P on the 
 diagram, represents the primary circuit, and the pulley marked 
 S on the diagram the secondary circuit. We cause a current to 
 begin to flow in the primary, or turn the pulley P; an opposite 
 current is induced in the secondary circuit, or the pulley S turns 
 in the opposite direction to that in which we began to move the 
 pulley P. The effect is only temporary, resistance speedily 
 stops the current in the secondary circuit, or, in the mechanical 
 model, friction the rotation of the pulley S. I now gradually 
 stop the motion of P ; the pulley S moves in the direction in 
 which P was previously moving, just as Faraday found that 
 the cessation of the primary current induced in the secondary 
 circuit a current in the same direction as that which had 
 existed in the primary. If there were a large number of con- 
 volutions or coils in the secondary circuit, but that circuit were 
 not completed, but had an air space interrupting its continuity, 
 an experiment with the well-known Ruhmkorff coil would show 
 you that when the current was suddenly made to cease to flow 
 
62 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 in the primary circuit, so great an electromotive force would be 
 exerted in the secondary circuit that the electricity would leap 
 across the space as a spark. I will now show you what corre- 
 sponds to a spark with this mechanical model. The secondary 
 pulley S shall be held by passing a thread several times round 
 it. I gradually produce the current in the primary circuit : 
 I will now suddenly stop this primary current: you observe 
 that the electromotive force is sufficient to break the thread. 
 The inductive effects of one electric circuit upon another depend 
 not alone on the dimensions and form of the two circuits, but 
 on the nature of the material between them. For example, if 
 we had two parallel circular coils, their inductive effects would 
 be very considerably enhanced by introducing a bar of iron in 
 their common axis. We can imitate this effect by moving out- 
 wards or inwards these brass weights. In the experiment I have 
 shown you the weights have been some distance from the axis in 
 order to obtain considerable effect, just as in the Ruhmkorff coil 
 an iron core is introduced within the primary circuit. I will now 
 do what is equivalent to removing the core : I will bring the 
 weights nearer to the axis, so that my fly-wheel shall have less 
 moment of inertia. You observe that the inductive 
 effects are very much less marked than they were 
 before. With the same electromagnet which we 
 used before, but differently arranged, we will show 
 wliat we have just illustrated the induction of 
 one circuit on another. Referring to Fig. 4, coil 
 AB corresponds to wheel P; CD to wheel $; 
 and the iron core to the fly-wheel and differential 
 gear. The resistance of a lamp takes the place 
 of the friction of the string on 8. As we make 
 and break the circuit you see the effect of the 
 induced current in rendering the lamp incandescent. 
 So far I have been illustrating the phenomena of 
 the induction of one current upon another. I will 
 now show on the model that a current in a single 
 electric circuit has momentum. The secondary 
 FIG wheel shall be firmly held; it shall have no con- 
 
 ductivity at all ; that is, its electrical effect shall be 
 as though it were not there. I now cause a current to begin to flow 
 in the primary circuit, and it is obvious enough that a certain 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 63 
 
 amount of work must be done to bring it up to a certain speed. The 
 angular velocity of the fly-wheel is half that of the pulley repre- 
 senting the primary circuit. Now suppose that the two pulleys 
 were connected together in such a way that they must have the 
 same angular velocity in the same direction. This represents the 
 coil having twice as many convolutions as it had before. A 
 little consideration will show that I must do four times as 
 much work to give the primary pulley the same velocity that it 
 attained before ; that is to say, that the coefficient of self-induc- 
 tion of a coil of wire is proportional to the square of the number 
 of convolutions. Again, suppose that these two wheels were so 
 geared together that they must always have equal and opposite 
 velocities, you can see that a very small amount of work must be 
 done in order to give the primary wheel the velocity which we 
 gave to it before. Such an arrangement of the model represents 
 an electric circuit, the coefficient of induction of which is exceed- 
 ingly small, such as the coils that are wound for 
 standard resistances ; the wire is there wound 
 double, and the current returns upon itself, as 
 shown in Fig. 5. 
 
 In the widest sense, the dynamo-electric 
 machine may be defined as an apparatus for 
 converting mechanical energy into the energy 
 of electro-static charge, or mechanical power into 
 its equivalent electric current through a con- 
 ductor. Under this definition would be included 
 the electrophorus and all frictional machines ; but 
 the term is used, in a more restricted sense, for 
 those machines which produce electric currents 
 by the motion of conductors in a magnetic field, 
 or by the motion of a magnetic field in the 
 neighbourhood of a conductor. The laws on 
 which the action of such machines is based 
 have been the subject of a series of discoveries. 
 Oersted discovered that an electric current in a 
 conductor exerted force upon a magnet ; Ampere 
 that two conductors conveying currents generally FlG - 5 - 
 
 exerted a mechanical force upon each other : Faraday discovered 
 what Helmholtz and Thomson subsequently proved to be the neces- 
 sary consequence of the mechanical reactions between conductors 
 
64 SOME POINTS IN ELECTRIC LIGHTING. 
 
 conveying currents and magnets that if a closed conductor move 
 in a magnetic field, there will be a current induced in that con- 
 ductor in one direction, if the number of lines of magnetic force 
 passing through the conductor was increased by the movement ; 
 in the other direction if diminished. Now all dynamo-electric 
 machines are based upon Faraday's discovery. Not only so ; but 
 however elaborate we may wish to make the analysis of the action 
 of a dynamo-machine, Faraday's way of presenting the pheno- 
 mena of electro-magnetism to the mind is in general our best 
 point of departure. The dynamo-machine, then, essentially con- 
 sists of a conductor made to move in a magnetic field. This 
 conductor, with the external circuit, forms a closed circuit in 
 which electric currents are induced as the number of lines of 
 magnetic force passing through the closed circuit varies. Since, 
 then, if the current in a closed circuit be in one direction when 
 the number of lines of force is increasing, and in the opposite 
 direction when they are diminishing, it is clear that the current in 
 each part of such circuit which passes through the magnetic field 
 must be alternating in direction, unless indeed the circuit be such 
 that it is continually cutting more and more lines of force, always 
 in the same direction. Since the current in the wire of the machine 
 is alternating, so also must be the current outside the machine, 
 unless something in the nature of a commutator be employed to 
 reverse the connections of the internal wires in which the current 
 is induced, and of the external circuit. We have then broadly 
 two classes of dynamo-electric machines ; the simplest, the alter- 
 nating-current machine, where no commutator is used ; and the 
 continuous- current machine, in which a commutator is used to 
 change the connection of the external circuit just at the moment 
 when the direction of the current would change. The mathematical 
 theory of the alternate-current machine is comparatively simple. 
 To fix ideas, I will ask you to think of the alternate-current 
 Siemens machine, which Dr Siemens exhibited here three weeks 
 ago. We have there a series of magnetic fields of alternate 
 polarity, and through these fields we have coils of wire moving; 
 these coils constitute what is called the armature; in them are 
 induced the currents which give a useful effect outside the 
 machine. Now, I am not going to trouble you to go through the 
 mathematical equations, simple though they are, by which the 
 following formulae are obtained: 
 
SOME POINTS IN ELECTRIC LIGHTING. 65 
 
 . . iirt /T v 
 
 l=Asrn -jr (I.) 
 
 E=^cos^ (H.) 
 
 COS 2-7T rn 
 
 *=^_ L_ an-) 
 
 2?TT 
 
 ^ n 
 
 " .................. 
 
 T represents the periodic time of the machine ; that is, in the 
 case of a Siemens machine having eight magnets on each side 
 of the armature, T represents the time of one-fourth of a revo- 
 lution. / represents the number of lines of force embraced by 
 the coils of the armature at the time t. I must be a periodic 
 function of t, in the simplest form represented by Equation I. 
 Equation II. gives E the electromotive force acting at time 
 t upon the circuit. Having given the electromotive force acting 
 at any time, it would appear at first sight that we had nothing 
 to do but to divide that electromotive force by the resistance R 
 of the whole circuit, to obtain the current flowing at that time. 
 But if we were to do so we should be landed in error, for 
 the conducting circuit has other properties besides resistance. 
 I pointed out to you that it had a property of momentum 
 represented by its coefficient of self-induction called 7 in the 
 formula ; and when we are dealing with rapid changes of current, 
 it plays as important a part as the resistance. Formula III. gives 
 the current x, flowing at any time, and you will observe that 
 it shows two things: first, the maximum current is less than 
 it would be if there were no self-induction ; secondly, it attains 
 its maximum at a later time. This retardation is represented 
 by the letter T, and its amount is determined by the Formula IV. 
 At a given speed of rotation, the amount of electrical work de- 
 veloped in the machine in any time <B) is given by Formula V. It 
 
 is greatest when R = ^ . From these formulae we see that the 
 H. i. 5 
 
66 SOME POINTS IN ELECTRIC LIGHTING. 
 
 current is diminished either by increasing 7 or increasing R ; also 
 the moment of reversal of current is not coincident with the 
 moment of reversal of electromotive force, but occurs later, by an 
 amount depending on the relative magnitudes of 7 and R. They 
 show us that although by doubling the velocity of the machine 
 we really double the electromotive force at any time, we do not 
 double the current passing, nor the work done by the machine; 
 but we may see that if we double the velocity of the machine, we 
 may work through double the external resistance, and still obtain 
 the same current. In what precedes, it has been assumed that the 
 copper wires are the only conducting bodies moving in the mag- 
 netic field. In many cases the moving wire-coils of these machines 
 have iron cores, the iron being in some cases solid, in others more 
 or less divided. It is found that if such machines are run on open 
 circuit, that is, so that no current circulates in the armatures ; the 
 iron becomes hot, very much hotter than when the circuit of the 
 copper wire is closed. In some cases this phenomenon is so 
 marked that the machine actually takes more to drive it, when 
 the machine is on open circuit, than when it is short-circuited. 
 The explanation is that on open circuit currents are induced in the 
 iron cores, but that when the copper coils are closed the current 
 in them diminishes by induction the current in the iron. The 
 effect of currents in the iron cores is not alone to waste energy and 
 heat the machine ; but for a given intensity of field and speed of 
 revolution, the external current produced is diminished. The cure 
 of the evil is to subdivide the moving iron as much as possible, 
 in directions perpendicular to those in which the current tends to 
 circulate. 
 
 There remains one point of great practical interest in con- 
 nection with alternate-current machines, How will they behave 
 when two or more are coupled together, to aid each other in 
 doing the same work ? With galvanic batteries, we know very 
 well how to couple them, either in parallel circuit or in series, 
 so that they shall aid, and not oppose, the effects of each other ; 
 but with alternate-current machines, independently driven, it 
 is not quite obvious what the result will be, for the polarity of 
 each machine is constantly changing. Will two machines, coupled 
 together, run independently of each other, or will one control 
 the movement of the other in such wise that they settle down 
 to conspire to produce the same effect, or will it be into mutual 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 67 
 
 opposition ? It is obvious that a great deal turns upon the answer 
 to this question, for in the general distribution of electric light, it 
 will be desirable to be able to supply the system of conductors 
 from which the consumers draw by separate machines, which can 
 be thrown in and out at pleasure. Now I know it is a common 
 impression that alternate-current machines cannot be worked 
 together, and that it is almost a necessity to have one enormous 
 machine to supply all the consumers drawing from one system of 
 conductors. Let us see how the matter stands. Consider two 
 machines independently driven, so as to have approximately the 
 same periodic time and the same electromotive force. If these 
 two machines are to be worked together they may be connected in 
 one of two ways ; they may be in parallel circuit with regard to 
 the external conductor, as shown by the full line in Fig. 6, that is, 
 
 Fio. 6. 
 
 their currents may be added algebraically and sent to the external 
 circuit, or they may be coupled in series, as shown by the dotted 
 line, that is, the whole current may pass successively through 
 the two machines, and the electromotive force of the two machines 
 may be added, instead of their currents. The latter case is simpler. 
 Let us consider it first. I am going to show that if you couple 
 two such alternate-current machines in series, they will so control 
 each other's phase as to nullify each other, and that you will get 
 no effect from them ; and, as a corollary from that, I am going to 
 show that if you couple them in parallel circuit, they will work 
 perfectly well together, and the currents they produce will be 
 added ; in fact, that you cannot drive alternate-current machines 
 tandem, but that you may drive them as a pair, or, indeed, any 
 
 52 
 
68 SOME POINTS IN ELECTRIC LIGHTING. 
 
 number abreast. In diagram, Fig. 7, the horizontal line of abscissae 
 represents the time advancing from left to right ; the full curves 
 represent the electromotive forces of the two machines not supposed 
 to be in the same phase. We want to see whether they will tend 
 to get into the same phase or to get into opposite phases. Now, if 
 the machines are coupled in series, the resultant electromotive force 
 
 linn iv 
 
 on the circuit will be the sum of the electromotive forces of the two 
 machines. This resultant electromotive force is represented by the 
 broken curve III ; by what we have already seen in Formula IV, 
 the phase of the current must lag behind the phase of the elec- 
 tromotive force, as is shown in the diagram by curve IV, thus 
 
 . . . Now the work done in any machine is represented 
 
 by the sum of the products of the currents and of the electromotive 
 forces, and it is clear that as the phase of the current is more near 
 to the phase of the lagging machine II than to that of the leading 
 machine I, the lagging machine must do more work in producing 
 electricity than the leading machine ; consequently its velocity will 
 be retarded, and its retardation will go on until the two machines 
 settle down into exactly opposite phases, when no current will pass. 
 The moral, therefore, is, do not attempt to couple two independently 
 driven alternate-current machines in series. Now for the corollary, 
 AB, Fig. 6, represent the two terminals of an alternate-current 
 machine ; ab the two terminals of another machine independently 
 driven. A and a are connected together, and B and b. So regarded, 
 the two machines are in series, and we have just proved that they 
 will exactly oppose each other's effects, that is, when A is positive, 
 a will be positive also; when A is negative, a is also negative. 
 Now, connecting A and a through the comparatively high resist- 
 ance of the external circuit with B and b, the current passing 
 through that circuit will not much disturb, if at all, the relations 
 of the two machines. Hence, when A is positive, a will be posi- 
 tive, and when A is negative, a will be negative also ; precisely 
 
SOME POINTS IN ELECTRIC LIGHTING. 69 
 
 the condition required that the two machines may work together 
 to send a current into the external circuit. You may, therefore, 
 with confidence, attempt to run alternate-current machines in 
 parallel circuit for the purpose of producing any external effect. 
 I might easily show that the same applies to a larger number: 
 hence, there is no more difficulty in feeding a system of conductors 
 from a number of alternate-current machines, than there is in 
 feeding it from a number of continuous-current machines. A 
 little care only is required that the machine shall be thrown in 
 when it has attained something like its proper velocity. A 
 further corollary is that alternate currents with alternate-current 
 machines as motors may theoretically be used for the transmission 
 of power*. 
 
 It is easy to see that, by introducing a commutator revolving 
 with the armature, in an alternate-current machine, and so ar- 
 ranged as to reverse the connection between the armature and the 
 external circuit just at the time when the current would reverse, 
 it is possible to obtain a current constant always in direction ; but 
 such a current would be far from constant in intensity, and would 
 certainly not accomplish all the results that are obtained in 
 modern continuous-current machines. This irregularity may, 
 however, be reduced to any extent by multiplying the wires of 
 the armature, giving each its own connection to the outer circuit, 
 and so placing them that the electromotive force attains a 
 maximum successively in the several coils. A practically uniform 
 electric current was first commercially produced with the ring 
 armature of Pacinotti, as perfected by Gramme. The Gramme 
 machine is represented diagrammatically in Fig. 8. The armature 
 consists of an anchor ring of iron wire, the strands more or less 
 insulated from each other. Round this anchor ring is wound a 
 continuous endless coil of copper wire ; the armature moves in 
 a magnetic field, produced by permanent or electro-magnets with 
 diametrically opposite poles, marked N and S. The lines of 
 magnetic force may be regarded as passing into the ring from N, 
 dividing, passing round the ring and across to 8. Thus the coils 
 of wire, both near to N and near to S, are cutting through a very 
 
 * Of coarse in applying these conclusions it is necessary to remember that the 
 machines only tend to control each other, and that the control of the motive 
 power may be predominant, and compel the two or more machines to run at 
 different speeds. 
 
70 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 strong magnetic field; consequently there will be an intense 
 inductive action ; the inductive action of 
 the coils near N being equal and op- 
 posite to the inductive action of the coils 
 near S, it results that there will be strong 
 positive and negative electric potential at 
 the extremities of a diameter perpen- 
 dicular to the line NS. The electro- 
 motive force produced is made use of 
 to produce a current external to the 
 machine thus, the endless coil of the 
 armature is divided into any number of 
 sections, in the diagram into six for con- 
 venience, usually into sixty or eighty, 
 and the junction of each pair of sections 
 is connected by a wire to a plate of the 
 commutator fixed upon the shaft which 
 carries the armature; collecting brushes 
 make contact with the commutator as 
 shown in the diagram. If the external 
 resistance were enormously high, so that 
 very little current, or none at all, passed 
 through the armature, the greatest difference of potential between 
 the two brushes would be found when they made contact at points 
 at right angles to the line between the magnets ; but when a 
 current passes in the armature, this current causes a disturbing 
 effect upon the magnetic field. Every time the contact of the 
 brushes changes from one contact-plate to the next, the current in 
 a section of the copper coil is reversed, and this reversal has an 
 inductive effect upon all the other coils of the armature. You 
 may take it from me that the net result on any one coil is ap- 
 proximately the same as if that coil alone were moved, and all 
 the other coils were fixed, and there were no reversals of current 
 in them. Now you can easily see that the magnetic effect of the 
 current circulating in the coils of the armature, will be to produce 
 a north pole at n, and a south pole at s. This will displace the 
 magnetic field in the direction of rotation. If, then, we were to 
 keep the contact points the same as when no current was passing, 
 we should short circuit the sections of the armature at a time 
 when they were cutting through the lines of magnetic force, with 
 
 FIG. 8. 
 
SOME POINTS IN ELECTRIC LIGHTING. 71 
 
 a result that there would be vigorous sparks between the col- 
 lecting brushes and the commutator. To avoid this, the brushes 
 must follow the magnetic field, and also be displaced in the 
 direction of rotation, this displacement being greater as the 
 current in the armature is greater in proportion to the magnetic 
 field. The net effect of this disturbing effect of the current 
 in the armature reacting upon itself is then to displace the 
 neutral points upon the commutator, and consequently somewhat 
 to diminish the effective electromotive force. It is best to adjust 
 the brushes to make contact at a point such that, with the 
 current then passing, flashing is reduced to a minimum, but 
 this point does not necessarily coincide with the point which 
 gives maximum difference of potential. The magnetic field in the 
 Gramme and other continuous dynamo- electric machines, may be 
 produced in several ways. Permanent magnets of steel may be 
 used, as in some of the smaller machines now made, and in all the 
 earlier machines; these are frequently called magneto-machines. 
 Electro-magnets excited by a current from a small dynamo- 
 electric machine, were introduced by Wilde; these may be de- 
 scribed shortly as dynamos with separate exciters. The plan 
 of using the whole current from the armature of the machine 
 itself, for exciting the magnets, was proposed almost simul- 
 taneously by Siemens, Wheatstone, and S. A. Vaiiey. A dynamo, 
 so excited, is now called a seiies dynamo. Another method is 
 to divide the current from the armature, sending the greater 
 part into the external circuit, and a smaller portion through the 
 electro-magnet, which is then of very much higher resistance ; 
 such an arrangement is called a shunt dynamo. A combination of 
 the two last methods has been recently introduced, for the purpose 
 of maintaining constant potential. The magnet is partly excited 
 by a circuit of high resistance, a shunt to the external circuit, and 
 partly by coils conveying the whole current from the armature. 
 All but the first two arrangements named depend on residual 
 magnetism to initiate the current, and below a certain speed of 
 rotation give no practically useful electromotive force. A dynamo 
 machine is, of course, not a perfect instrument for converting 
 mechanical energy into the energy of electric current. Certain 
 losses inevitably occur. There is, of course, the loss due to friction 
 of bearings, and of the collecting brushes upon the commutator ; 
 there is also the loss due to the production of electric currents in 
 
72 SOME POINTS IN ELECTRIC LIGHTING. 
 
 the iron of the machine. When these are accounted for, we have 
 the actual electrical effect of the machine in the conducting wire ; 
 but all of this is not available for external work. The current has 
 to circulate through the armature, which inevitably has electrical 
 resistance ; electrical energy must, therefore, be converted into 
 heat in the armature of the machine. Energy must also be ex- 
 pended in the wire of the electro-magnet which produces the field, 
 for the resistance of this also cannot be reduced beyond a certain 
 limit. The loss by the resistance of the wires of the armature and 
 of the magnets greatly depends on the dimensions of the machine. 
 About this I shall have to say a word or two presently. To know 
 the properties of any machine thoroughly, it is not enough to know 
 its efficiency and the amount of work it is capable of doing ; we 
 need to know what it will do under all circumstances of varying 
 resistance or varying electromotive force. We must know, under 
 any given conditions, what will be the electromotive force of the 
 armature. Now this electromotive force depends on the intensity of 
 the magnetic field, and the intensity of the magnetic field depends 
 on the current passing round the electro-magnet and the current 
 in the armature. The current then in the machine is the proper 
 independent variable in terms of which to express the electro- 
 motive force. The simplest case is that of the series dynamo, in 
 which the current in the electro-magnet and in the armature is 
 the same, for then we have only one independent variable. The 
 relation between the electromotive force and current is repre- 
 sented by such a curve as is shown in the diagram, Fig. 9 (p. 73). 
 The abscissae, measured along OX, represent the current, and 
 the ordinates represent the electromotive force in the armature. 
 When four years ago I first used this curve, for the purpose of 
 expressing the results of my experiments on the Siemens dynamo 
 machine, I pointed out that it was capable of solving almost any 
 problem relating to a particular machine, and that it was also 
 capable of giving good indications of the results of changes in the 
 winding of the magnets, or of the armatures of such machines. 
 Since then M. Marcel Deprez has happily named such curves 
 " characteristic curves." I will give you one or two illustrations of 
 their use. A complete characteristic of a series dynamo does not 
 terminate at the origin, but has a negative branch, as shown in 
 the diagram ; for it is clear that by reversing the current through 
 the whole machine, the electromotive force is also reversed. 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 73 
 
 Suppose a series dynamo is used for charging an accumulator, 
 and is driven at a given speed, what current will pass through 
 it? The problem is easily solved. Along OF, Fig. 9, set off 
 OE to represent the electromotive force of the accumulator, 
 and through E draw the line CEBA, making an angle with OX, 
 
 FIG. 9. 
 
 such that its tangent is equal to the resistance of the whole 
 circuit, and cutting the characteristic curve, as it in general 
 will do, in three points, A, B, and G. We have then three 
 answers to the question. The current passing through the 
 dynamo will be either OL, OM, or ON the abscissae of the points 
 where the line cuts the curve. OL represents the current when 
 the dynamo is actually charging the accumulator. OM repre- 
 sents a current which could exist for an instant, but which would 
 be unstable, for the least variation would tend to increase. ON is 
 the current which passes, if the current in the dynamo should get 
 reversed, as it is very apt to do when used for this purpose. The 
 next illustration is rather outside my subject, but shows another 
 method of using the characteristic curve. Many of you have 
 heard of Jacobi's law of maximum effect of transmitting work by 
 dynamo machines. It is this. Supposing that the two dynamo 
 machines were perfect instruments for converting mechanical 
 energy into electrical energy, and that the generating machine 
 were run at constant velocity, whilst the receiving machine had 
 a variable velocity, the greatest amount of work would be de- 
 veloped in the receiving machine when its electromotive force 
 
SOME POINTS IN ELECTRIC LIGHTING. 
 
 was one-half that of the generating machine, then the efficiency 
 would be one-half, and the electrical work done by the gene- 
 rating machine would be just one-half of what it would be if the 
 receiving machine were forcibly held at rest. Now this law 
 is strictly true if, and only if, the electromotive force of the 
 generating machine is independent of the current passing through 
 its armature. What I am now going to do is to give you a con- 
 struction for determining the maximum work which can be trans- 
 mitted when the electromotive force of the generating machine 
 depends on the current passing through the armature, as, indeed, 
 it nearly always does, referring to Fig. 10. OPB is the character- 
 istic curve of the generating machine ; construct a derived curve 
 Y 
 
 L 
 
 V 
 
 O 
 
 C 
 FIG. 10. 
 
 thus, at successive points P of the characteristic curve, draw 
 tangents PT, draw TN parallel to OX, cutting PM in N, produce 
 MP to L, making LP equal PN ; the point L gives the derived 
 curve, which I want. Now, to find the maximum work which 
 can be transmitted, draw OA at such an angle with OX that its 
 tangent is equal to twice the resistance of the whole circuit, 
 cutting the derived curve in A. Draw the ordinate AC, cutting 
 the characteristic curve in B; bisect AC at D. The work ex- 
 pended upon the generating machine would be represented by the 
 parallelogram OGBR, the work wasted in resistance by OCDS, 
 and the work developed in the receiving machine by the parallelo- 
 gram SDBR. 
 
 When the dynamo-machine is not a series dynamo, but the 
 currents in the armature and in the electro-magnet, though possibly 
 
SOME POINTS IX ELECTRIC LIGHTING. 
 
 75 
 
 dependent upon each other are not necessarily equal, the problem 
 is not quite so simple. We have, then, two variables, the current 
 in the electro-magnet and the current in the armature ; and the 
 proper representation of the properties of the machine will be by a 
 characteristic surface such as that illustrated by this model, Fig. 11. 
 Of the three coordinate axes, OX represents the current in the 
 
 FIG. 11. OX is current round magnet. 
 
 magnet ; Y represents the current in the armature not necessarily 
 to the same scale, and OZ the electromotive force. By the aid of 
 such a surface as this one may deal with any problem relating to 
 a dynamo-machine, no matter how its electro-magnets and its 
 armature are connected together. Let us apply the model to find 
 the characteristic of a series dynamo. Take a plane through OZ 
 the axis of electromotive force, and making such an angle with 
 the plane OX, OZ, that its tangent is equal to current unity on 
 axis T, divided by current unity on axis OX. This plane cuts 
 the surface in a curve. The projection of this curve on the plane 
 OX, OZ is the characteristic curve of the series dynamo. This 
 model only shows an eighth part of the complete surface. If any 
 of you should interest yourselves about the other seven parts, 
 which are not without interest, remember that it is assumed that 
 the brushes always make contact with the commutator at the 
 point of no flashing, if there is one. Of course in actual practice one 
 would not use the model of the surface, but the projections of its 
 sections. While I am speaking of characteristic curves there is 
 
76 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 one point I will just take this opportunity of mentioning. Three 
 years ago Mr Shoolbred exhibited the characteristic curve of a 
 Gramme machine, in which, after the current attained to a certain 
 amount, the electromotive force began to fall. I then said that I 
 thought there must be some mistake in the experiment. However, 
 subsequent experiments have verified the fact ; and when one con- 
 siders it, it is not very difficult to see the explanation. It lies in 
 this : after the current attains to a certain amount the iron in 
 the machines becomes magnetically nearly saturated, and conse- 
 quently an increase in the current does not produce a corre- 
 sponding increase in the magnetic field. The reaction, however, 
 between the different sections of the wire on the armature goes 
 on increasing indefinitely, and its effect is to diminish the electro- 
 motive force. 
 
 A little while ago I said that the dimensions of the machine 
 had a good deal to do with its efficiency. Let us see how the 
 properties of a machine depend upon its dimensions. Suppose two 
 machines alike in every particular excepting that the one has all 
 its linear dimensions double that of the other ; obviously enough 
 all the surfaces in the larger would be four times the correspond- 
 ing surfaces in the smaller, and the weights and volumes of the 
 
 larger would be eight times the corresponding weights in the 
 smaller machine. The electrical resistances in the larger machine 
 would be one-half those of the smaller. The current required to 
 produce a given intensity of magnetic field would be twice as 
 great in the larger machine as in the smaller. In the diagram, 
 Fig. 12, are shown the comparative characteristic curves of the 
 two machines, when driven at the same speed. You will observe 
 
SOME POINTS IX ELECTRIC LIGHTING. 77 
 
 that the two curves are one the projection of the other, having 
 corresponding points with abscissae in the ratio of one to two, and 
 the ordinates in the ratio of one to four. Now at first sight it 
 would seem as though, since the wire on the magnet and arma- 
 ture of the larger machine has four times the section of that of 
 the smaller, that four times the current could be carried, that con- 
 sequently the intensity of the magnetic field would be twice as 
 great, and its area would be four times as great, and hence the 
 electromotive force eight times as great ; and since the current in 
 the armature also is supposed to be four times as great, that the 
 work done by the larger machine would be thirty-two times as 
 much as that which would be done by the smaller. Practically, 
 however, no such result can possibly be attained, for a whole series 
 of reasons. First of all, the iron of the magnets becomes saturated, 
 and consequently instead of getting eight times the electromotive 
 force, we should only get four times the electromotive force. 
 Secondly, the current which we can carry in the armature is 
 limited by the rate at which we can get rid of the heat generated 
 in the armature. This we may consider as proportional to its 
 surface, consequently we must only waste four times as much 
 energy in the armature of the larger machine as in the smaller 
 one, instead of eight times, as would be the case if we carried the 
 current in proportion to the section of the wire. Again, the larger 
 machine cannot run at so great an angular velocity as the smaller 
 one. And lastly, since in the larger machine the current in the 
 armature is greater in proportion to the saturated magnetic field 
 than it is in the small one, the displacement of the point of 
 contact of the brushes with the commutator will be greater. 
 However, to cut short the matter, about which one might say a 
 great deal, one may say that the capacity of similar dynamo- 
 machines is pretty much proportionate to their weight, that is, to 
 the cube of their linear dimensions; that the work wasted in 
 producing the magnetic field will be directly as the linear di- 
 mensions ; and that the work wasted in heating the wires of the 
 armature will be as the square of the linear dimensions. Now let 
 us see how this would practically apply. Suppose we had a small 
 machine capable of producing an electric current of 4 H.-R, that 
 of this 4 H.-P. 1 was wasted in heating the wires of the arma- 
 ture, and 1 in heating the wires of the magnet, 2 would be 
 usefully applied outside. Now, if we doubled the linear dimensions 
 
78 SOME POINTS IN ELECTRIC LIGHTING. 
 
 we should have a capacity of 32 H.-R, of which 2 only, if 
 suitably applied, would be required to produce the magnetic field, 
 and 4 would be wasted in heating the wires of the armature, 
 leaving 26 H.-P. available for useful work outside the machine a 
 very different economy from that of the smaller machines. But if 
 we again doubled the linear dimensions of our machine, we should 
 by no means obtain a similar increase of effect. A consideration 
 of the properties of similar machines has another very important 
 practical use. As you all know, Mr Froude 'was able to control 
 the design of ironclad ships by experiments upon models made in 
 paraffin wax. Now, it is a very much easier thing to predict 
 what the performance of a large dynamo-machine will be, from 
 laboratory experiments made upon a model of a very small fraction 
 of its dimensions. As a proof of the practical utility of such 
 methods, I may say that by laboratory experiments I have 
 succeeded in increasing the capacity of the Edison machines 
 without increasing their cost, and with a small increase of their 
 percentage of efficiency, remarkably high as that efficiency already 
 was. 
 
 I might occupy your time with considerations as to the proper 
 proportion of conductors, and explain Sir W. Thomson's law, that 
 the most economical size of a copper conductor is such that the 
 annual charge for interest and depreciation of the copper of 
 which it is made, shall be equal to the cost of producing the 
 power which is wasted by its resistance. But the remaining 
 time will, perhaps, be best spent in considering the production of 
 light from the energy of electric currents. You all know that 
 this is done commercially in two ways, by the electric arc, and 
 by the incandescent lamp; as the arc lamp preceded the in- 
 candescent lamp historically, we will examine one or two points 
 connected with it first. 
 
 I have here all that is necessary to illustrate the electric arc, 
 viz., two rods of carbon supported in line with each other, and so 
 mounted that they can be approached or withdrawn. Each carbon 
 is connected with one of the poles of the Edison dynamo-machine, 
 which is supplying electricity to the incandescent lamps which 
 illuminate the whole of this building. A resistance is interposed 
 in the circuit of the lamp, because the electromotive force of the 
 machine is much in excess of what the lamp requires. I now 
 
SOME POINTS IN ELECTRIC LIGHTING. 79 
 
 approach the carbons, bring them into contact, and again separate 
 them slightly ; you observe that the break does not stop the current 
 which forces its way across the space. I increase the distance 
 between the carbons, and you observe the electric arc between 
 their extremities; at last it breaks, having attained a length of 
 about 1 inch. Now the current has hard work to cross this air- 
 space between the carbons, and the energy there developed is 
 converted into heat, which raises the temperature of the ends of 
 the carbon beyond any other terrestrial temperature. There are 
 several points of interest I wish to notice in the electric arc. Both 
 carbons burn away in the air, but there is also a transference of 
 carbon from the positive to the negative carbon ; therefore, although 
 both waste away, the positive carbon wastes about twice as fast as 
 the negative. With a continuous current, such as we are using 
 now, the negative carbon becomes pointed, whilst the positive 
 carbon forms a crater or hollow ; it is this crater which becomes 
 most intensely hot and radiates most of the light, hence the light 
 is not by any means uniformly distributed in all directions, but is 
 mainly thrown forward from the crater in the positive carbon. 
 This peculiarity is of great advantage for some purposes, such, for 
 example, as military or naval search-lights, but it necessitates, in 
 describing the illuminating power of an arc-light, some statement 
 of the direction in which the measurement was made. On account 
 of its very high temperature the arc-light sends forth a very large 
 amount of visible radiation, and is therefore very economical of 
 electrical energy. For the same reason its light contains a very 
 large proportion of rays of high refrangibility, blue and ultra- 
 violet. I have measured the red light of an electric arc against 
 the red of a candle, and have found it to be 4,700 times as great, 
 and I have measured the blue of the same arc-light against the 
 blue of the same candle, and found it to be 11,380 times as great. 
 The properties of an electric arc are not those of an ordinary 
 conductor. Ohm's law does not apply. The electromotive force 
 and the current do not by any means bear to each other a constant 
 ratio. Strictly speaking, an electric arc cannot be said to have 
 an electric resistance measurable in ohms. We will now examine 
 the electrical properties of the arc experimentally. In the circuit 
 with the lamp is a Thomson graded current galvanometer for 
 measuring the current passing in amperes ; connected to the two 
 carbons is a Thomson graded potential galvanometer, for measuring 
 
80 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 the difference of potential between them in volts. We have the 
 means of varying the current by varying the resistance, which I 
 have already told you is introduced into the circuit. We will first 
 put in circuit the whole resistance available, and will adjust the 
 carbons so that the distance between them is, so near as I can 
 judge, J inch. We will afterwards increase the current, and 
 repeat the readings. The results are given in the following 
 Table : 
 
 TABLE III. 
 
 Current 
 Galvanometer 
 
 Potential 
 Galvanometer 
 
 Amperes 
 
 Volts 
 
 Watts 
 
 H.-P. 
 
 6-2 
 
 12-0 
 
 9-9 
 
 35 
 
 346 
 
 0-46 
 
 9-3 
 
 12-0 
 
 14-9 
 
 35 
 
 521 
 
 0-70 
 
 11-5 
 
 11-8 
 
 18-4 
 
 34 
 
 626 
 
 0-84 
 
 If the electrical properties of the arc were the same as those of 
 a continuous conductor, the volts would be in proportion to the 
 amperes, if correction were made for change of temperature ; you 
 observe that instead of that the potential is nearly the same in the 
 two cases. We may say, with some approach to accuracy, that 
 with a given length of arc, the arc opposes to the current an 
 electromotive force nearly constant, almost independent of the 
 current. This was first pointed out by Edlund. If you will speak 
 of the resistance of the electric arc, you may say that the resist- 
 ance varies inversely as the current. Take the last experiment ; 
 by burning 4 cubic feet of gas per hour we should produce heat- 
 energy at about the same rate. I leave any of you to judge of the 
 comparative illuminating effects. It is not my purpose to describe 
 the mechanisms which have been invented for controlling the 
 feeding of the carbons as they waste away. Several lamps lent by 
 Messrs Siemens Brothers to whom I am indebted for the lamp 
 and resistance I have just been using lie upon the table for 
 inspection. An electric arc can also be produced by an alternate 
 current. Its theory may be treated mathematically, and is very 
 interesting, but time will not allow us to go into it. I will merely 
 point out this, there is some theoretical reason to suppose that 
 an alternate-current arc is in some measure less efficient than one 
 produced by a continuous current. The efficiency of a source of 
 light is greater, as the mean temperature of the radiating surface 
 
SOME POINTS IN ELECTRIC LIGHTING. 81 
 
 is greater. The maximum temperature in an arc is limited 
 probably by the temperature of volatilisation of carbon ; in an 
 alternate-current arc the current is not constant, therefore the 
 mean temperature is less than the maximum temperature ; in a 
 continuous-current arc, the current being constant, the mean and 
 maximum temperatures are equal, therefore in a continuous- 
 current arc the mean temperature is likely to be somewhat higher 
 than in an alternate-current arc. 
 
 We will now pass to the simpler incandescent light. When a 
 current of electricity passes through a continuous conductor, it 
 encounters resistance, and heat is generated, as was shown by 
 Joule, at a rate represented by the resistance multiplied by the 
 square of the current. If the current is sufficiently great, the 
 heat will be generated at such a rate that the conductor rises in 
 temperature so far that it becomes incandescent and radiates light. 
 Attempts have been made to use platinum and platinum-iridium 
 as the incandescent conductor, but these bodies are too expensive 
 for general use, and besides, refractory though they are, they 
 are not refractory enough to stand the high temperature re- 
 quired for economical incandescent lighting. Commercial success 
 was not realised until very thin and very uniform threads or 
 filaments of carbon were produced and enclosed in reservoirs of 
 glass, from which the air was exhausted to the utmost possible 
 limit. Such are the lamps made by Mr Edison with which this 
 building is lighted to-night. Let us examine the electrical pro- 
 perties of such a lamp. Here is a lamp intended to carry the 
 same current as those overhead, but of half the resistance, selected 
 because it leaves us a margin of electromotive force wherewith 
 to vary our experiment. Into its circuit I am able to intro- 
 duce a resistance for checking the current, composed of other 
 incandescent lamps for convenience, but which I shall cover over 
 that they may not distract your attention. As before, we have 
 two galvanometers, one to measure the current passing through 
 the lamp, the other the difference of potential at its terminals. 
 First of all, we will introduce a considerable resistance ; you 
 observe that, although the lamp gives some light, it is feeble and 
 red, indicating a low temperature. We take our galvanometer 
 readings. We now diminish the resistance, the lamp is now a 
 little short of its standard intensity; with this current it would 
 last 1000 hours without giving way. We again read the galvano- 
 H. i. 6 
 
82 
 
 SOME POINTS IN ELECTRIC LIGHTING. 
 
 meters. The resistance is diminished still further. You observe 
 a great increase of brightness, and the light is much whiter than 
 before. With this current, the lamp would not last very long. 
 The results are given in the following Table: 
 
 TABLE IV. 
 
 Current 
 Galvanometer 
 
 Potential 
 Galvanometer 
 
 Amperes 
 
 Volts 
 
 Watts 
 
 Resistance 
 Ohms 
 
 5-2 
 
 12-8 
 
 0-38 
 
 37 
 
 14 
 
 97 
 
 6-0 
 
 14-3 
 
 0-44 
 
 41 
 
 18 
 
 93 
 
 11-5 
 
 23-4 
 
 0-84 
 
 68 
 
 57 
 
 81 
 
 There are three things I want you to notice in these experi- 
 ments : first, the light is whiter as the current increases ; second, 
 the quantity of light increases very much faster than the power 
 expended increases; and thirdly, the resistance of the carbon 
 filament diminishes as its temperature increases, which is just 
 the opposite of what we should find with a metallic conductor. 
 This resistance is given in ohms in the last column. To the 
 second point, which has been very clearly put by Dr Siemens 
 in his British Association address, I shall return in a minute 
 or two. 
 
 The building is this evening lighted by about 200 lamps, each 
 giving sixteen candles' light, when 75 watts of power are de- 
 veloped in the lamp. To produce the same sixteen candles' light 
 in ordinary flat-flame gas-burners, would require between seven 
 and eight cubic feet of gas per hour, contributing heat to the 
 atmosphere at the rate of 3,400,000 foot-pounds per hour, equiva- 
 lent to 1250 watts, that is to say, equivalent gas lighting would 
 heat the air nearly seventeen times as much as the incandescent 
 lamps. 
 
 Look at it another way. Practically, about eight of these 
 lamps take one indicated horse-power in the engine to supply 
 them. If the steam-engine were replaced by a large gas-engine 
 this 1 H.-P. would be supplied by 25 cubic feet of gas per hour, or 
 by rather less ; therefore by burning gas in a gas-engine driving 
 a dynamo, and using the electricity in the ordinary way in incan- 
 descent lamps, we can obtain more than 5 candles per cubic foot 
 
SOME POINTS IX ELECTRIC LIGHTING. 83 
 
 of gas, a result you would be puzzled to obtain in 16-candle gas- 
 burners. With arc lights instead of incandescent lamps many 
 times as much light could be obtained. 
 
 At the present time lighting by electricity in London must 
 cost something more than lighting by gas. Let us see what are 
 the prospects of reduction of this cost. Beginning with the 
 engine and boiler, the electrician has no right to look forward to 
 any marked and exceptional advance in their economy. Next 
 comes the dynamo : the best of these are so good, converting 80 
 per cent, of the work done in driving the machine into electrical 
 work outside the machine, that there is little room for economy 
 in the conversion of mechanical into electrical energy ; but the 
 prime cost of the dynamo machine is sure to be greatly reduced. 
 Our hope of greatly increased economy must be mainly based 
 upon probable improvements in the incandescent lamp, and to this 
 the greatest attention ought to be directed. You have seen that 
 a great economy of power can be obtained by working the lamps 
 at high-pressure, but then they soon break down. In ordinary 
 practice, from 140 to 200 candles are obtained from a horse-power 
 developed in the lamps, but for a short time I have seen over 
 1000 candles per horse-power from incandescent lamps. The 
 problem, then, is so to improve the lamp in details, that it will 
 last a reasonable time when pressed to that degree of efficiency. 
 There is no theoretical bar to such improvements, and it must be 
 remembered that incandescent lamps have only been articles of 
 commerce for about three years, and already much has been done. 
 If such an improvement were realised, it would mean that you 
 would get five times as much light for a sovereign as you can 
 now. As things now stand, so soon as those who supply electricity 
 have reasonable facilities for reaching their customers, electric 
 lighting will succeed commercially where other considerations than 
 cost have weight. We are sure of some considerable improvement 
 in the lamps, and there is a probability that these improvements 
 may go so far as to reduce the cost to one-fifth of what it now 
 is. I leave you to judge whether or not it is probable, nay, 
 almost certain, that lighting by electricity is the lighting of the 
 future. 
 
 62 
 
6. 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 [From the Philosophical Transactions of the Royal Society \ 
 Part I. 1886.] 
 
 Received April 19, Read May 6, 1886. 
 
 THEOEETICAL CONSTRUCTION OF CHARACTERISTIC CURVE. 
 
 OMITTING the inductive effects of the current in the armature 
 itself, all the properties of a dynamo machine are most con- 
 veniently deduced from a statement of the relation between the 
 magnetic field and the magnetising force required to produce that 
 field, or, which comes to the same thing but is more frequently 
 used in practice, the relation between the electromotive force of 
 the machine at a stated speed and the current around the magnets. 
 This relation given, it is easy to deduce what the result will be in 
 all employments of the machine, whether as a motor or to produce 
 a current through resistance, through an electric arc, or in charg- 
 ing accumulators; also the result of varying the winding of the 
 machine whether in the armature or magnets. The proper inde- 
 pendent variable to choose for discussing the effect of a dynamo 
 machine is the current around the magnets, and the primary 
 relation it is necessary to know concerning the machine is the 
 relation of the electromotive force of the armature to the magnet 
 current. This primary relation may be expressed by a curve 
 (Hopkinson, Mechan. Engin. Instit Proc., 1879, pp. 246 et seq., 
 1880, p. 266), now called the characteristic of the machine, and 
 all consequences deduced therefrom graphically ; or it may be 
 expressed by stating the E.M.F. as an empirical function of the 
 
DYNAMO-ELECTRIC MACHINERY. 85 
 
 magnetising current. Many such empirical formulae have been 
 proposed ; as an instance we may mention that known as Frohlich's, 
 according to whom, if c be the current in the magnets, E the 
 
 ft f* 
 
 resulting E.M.F., E = V. For some machines this formula is 
 J. T~ oc 
 
 said to express observed results fairly accurately, but in our 
 experience it does not sufficiently approximate to a straight line 
 in the part of the curve near the origin. The character of the 
 error in Frohlich's formula is apparent by reference to Fig. 1, 
 which gives a series of observations on a dynamo machine, and for 
 comparison therewith a hyperbola F, drawn as favourably as possible 
 to accord with the observations*. Such empirical formulae possess 
 no advantage over the graphical method aided by algebraic pro- 
 cesses, and tend to mask much that is of importance. 
 
 One purpose of the present investigation is to give an approxi- 
 mately complete construction of the characteristic curve of a 
 dynamo of given form from the ordinary laws of electro- magnetism 
 and the known properties of iron, and to compare the result of 
 such construction with the actual characteristic of the machine. 
 The laws of electro-magnetism needed are simply (Thomson, 
 papers on Electrostatics and Magnetism; Maxwell, Electricity and 
 Magnetism, vol. II., pp. 24, 26, and 143), (1) that the line integral 
 of magnetic force around any closed curve, whether in iron, in air, 
 or in both, is equal to 4?rnc where c is the current passing through 
 the closed curve, and n is the number of times it passes through ; 
 (2) the solenoidal condition for magnetic induction, that is, if the 
 lines of force or of induction be supposed drawn, then the induc- 
 tion through any tube of induction is the same for every section. 
 Kegarding the iron itself, we require to know from experiments 
 on the material in any shape the relation between a, the induction, 
 and a, the magnetic force at any point ; for convenience write 
 a =/ -1 (a), or a =f(a). From these premises, without any further 
 assumption, it is easy to see that a sufficiently powerful and 
 
 * [Added Aug. 17. That Frohlich's formula cannot be a thoroughly satisfactory 
 expression of the characteristic of a dynamo machine is evident from the considera- 
 tion that E should simply change its sign with c, that is, be an odd function of c. 
 There should be a point of inflexion in the characteristic curve at the origin. 
 
 Another empirical formula rrtan" 1 ^ is free from this objection, but still fails to 
 
 fully represent the approximation of the curve to a straight line on either side of 
 the origin, and it is equally uninstructive with any other purely empirical formula.] 
 
86 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 w 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 [ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 & 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 e 
 
 
 
 
 
 
 
 
 
 
 
 :( 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ff 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r* 
 
 
 
 \ 
 
 
 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 j 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 '\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 PQ 
 
 
 
 
 \\ 
 
 
 
 (i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 \ 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 \V 
 
 
 e 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 ' t \ 
 
 \ 
 
 
 F 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x \ 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 ^ 
 
 4 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ l 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ \ 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Sy 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V\^ 
 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 F^i v 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 v 4 
 
 X ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (j 1 " 
 
 Si 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 e 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 P 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 5 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 + 
 
 \ \ 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,5j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V^ 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^4 
 
 
 
 
 
 
 
 
 
 
 \> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s, * 
 
 
 
 
 
 
 
 
 
 
 \J- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 *v 
 
 
 
 
 
 1C 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 I 
 
 
 
 
 g 
 
 
 
 
 
 \\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 ^ 
 
 
 i 
 
 
 
 
 
 
 
 N 
 
 ^ 
 
 s" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 I 
 
 
 
 
 
 
 
 
 
 
 f- 
 
 ti 
 
 i". 
 
 _- 
 
 j 
 
 ... 
 
 ... 
 
 -J. 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 $2 
 
 to 
 
 **~ 
 
 8 
 
 3 
 
 U 
 
 
 ^ 
 
 
 
 i 
 
 
 
 c 
 
 
 CT> 
 
 a 
 
 
 ^~. 
 
 l 
 
 
 m 
 
 <r 
 
 1 
 
 3 
 
 C\ 
 
 
 
 o 
 
 II 
 
 -S 
 
 I Q 
 
 s . 
 
 I! 
 
DYNAMO-ELECTRIC MACHINERY. 87 
 
 laborious analysis would be capable of deducing the characteristic 
 of any dynamo to any desired degree of accuracy. This we do 
 not attempt, as, even if successful, the analysis would not be likely 
 to throw any useful light on the practical problem. We shall 
 calculate the characteristic, first making certain assumptions to 
 simplify matters. We shall next point out the nature of the 
 errors introduced by these assumptions, and make certain small 
 corrections in the method to account for these sources of error, 
 merely proving that the amount of these corrections is probable 
 or deducing it from a separate experiment, and again compare the 
 theoretical and the actual characteristic. 
 
 First approodmation. Assume that by some miracle the tubes 
 of magnetic induction are entirely confined to the iron excepting 
 that they pass directly across from the bored faces of the pole- 
 pieces to the cylindrical face of the armature core. This, we shall 
 find, introduces minor sources of error, affecting different parts of 
 the characteristic curve to a material extent. Let / be total 
 induction through the armature, A l the area of section of the 
 iron of the armature, h the mean length of lines of force in the 
 armature ; A z the area of each of the two spaces between core of 
 armature and the pole-pieces of the magnets, l z the distance 
 between the core and the pole-piece; A 3 the area of core of 
 magnet, 1 8 the total length of the magnets. All the tubes of 
 induction which pass through the armature pass through the 
 space A and the magnet cores, and by our assumption there are 
 no others. We now assume further that these tubes are uniformly 
 distributed over these areas. The induction per square centi- 
 metre is then : - in the armature core, -r- in the non-magnetic 
 
 -0-1 ^2 
 
 spaces, - - in the magnet cores ; the corresponding magnetic 
 ** 
 
 forces per centimetre linear must be /(-j"), -j-, /{-*-} The 
 
 Vi/ A. 2 ' \-a. 3 / 
 
 line integral of magnetic force round a closed curve must be 
 ^i/(-j-J + 2^-7- + ^ 3 /f-i-J . In this approximation we neglect 
 
 the force required to magnetise pole-pieces and other parts not 
 within the magnet coils to avoid complication. The equation of 
 
 the characteristic curve is then 4>7rnc = lif(-r\ + 2/ 2 -j- + l s f(-r } . 
 
 \A 1 / A 2 \A 3 / 
 
88 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 This curve is, of course, readily constructed graphically from the 
 magnetic property of the material expressed by the curve a =/(a). 
 
 In Fig. 1 curve A represents =A/{ir]> tne straight line B 
 
 \-"-i/ 
 
 x 2 2 Jf~ , curve C x = I 3 f ( -j- ) , and curve D the calculated 
 A 2 \A 3 / 
 
 characteristic. When we compare this with an actual character- 
 istic E, we shall see that, broadly speaking, it deviates from truth 
 in two respects: (1) it does not rise sufficiently rapidly at first; 
 (2) it attains a higher maximum than is actually realised. Let 
 us examine these errors in detail. 
 
 (1) The angle the characteristic makes with the axis of 
 abscissae near the origin is mainly determined by the line B. We 
 have in fact a very considerable extension of the area of the field 
 beyond that which lies under the bored face of the pole-piece. 
 The following consideration will show that the extension may be 
 considerable. Imagine an infinite plane slab, and parallel with it 
 
 FIG. 2. 
 
 a second slab cut off by a second plane making an angle a. We 
 want a rough idea of the extension of the area between the plates 
 by the spreading of the lines of induction beyond the boundary. 
 We know that the actual extension of the area will be greater 
 than we shall calculate it to be if we prescribe an arbitrary distri- 
 bution of lines of force other than that which is consistent with 
 Laplace's equation. 
 
DYNAMO-ELECTRIC MACHINERY. 89 
 
 Assume, then, the lines of force to be segments of circles centre 
 
 0, and straight lines perpendicular to OA. The induction along a 
 
 y 
 
 line PQR will be - f r , V being difference of potential be- 
 tween the planes, and the added induction from OPB will be 
 
 Vdx V , (TT ot)x + t ^ . r TT , 
 
 if a. we have 
 
 for x = t, 2t, &c. 
 
 1 . (TT 
 x . . . . -log v 
 
 TT -a t 
 
 t /. . . . '599 
 
 2* . -904 
 
 3 . . . . - 1109 
 
 4* . . . . 1-263 
 
 ot . . . .. 1*387 
 
 lOt . ... 1-792 
 
 showing that the extension of the area of the field is likely to be 
 considerable. 
 
 (2) The failure of the actual curve to reach the maximum 
 indicated by approximate theory is because the theory assumes 
 that all tubes of induction passing through the magnets pass also 
 through the armature. Familiar observations round the pole- 
 pieces of the magnets show that this is not the case. If v be the 
 ratio of the total induction through the magnets to the induction 
 in the armature we must, in our expression for the line integral of 
 
 magnetising force, replace the term f( -j- j by/(V); v is not 
 
 strictly a constant, as we shall see later ; it is somewhat increased 
 as / increases owing to magnetisation of the core of the armature, 
 and it is also affected by the current in the armature. For our 
 present purpose we treat it as constant. 
 
 There is yet another source of error which it is necessary to 
 examine. Some part of the induction in the armature may pass 
 through the shaft instead of through the iron plates. An idea of 
 the amount of this disturbance may be readily obtained. Consider 
 the closed curve ABCDEF, AB and FEDG are drawn along lines 
 of force, AF and BC are orthogonal to lines of force. Since this 
 closed curve has no currents passing through it, the line integral 
 of force around it is nil ; therefore, neglecting force along ED, we 
 
90 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 have force along AB is equal to force along FE and DC. In the 
 machine presently described we may safely neglect the induction 
 through the shaft ; the error is comparable with the uncertainty 
 as to the value of ^ ; but in another machine, with magnets of 
 much greater section, the effect of the shaft would become very 
 sensible when the core is practically saturated. 
 
 FIG. 3. 
 The amended formula now becomes 
 
 where 1 4 is the mean length of lines of force in the wrought-iron 
 yoke, A 4 the area of the yoke, l s and A 5 corresponding quantities 
 for the pole-pieces, the last two terms being introduced for the 
 forces required to magnetise the yoke and the two pole-pieces. 
 
 We now repeat the graphical method of construction exactly 
 as before, the actual observations of induction in armature and 
 current being plotted on the same diagram (Fig. 1), in which 
 curve G represents the force required to magnetise the yoke, and 
 curve H that required to magnetise the pole-pieces. Before 
 discussing these curves further, and comparing the results with 
 those of actual observation, it may be convenient to describe the 
 machine upon which the experiments have been made, confining 
 the description strictly to so much as is pertinent to our present 
 inquiry. 
 
DYNAMO-ELECTRIC MACHINERY. 91 
 
 DESCRIPTION OF MACHINE. 
 
 The dynamo has a single magnetic circuit, consisting of two 
 vertical limbs, extended at their lower extremities to form the 
 pole-pieces, and having their upper extremities connected by a 
 yoke of rectangular section. Each limb, together with its pole- 
 piece, is formed of a single forging of wrought-iron. These 
 forgings, as also that for the yoke, are built up of hammered 
 scrap and afterwards carefully annealed, and have a magnetic 
 permeability but little inferior to the best Swedish charcoal iron. 
 The yoke is held to the limbs by two bolts, the surfaces of contact 
 being truly planed. In section the limb is oblong, with the 
 corners rounded in order to facilitate the winding of the mag- 
 netising coils. A zinc base, bolted to the bed-plate of the machine, 
 supports the pole-pieces. 
 
 The magnetising coils are wound directly on the limbs, and 
 consist of 11 layers on each limb of copper wire 2*413 mms. 
 diameter (No. 13, B.W.G.), making 3260 convolutions in all, the 
 total length being approximately 4570 metres. The pole-pieces 
 are bored to receive the armature, leaving a gap above and below, 
 subtending an angle of 51 at the centre of the fields. The 
 opposing surfaces of the gap are 8 mms. deep. 
 
 The following table gives the leading dimensions of the 
 machine : 
 
 cms. 
 
 Length of magnet limb ,....= 457 
 
 Width of magnet limb . . . = 22*1 
 
 Breadth of magnet limb . ... . = 44*45 
 
 Length of yoke . . . . . = 61*6 
 
 Width of yoke . . ; . . . . = 48*3 
 
 Depth of yoke . ... . . . = 23*2 
 
 Distance between centres of limbs = 38*1 
 
 Bore of fields . . . . . . . = 27*5 
 
 Depth of pole-piece . . . . . == 25*4 
 
 Width of pole-piece measured parallel to the shaft = 48*3 
 
 Thickness of zinc base . . . . . . =12*7 
 
 Width of gap . , . . . . . = 12*7 
 
 The armature is built up of about 1000 iron plates, insulated 
 one from another by sheets of paper, and held between two end 
 plates, one of which is secured by a washer shrunk on to the 
 
92 
 
 DYNAMO-ELECTKIC MACHINERY. 
 
 ^\ 
 
 " """~""w" =";::" 
 
 \ 
 
 II 
 
 to 
 
 & C 
 
 O 
 
 t) 03 
 
 I 'I 
 
 si 
 
 I Kf 
 W .- 
 
 I > 
 
 B T3 
 
 I II 
 
 * n 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 93 
 
 shaft, and the other by a nut and lock-nut screwed on the shaft 
 itself. The plates are cut from sheets of soft iron, having probably 
 about the same magnetic permeability as the magnet cores. The 
 shaft is of Bessemer steel, and is insulated before the plates are 
 threaded on. 
 
 The following table gives the leading dimensions of the 
 
 armature : 
 
 cms. 
 
 Diameter of core = 24'5 
 
 Diameter of internal hole . . . . = 7'62 
 
 Length of core over the end plates . . = 50*8 
 
 Diameter of shaft = 6*985 
 
 The core is wound longitudinally according to the Hefner von 
 Alteneck principle with 40 convolutions, each consisting of 16 
 strands of wire 1753 mm. diameter, the convolutions being placed 
 in two layers of 20 each. The commutator is formed of 40 copper 
 bars, insulated with mica, and the connections to the armature 
 so made that the plane of commutation in the commutator is 
 horizontal, when no current is passing through the armature. 
 
 Fig. 5 shows a side elevation of the dynamo ; Fig. 6 a cross- 
 section through the centres of the magnets ; Fig. 7 a section of 
 
 rm 
 
 FIG. 5. 
 
 the core of the armature, in a plane through the axis of the 
 shaft. 
 
94 DYNAMO-ELECTRIC MACHINERY. 
 
 The dynamo is intended for a normal output of 105 volts 320 
 amperes at a speed of 750 revolutions per minute. The resistance 
 
 m 
 
 FIG. 6. 
 
 of the armature measured between opposite bars of the com- 
 mutator is 0-009947 ohm, and of the magnet coils 16'93 ohms, 
 both at a temperature of 13*5 Centigrade; Lord Rayleigh's 
 determination of the ohm being assumed. 
 
 FIG. 7. 
 
 We have now to estimate the lengths and areas required in 
 the synthesis of the characteristic curve. 
 
 A l ; from the length of the core of the armature (50'8 cms.) 
 must be deducted 3'4 cms. for the thickness of insulating material 
 between the plates ; the resultant area is, on the other hand, 
 as has already been stated, slightly augmented by the presence of 
 the steel shaft. A l is taken as 810 sq. cms. 
 
 ^ ; this is assumed to be 13 cms. : i.e., slightly in excess of 
 the shortest distance (12- 6 cms.) between the pole-pieces. 
 
DYNAMO-ELECTRIC MACHINERY. 95 
 
 A z ; the angle subtended by the bored face of the pole-piece 
 at the axis is 129, the breadth of the pole-piece is 48'3 cms., 
 the diameter of the bore of the field is 27'5 cms., and, as already 
 stated, the diameter of core 25*5 cms., thus, the area of pole-piece 
 is 1513 sq. cms., and the area of 129 of the cylinder at the mean 
 radius of 13*0 cms. is 1410 sq. cms. ; this value is taken for A 2 in 
 the curves drawn in Fig. 1. In Fig. 4, A z is taken as 1600, an 
 allowance of 190 sq. cms. being made for the spreading of the 
 field at the edges of the pole-pieces, or |f$ = 1*2 cm. all round 
 
 1'2 
 
 the periphery, that is =0'8 of the distance from iron of pole- 
 pieces to iron of core. 
 1. 2 is 1*5 cm. 
 
 A 3 is a little uncertain, as the forgings are not tooled all over, it 
 is here taken as 980 sq. cms., but this value may be slightly too high. 
 
 1 3 is 91 '4 cms. 
 
 A 4 is 1120 sq. cms. 
 
 1 4 is 49 cms., being measured along a quadrant from the centre 
 of the magnet, thus : 
 
 FIG. 8. 
 
 A 5 is 1230 sq. cms., intermediate between the area of magnet 
 and face of pole-piece. 
 
 1 5 is 11 cms. 
 
 v was determined by experiment as described below, and its 
 value is taken as 1'32 ; when the magnetising current is more 
 than 5 '62 amperes its value should be a little greater. 
 
 The function f(a) is taken from Hopkinson, Phil. Trans., 
 vol. CLXXVI. (1885), p. 455*; the wrought-iron there referred to 
 was not procured at the same time as, and its properties may 
 differ to a certain extent from, the wrought-iron of these magnets. 
 
 The curves now explain themselves ; the abscissae in each case 
 represent the line integral of magnetising force in the part of 
 
 * The material parts of this paper are printed at the end of this volume for 
 convenience of reference. 
 
96 DYNAMO-ELECTRIC MACHINERY. 
 
 the magnetic circuit referred to, the ordinates, the number of 
 lines of induction which also pass through the armature. 
 
 The results of the actual observations on the machine are 
 indicated, those when the magnetising force is increasing +, when 
 it is decreasing . The measurements of the currents in the 
 magnets which were separately excited, and of the potential differ- 
 ence between the brushes, the circuit being open, were made 
 with Sir W. Thomson's graded galvanometers, standardised at the 
 time of use. The irregularities of the observations are probably 
 due to the variation of speed, the engine being not quite perfectly 
 governed. The second construction exhibits quite as close an 
 agreement between observation and calculation as could be ex- 
 pected ; the deviation at high magnetising forces is probably due 
 to three causes, increase in the value of v when the core of the 
 armature is partially saturated, uncertainty as to the area A 3 , 
 difference in the quality of the iron. It is interesting to see how 
 clearly theory predicts the difference between the ascending and 
 descending curves of a dynamo. Consideration of the diagram 
 proves that this machine is nearly perfect in its magnetic pro- 
 portions. The core might be diminished by increasing the hole 
 through it to a small, but very small, extent without detriment. 
 Any reduction of area of magnets would be injurious; they might, 
 indeed, be slightly increased with advantage. An increase in the 
 length of the magnets would be very distinctly detrimental. 
 Again, little advantage results from increasing the magnetising 
 force beyond the point at which the permeability of the iron of 
 the magnets begins to rapidly diminish. For iron of the same 
 quality as that of the machine under consideration, a magnetising 
 force of 2 '6 x 10 3 or 28*4 per centimetre is suitable. To get the 
 same induction in other parts of the circuit, the diagram shows that 
 for the air space a magnetising force of 21 x 10 3 is required, for 
 the pole-pieces O'l x 10 3 , for the armature 0*2 x 10 3 , for the yoke 
 0'6 x 10 3 , making a total force required of 24*5 x 10 3 . Any alter- 
 ation in the length or the area of any portion of the magnetic 
 circuit entails a corresponding alteration in the magnetising forces 
 required for that portion, at once deducible from the diagram. 
 Similar machines must have the magnetising forces proportional 
 to the linear dimensions, and, consequently, if the electromotive 
 force of the machines is the same, the diameter of the wire of the 
 magnet coils must be proportional to the linear dimensions. If 
 
DYNAMO-ELECTRIC MACHINERY. 97 
 
 the lengths of the several portions of the magnetic circuit remain 
 the same, but the areas are similarly altered, the section of the 
 wire must be altered in proportion to the alteration in the peri- 
 phery of the section. 
 
 EXPERIMENT TO DETERMINE v. 
 
 Around the middle of one of the magnet limbs a single coil of 
 wire was taken, forming one complete convolution, and its ends 
 connected to a Thomson's mirror galvanometer rendered fairly 
 ballistic. If the circuit of the field magnets, while the exciting 
 current is passing, be suddenly short-circuited, the elongation of 
 the galvanometer is a measure of the total induction within the 
 core of the limbs, neglecting the residual magnetisation. If the 
 short circuit be suddenly removed, so that the current again 
 passes round the field-magnets, the elongation of the galvanometer 
 will be equal in magnitude and opposite in direction. 
 
 The readings taken were : 
 
 Zero . . 71 left. 
 
 Deflection . . . . . 332 magnets made. 
 
 . . . .196 right; magnets short-circuited. 
 Hence, deflection to right = 267 
 left = 261 
 Mean deflection = 264 
 
 To determine the induction through the armature, the leads 
 to the ballistic galvanometer were soldered to consecutive bars of 
 the commutator, connected to that convolution of the armature, 
 which lay in the plane of commutation. 
 
 The readings taken were : 
 
 Zero . . . . . . 23 left 
 
 Deflection . . ... . 223 magnets made. 
 
 . . * . . 176) right; magnets 
 
 . . . . 178J short-circuited. 
 
 Hence, deflection to right and left = 200 
 
 It thus appears that out of 264 lines of force passing through 
 
 the cores of the magnet limbs at their centre, 200 go through the 
 
 core of the armature, whence v equals 1*32. The magnetising 
 
 current round the fields during these experiments was 5 '6 amperes. 
 
 H. i. 7 
 
98 DYNAMO-ELECTRIC MACHINERY. 
 
 EXPERIMENTS ON WASTE FIELD NOT PASSING THROUGH 
 ARMATURE. 
 
 As in the determination of v a single convolution was taken 
 around the middle of one of the limbs, and connected to the 
 ballistic galvanometer; the deflections, when a current of 5*6 
 amperes was suddenly passed through the fields or short-circuited, 
 were: 
 
 Zero . . 34 left. 
 
 Deflection ;.. . . 148 magnets made. 
 
 . .... . V .. : *' 82 right; magnets short-circuited. 
 
 Hence, deflection to right = 116 
 
 left =114 
 
 Mean deflection = 115 
 
 I. Four convolutions were then wound round the zinc plate 
 and the cast-iron bed in a vertical plane, passing through the axis 
 of the armature ; and the deflections noted. The mean deflection 
 was 50*25 ; or, reducing to one convolution, = 12*6. 
 
 II. A square wooden frame, 38 cms. x 38 cms., on which 
 were wound ten convolutions, was then inserted between the 
 magnet limbs, with one side resting on the armature, and an 
 adjacent side projecting 5 cms. beyond the coils on the limbs, or 
 about 7*6 cms. beyond the cores of the limbs. The mean de- 
 flection was 55 ; or, reducing to one convolution, = 5'5. 
 
 III. The same frame was raised a height of 6 '3 5 cms. above 
 the armature in a vertical plane. The mean deflection was 46'5 
 or, reducing to one convolution, = 4'6. 
 
 IV. The same frame was again lowered on the armature 
 and pushed inwards so as to lie symmetrically within the space 
 between the limbs. The deflections were noted and the mean 
 was 80 ; or, reducing to one convolution, = 8'0. 
 
 Let G represent the leakage through a vertical area bounded 
 by the armature, and a line 7 '6 cms. above the armature, and of 
 the same width as the pole-pieces ; let R be the remainder of the 
 leakage between the limbs ; then II. and III. give 
 
DYNAMO-ELECTKIC MACHINERY. 
 
 99 
 
 whence 
 
 G 
 R 
 
 T35 
 6-9. 
 
 Again, IV. gives 
 
 therefore 
 
 G + R = 9-6 
 
 8-0 
 
 which shows an agreement as near as might be expected con- 
 sidering the rough nature of the experiment, and that the leakage 
 is assumed uniform over the areas considered. 
 
 We take 
 
 R = 8-0. 
 Reducing these losses to percentages we have 
 
 . . . . . - . = 1'4 per cent. 
 
 7-0 
 
 And from I. the leakage through the zinc) _ - . _ 
 
 plate and iron base . . . .J 
 
 Hence the two gaps account for . . , 2'8 
 
 The zinc plate and iron base account for . 10'3 
 
 And the area between the limbs . . 7*0 
 
 Making a total loss accounted for . . 201 
 
 Out of an observed loss of . . 24'24 
 
 The leakage through the shaft and from pole-piece to yoke, 
 and one pole-piece to the other by exterior lines, will account for 
 the remainder. 
 
 EFFECT OF THE CURRENT IN THE ARMATURE. 
 
 The currents in the fixed coils around the magnets are not the 
 only magnetising forces applied in a dynamo machine ; the currents 
 in the moving coils of the armature have also their effect on the 
 resultant field. There are in general two independent variables 
 in a dynamo machine, the current around the magnets and the 
 current in the armature, and the relation of E.M.F. to currents is 
 
 72 
 
100 DYNAMO-ELECTRIC MACHINERY. 
 
 fully represented by a surface. In well-constructed machines the 
 effect of the latter is reduced to a minimum, but it can be by no 
 means neglected. When a section of the armature coils is commu- 
 tated it must inevitably be momentarily short-circuited, and if 
 at the time of commutation the field in which the section is 
 moving is other than feeble, a considerable current will arise 
 in that section, accompanied by waste of power and destructive 
 sparking. It may be well at once to give an idea of the possible 
 magnitude of such effects. In the machine already described the 
 mean E.M.F. in a section of the armature at a certain speed may 
 be taken as 6 volts, its resistance 0*000995 ohm. Setting aside, 
 then, for the moment questions of self-induction, if a section were 
 commutated at a time when it was in a field of one-tenth part of 
 the mean intensity of the whole field there would arise in that 
 section, whilst short-circuited by the collecting brush, a current of 
 600 amperes, four times the current when the section is doing its 
 normal work. The ideal adjustment of the collecting brushes is 
 such that during the time they short-circuit the sections of the 
 armature the magnetic forces shall just suffice to stop the current 
 in the section, and to reverse it to the same current in the opposite 
 direction. 
 
 Suppose the commutation occurs at an angle A, in advance of 
 the symmetrical position between the fields, and that the total 
 current through the armature be (7, reckoned positive in the 
 direction of the resultant E.M.F. of the machine, i.e., positive 
 when the machine is used as a generator of electricity. Taking 
 any closed line through magnets and armature, symmetrically 
 drawn as ABCDEFA (fig. 9), it is obvious that the line integral 
 of magnetic force is diminished by the current in the armature 
 included between angle X in front and angle X behind the plane 
 of symmetry. If m be the number of convolutions of the armature, 
 
 the value of this magnetising force is 4t7rC -^ - = 4Xm(7 opposed 
 
 to the magnetising force of the fixed coils on the magnets. Thus, 
 if we know the lead of the brushes and the current in the 
 armature we are at once in a position to calculate the effect 
 on the electromotive force of the machine. A further effect of 
 the current in the armature is a material disturbance in the dis- 
 tribution of the induction over the bored face of the pole-piece ; 
 the force along JBC (fig. 9) is by no means equal to that along 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 101 
 
 DE. Draw the closed curve BCGHB, the line integral along CG 
 and HB is negligible. Hence the difference between force EG 
 
 and BC is equal to 47rC^ - = 2/cmC where K is the angle COG. 
 
 2t 7T 
 
 This disturbance has no material effect upon the performance of 
 
 FIG. 9. 
 
 the machine. But the current in the armature also distorts the 
 arrangement of the comparatively weak field in the gap between 
 the pole-pieces, displacing the point of zero field in the direction 
 of rotation in a generator and opposite to the direction of rotation 
 in a motor ; and it is due to this that the non-sparking point for 
 the brushes is displaced. A satisfactory mathematical analysis 
 of the displacement of the field in the gap between the pole- 
 pieces by the current in the armature would be more troublesome 
 than an a priori analysis of the distribution of field in this space 
 when the magnet current is the only magnetising force. Owing 
 to the fact that the armature is divided into a finite number 
 of sections there is a rapid diminution of the displacement of the 
 field during the time that a section is being commutated, the 
 diminution being recovered whilst the brush is in contact with 
 only one bar of the commutator. The field thus oscillates slightly, 
 owing to the disturbance caused by reversing the direction of the 
 current in the successive sections of the armature. The number 
 of oscillations in a gramme armature or in a Siemens' armature 
 with an even number of sections will be pm, where p is the 
 
102 DYNAMO-ELECTRIC MACHINERY. 
 
 number of revolutions per second, but in a Siemens' armature 
 with an odd number of sections it will be 2pm.* This oscillation 
 of the field is only another way of expressing the effect of the 
 self-induction of the section, but it must be remembered that 
 if the self-induction, multiplied by change of current, is expressed 
 as a change in the field we must omit self-induction as a separate 
 term in our electrical equations. The precise lead to be given to 
 the brushes in order to avoid sparking in any given case depends 
 on many circumstances the form and extent of the pole-pieces, 
 the number of sections in the armature, and the duration of the 
 short circuit which the brushes cause in any section of the 
 armature. The adjustment of the position of the collecting 
 brushes is generally made by hand at the discretion of the 
 attendant, and is in some cases fixed once for all to suit an 
 average condition of the machine. We shall, therefore, treat X 
 the lead as an independent variable, controlled by the attendant. 
 
 Let / be total induction through the armature, 1 ' + 1' total 
 induction through the magnets, /' being the waste field. Let G 
 be current in armature, c in the magnets. Let gl' be the line 
 integral of magnetic force from a point on one pole-piece to a 
 point on the other, the line being drawn external to the armature, 
 g will be approximately constant. Omitting as comparatively 
 unimportant the magnetising force in the pole-pieces and iron 
 core of the armature we have the following equations : 
 
 4,\mC + 21 2 
 
 * [Added Aug. 17. Armatures with an odd number of convolutions are open to 
 one theoretical objection, which would be a practical one if the number of con- 
 volutions were very small. The 2m + 1 convolutions constitute in themselves a 
 closed circuit, having a resistance four times the mean actual resistance of the 
 armature measured between the collecting brushes. When any one convolution is 
 exactly in the middle of the field, the E.M.F. of the other 2m convolutions exactly 
 balance, so that there is upon the closed circuit an E.M.F. due to the single convo- 
 
 lution somewhat in excess of th part of the actual E.M.F. of the machine. Thus 
 m 
 
 there will be an alternating E.M.F. around the closed circuit of the armature 
 capable of causing a considerable waste of power. This waste is materially checked 
 by the self-induction of the circuit.] 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 When C = we observed 
 
 /= _1 r. 
 V 
 
 whence 
 
 9 
 eliminating /' 
 
 103 
 
 1 
 
 -4Xra(7-. 
 z/ 
 
 The characteristic curve when (7 = being / = F (4s7rnc) we 
 may write the above as the equation of the characteristic surface 
 thus 
 
 r v 1 A* f 4Xm(7\ 
 
 1 + - - 4>\mC f = F[ 4i7rnc 
 
 v 2/ 2 V v J 
 
 In applying this equation it must not be forgotten that the 
 E.M.F. of the machine cannot be determined from 7 unless the 
 
 commutation occurs at such a time that the coil being commutated 
 embraces all, or nearly all, the lines of induction in the armature. 
 
104 DYNAMO-ELECTKIC MACHINEKY. 
 
 This equation enables the characteristic surface to be 
 constructed from the characteristic curve. Let OL 4>7rnc, 
 
 KL 1 
 
 LM = 4m\(7, draw MK so that y-^- = - , through K draw ordi- 
 
 nate KR meeting characteristic curve in R, draw RQ parallel to 
 OL meeting ordinate QL in Q, draw QS parallel to LM ; draw QP 
 
 so that on = ~ ~ of Then P is a point on the characteristic 
 o(tf v 1% 
 
 surface. 
 
 A very important problem is to deduce the characteristic curve 
 of a series wound machine from the normal characteristic ; in this 
 case c = C, and we have 
 
 T v l A - n Az -r,(( A 4Xm\ 
 / H 4i\mU QJ- F K 47rn 
 
 V 1/2 I \ V / 
 
 taking P-R as ordinate of any point in the normal characteristic, 
 cut off QR equal to 4Xm(7 -^ , that is, draw OQ so that 
 
 r>r\ V ~^-A n^-z/A ( m ^ 
 
 tan QOx = - 4Xm(7 ^y 2 4>7r in -- 
 v 2/2 / \ VTT 
 
 7T?l -- 
 Z^ 
 
 then PQ will represent the induction corresponding to magnetis- 
 
 ing force 4?r (n -- - )(7. It is noteworthy that as the current (7, 
 \ ^TT/ 
 
 and therefore OR increases, PQ, the induction, will attain a maxi- 
 mum and afterwards diminish, vanish, and become negative. That 
 in series wound machines the E.M.F. has a maximum value has 
 been many times observed. The cause lies in the existence of a 
 waste field not passing through the armature, and in the satura- 
 tion of the magnet core. 
 
 The effect of the current in the armature on the potential 
 between the brushes of any machine is the same as that of an 
 addition to the resistance of the armature proportional to the lead 
 of the brushes, and to the ratio of the waste field to the total field, 
 
 combined with that of taking the main current times round 
 
 6 I/TT 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 105 
 
 the magnets in direction opposite to the current c. The preceding 
 investigation tells the whole story of a dynamo machine, except- 
 ing only the relation of X to C in order that the brushes may be 
 so placed as to avoid sparking. The only constant or function 
 which has to be determined experimentally for any particular 
 machine is v, the ratio of total to effective field, all the rest 
 follows from the configuration of the iron and the known proper- 
 ties of the material. 
 
 The following illustrations of the effect of the current in the 
 armature and the lead of the brushes are interesting. In both 
 cases the magnet coils are supposed to be entirely disconnected so 
 that c is zero. First, let X be negative, short-circuit the brushes 
 and drive the machine at a certain speed, a large current will be 
 produced, the current in the armature itself forming the magnet*. 
 Second, let X be positive, cause a current to pass through the 
 armature, the armature will turn in the positive direction and will 
 
 * [Added Aug. 17. This experiment was tried upon a dynamo machine of 
 construction generally similar to that shown in Figs. 5, 6, and 7, but with an 
 armature of half the length intended in normal work to give 400 amperes, 50 volts, 
 at 1,000 revolutions. The magnet coils were disconnected, and the terminals of 
 the armature were connected through a Siemens' electrodynamometer, and the 
 machine was run at 1,380 revolutions. When the brushes were placed in the 
 normal position (X = 0) the current due to residual magnetism was 52 amperes. By 
 giving the brushes a small positive lead the current was reduced to nearly zero. 
 By giving the brushes a small negative lead a current of over 234 amperes, the 
 maximum measured by the dynamometer, was obtained, and by varying the lead it 
 was easy to maintain a steady current of any desired amount.] 
 
106 DYNAMO-ELECTRIC MACHINERY. 
 
 act as a motor capable of doing work. In either case, particularly 
 the former, such use of the machine would not be practical owing 
 to violent sparking on the commutator. The following is a further 
 illustration of the formula given above. If we could put up with 
 the sparking which would ensue, it would be possible to make X 
 negative in a generator of electricity, and thereby obtain by the 
 reactions of the armature itself all the results usually obtained by 
 compound winding. 
 
 EFFICIENCY EXPERIMENTS. 
 
 Having discussed the relations subsisting between the con- 
 figuration of the magnetic circuit of a dynamo machine and the 
 induction obtained for given magnetising forces, and having com- 
 pared the results obtained by direct calculation with the results of 
 actual observation on a particular machine, the construction of 
 which we have described at length, it appeared of importance to 
 determine the efficiency of the machine under consideration as a 
 converter of energy, when used either as a generator of electricity 
 or as a motor. An accurate determination of the mechanical 
 power transmitted to a dynamo by a driving belt, or of the power 
 given by a motor presents formidable experimental difficulties. 
 Moreover, if the mechanical power absorbed in driving the dynamo 
 be measured directly, any error in measurement will involve an 
 error of the same magnitude in the determination of the efficiency. 
 To avoid this difficulty we employed the following device. 
 
 Let two dynamos, approximately equal in dimensions and 
 power, have their shafts coupled by a suitable coupling, which 
 may serve also as a driving pulley ; and let the electrical connex- 
 ions between the dynamos be made so that the one drives the 
 other as a motor. If the combination be driven by a belt passing 
 over the coupling pulley, the power transmitted by the belt is the 
 waste in the two dynamos and the connexions between them. By 
 suitably varying the magnetic field of one of the dynamos, the 
 power passing between the two machines can be adjusted as 
 desired. If, then, the electrical power given out by the generator 
 is measured, and also the power transmitted by the belt, the 
 efficiency of the combination can be at once determined. By 
 this arrangement the measurement, which presents experimental 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 107 
 
 difficulties, viz., of the power transmitted by the belt, is of a small 
 quantity. Consequently, even a considerable error in the deter- 
 mination has but a small effect on the ultimate result. On the 
 other hand, the measurement of the large quantity involved, viz., 
 the electrical power passing between the two machines, can with- 
 out difficulty be made with great accuracy. 
 
 The second machine was similar in all respects to that already 
 described, and each is intended for a normal output of 110 volts, 
 320 amperes, at a speed of 780 revolutions per minute. 
 
 The power transmitted by the belt was measured by a dyna- 
 mometer of the Hefner- Alteneck type, the general arrangement 
 being as shown in the diagram, Fig. 12. A is the driving pulley 
 of the engine, B the driven coupling of the dynamos ; D, D are 
 
 FIG. 12. 
 
 the guide pulleys of the dynamometer carried on a double frame 
 turning about the fulcrum C, and supported by a spiral spring, 
 the suspension of which can be varied by a pair of differential 
 pulley-blocks attached to a fixed support overhead. When a 
 reading is made the suspension of the spring is adjusted until the 
 index of the dynamometer comes to a fiducial mark on a fixed 
 scale, the extension of the spring is then read by a second index 
 attached to its upper extremity ; F, F-are two fixed guide pulleys 
 of the same diameter as the pulleys D, D, and having the same 
 distance between their centres, in order that the two portions of 
 the belt may be parallel and the sag as far as possible taken up. 
 The normal from C to the centre line of either portion of the belt 
 
108 DYNAMO-ELECTRIC MACHINERY. 
 
 between the pulley A and the guide pulleys = 31'9 cms. The 
 normal from C to the centre line of either of the parallel portions 
 of the belt = 2 '4 cms.; and from C to the centre line of the spring 
 = 92-7 cms. 
 
 Take moments about C ; then 
 
 92*7 
 
 Tension of the belt = ^-^ x tension of spring, 
 ' 
 
 = 2*7 x tension of spring. 
 
 Also the diameter of the pulley B = 33 '6 cms. and the thick- 
 ness of the belt =1*6 cm. 
 
 Hence the velocity of the centre of the belt in centimetres per 
 second = 1*845 x revolutions of dynamo per minute, and, therefore, 
 
 Power transmitted by the belt in ergs per second 
 
 = 2*7 x 1*845 x 981 x tension of spring x revolutions per minute, 
 assuming the value of g to be 981. 
 
 We may more conveniently express the power in watts 
 (= 10 7 ergs per second), and write 
 
 Power in watts 
 
 = '0004887 x tension of spring x revolutions per minute. 
 
 The potential between the terminals of the generator was 
 measured by one of Sir William Thomson's graded galvanometers, 
 previously standardised by a Clark's cell, which had been compared 
 with other Clark's cells, of which the electromotive force was 
 known by comparison with Lord Rayleigh's standard. The current 
 between the two machines was measured by passing it through a 
 known resistance, the difference of potential between the ends of 
 the resistance being determined by direct comparison with the 
 Clark's standard cell, according to Poggendorffs method. As 
 experiments were made with currents of large magnitude, it was 
 important that the temperature coefficient of the resistance should 
 be as low as possible. To this end we found a resistance-frame 
 constructed of platinoid wire of great value. The temperature 
 coefficient of this alloy is only 0*021 per cent, per degree Centi- 
 grade. (Proc. Roy. Soc., vol. 38, p. 265 (1885).) 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 109 
 
 The resistances of the armatures and magnets of the two 
 
 machines are as follows : 
 Generator . . 
 Motor 
 
 armature 
 magnets 
 armature 
 magnets 
 
 Ohms. 
 
 0-009947 
 16-93 
 
 0-009947 
 16-44. 
 
 The resistance of the leads connecting the two machines was 
 0'00205 ohm, and of the standard resistance 0'00586 ohm. 
 
 In all determinations of resistance, the value of the B.A. ohm 
 was taken as 0'9867 x 10 9 c.g.s. units, according to Lord Rayleigh's 
 determination. 
 
 The diagram shows the electrical connexions between the two 
 machines with the rheostat r inserted in the magnets of the motor 
 dynamo. 
 
 Resistance 
 for measuring current 
 
 P 
 
 Magnet coils 
 l VSA/VVVV\AAAAAA / v 
 
 Terminals of machine 
 acting as-motor 
 
 |V^AAA/^/WV^VWV^A 
 
 Magnet coils 
 
 'WVWWWWWVAA-O 
 
 Terminals of machine 
 acting as generator 
 
 vwwwwwwv 
 
 Resistance-for adjusting 
 
 field of motor 
 
 /VVW\AAA/VWW\A/H 
 
 FIG. 13. 
 
 In order to ascertain the friction of bending the belt round 
 the pulley B, and of the journals of the dynamo, a preliminary 
 experiment was made with the dynamometer. The combination 
 was run at a speed of 814 revolutions per minute with the 
 dynamos on open circuit and the tension of the spring observed 
 9979 grammes. The engine was then reversed, and the dynamos 
 run at the same speed and the tension of the spring again 
 
110 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 observed 3629 grammes. The difference of the two readings 
 gives twice the power absorbed in friction, viz.: 1262 watts for 
 the two machines, or 631 watts per machine. This is excluded 
 entirely from the subsequent determinations of efficiency, as 
 being a quantity dependent on such arbitrary conditions as the 
 lubrication of the journals, the weight of the belt, and the angle 
 it makes with the horizontal. 
 
 In Table I. column I. is the speed of the dynamos ; column II. 
 is the reading of the spring in grams; column III. is the power 
 transmitted by the belt in watts ; column IV. is the potential at 
 the terminals of the generator ; column V. is the current passing 
 
 TABLE I. 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 
 Revolutions 
 
 
 
 
 
 
 
 
 per 
 
 Grams. 
 
 Watts 
 
 Volts 
 
 Amperes 
 
 Ohms 
 
 Watts 
 
 
 minute 
 
 
 
 
 
 
 
 1 
 
 810 
 
 8,392 
 
 3,322 
 
 129-1 
 
 21-6 
 
 1-39 
 
 13 
 
 2 
 
 801 
 
 9,299 
 
 3,640 
 
 127-2 
 
 72-0 
 
 1-39 
 
 75 
 
 3 
 
 811 
 
 11,113 
 
 4,405 
 
 125-8 
 
 150-0 
 
 2-72 
 
 267 
 
 4 
 
 808 
 
 10,433 
 
 4,119 
 
 124-4 
 
 186-0 
 
 2-72 
 
 397 
 
 5 
 
 792 
 
 10,660 
 
 4,124 
 
 116-5 
 
 211-0 
 
 2-72 
 
 499 
 
 6 
 
 798 
 
 16,897 
 
 6,589 
 
 110-6 
 
 351-0 
 
 4-59 
 
 1,309 
 
 7 
 
 764 
 
 17,690 
 
 6,605 
 
 110-12 
 
 358-0 
 
 4-09 
 
 1,360 
 
 8 
 
 766 
 
 17,804 
 
 6,665 
 
 110-6 
 
 360-0 
 
 4-59 
 
 1,375 
 
 9 
 
 778 
 
 16,556 
 
 6,294 
 
 102-3 
 
 369-0 
 
 4-09 
 
 1,436 
 
 10 
 
 756 
 
 20,412 
 
 7,541 
 
 96-8 
 
 446-0 
 
 4-59 
 
 2,070 
 
 11 
 
 808 
 
 9,526 
 
 3,765 
 
 119-3 
 
 36-8 
 
 2-72 
 
 25 
 
 12 
 
 802 
 
 3,855 
 
 1,512 
 
 113-5 
 
 No current 
 
 
 
 
 13 
 
 814 
 
 3,175 
 
 1,262 
 
 
 
 
 
 
 
 VIII. 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 1 
 
 4 
 
 984 
 
 861 
 
 77 
 
 4,720 
 
 691 
 
 5,411 
 
 2 
 
 51 
 
 955 
 
 837 
 
 112 
 
 11,096 
 
 805 
 
 11,901 
 
 3 
 
 223 
 
 935 
 
 709 
 
 295 
 
 20,896 
 
 988 
 
 21,884 
 
 4 
 
 344 
 
 914 
 
 695 
 
 388 
 
 25,256 
 
 691 
 
 25,949 
 
 5 
 
 443 
 
 801 
 
 608 
 
 453 
 
 26,590 
 
 660 
 
 27,250 
 
 6 
 
 1,222 
 
 722 
 
 455 
 
 1,101 
 
 41,433 
 
 890 
 
 42,323 
 
 7 
 
 1,268 
 
 716 
 
 473 
 
 1,131 
 
 42,087 
 
 828 
 
 42,915 
 
 8 
 
 1,289 
 
 722 
 
 455 
 
 1,152 
 
 42,494 
 
 836 
 
 43,330 
 
 9 
 
 1,354 
 
 618 
 
 408 
 
 1,178 
 
 40,314 
 
 650 
 
 40,964 
 
 10 
 
 1,979 
 
 554 
 
 348 
 
 1,670 
 
 46,244 
 
 459 
 
 46,704 
 
 11 
 
 13 
 
 841 
 
 637 
 
 116 
 
 5,998 
 
 1,066 
 
 7,064 
 
 12 
 
 
 
 
 
 
 756 
 
 
 13 
 
 
 
 
 
 
 631 
 
 
 
 
 
 
 
 
 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 Ill 
 
 in the external circuit between the two machines ; column VI. is 
 the resistance introduced into the magnets of the motor by the 
 rheostat ; column VII. is the power absorbed in the armature of 
 the generator ; column VIII. is the power absorbed in the arma- 
 ture of the motor; column IX. is the power absorbed in the 
 magnets of the generator; column X. is the power absorbed in the 
 magnets of the motor ; column XI. is the power absorbed in the 
 connecting leads between the two dynamos, in the rheostat resist- 
 ance r, and in the standard resistance used for measuring the 
 current; column XII. is the total electrical power developed in 
 the generator ; column XIII. is half the power absorbed by the 
 combination less the known losses in the armatures, magnets, and 
 external connexions of the two machines ; column XIV. is the 
 total mechanical power given to the generator, being the sum of 
 the powers given in columns XII. and XIII. 
 
 In Table II. the percentage losses in the armature and mag- 
 nets of the generator are given, as also the sum of all other losses 
 as obtained from column XIII. in the foregoing table ; also the 
 percentage efficiency of the generator, of the motor, and of the 
 
 TABLE II. 
 
 
 I. 
 
 Per cent. 
 
 II. 
 
 Per cent. 
 
 in. 
 
 Per cent. 
 
 IV. 
 
 Per cent. 
 
 V. 
 
 Per cent. 
 
 VI. 
 
 Percent. 
 
 1 
 
 0-24 
 
 18-20 
 
 12-76 
 
 68-8 
 
 
 
 57-28 
 
 39-40 
 
 2 
 
 0-63 
 
 8-93 
 
 6-76 
 
 84-58 82-99 
 
 70-19 
 
 3 
 
 1-22 
 
 4-27 
 
 4-52 
 
 90-00 
 
 90-15 
 
 81-13 
 
 4 
 
 1-53 
 
 3-52 
 
 2-66 
 
 92-28 
 
 92-65 
 
 85-49 
 
 5 
 
 1-83 
 
 2-94 
 
 2-415 
 
 92-80 
 
 93-12 
 
 86-42 
 
 6 
 
 3-09 
 
 1-71 
 
 2-10 
 
 93-10 
 
 93-30 
 
 86-86 
 
 7 
 
 3-17 
 
 1-67 
 
 1-93 
 
 93-23 1 93-39 
 
 87-07 
 
 8 
 
 3-17 
 
 1-67 
 
 1-93 
 
 93-23 i 93-43 
 
 87-10 
 
 9 
 
 3-51 
 
 1-75 
 
 1-59 
 
 93-39 : 93-50 
 
 87-32 
 
 10 
 
 4-43 
 
 1-19 
 
 0-98 
 
 93-39 i 93-36 
 
 87-19 
 
 11 
 
 0-35 
 
 11-9 
 
 15-1 
 
 72-65 65-77 
 
 47-78 
 
 
 
 1 
 
 
 double conversion. Column I. is the percentage loss in the 
 generator armature; column II. is the percentage loss in the 
 generator magnets; column III. is the percentage sum of all 
 other losses in the generator; column IV. is the percentage 
 efficiency of the generator ; column V. is the percentage efficiency 
 of the motor; column VI. is the percentage efficiency of the 
 double conversion. 
 
112 DYNAMO-ELECTRIC MACHINERY. 
 
 In this series of experiments in all cases, from Nos. 1 to 10 
 inclusive, the brushes, both of the generator and motor, were set 
 at the non-sparking point ; but in No. 1 1 no lead was given to 
 the brushes of the generator, and, consequently, there was violent 
 sparking throughout the duration of the experiment. 
 
 In No. 12 the magnets were separately excited with a current 
 giving 113'5 volts across their terminals. The power absorbed 
 must be due entirely to local currents in the core of the armature, 
 and the energy for the reversal of magnetisation of the core twice 
 in every revolution of the armature. 
 
 No. 13 gives the results of the experiments on the friction of 
 the bearings and in bending the belt already referred to. 
 
 It will be observed that the figures in column XIII. are calcu- 
 lated by deducting the power absorbed in the armatures and 
 magnets, and extraneous resistances from the total power given to 
 the combination as measured by the dynamometer. They must 
 therefore include all the energy dissipated in the core of the 
 armature, whether in local currents or in the reversal of its 
 magnetisation ; also the energy dissipated in local currents in the 
 pole-pieces, if such exist ; also the energy spent in reversing the 
 direction of the current in each convolution of the armature as 
 they are successively short circuited by the brushes. Further, it 
 will include the waste in all the connexions of the machine from 
 the commutator to its terminals and the friction of the brushes 
 against the commutator. A separate experiment was made to 
 determine the amount of this last constituent, but it was found to 
 be too small to be capable of direct measurement by the dynamo- 
 meter. Moreover, from the manner in which the figures in this 
 column are deduced, any error in the dynamometric measurement 
 will appear wholly in them. Since, undoubtedly, the first two 
 components enumerated are the" most important, and the condi- 
 tions determining their amount are practically the same through- 
 out the series, the close agreement of the figures in the column 
 are a fair criterion of the accuracy of the observations. Probably 
 100 watts is the limit of error in any of the measurements. Such 
 an error would affect the determination of the efficiency when the 
 machines were working up to their full power to less than i per 
 cent. 
 
 It has been assumed that the sum of these losses is equally 
 
DYNAMO-ELECTRIC MACHINERY. 113 
 
 divided between the two machines. This will not accurately 
 represent the facts, as the intensities of the fields and the currents 
 passing through the armatures differ to some extent in the two 
 machines. The inequality, however, cannot amount to a great 
 quantity, and if it diminishes the efficiency of the generator it will 
 increase the efficiency of the motor by a like amount, and con- 
 trariwise. In No. 11 of the series the effect of the sparking at 
 the brushes of the generator is very marked, the power wasted 
 amounting to at least 250 watts. 
 
 If it be assumed that the dissipation of energy is the same 
 whether the magnetisation of the core is reversed by diminishing 
 and increasing the intensity of magnetisation without altering its 
 direction, or whether it is reversed by turning round its direction 
 without reducing its amount to zero, a direct approximation may 
 be made to the value of this component. (J. Hopkinson, Phil. 
 Trans., vol. 176 (1885), p. 455.) 
 
 The core has about 16,400 cubic centims. of soft iron plates, 
 hence loss in magnetising and demagnetising when the speed is 
 800 revolutions per minute = 16,400 x ^ x 13,356 ergs per second 
 = 292 watts. 
 
 Referring to Table II. it appears that the efficiency approaches 
 a maximum when the current, passing externally between the 
 two machines, is about 400 amperes. Let C be the current 
 in the armature, p its resistance, W the power absorbed in all 
 parts of the machine other than the armature, then, if the speed 
 
 is constant, the efficiency is approximately - j=^ , where 
 
 W 
 
 E is the electromotive force. This is a maximum when -^ + Cp 
 
 is a minimum, which occurs when W= C z p ; when the loss in the 
 armature is equal to the sum of all other losses. For the machines 
 under consideration the experimental results verify this deduction. 
 But in actual practice the rate of generation of heat in the 
 armature conductors, when a current of 400 amperes was passed 
 for a long period, would be so great as to trench upon the margin 
 of safety desirable in such machines. Of the total space, however, 
 available for the disposition of the conductors only about one- 
 fourth part is actually occupied by copper, the remainder being 
 taken up with insulation, and the interstices left by the round 
 H. i. 8 
 
114 DYNAMO-ELECTRIC MACHINERY. 
 
 wire. If the space occupied by the copper could be increased 
 to three-fourths of the total space available, while the cooling 
 surface remained the same, the current could be increased 75 per 
 cent, and the efficiency increased T3 per cent, approximately, as 
 all losses other than that in the armature-wires would not be 
 materially altered. 
 
 The loss in the magnets is also susceptible of reduction. It 
 has already been shown that for a given configuration of the 
 magnetic circuit and a given electromotive force the section of 
 the wire of the magnet coils is determinate. The length is, 
 however, arbitrary, since within limits the number of ampere 
 convolutions is independent of the length. An increase in the 
 length will cause a proportionate diminution in the power absorbed 
 in the magnet coils. If the surface of the magnets is sufficient to 
 dissipate all the heat generated, then the length of wire is 
 properly determined by Sir William Thomson's rule that the cost 
 of the energy absorbed must be equal to the continuing cost of 
 the conductor. 
 
 APPENDIX. 
 
 (Added Aug. 17.) 
 
 Since the reading of the present communication experiments 
 have been tried on machines having armatures wound on the plan 
 of Gramme and with differently arranged magnets; the experi- 
 ments were carried out in a closely similar manner to that already 
 described. 
 
 DESCRIPTION OF MACHINES. 
 
 The construction of these machines is shown in figs. 14, 15, and 
 16, in which fig. 14 shows an elevation, fig. 15 a section through 
 the magnets, fig. 16 a longitudinal section of the armature. It 
 will be observed that the magnetic circuit is divided. The pole- 
 pieces are of cast-iron and are placed above and below the 
 armature, and are extended laterally. The magnet cores are of 
 wrought-iron of circular section and fit into the extensions of the 
 cast-iron pole-pieces, so that the area of contact of the cast-iron is 
 greater than the area of section of the magnet. The magnetising 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 115 
 
 coils consist of 2196 convolutions on each limb of copper wire, 
 No. 17, B.W.G., in No. 1 machine, and 2232 convolutions in No. 2 
 
 FIG. 14. 
 
 machine. The pole-pieces are bored to receive the armature, 
 leaving a gap on either side subtending an angle of 41 at the axis. 
 
 FIG. 15. 
 
 The bearings are carried upon an extension of the lower pole- 
 piece. 
 
 
 
 FIG. 16. 
 
 82 
 
116 DYNAMO-ELECTRIC MACHINERY. 
 
 The following table gives the principal dimensions of the 
 
 magnets in No. 1 machine : 
 
 cms. 
 
 Length of magnet limbs between pole-pieces . 26*0 
 
 Diameter of magnet limb 15'24 
 
 Bore of fields 257 
 
 Width of pole-piece parallel to the shaft . . 24*1 
 Width of gap between poles . . . .8*6 
 
 The armature is built up of plates as in the machine already 
 described, and is carried from the shaft by a brass frame between 
 the arms of which the wires pass. 
 
 The principal dimensions are as follows : 
 
 cms. 
 
 Diameter of core . . . . . . . 241 
 
 Diameter of hole through core . . . . 14'0 
 
 Length of core over end plates . . . . 24*1 
 
 The core is wound on Gramme's principle with 160 con- 
 volutions, each consisting of a single wire, No. 10, B.W.G., the 
 wire lying on the outside of the armature in a single layer. The 
 commutator has 40 bars. 
 
 This dynamo is compound wound, and is intended for a normal 
 output of 105 volts 130 amperes, at a speed of 1050 revolutions 
 per minute. The resistance of the armature is 0'047 ohm, and of 
 the magnet shunt coils 53*7 ohms. 
 
 There is here no yoke, and consequently A 4 and 1 4 do not 
 appear in the equation. 
 
 It is necessary to bear in mind that the magnetising force 
 is that due to the convolutions on one limb, and that the areas 
 are the sums of the areas of the two limbs. In calculating in- 
 duction from E.M.F. it is also necessary to remember that two 
 convolutions in a Gramme count as one in a Hefner- Alte neck 
 armature. 
 
 A-L ; the section of the core is 245 sq. cms., allowances for 
 insulation reduce this to 220'5 sq. cms. 
 
 h ; this is assumed to be 10 cms., but it will be seen that an 
 error in this value has a much more marked effect on the 
 characteristic in this machine than in the other. 
 
 A 2 ; the angle subtended by the bored face of the pole-pieces 
 is 139, the mean of the radii of the pole-pieces and the core 
 

 DYNAMO-ELECTRIC MACHINERY. 117 
 
 is 12*45 cms. Hence the area of 139 of the cylinder of this 
 radius is 768'3 sq. cms., add to this a fringe of a width 0'8 of the 
 distance from core to pole-pieces as already found necessary for 
 the other machine, and we have 839'5 sq. cms. as the value of A 2 . 
 
 1 2 is 0*8 cm. 
 
 A 3 is 365 sq. cms. (i.e., the area of two magnet cores). 
 
 l s is 26'0 cms. 
 
 A i is taken to be 955 sq. cms., viz., double the smallest section 
 of the pole-piece. 
 
 l s is a very uncertain quantity ; it is assumed to be 15 cms. 
 
 The expression already used requires slight modification. In- 
 asmuch as the pole-pieces are of cast-iron a different function 
 must be used. Different constants for waste field must be used 
 for the field, the pole-pieces and the magnet core. We write 
 
 the function /' is taken from Hopkinson, Phil Tram., vol. CLXXVI. 
 (1885), p. 455, Plate 52. v 2 , v 3 , and v 5 were determined by experi- 
 ment as described below, their values are 
 
 v a = 1-05 
 
 v, = 1-18 
 
 v, = 1-49. 
 
 Comparing the curves in Fig. 4 with that in Fig. 17, the 
 most notable difference is that in the present case the armature 
 core is more intensely magnetised than the magnet cores. No 
 published experiments exist giving the magnetising force required 
 to produce the induction here observed in the armature core, 
 amounting to a maximum of 20,000 per sq. cm. We might, 
 however, make use of such experiments as the present to con- 
 struct roughly the curve of magnetisation of the material ; thus 
 we find that with this particular sample of iron a force of 740 
 per cm. is required to produce induction 20,000 per sq. cm. ; 
 this conclusion must be regarded as liable to considerable un- 
 certainty. 
 
 The observations on the two machines are plotted, together, 
 but are distinguished from each other as indicated. They are 
 unfortunately less accurate than those of fig. 4, and are given 
 here merely as illustrating the method of synthesis. 
 
118 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 a 
 
 
 
 
 + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S 6 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .5 
 
 
 
 
 
 + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 L 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 Q\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 tj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 \\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 * 
 
 ^+ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 \v 
 
 + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \^> 
 
 *> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ N 
 
 N 
 
 + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 N^ 1 . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 k 
 
 
 
 
 
 
 
 
 
 
 
 
 
 u 
 
 
 
 
 
 
 
 
 \ 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 ^ 
 
 fc 
 
 
 
 
 
 
 
 
 
 
 
 j 
 
 
 
 
 
 
 
 
 
 L 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 VI 
 
 < 
 
 
 
 
 
 
 
 
 
 
 _ 
 
 "\\^ 
 
 
 
 
 
 2 
 
 
 
 
 1 
 
 La 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 JS 
 
 c 
 
 
 
 
 
 \\ 
 
 
 
 
 
 
 
 
 
 
 
 
 ^j^ 
 
 ^ 
 
 
 
 
 
 I 
 
 
 ^ 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 % 
 
 V 
 
 | 
 
 
 
 
 
 ^= 
 
 __. 
 
 
 
 ^ 
 
 ^s? 
 
 ^r 
 
 
 _:m 
 
 
 === 
 
 =it 
 
 ^d^ 
 
 M 
 
 _, 
 
 - 'V 
 
 C 
 
 ooo'si >r 
 
 B 
 
 H^ 
 
 OOQ'91 | J I 
 
 ^ "a'S* 
 go 
 
 ooo'gi S s'o 
 
 S c3 Q. 
 
 OOO'frl O g" 
 
 W 
 
 sie 
 
 C H 
 
 ooo'ei ^ a E 
 
 OOO'Z. S "^ 
 
 'i 
 
 OOO'Ll o ,g Q 
 P ^ .. 
 
 1-2 
 
 OOO'O! oil 
 
 S 2 
 ooo'e S 
 
 ooo's | | | 
 
 ^ 2 h 
 
 OOO'i gj t'5 
 
 000'9 
 
 s-s 
 
 K 
 
 III 
 
 02 
 
 OOO'f - 
 
 si 
 
 OO'E 
 
 OO'Z 
 
 OO'L 
 
 8 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 119 
 
 EXPERIMENTS TO DETERMINE v 2 , v 3 , AND v s . 
 
 The method was essentially the same as is described on 
 pp. 97 and 98, and was only applied to No. 1 machine. Re- 
 ferring to fig. 18 a wire A A was taken four times round the middle 
 of one limb of the magnet, a known current was suddenly passed 
 round the magnets, the elongation of the reflecting galvanometer 
 
 A 
 
 FIG. 18. 
 
 was observed, it was found to be 214 scale divisions, giving 107 as 
 the induction through the two magnet limbs in terms of an 
 arbitrary unit. The coil was moved to the top of the limb as 
 at BE the elongation was reduced to 206 or 103 for the two 
 limbs. We take the mean induction in the magnet to be 105. 
 A wire was taken three times round the whole armature in a 
 horizontal plane as at 0(7; the elongation observed was 222 
 divisions or 74 in terms of the same units. A wire was taken four 
 times round one-half of the armature as at DD] the elongation 
 was 141, or induction in the iron of the armature 70'5, whence we 
 have 
 
 ' 
 
 It may be well to recall here that i> 2 is essentially dependent 
 on the intensity of the field, strictly the line B in fig. 17 should 
 not be straight but slightly curved. 
 
120 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 Four coils were taken round the upper pole-piece at EE ; the 
 elongation was 159, giving 79*5 on the two sides. Coils at FF 
 give a higher result, 87 '5, owing to the lines of induction which 
 pass round by the bearings of the machine, and across to the 
 
 upper ends of the magnets v 6 is taken to be 
 
 
 ^ = 118. 
 'o 
 
 EFFICIENCY EXPERIMENTS. 
 
 The method and instruments were those already described, 
 pp. 106 and 107, excepting that the current was measured by a 
 Thomson's graded galvanometer, which had been standardised 
 against a Clark's cell in the position and at the time when used. 
 The resistance of leading wires and galvanometer was 0'034 ohm, 
 the series coils introduced for compounding the machines were 
 also brought into use, and the losses due to their resistance find a 
 place in columns XII. and XIII. of the following Table III., 
 
 TABLE III. 
 
 
 
 
 
 
 
 
 i 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 .VII. 
 
 VIII. 
 
 
 Degrees 
 
 Revolutions 
 
 Grams 
 
 Watts 
 
 Volts 
 
 Amperes 
 
 Ohms 
 
 Watts 
 
 1 
 
 17-5 
 
 1098 
 
 7711 
 
 4419 
 
 100-1 
 
 139-0 
 
 00 
 
 955 
 
 2 
 
 5 
 
 1094 
 
 2722 
 
 1554 
 
 103-8 
 
 41-2 
 
 18-8 
 
 105 
 
 3* 
 
 
 
 1144 
 
 1814 
 
 1083 
 
 104-7 
 
 7-85 
 
 
 
 11 
 
 1 
 
 
 IX. 
 
 X. 
 
 XL 
 
 XII. 
 
 XIII. 
 
 XIV. 
 
 XV. 
 
 XVI. 
 
 XVII. 
 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 Watts 
 
 1 
 
 895 
 
 372 
 
 
 
 497 
 
 464 
 
 657 
 
 16,395 
 
 289 
 
 16,684 
 
 2 
 
 78 
 
 400 
 
 138 
 
 55 
 
 41 
 
 148 
 
 5,015 
 
 294 
 
 5,309 
 
 3* 
 
 3 
 
 395 
 
 409 
 
 6 
 
 1 
 
 2 
 
 1,637 
 
 128 
 
 1,765 
 
 in which column I. is lead of brushes of the dynamo, positive for 
 the generator, negative for the motor ; column II., revolutions per 
 minute ; column III., deflection of spring in grammes ; column IV., 
 watts by dynamometer ; column V., volts at terminals of generator ; 
 
 * In this experiment the direction of the current had become reversed, and 
 No. 2 machine was generator. 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 121 
 
 column VI., amperes in external circuit ; column VII., rheostat 
 resistance ; column VIII., watts in generator armature ; column IX., 
 watts in motor armature ; column X., watts in generator shunt 
 magnet coils; column XL, watts in motor shunt; column XII., 
 watts in generator series magnet coils; column XIII., watts in 
 motor series ; column XIV., watts in external resistances ; column 
 XV., total electrical power of generator ; column XVI., half the 
 sum of losses unaccounted for; column XVIL, total mechanical 
 power applied to generator. 
 
 TABLE IV. 
 
 
 Generator 
 Armature 
 
 Generator 
 Shunt 
 Coils 
 
 Generator 
 Series 
 Coils 
 
 Other 
 
 Losses 
 
 Efficiency 
 of 
 Generator 
 
 Efficiency 
 of 
 Motor 
 
 Efficiency 
 of Double 
 Conversion 
 
 1 
 
 5-8 
 
 2-2 
 
 3-0 
 
 1-9 
 
 87-1 
 
 89-0 
 
 77-5 
 
 2 
 
 2-0 
 
 7'5 
 
 1-0 
 
 5-5 
 
 84-0 
 
 92-0 
 
 77-3 
 
 Table IV. gives the losses and efficiencies as percentages in 
 exactly the same way as in Table II., excepting that another 
 column is introduced for the loss in the series coils of the magnets 
 of the generator. 
 
 [The core of the armature contains about 6500 cub. cms. of 
 iron. Hence energy of magnetising and demagnetising when the 
 speed =1100 revolutions per minute =6500 x ^^ x 13,356 in 
 ergs per second =159 watts.] 
 
 In conclusion we desire to express our indebtedness to Messrs. 
 Mather and Platt, by whom the machines we have used were 
 manufactured, and who, in placing the same at our disposal, 
 together with all facilities for carrying out our experiments at 
 their Salford Iron Works, have enabled us to put theory to the 
 test of experiment on an engineering scale. 
 
7. 
 
 DYNAMO-ELECTRIC MACHINERY*. 
 
 [From the Proceedings of the Royal Society, Vol. LI.] 
 
 Received February 15, 1892. 
 
 THE following is intended as the completion of a Paper-)- by 
 Drs J. and E. Hopkinson (Phil. Trans., 1886)f. The motive 
 is to verify by experiment theoretical results concerning the 
 effect of the currents in the armature of dynamo machines on the 
 amount and distribution of the magnetic field which were given 
 in that Paper, but which were left without verification. For the 
 sake of completeness, part of the work is given over again. 
 
 The two dynamos experimented upon were constructed by 
 Messrs Siemens Brothers and Co., and are identical as far as it is 
 possible to make them. They are mounted upon a common base 
 plate, their axles being coupled together, and are referred to in 
 this Paper respectively as No. 1 and No. 2. 
 
 Each dynamo has a single magnetic circuit consisting of two 
 vertical limbs extended at their lower extremities to form the 
 pole-pieces, and having their upper extremities connected by a 
 yoke of rectangular section. Each limb, together with its pole- 
 piece, is formed of a single forging of wrought-iron. These 
 forgings, as also that of the yoke, are built up of hammered 
 scrap iron, and afterwards carefully annealed. Gun-metal castings 
 bolted to the base plate of the machine support the magnets. 
 
 * It must not be supposed from his name not appearing in this short Paper 
 that my brother, Dr E. Hopkinson, had a minor part in the earlier Paper. He not 
 only did the most laborious part of the experimental work, but contributed his 
 proper share to whatever there may be of merit in the theoretical part of the Paper. 
 J. H. 
 
 t The Paper here referred to is that reprinted on pages 84 to 121 of this volume. 
 
DYNAMO-ELECTRIC MACHINERY. 123 
 
 The magnetizing coils on each limb consist of sixteen layers of 
 copper wire 2 mms. in diameter, making a total of 3,968 con- 
 volutions for each machine. The pole-pieces are bored out to 
 receive the armature, leaving a gap above and below subtending 
 an angle of 68 at the centre of the shaft. The opposing surfaces 
 of the gap are 1*4 cm. deep. 
 
 The following table gives the leading dimensions of the 
 machine : 
 
 cms. 
 
 Length of magnet limb 66*04 
 
 Width of magnet limb 11-43 
 
 Breadth of magnet limb 38*10 
 
 Length of yoke 38*10 
 
 Width of yoke 12*06 
 
 Depth of yoke 11*43 
 
 Distance between centres of limbs 23*50 
 
 Bore of fields 21*21 
 
 Depth of pole-piece 20*32 
 
 Thickness of gun-metal base 1 0*80 
 
 Width of gap 12'06 
 
 The armature core is built up of soft iron disks, No. 24 
 B. W. G., which are held between two end plates screwed on 
 the shaft. 
 
 The following table gives the leading dimensions of the 
 armature : 
 
 cms. 
 
 Diameter of core 18*41 
 
 Diameter of shaft 476 
 
 Length of core 38*10 
 
 The core is wound longitudinally according to the Hefner von 
 Alteneck principle with 208 bars made of copper strip, each 
 9 mms. deep by 1*8 mm. thick. The commutator is formed of 
 fifty-two hard drawn copper segments insulated with mica, and 
 the connections to the armature so made that the plane of 
 commutation in the commutator is vertical when no current is 
 passing through the armature. 
 
 Each dynamo is intended for a normal output of 80 amperes, 
 140 volts, at 880 revolutions per minute. The resistance of the 
 
124 DYNAMO-ELECTRIC MACHINERY. 
 
 armature measured between opposite bars of the commutator is 
 0'042 ohm, and of each magnet coil 13'3 ohms. 
 
 In the machine the armature core has a greater cross section 
 than the magnet cores, and consequently the magnetizing force 
 used therein may be neglected. The yoke has the same section 
 as the magnet cores, and is therefore included therein, as is also 
 the pole-piece. The formula connecting the line integral of the 
 magnetizing force and the induction takes the short form 
 
 where 
 
 n is the number of turns round magnet ; 
 
 c is the current round magnet in absolute measure ; 
 
 h the distance from iron of armature to rim of magnet; 
 
 A 2 the corrected area of field ; 
 
 / the total induction through armature; 
 
 / 3 the mean length of lines of magnetic force in magnets; 
 
 A 3 the area of section of magnets; 
 
 v the ratio of induction in magnets to induction in armature ; 
 
 / the function which the magnetizing force is of the induction 
 in the case of the machine actually taken from Dr J. 
 Hopkinson on the " Magnetization of Iron," Phil. Trans., 
 1885, Figs. 4 and 5, Plate 47. 
 
 In estimating A z we take the mean of the diameter of the 
 core and of the bore of the magnets 19'8 cms., and the angle 
 subtended by the pole face 112, and we add a fringe all round 
 the area of the pole face equal in width to the distance of the 
 core from the pole face. This is a wider fringe than was used in 
 the earlier experiments f, because the form of the magnets differs 
 slightly. The area so estimated is 906 sq. cms. 
 
 1 3 is taken to be 108'8 cms. 
 A 3 is 435*5 sq. cms. 
 
 v was determined .by the ballistic galvanometer to be 1'47. It 
 is to be expected that, as the core is actually greater in area than 
 
 * Phil. Trans. 1886; page 90 of this volume. 
 t Phil. Trans. 1886; page 95 of this volume. 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 125 
 
 the magnets, v will be more nearly constant than in the earlier 
 experiments. It was found to be constant within the limits of 
 errors of observation. 
 
 Referring to Fig. 1, the curve C is the curve # = I 3 f ( ^M , 
 
 voV 
 
 and the straight line B is the curve x = 21 2 -j- , while the full 
 
 -0.2 
 
 line D is the characteristic curve of the machine, 
 
 as given by calculation. 
 
 The marks + indicate the results of actual observations on 
 machine No. 1, and the marks the results on machine No. 2, 
 the total induction / being given by the equation : 
 
 T _ potential difference in volts x 10 s 
 208 x revolutions per second 
 
 Experiments made upon the power taken to drive the machine 
 under different conditions show that it takes about 250 watts 
 
 | Line integral of Magnetising Force 
 
 20,000 30,000 
 
 FIG. 1. 
 
 40,000 
 
 more power to turn the armature at 660 revolutions when the 
 magnets are normally excited than when they are not excited 
 at all. The volume of the core is 9,465 cub. cms., or in each 
 complete cycle the loss per cubic centimetre is 
 
 The loss by hysteresis is about 13,000 (Phil. Trans., 1885, 
 p. 463) if the reversals are made by variation of intensity of the 
 magnetizing force and the iron is good wrought-iron. This result 
 
126 DYNAMO-ELECTRIC MACHINERY. 
 
 is similar to that in the earlier Paper*, where it is shown that the 
 actual loss in the core, when magnetized, is greater than can be 
 accounted for by the known value of hysteresis. 
 
 EFFECTS OF THE CURRENT IN THE ARMATURE. 
 
 Quoting from the Royal Society Paper [page 99 of this 
 volume], "The currents in the fixed coils around the magnets 
 are not the only magnetizing forces applied in a dynamo machine 
 the currents in the moving coils of the armature have also their 
 effect on the resultant field. There are in general two inde- 
 pendent variables in a dynamo machine the current around the 
 magnets and the current in the armature; and the relation of 
 E.M.F. to currents is fully represented by a surface. In well- 
 constructed machines the effect of the latter is reduced to a 
 minimum, but it can be by no means neglected. When a section 
 of the armature coils is commutated, it must inevitably be 
 momentarily short circuited ; and if at the time of commutation 
 the field in which the section is moving is other than feeble, 
 a considerable current will arise in that section, accompanied by 
 waste of power and destructive sparking 
 
 " Suppose the commutation occurs at an angle \ in advance of 
 the symmetrical position between the fields, and that the total 
 current through the armature be C, reckoned positive in the 
 direction of the resultant E.M.F. of the machine, i.e., positive when 
 the machine is used as a generator of electricity. Taking any 
 closed line through magnets and armature, symmetrically drawn as 
 ABCDEFA [Fig. 9, p. 101], it is obvious that the line integral of 
 magnetic force is diminished by the current in the armature 
 included between angle X in front and angle X behind the plane 
 of symmetry. If m be the number of convolutions of the arma- 
 ture, the value of this magnetizing force is 4?r(7 - = 4Xm(7 
 
 opposed to the magnetizing force of the fixed coils on the magnets. 
 Thus if we know the lead of the brushes and the current in the 
 armature we are at once in a position to calculate the effect on 
 the electromotive force of the machine. A further effect of the 
 current in the armature is a material disturbance of the distri- 
 bution of the induction over the bored face of the pole-piece ; the 
 force along BC [Fig. 9] is by no means equal to that along DE. 
 * See page 113 of this volume. 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 127 
 
 Draw the closed curve BCGHB, the line integral along CG, and 
 HE is negligible. Hence the difference between force HG and 
 
 EG is equal to 4^0 ^ - = 2tcmC, where K is the angle COG" 
 
 To verify this formula is one of the principal objects of this 
 Paper. 
 
 A pair of brushes having relatively fixed positions near 
 together, and insulated froiri the frame and from one another, 
 are carried upon a divided circle, and bear upon the commu- 
 tator. The difference of potential between these brushes was 
 measured in various positions round the commutator, the current 
 in the armature, the potential difference of the main brushes, and 
 the speed of the machine being also noted. 
 
 The results are given in Figs. 2, 3, 4, and 5, in which the 
 ordinates are measured potential differences, and the abscissae are 
 angles turned through by the exploring brushes. The potential 
 differences in Fig. 2 were measured by a Siemens voltmeter, and 
 each ordmate is therefore somewhat smaller than the true value* 
 owing to the time during which the exploring brushes were not 
 actually in contact with the commutator segments. But this does 
 not affect the results, because the area is reduced in the same 
 proportion as the potential differences. In Figs. 3, 4, and 5 
 the potential differences were taken on one of Sir William 
 Thomson's quadrant electrometers, and are correct. 
 
 Take Fig. 2, in which machine No. 1 is a generator. A 
 centimetre horizon tally represents 10 of lead*, and the ordinates 
 
 200 
 
 represent differences of potential between the brushes. The area 
 of the curve is 61*3 sq. cms., and represents 130 volts and a total 
 
 * In this paper the diagrams are on half the scale of the original, so that 10 
 of lead is really represented by half a centimetre horizontally. 
 
128 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 field of -. x x 10 8 = 4'31 x 10 6 lines of induction. This is, 
 
 of course, not the actual field, which is 3 per cent, greater on 
 account of the resistance of the armature, but is represented by 
 an area 3 per cent, greater. An ordinate of 1 cm. will represent 
 
 4*31 
 
 an induction of -^-^ x 10 6 
 bl'o 
 
 7'0 x 10 4 lines in 10. The area of 
 
 10 is 39'5 x 1-73 = 68'3 sq. cms.* Hence an ordinate of 1 cm. 
 represents an induction of 1,024 lines per square centimetre. The 
 difference between ordinates at 50 and 140 is 2'5 ; hence the 
 difference of induction is actually 2,560. Theoretically, we have 
 * = ITT, ra = 104, 0=9-4. Therefore 2*m(7= 3,072, and this is the 
 line integral of magnetizing force round the curve. 
 
 Let A be the induction at 50 and A + 8 at 140 : these also 
 are the magnetizing forces. Hence (A + ) 1*4 -41*4 = 2/cmC ; 
 S = 2,200, as against 2,560 actually observed. 
 
 Take Fig. 3, in which No. 2 machine is a motor. The 
 
 total field = x ^ x 10 8 = 515 x 10 6 lines of induction. Since 
 104 20 
 
 210 
 
 FIG. 3. 
 
 the area of the diagram is 53'5 sq. cms., an ordinate of 1 cm. 
 x 10 6 = 96 x 10 4 lines of induction in 10. Hence an 
 
 ordinate of 1 cm. represents an induction of - = 1,400 lines 
 
 oo'o 
 
 per square centimetre. The difference between ordinates at 320 
 and at 230 is 2'0 ; hence the difference of induction is actually 
 
 o^rv rm. j.- n 2/cmC 34 x 104 x 1T4 
 
 2,800. Theoretically, we have * = - ; - =2,666, 
 
 I 1'4 
 
 as against 2,800 actually observed. 
 
 * In calculating this area, the allowance for fringe at ends of armature is taken 
 less than before, because the form of opposing faces differs. 
 
DYNAMO-ELECTRIC MACHINERY. 
 
 129 
 
 In Fig. 4, No. 1 machine is a generator. The total field 
 
 x i * x 10* = 3-97 x 10 6 lines. The area of the diagram 
 l^*o 
 
 3'97 
 is 90'9 sq. cms., and therefore an ordinate of 1 cm. = - x 10 6 
 
 4'37 x 10 4 lines in 10. Hence an ordinate of 1 cm. represents 
 
 200 
 
 an induction of - ' aQ = 639 lines per square centimetre, 
 boo 
 
 The difference between ordinates at 50 and at 140 is 4*5 ; hence 
 the difference of induction is actually 2,877. Theoretically, we 
 
 ZfcmC 3fx 104x12-9 OA1 . 
 
 have j = -^fTT- - = 3,010, as against 2,877. 
 * 
 
 310 
 
 260 
 
 310 
 
 FIG. 5. 
 
 In Fig. 5, No. 2 machine is a motor. The total field 
 
 1 
 
 area ^ t ^ ie Diagram is 
 
 
 
 104 X 12-3 
 
 x = 
 
 i. 
 
 9 
 
130 
 
 DYNAMO-ELECTKIC MACHINERY. 
 
 4'96 
 
 112*2 sq. cms., and therefore an ordinate of 1 cm. = ^r~ x 10 6 
 
 * 
 
 4'42 x 10 4 lines in 10. Hence an ordinate of 1 cm. represents 
 
 4*42 
 an induction of - x 10 4 = 647 lines per square centimetre. 
 
 Oo'o 
 
 The difference between ordinates at 323 and at 233 is 4'2; 
 hence the difference of induction is actually 2,718. Theoretically, 
 
 2/cmG 3| x 104 x 12 3 
 
 we have j = - r-j = 2,8/0, as against 2,718 actually 
 I 14 
 
 observed. 
 
 At page 103 of the preceding Paper on Dynamo-Electric 
 Machinery it is shown that 
 
 .,/ 4Xm(7\ 
 
 F 4tirnc -- - 1 , 
 
 21 2 
 
 where I F (4nrnc) is the characteristic curve when 0=0, and X 
 is the lead of the brushes. 
 
 The following is an endeavour to verify this formula. The 
 potentials both upon the magnets and upon the brushes were 
 taken by a Siemens voltmeter, and are rough. The speeds were 
 taken by a Buss tachometer, and there is some uncertainty about 
 the precise lead of the brushes, owing to the difficulty in de- 
 termining the precise position of the symmetrical position between 
 the fields, and also to the width of the contacts on the com- 
 mutator. 
 
 It was necessary, in order to obtain a marked effect of the 
 armature reaction, that the magnet field should be comparatively 
 small, that the current in the armature should be large, and the 
 leads of the brushes should be large. 
 
 The two machines had their axles coupled so that No. 1 could 
 be run as a generator, and No. 2 as a motor. The magnets were 
 in each case coupled parallel, and excited by a battery each 
 through an adjustable resistance. The two armatures were 
 coupled in series with another battery, and the following ob- 
 servations were made : 
 
 
 Potential on 
 Magnets in volts 
 
 Potential on 
 Brushes 
 
 Speed per 
 Minute 
 
 Current in 
 Amperes 
 
 Lead of 
 Brushes 
 
 No. 1 
 
 No. 2 
 
 2424 
 2929 
 
 6667 
 
 8684 
 
 880 
 
 880 
 
 102103 
 102103 
 
 26 
 
 29 
 
DYNAMO-ELECTRIC MACHINERY. 
 From which we infer: 
 
 131 
 
 
 Current in 
 Magnets 
 
 vnc 
 
 Corrected Potential 
 for Resistance of 
 Armature 
 
 Total 
 Induction, 
 
 I 
 
 No. 1 
 
 1-78 
 
 8,900 
 
 70-8 
 
 2-30xlO 
 
 No. 2 
 
 2-15 
 
 10,750 
 
 80-7 
 
 2-65xlO 
 
 As there was uncertainty as to the precise accuracy of the 
 measurements of potential, it appeared best to remeasure the 
 potentials with no current through the armature with the Siemens 
 voltmeter placed as in the last experiment. Each machine was 
 therefore run on open circuit with its magnets excited, and its 
 potential was measured. 
 
 
 Potential on Magnets 
 in volts 
 
 Potential on 
 Brushes 
 
 Speed per 
 Minute 
 
 Potential at 
 880 Revs. 
 
 No. 1 
 
 2525 
 
 9090 
 
 880 
 
 90-0 
 
 No. 2 
 
 2828 
 
 7980 
 
 715710 
 
 98-2 
 
 From which, since the formula is reduced to 
 
 - 4\mC), 
 the characteristic being practically straight, we infer : 
 
 I = 4* 
 
 _& 2 
 
 
 Potential on 
 Magnets 
 
 Potential on 
 Brushes 
 
 Induction, 
 
 I = F (47TOC) 
 
 No. 1 
 
 24 
 
 86-4 
 
 2-82xl0 6 
 
 No. 2 
 
 29 
 
 101-7 
 
 3 -30 x 10* 
 
 We have further : 
 X = 0'45 for No. 1; 
 
 = 2,920; 
 
 5 for No. 2; 
 
 4- 2 = 443,800. 
 21s 
 
 92 
 
132 
 
 DYNAMO-ELECTRIC MACHINERY. 
 
 
 
 
 
 
 / 4X771^7 \ 
 
 
 4XmC 
 
 V \\rnC 2 
 
 4Xm(7 
 
 _,/ 4Xm(7\ 
 F I d-jrwr* 1 
 
 \ " / 
 
 
 V 
 
 v 2Z 3 
 
 v 
 
 
 -^4xa| 
 
 No. 1 
 
 1,314 
 
 199,700 
 
 7,586 
 
 2-41 x 10 
 
 2-21 x 10 
 
 No. 2 
 
 1,460 
 
 221,900 
 
 9,290 
 
 2-90xlO 
 
 2-68xlO 
 
 It has already appeared that experiment gives for / in No. 1 
 2-3 x 10 6 , and in No. 2 2'65 x 10 6 . The difference is probably due 
 to error in estimating the lead of the brushes, which is difficult, 
 owing to uncertainty in the position of the neutral line on open 
 circuit. 
 
8. 
 
 ON THE THEORY OF ALTERNATING CURRENTS, 
 PARTICULARLY IN REFERENCE TO TWO ALTER- 
 NATE-CURRENT MACHINES CONNECTED TO THE 
 SAME CIRCUIT. 
 
 [From the Proceedings of the Institution of Electrical 
 Engineers, pp. 321. Nov. 13, 1884.] 
 
 IN my lecture on Electric Lighting, delivered before the 
 Institution of Civil Engineers last year*, I considered the 
 question of two alternate-current dynamo machines connected 
 to the same circuit, but having no rigid mechanical connection 
 between them, and I showed that, if two such machines be 
 coupled in series, they will tend to nullify each other's effect ; if 
 parallel, to add their effects f. The subject is one which already 
 has practical importance and application, and may have much 
 more in the future; it is also one suited for discussion, and 
 upon which discussion is desirable. I therefore venture to bring 
 before the Society what I said in my lecture, some other ways of 
 looking at the same subject, and an experimental verification, 
 
 * This Paper is reprinted on pages 57 to 83 of this volume. 
 
 t '22nd November, 1884. My attention has only to-day been called to a paper by 
 Mr Wilde, published by the Literary and Philosophical Society of Manchester, 
 December 15, 1868, also Philosophical Magazine, January, 1869. Mr Wilde fully 
 describes observations of the synchronising control between two or more alternate- 
 current machines connected together. I am sorry I did not know of his obser- 
 vations when I lectured before the Institution of Civil Engineers, that I might have 
 given him the honour which was his due. If his paper had been known to those 
 who have lately been working to produce large alternate-current machines, it would 
 have saved them both labour and money. 
 
134 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 together with solutions of other problems requiring similar 
 treatment. 
 
 The general explanation amounting to proof, so far as machines 
 in series are concerned, is given in the following extract from my 
 lecture : 
 
 "There remains one point of great practical interest in 
 connection with alternate-current machines, How will they 
 behave when two or more are coupled together, to aid each other 
 in doing the same work ? With galvanic batteries, we know very 
 well how to couple them, either in parallel circuit or in series, so 
 that they shall aid, and not oppose the effects of each other ; but 
 with alternate-current machines, independently driven, it is not 
 quite obvious what the result will be, for the polarity of each 
 machine is constantly changing. Will two machines coupled 
 together run independently of each other, or will one control the 
 movement of the other in such wise that they settle down to 
 conspire to produce the same effect, or will it be into mutual 
 opposition ? It is obvious that a great deal turns upon the 
 answer to this question, for in the general distribution of electric 
 light it will be desirable to be able to supply the system of 
 conductors from which the consumers draw by separate machines, 
 which can be thrown in and out at pleasure. Now I know it is 
 a common impression that alternate-current machines cannot be 
 worked together, and that it is almost a necessity to have one 
 enormous machine to supply all the consumers drawing from one 
 system of conductors. Let us see how the matter stands. 
 Consider two machines independently driven, so as to have 
 approximately the same periodic time and the same electro- 
 motive force. If these two machines are to be worked together, 
 they may be connected in one of two ways: they may be in 
 parallel circuit with regard to the external conductor, as shown 
 by the full line in Fig. 1, that is, their currents may be added 
 algebraically and sent to the external circuit ; or they may be 
 coupled in series, as shown by the dotted line, that is, the whole 
 current may pass successively through the two machines, and the 
 electromotive force of the two machines may be added, instead of 
 their currents. The latter case is simpler. Let us consider 
 it first. I am going to show that if you couple two such 
 alternate-current machines in series, they will so control each 
 
ON THE THEORY OF ALTERNATING CURRENTS. 
 
 135 
 
 other's phase as to nullify each other, and that you will get no 
 effect from them ; and, as a corollary from that, I am going to 
 show that if you couple them in parallel circuit, they will work 
 perfectly well together, and the currents they produce will be 
 
 Fm. 1. 
 
 added; in fact, that you cannot drive alternate-current machines 
 tandem, but that you may drive them as a pair, or, indeed, any 
 number abreast. In diagram, Fig. 2, the horizontal line of 
 abscissae represents the time advancing from left to right ; the 
 full curves represent the electromotive forces of the two machines 
 
 T ni II iv 
 
 FIG. 2. 
 
 not supposed to be in the same phase. We want to see whether 
 they will tend to get into the same phase or to get into opposite 
 phases. Now, if the machines are coupled in series, the resultant 
 electromotive force on the circuit will be the sum of the electro- 
 motive forces of the two machines. This resultant electromotive 
 force is represented by the broken curve III ; by what we have 
 already seen in Formula IV (p. 65), the phase of the current must 
 lag behind the phase of the electromotive force, as is shown in the 
 
 diagram by curve IV, thus . . . Now, the work done 
 
 in any machine is represented by the sum of the products of 
 
136 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 the currents and of the electromotive forces, and it is clear 
 that as the phase of the current is more near to the phase of 
 the lagging machine // than to that of the leading machine 
 /, the lagging machine must do more work in producing elec- 
 tricity than the leading machine; consequently its velocity will 
 be retarded, and its retardation will go on until the two machines 
 settle down into exactly opposite phases, when no current will 
 pass. The moral therefore is, do not attempt to couple two 
 independently driven alternate-current machines in series. Now 
 for the corollary. A, B, Fig. 1, represent the two terminals of 
 an alternate-current machine ; a, b the two terminals of another 
 machine independently driven. A and a are connected together, 
 and B and b. So regarded, the two machines are in series, and 
 we have just proved that they will exactly oppose each other's 
 effects that is, when A is positive, a will be positive also ; when 
 A is negative, a is also negative. Now, connecting A and a 
 through the comparatively high resistance of the external circuit 
 with B and b, the current passing through that circuit will not 
 much disturb, if at all, the relations of the two machines. Hence, 
 when A is positive, a will be positive, and when A is negative, a 
 will be negative also; precisely the condition required that the 
 two machines may work together to send a current into the 
 external circuit. You may therefore, with confidence, attempt to 
 run alternate-current machines in parallel circuit for the purpose 
 of producing any external effect. I might easily show that the 
 same applies to a larger number : hence, there is no more difficulty 
 in feeding a system of conductors from a number of alternate- 
 current machines than there is in feeding it from a number of 
 continuous-current machines. A little care only is required that 
 the machine shall be thrown in when it has attained something 
 like its proper velocity. A further corollary is that alternate 
 currents with alternate- current machines as motors may theoreti- 
 cally be used for the transmission of power*." 
 
 Although the proof of this corollary regarding motors is similar 
 to what we have just been going through, it may be instructive to 
 give it. In the accompanying diagrams, Figs. 3 and 4, the full 
 
 * " Of course, in applying these conclusions, it is necessary to remember that 
 the machines only tend to control each other, and that the control of the motive 
 power may be predominant, and compel the two or more machines to run at different 
 speeds." 
 
ON THE THEORY OF ALTERNATING CURRENTS. 
 
 137 
 
 lines I and II represent the electromotive forces of the two 
 machines (generator and receiver); the dotted line, curve III 
 (. . . .), the resultant electromotive force; and the curve IV, 
 the resulting current, each in terms of the time, as abscissae. 
 The only difference between the two diagrams is, that in Fig. 3 
 
 FIG. 3. 
 
 the two machines have equal electromotive forces, whilst in Fig. 4 
 the receiving machine has double the electromotive force of the 
 generator. In both figures the receiving machine lags behind 
 the phase of direct opposition to the generator by one quarter of 
 
 FIG. 4. 
 
 a period, or something less. Now observe, the resultant electro- 
 motive force must be in phase behind the receiver, but in advance 
 of the generator. Also observe, the current must be in phase 
 behind the resultant electromotive force, and may be one quarter 
 of a period behind, provided only the self-induction be large 
 enough compared with the resistance. The current will then be 
 less than a quarter period behind the generator. This machine 
 will do work upon the current, but the current will be more than 
 a quarter period behind the receiving machine ; therefore in the. 
 receiver the current does work upon the machine. 
 
138 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 The subject is illustrated by the following problems. Of 
 course any of them may be treated more generally by considering 
 the machines as unequal, or by introducing other periodic terms, 
 but I do not see that this would throw more light on the 
 subject : 
 
 I. Two alternate-current machines, equal in all respects, are 
 connected in series and independently driven at the same speed, 
 to determine the current, etc., in each. 
 
 Let 7 be the coefficient of self-induction of each, r the 
 resistance, x the current at time t, and E sin ~- (t 4- T) and 
 
 o 
 
 E sin -~j (t r) the electromotive forces. Then regarding the co- 
 efficient of self-induction as constant, which it is not exactly, and 
 neglecting the effect of currents other than those in the copper 
 wire, the equation of motion is 
 
 27^' + 2nc = E I sin ~ (t + r) + sin (t - T) 
 
 , T-, . a ii v ZTTT 
 
 or yx + rx = E sin =,- cos -~- ; 
 
 whence 
 
 * W ?/ f 2irf 2^7 
 
 {rsm-^-- -^cos -^ 
 
 Work done by the leading machine per second 
 
 27TT 
 
 T~ f 2-7TT 27T7 . 27TT) 
 
 rcos -jr - ^'siii -yj 
 
 4 
 
 . 
 
 47TT 
 
 From this at once follows that the leading machine does least 
 
 T 
 work, and will tend to increase its lead until r = -T , when the two 
 
 T< 
 
 machines will neutralise each other, as already proved geometri- 
 cally. The leading machine may actually become a motor and do 
 
ON THE THEORY OF ALTERNATING CURRENTS. 139 
 
 mechanical work, although its electromotive force is precisely equal 
 to that of the following machine. 
 
 Considering the important case when r is negligible, we have 
 
 2-7TT 2-n-t 
 
 Ecos 
 
 27T 7 
 
 T 
 
 . 47TT 
 T 
 
 rate of working = 
 
 T 
 This is the maximum when T = , and then it is equal to the maxi- 
 
 o 
 
 mum work which can be obtained from either machine when 
 connected to a resistance only, which occurs when that resistance 
 
 is -^7; the current, also, is the same as when the maximum 
 
 work is being done on resistance, and is -j= of the current the 
 
 y2 
 
 machine will give if short-circuited. The difference of potential 
 between the two leads connecting the machines, whether r = 
 
 O 4- O 
 
 or not, is E cos -~- sin -^- . If there be no work done on the 
 
 T 
 receiving machine and r = 0, T = -j , and the amplitude of the 
 
 difference of potential between the leads is E\ if, on the other 
 hand, the maximum work is being transmitted, the potential 
 
 measured will be -j= of that observed when either machine is run 
 on open circuit. 
 
 II. Two machines are coupled parallel and connected to an 
 external circuit resistance R. 
 
 Let a?!, #2 be currents in the two machines. The external 
 current will be ^ + #2, and consequently the difference of potential 
 at the junction, R (x l + # 2 ). 
 
 Let the electromotive forces of the two machines regarded in 
 this case as connected parallel be E sin tr^- and let the self- 
 induction and resistance of each be 2y and 2r. 
 
140 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 The equations of motion then are 
 
 E sin 27r+r) -R 
 
 = E sin E (^ + # 2 ) ; 
 
 whence 
 
 7 (a?/ -f # 2 ') + (E + r) (x l + x 2 ) = E sin ~ . cos -^r 
 and 
 
 7 (#/ - a?/) + r (x l - x z ) = E cos ^- sin ^7- . 
 
 Solving these 
 
 ^ 2-7TT 
 
 S ~~ 27T7 
 
 . 
 
 ~ 
 
 ( 2ir 
 
 V C S ~T 
 
 2 
 
 Electrical work done by the leading machine 
 2?r (^ + T) 
 
 2-7TT 2?T7 . 2-7TT 2-7TT 
 
 + R ) cos2 -^ --- ^r sin -JIT cos -^- 
 
 2-7TT 2?T . 2-7TT 2-7TT 
 
 This expression shows that ^e leading machine does most ^vork 
 
 2^ 
 m aW cases. Suppose r is small compared with R and -^ , also 
 
 O 
 
 that .R = ^, we have the work done per second 
 
 , 2-7TT 2-7TT 27TT) 
 
 -~- 
 
ON THE THEORY OF ALTERNATING CURRENTS. 141 
 T 
 
 Make r = ^-, and we see that the following machine will then 
 
 o 
 
 do no work ; when r exceeds this, the following machine becomes a 
 motor and absorbs electrical work. 
 
 III. Suppose the terminals of an alternate-current machine 
 are connected to a pair of conductors, the difference of potential 
 between which is completely controlled by connection with other 
 alternate-current machines. 
 
 Let 7 and R be the coefficient of self-induction and the 
 resistance of the machine and its own conductors up to the point 
 at which the potential is completely controlled. Let the differ- 
 
 ence of potential of the main conductors be A sin ~ , and let the 
 
 electromotive force of the machine be B sin ^ - . 
 Equation of motion is 
 
 7 
 whence 
 
 D . 2?r (t - T) 
 
 B sin - ^ A sin -_- 
 
 . 27T (t T) %7Ty 2-7T (t T) 
 
 
 Electrical work done by the machine in unit of time 
 
 D . 27T (t-r) 
 = ic5sin - -TJ 
 
 If T be positive, that is, if the machine be lagging in its phase, 
 work done is less than if it be negative ; hence r will tend to zero, 
 or the machine will tend to adjust itself to add its currents to that 
 of the system of conductors. The machine may act as a motor 
 even though its electromotive force be greater than that of the 
 system, for let 
 
 R 27T<f> 
 
 T 
 
142 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 work (electric) done by machine 
 
 B*R AB 
 
 sin - 
 
 T 
 
 this has a minimum value when <j> + r = , and then the me- 
 chanical work done by machine or electrical work received by the 
 machine 
 
 B 
 
 RB 
 
 and this is positive provided 
 
 A R 
 B> 
 
 There are two or three other problems of sufficient interest 
 to make it worth while giving them here, although not directly 
 relating to alternate-current machines coupled together. 
 
 IV. To determine the law of an alternate current through an 
 electric arc. 
 
 It has been shown by Joubert that in an arc the difference of 
 potential is of approximately constant numerical value, reversing 
 its value discontinuously with the reversal of the current, probably 
 at the instant of reversal of current. We shall assume, then, 
 that there is in the arc a constant electromotive force, A, always 
 opposed to the current, except when the current ceases, and that 
 then its value is zero. 
 
 The equation of motion is 
 
 / T-V n ^Trt 
 
 70? -)- Rx E sin-^r + A, 
 
 the negative sign being taken when x is positive, the positive 
 when x is negative. Solving generally 
 
 _ A E 
 
ON THE THEORY OF ALTERNATING CURRENTS. 143 
 
 this equation will continuously hold good for a half period from 
 x = to x = again, but at each half period the arbitrary 
 constant C is changed with the sudden change of sign of A. 
 It is determined by the consideration that, if for a certain value 
 
 T 
 
 t of t, x should vanish, it shall vanish again when t = t + ^ . This 
 
 2i 
 
 applies to the case when E is sufficiently large, as is practically 
 the case, but if the current should cease for a finite time this 
 condition will be varied, and instead of it we have the condition 
 
 x = when E sin -~- = A. This latter case I do not propose to 
 consider further. 
 
 27PY 27T^ 
 
 Let -j* = tan 
 
 A* E 
 
 T 
 
 Putting t = t and t = +- we have 
 
 -i ^ 
 
 '~ 
 
 _R nr 
 
 + Ce y . e * ' 
 
 equations to determine and C. 
 Eliminating C, 
 
 RE . 27r(t -t l ) ,RT 
 
 Having obtained t 0) C is given by equation 
 
 This gives the complete solution of the problem. 
 
 * That is, taking a half-period in which x is positive and the negative sign 
 affixed to A. [Eo.] 
 
144 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 A case of special importance is that in which R is small ; let 
 us therefore consider the case R = 0, the solution then is 
 
 T 
 
 yx = - E cos T~- - At 4- G. 
 LIT 2 
 
 In the same way as before 
 
 ATT 
 
 The limiting case to which the solution applies is given by 
 
 T 
 x = when t = t + ^ 
 
 c 
 
 E sin - f 
 
 whence E Z A 
 
 or A = E x 0-538. 
 
 Roughly, we may say that, in order that the current may not 
 cease for a finite time, E must be at least double of A ; A will of 
 course depend upon the length of the arc. The work done in the 
 arc will be proportional to the arithmetical mean value of the 
 current taken without regard to sign. This is of course quite a 
 different thing from the mean current as measured by an electro- 
 dynamometer. Let us examine what error is caused by estimat- 
 ing the work done in the arc as equal to the current measured by 
 the dynamometer multiplied by the mean difference of potential. 
 
 The actual work done per second 
 
 T 
 2 
 xdt 
 
 * A T / 
 = ' &' V ^ ~ 
 
 4 
 
 The mean square of the current, as measured by the electro- 
 dynamometer, is 
 
 <0 + ? 
 
 2 , T 
 
 2 * ) ' 48 7 2 ' 
 and the work done by this current is apparently the square root 
 of the above expression multiplied by A. It is easy to see that 
 this is greater in all cases than the work done, but it is worth 
 
ON THE THEORY OF ALTERNATING CURRENTS. 145 
 
 while to examine the extent of the error. If we treated the arc 
 as an ordinary resistance, we should assume work per second 
 
 A 
 
 2 
 
 Taking a fairly practical case, assume A = - E, we have actual 
 
 o 
 
 work per second 
 
 ~T~ ' 9r*V T~T 
 
 work done estimated by electro-dynamometer 
 
 nearly 
 40 V2 4 / 48 
 
 A*T 20 / 
 
 ~y TV 
 
 235 
 12"' 
 
 or nearly part too much. This will suffice to show that the 
 matter is not a mere theoretical refinement. Another erroneous 
 method of estimating the power developed in an arc is, to replace 
 by a resistance and adjust this resistance till the current, as 
 measured by an electro-dynamometer, is the same as with the 
 arc, and assume that the work done in the resistance is the same 
 as the work done in the arc. 
 
 Returning to the expression 
 
 TT 2 ^! 2 
 
 Tny ZTT v 4 
 
 we may enquire, given TA and the dimensions of the machine, 
 how ought it to be wound or its coils connected, that most work 
 may be done in the arc ? If the number of convolutions be varied, 
 E will vary as the convolutions, 7 as their square, therefore 7 x E* ; 
 
 we are therefore to determine E so that A / E 2 
 
 A 2 V 4 
 
 maximum which occurs when E=7rA. When the resistance of 
 the circuit is taken into account this result will be modified. It 
 suffices to prove that it is desirable that the potential of the 
 machine should be materially in excess of that required to main- 
 tain the arc. 
 
 H. i. 10 
 
 s a 
 
146 
 
 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 V.* In all that precedes it is assumed, not only that 7 is 
 constant, but that the copper conductor of the armature is the 
 only conductor moving in the field. If there be iron cores in the 
 armature, we shall approximate to the effect by regarding such 
 cores as a second conducting circuit. Slightly changing the 
 notation, let L be coefficient of self-induction of the copper 
 circuit, N coefficient of self-induction of the iron circuit and R 
 its resistance, /' the magnetic induction of the field magnets upon 
 the iron circuit and M the coefficient of mutual induction of the 
 two circuits, y the current in the iron. The equations of motion 
 are obtained from the expression for the energy, viz. 
 
 and are 
 
 J [La? + ZMxy + Ny* - 2/# - 2/'y}, 
 
 T > , K/r ' , T> dl 2 
 Lx' + My + Rx = -= 
 
 for in general the iron cores and the copper conductor are 
 symmetrically arranged. Assume 
 
 . 
 x = a sin j- + b cos r, 
 
 y=a sui-r 
 
 cos 
 
 and substitute in the equations of motion, we have the following 
 four equations to determine the constants, a, b, a', b', 
 
 or 
 
 and 
 
 m-p 
 
 aL + a'M+b =A\ 
 
 bL+b'M-a~mO 
 
 2?r 
 
 * Vide also Encyclopedia Britannica, article " Lighting." 
 
ON THE THEORY OF ALTERNATING CURRENTS. 
 
 147 
 
 These equations contain the solution of the problem, but are 
 too cumbersome to be worth while solving generally ; we will 
 however prove the statements made in the lecture before the 
 Civil Engineers. 
 
 1st. Compare short circuit and open circuit, that is .R = 0, 
 very nearly, and R = oo *. In the former case we find that work 
 
 done in the iron is diminished, and if B 
 
 A.M 
 
 we have the 
 
 paradoxical result that there are no currents induced in the iron 
 of the cores and no work is required to drive the machine. This 
 of course can never actually occur, because R can never absolutely 
 vanish. It suffices to show, however, that the current in the 
 copper circuit may dimmish the whole power required to drive 
 the machine, to an amount less than the power required to drive 
 the machine on open circuit. 
 
 2nd. The other statement related to the effect of the currents 
 in the iron upon the currents produced in the copper circuit. 
 Assume that the effect is a small one, for a first approximation. 
 Neglect it, that is, treat the currents in the iron and the currents 
 in the copper as independent of each other, and then see how 
 each would disturb the other. 
 
 The first approximation then is 
 AL 
 
 EN 
 
 47T 2 
 
 TR 
 
 4?r 2 
 TR 
 
 2-7T 
 
 ' 47T* 47T 2 
 
 If we substitute these in the general equations as corrections, we 
 have 
 
 ,TR BNM 
 
 aL+b ' f>frr = A 
 
 M*/r ITrt 
 
 TR 
 
 102 
 
148 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 which shows that the disturbing effect of each circuit upon the 
 other is to dimmish the apparent electromotive force, and to 
 accelerate its phase. 
 
 VI. A very similar problem is that of secondary generators 
 or induction coils, whether used for the conversion of high 
 potentials to low, or the reverse. To treat it generally, taking 
 the magnetisation of the iron cores, which are always used, as a 
 non-linear function of the currents in the coils, would be a matter 
 of much difficulty ; we therefore assume, as is usual, that the co- 
 efficients of induction are constants, noting in passing that this is 
 not strictly the fact, though it is very nearly the fact, when the 
 cores are not saturated, and when the lines of magnetic induction 
 pass through non-magnetic space. 
 
 Let, then, R, r be the resistances of the primary and secondary 
 
 circuits, 
 
 L coefficient of self-induction of the primary, 
 N coefficient of self-induction of the secondary, 
 M coefficient of mutual induction of the two circuits, 
 x and y the currents in the two circuits at time t, 
 X the electromotive force applied in the primary circuit by 
 
 an alternate-current dynamo machine or otherwise, 
 
 the equations of motion will be 
 
 Lot + My'+Rx = 
 
 Various assumptions may be made as to X, but that most likely 
 to be adopted in the practical work of secondary generators is 
 that X is kept so adjusted that 
 
 2-7T 
 
 x = A cos nt, where n -^ , 
 
 and to enquire how X will depend on the resistances. 
 Ny' + ry = nAM sin nt, 
 nAM 
 
 r* 
 
 ~ C S nt + r Sm }> 
 
 v , I [ T n*NM* } ( MWr D ) . 1 
 
 X = A N - nL + .. \ sm nt -f \ , ro - + R [ cos nt . 
 L i fra* + r 2 j ( n 2 N 2 -h r 2 J 
 
 As in the case of the dynamo machine, the work done in the 
 secondary circuit is greatest when r = nN. The expression for 
 
ON THE THEORY OF ALTERNATING CURRENTS. 149 
 
 X serves to show that when the secondary is short-circuited a 
 lower electromotive force of the generating circuit is required 
 than when it is on open circuit. In induction coils the electro- 
 static capacity of the coils themselves has important effects. 
 An illustration of the effect of electrostatic induction is found 
 in the old-fashioned Ruhmkorff coils. These were not wound 
 symmetrically, but in such wise that one end of the secondary 
 coil was on the whole towards the inside, the other towards the 
 outside of the bobbin. In such coils a spark to earth may be 
 obtained from the outside end, but not from the inside. The 
 reason is that the outer convolutions have smaller electrostatic 
 capacity than the inner ones. The terminals may be made to 
 give equal sparks by the simple expedient of laying a piece of 
 tinfoil around the whole coil and connecting it to earth. 
 
 VII. Some time ago Dr Muirhead told me that he had 
 observed that the effect of an alternate-current machine could 
 be increased by connecting it to a condenser. This is not difficult 
 to explain : it is a case of resonance analogous to those which 
 are so familiar in the theory of sound and in many other 
 branches of physics. 
 
 Take the simplest case, though some others are almost as easy 
 to treat. Imagine an alternate-current machine with its terminals 
 connected to a condenser ; it is required to find the amplitude of 
 oscillation of potential between the two sides of the condenser. 
 Let Ry be the resistance and self-induction of the machine, 
 
 E sin ^- its electromotive force, C the capacity of the condenser, 
 
 V the difference of potential sought, and x the current in the 
 machine, then 
 
 CV = x 
 
 O J. 
 
 and yx + RxE sin - V, 
 
 , 2-7T r, 
 
 whence yx + Rx = -^ E cos -=- ~ , 
 
 J. JL 
 
 f, r 27T 2 !) 2-TTt 
 
 jl -CV-jr 4 cos jr 
 
 27T . 
 
 -T**-T 
 
 T 
 
150 ON THE THEORY OF ALTERNATING CURRENTS. 
 
 amplitude of V is therefore 
 
 Now suppose ^ = 100 volts, the machine would light up an 
 incandescent lamp of about 69 volts; let T=^ second, (7=100 
 
 microfarads, and ~- = eight ohms, and R T \j- ohm, all figures 
 
 which could be practically realised, we have amplitude of F= 80 E 
 roughly, or the apparent electromotive force would be increased 
 eighty-fold. 
 
 We now return to the principal subject of the present com- 
 munication. Some attempts have been made to verify the 
 proposition that two alternate-current machines can be advan- 
 tageously connected parallel, but I believe, till recently, without 
 success. I had no convenient opportunity for testing the point 
 myself till last summer, when I had two machines of De Meritens, 
 intended for the lighthouse of Tino*, in my hands. I have made 
 no determinations of the constants of these machines, but between 
 three and four years ago I thoroughly tested a pair of similar 
 machines now in use at a lighthouse in New South Wales*. Each 
 machine has five rings of sixteen sections, and 40 permanent 
 magnets. The resistance of the whole machine as connected for 
 lighthouse work (a single arc) was 0*0313, its electromotive force 
 (E) when running 830 revolutions per minute, 95 volts and 
 
 ohms. It was further remarked that the loss of 
 
 power was least with a maximum load, as is shown in the follow- 
 ing table : 
 
 Power applied as measured in belt 3*1, 4*8, 5'6, 6'5, 5 '4 
 Electric power developed ............ 07, 3'4, 4'3, 57, 3'4 
 
 Mean current in amperes ............ 77, 38'6, 517, 73'6, 151 
 
 * The engines, dynamos, lamps, optical apparatus, and lanterns of both these 
 lighthouses have been supplied by Messrs Chance Bros. & Co. 
 
ON THE THEORY OF ALTERNATING CURRENTS. 151 
 
 This result illustrates well the conclusion arrived at in Problem V 
 above. 
 
 Last summer the two machines for Tino were driven from 
 the same countershaft by link bands, at a speed of 850 to 900 
 revolutions per minute; the pulleys on the countershaft were 
 sensibly equal in diameter, but those on the machines differed by 
 rather more than a millimetre, one being 300, the other 299 mm. 
 in diameter (about) ; thus the two machines had not when un- 
 connected exactly the same speed. The pulleys have since been 
 equalised. The bands were of course put on as slack as prac- 
 ticable, but no special appliance for adjusting the tightness of 
 the bands was used. The experiment succeeded perfectly at the 
 very first attempt. The two machines, being at rest, were coupled 
 in series with a pilot incandescent lamp across the terminals, the 
 two bands were then simultaneously thrown on : for some seconds 
 the machines almost pulled up the engine. As the speed began 
 to increase, the lamp lit up intermittently, but in a few seconds 
 more the machines dropped into step together, and the pilot 
 lamp lit up to full brightness and became perfectly steady and 
 remained so. An arc lamp was then introduced, and a perfectly 
 steady current of over 200 amperes drawn off without disturbing- 
 the harmony. The arc lamp being removed, a Siemens electro- 
 dynamometer was introduced between the machines, and it was 
 found that the current passing was only 18 amperes, whereas, if 
 the machines had been in phase to send the current in the same 
 direction, it would have been more than ten times as great. On 
 throwing off the two bands simultaneously, the machines continued 
 to run by their own momentum, with retarded velocity. It was 
 observed that the current, instead of diminishing from diminished 
 electromotive force, steadily increased to about 50 amperes, 
 owing to the diminished electrical control between the machines, 
 and then dropped off to zero as the machines stopped. Professor 
 Adams will, I hope, give an account of experiments he has tried 
 with me, and on other occasions, at the South Foreland. With 
 De Meritens' machines, I regard coupling two or more machines 
 parallel as practically the best way of obtaining exceptionally 
 great currents when required in a lighthouse for penetrating a 
 thick atmosphere. 
 
9. 
 
 NOTE ON THE THEORY OF THE ALTERNATE 
 CURRENT DYNAMO. 
 
 [From the Proceedings of the Royal Society, Vol. XLII., 
 pp. 167170.] 
 
 Received February 17, 1887. 
 
 ACCORDING to the accepted theory of the alternate-current 
 dynamo, the equation of electric current in " the armature is 
 yy + Ry = periodic function of t, where 7 is a constant coefficient 
 of self-induction. This equation is not strictly true, inasmuch as 
 7 is not in general constant*, but it is a most useful approxima- 
 tion. My present purpose is to indicate how the values of 7 and 
 of the periodic function representing the electromotive force can 
 be calculated in a machine of given configuration. 
 
 To fix ideas, we will suppose the machine considered to have 
 its magnet cores arranged parallel to the axis of rotation, that the 
 cores are of uniform section, also that the armature bobbins have 
 iron cores, so that we regard all the lines of induction as passing 
 either through an armature coil, or else between adjacent poles 
 entirely outside the armature. The sketch shows a development 
 of the machine considered. The iron is supposed to be so arranged 
 that the currents induced therein may be neglected. We further 
 suppose for simplicity that the line integral of magnetic force 
 within the armature core may be neglected. 
 
 Let A l be the effective area of the space between the pole 
 piece and armature core when the cores are in line, ^ the distance 
 from iron to iron. 
 
 * "On the Theory of Alternating Currents," Telegr. Engin. Journ. vol. xui, 
 1884, p. 496. 
 
ON THE THEORY OF THE ALTERNATE CURRENT DYNAMO. 153 
 
 Let A z be the section of magnet core, 4 the effective length of 
 a pair of magnet limbs, so that L 2 may be regarded as the length 
 of the lines of force as measured from one pole face to the next. 
 
 Let ra be the number of convolutions in a pair of magnet 
 limbs, and 
 
 n, the convolutions in one armature section, 
 T, the periodic time. 
 
 The time is measured from an epoch when the armature coil 
 we shall consider is in a symmetrical position in a field which we 
 shall regard as positive. 
 
 x and y are the currents in the magnet and armature coils, the 
 positive direction being that which produces the positive field at 
 time zero. 
 
 At time t the armature coil considered has area AI, 
 
 = + l cos 7rt + cos 
 in a positive field ; and area A", 
 
 = b -b l cos (tort/T) + 6. 2 cos (4irf/T) - &c. 
 in a negative field, where 
 
 and &0-&J + &2+ ... = 0. 
 
 The coefficients & > &i> &c., are deducible by Fourier's theorem 
 from a drawing of the machine under consideration. 
 
 Let / be the total induction in the magnet core, and let, at 
 time t, I be distributed into /' through A^ I" through A" and 
 I'" as a waste field to the neighbouring poles. 
 
 The line integral of magnetic force from the pole to either 
 adjacent pole is /'"/&, where k is a constant. 
 
154 ON THE THEORY OF THE ALTERNATE CURRENT DYNAMO. 
 
 We have first to determine /', I", I"', in terms of x and y. 
 
 Take the line integral of magnetic force in three ways through 
 the magnets, and respectively through area AI, through area J./' 
 and across between the adjacent poles 
 
 r 
 
 1\ I" 
 
 2 ^ 'A 7 ' 
 i\ i'" 
 
 whence /' + 1" + 1'" = I 
 
 . ! 
 
 *** - 
 
 When t, x, and y are given, this would suffice to determine / by 
 means of the known properties of the material of the magnets as 
 represented by the function f. We will, however, consider two 
 extreme cases between which other cases will lie. 
 
 First. Suppose that the intensity of induction in the magnet 
 cores is small, so that l 2 f(I/A 2 ) may be neglected, the iron being 
 very far from saturation. We have 
 
 - 1" = y m (4/ - A,") x + n (AS + A,") y 
 
 Ml ( 
 
 47rf /, %7rt , 
 
 = m lCOS ~ 3C 
 
 + n U> + 2 cos --+... y K 
 
 We see that the coefficient of self-induction 7 in general contains 
 terms in cos (4-Trtf/T). 
 
 Second. In actual work it would be nearer the truth to sup- 
 pose that the magnetising current x is so great that the induction 
 / may be regarded as constant, and the quantity I 2 f(l/A<i) as 
 considerable. But as small changes in I imply very great changes 
 
OX THE THEORY OF THE ALTERNATE CURRENT DYNAMO. 155 
 
 in l 2 f(I/A 2 ), its value cannot be regarded as known. We have 
 then 
 
 whence 
 
 (A1-A?)I f (Aj-AlJ , _ 4 ^ 
 
 ~"' " v ; 
 
 ./ - ^/Q / Jyi/^* + 2H (^/ + A,") 
 
 For illustration, consider the simplest possible case: let b = b l =^A 1 , 
 and b., = b s = ... = 0, and let 2Hj be negligible ; we have 
 
 T , , r . ^ 
 
 I - 1 = /cos -^ + A l sm 2 
 
 and the equation of current will be 
 
 (27T , Znt ZirnAi d / . 2?r^ \) 
 % - { T / sm -^-- -^ ^ (sm* ^ . yj j, 
 
 instead of the simple and familiar linear equation. 
 
10. 
 
 ALTERNATE CURRENT DYNAMO-ELECTRIC 
 MACHINES. 
 
 [From the Philosophical Transactions of the Royal Society, 1896, 
 
 pp. 229252.] 
 
 Received April 4, Read May 2, 1895. 
 
 THIS paper deals experimentally with the current induced in 
 the coils and in the cores of the magnets of alternate current 
 machines by the varying currents and by the varying positions of 
 the armature. It is shown that such currents exist, and that they 
 have the effect of diminishing to a certain extent the electro- 
 motive force of the machine when it is working on resistances as 
 a generator without having a corresponding effect upon the phase 
 of the armature current. It is also shown that preventing varia- 
 tions in the coils of the electromagnet does not, in the machine 
 experimented upon, greatly affect the result, and that the effect 
 of introducing copper plates between the magnets and the arma- 
 ture has not a very great effect upon the electromotive force of the 
 armature, the conclusion being that the conductivity of the iron 
 cores is sufficient to produce the main part of the effect. A method 
 of determining the efficiency of alternate current machines is illus- 
 trated and the results of the experiments for this determination 
 are utilised to show that in certain cases of relation of phase of 
 current to phase of electromotive force the effect of the local 
 currents in the iron cores is to increase instead of to diminish 
 the electromotive force of the machine. 
 
 * The large majority of the experiments herein described were made in the 
 summer of 1893 and a considerable part of the paper was then written. We have 
 to thank Mr F. Lydall, one of the student demonstrators at King's College at that 
 time, for much assistance. 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 157 
 
 I. 
 
 In algebraic discussions of the theory of alternate current 
 machines, it has usually been assumed that the electromotive 
 force due to the magnets is a periodic function, the same whether 
 there is a current in the arma'ture or not, and that the effect of 
 the current in the armature can be represented by regarding the 
 armature as having self-induction. It has been pointed out, too, 
 that the coefficient of self-induction will generally vary with the 
 position of the armature in the field. To state exactly the same 
 thing in another way it has been assumed that the electromotive 
 force of the magnets is a periodic function independent of the 
 current in the armature, and that the effect of the armature 
 current on the induction through the armature can be represented 
 as an armature reaction which vanishes at the moment when the 
 current in the armature vanishes. 
 
 To state the matter in the form of an equation, let E be the 
 electromotive force of the machine on open circuit, R the resist- 
 ance of the armature circuit, x the current in the armature, T the 
 periodic time, then it is assumed that 
 
 Rx = E- (Lx)' ; 
 
 E being independent of #, L being, if you please, a coefficient of 
 self-induction constant or variable, or, if you prefer it, Lx repre- 
 senting the change in the induction through the armature due to 
 the current in the armature, vanishing with x. 
 
 It is easy to see that this statement is true in some cases. 
 For example, it is very nearly true in the older machines with 
 permanent magnets. Or imagine a machine without iron in the 
 magnets or armature, consisting merely of two circuits one the 
 magnet circuit, the other the armature circuit moveable in rela- 
 tion to each other. If the current in the magnet circuit is kept 
 precisely constant, either by inserting a great self-induction in its 
 circuit external to the machine, or by inserting such a resistance 
 and using so high an electromotive force that any disturbing 
 electromotive forces are inappreciable compared with it, the pre- 
 ceding statement is strictly accurate. But if the magnet current 
 is not forced to be constant the problem is more complicated. 
 
 Stating the matter in the language of self- and mutual-induc- 
 tion, let x and y be the currents in armature and magnet circuits, 
 
158 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 R and r their resistances, L and N their self-induction, M sin 27rt/T 
 their mutual-induction, F the constant electromotive force applied 
 to the magnet, the equations for the system are : 
 
 Rx = -M(y sin Z-n-t/T)' - Lx' } 
 ry = F-M(x sin ^Trt/T)' - Ny } ' 
 
 These equations can be solved by approximations if the varia- 
 tions in the value of y are small. 
 
 First, 
 
 _ F MF 2?r R cos ZTrt/T + 2-rrL/T sin 27rt/T 
 
 T T J. Xl 2 4" (27TJL//./ ) 2 
 
 Second, substituting this value of x, we obtain 
 
 M 2 F 27T/T 
 
 r ' E 2 + 
 
 R . 
 
 This gives periodic terms in y, the period being one-half the 
 period of the mutual induction. 
 
 Introducing these terms into the first equation, we see that 
 the term in 27rt/T in the electromotive force of the machine is 
 modified, and that terms in 67rt/T are introduced. The former 
 may have real practical importance, and it is one of the objects of 
 the present paper to ascertain how far it exists and is of import- 
 ance in actual machines. 
 
 Returning to machines as ordinarily constructed, in these the 
 current in the magnet coils is not compelled to be constant, and 
 any rapid variation of the induction in the magnet cores will 
 induce currents in those cores. The variations in the current in 
 the magnet coils and the currents in the cores both tend to annul 
 the variations in the induction in the core arising from the current 
 in the armature, but they will not tend to alter the average effect 
 of the currents in the armature on the induction through the 
 magnets. That there will be such an average effect is not difficult 
 to see. Suppose the armature coils to be fixed in line with the 
 magnets of the machine, any current in the armature will have 
 its full effect in increasing or diminishing the field through the 
 magnets. Suppose the armature coils to be fixed midway between 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 159 
 
 the magnets, any current in the armature will then have practi- 
 cally little or no effect in increasing or diminishing the field 
 through the magnets. If the armature be connected through 
 resistance, inductive or non-inductive, and the machine run in the 
 ordinary way, the current in the armature will lag in phase 
 behind the electromotive force E. The result is that when the 
 armature is opposite to the magnets there is a current in the 
 armature tending to demagnetise the magnets, and adding 
 together the effects of the armature in all positions, there is an 
 average effect tending to demagnetise the magnets. If the 
 machine had a constant current round the magnets and divided 
 iron in the magnets, this average effect, as well as its variations, 
 would be fully accounted for by the term (La;)', call it self-induc- 
 tion or call it armature reaction, as you please. But inasmuch as 
 the variations are in part annulled by the variations of current 
 in the magnet-winding and the local currents in the magnet cores, 
 we have a part of the diminution of the electromotive force E of 
 the machine unaccompanied by retardation of phase of the current 
 in the armature. 
 
 Before giving any experimental results, it will be well to 
 describe the machines used and the general method of experi- 
 ment adopted. 
 
 The two dynamos experimented upon were constructed by 
 Messrs Siemens Bros., and are of the same pattern and size but 
 are of an old type. They are mounted upon a common base-plate, 
 their pulleys being provided with flanges and bolts, so that any 
 desired phase difference can be given to the armatures, for the 
 accurate setting of which a graduated circle is provided, or so that 
 the armatures can be run independently of each other. The 
 pulleys have each a diameter of 12 inches, and are suited for a 
 6-inch belt the shaft is prolonged for the purpose of carrying a 
 revolving contact-maker and a small pulley for driving a Buss 
 tachometer. 
 
 Each dynamo has a series of 24 electromagnets (see fig. 1), 
 there being 12 on either side of the armature. The core of each 
 magnet (A) is of wrought-iron 2^- inches diameter, and 6J inches 
 long: and is wound with 5 layers, 35 convolutions per layer, of 
 copper wire 3*5 millims. diameter. The electromagnets are bolted 
 to circular cast-iron frames (J5), which serve also for supporting 
 
160 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 the bearings of the armature shaft. The centres of the 12 electro- 
 magnets on each frame are equally spaced out on a circle 8| inches 
 radius concentric with the axle of the machine. Each cast-iron 
 frame has a cross-sectional area of 4r8 sq. inches. The opposing 
 pole pieces of the electromagnets have an air space of 1J inch 
 
 FIG. 1. 
 
 between them, through which the armature coils rotate. The 24 
 electromagnet windings are coupled in series, and have a total 
 resistance of 1*8 ohms, the normal existing current being about 
 22 amperes. 
 
 The armature of each dynamo consists of 12 coils or bobbins 
 (C) with wooden cores (D) J inch thick. Each core is 7 inches 
 long (radially), with rounded ends the outer being struck to a 
 circle 3 inches and the inner 1 J inches diameter. The ends of 
 the respective coils are brought to a screw-plug commutator 
 board fixed to the shaft, by means of which a series of combina- 
 tions can be made. Each coil consists of 10 layers, 8 convolutions 
 per layer, 2 '2 millims. copper wire, having a resistance (cold) of 
 "187 ohm, and at a speed of 1000 revolutions per minute, with 
 normal excitation and fully loaded, is intended to give 50 volts at 
 its extremities. The full load current for each coil is 16 6 amperes, 
 so that at 1000 revolutions per minute, or a frequency of 100 com- 
 plete periods per second, the machine should give, with its 12 
 armature coils in parallel, an output of 200 amperes 50 volts. 
 The two terminal rings of the screw-plug commutator are con- 
 nected by conductors to two gun-metal collector rings, insulated 
 from one another and from the shaft by means of ebonite. Each 
 collector ring is provided with two 1-inch copper-wire brushes 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 161 
 
 carried by adjustable bar-holders fixed to the terminal blocks of 
 the dynamo. 
 
 The potential difference between any two points at any epoch 
 is determined by means of a Kelvin quadrant electrometer and a 
 revolving con tact- maker fixed to the shaft of the dynamo. The 
 contact-maker consists of a disc of gun-metal which carries two 
 rings, one of gun-metal insulated from the disc, the other of 
 ebonite. Into the latter is inserted a strip of metal ^\ inch wide, 
 which is in permanent contact with the gun-metal ring. Two 
 insulated brushes are attached to a moveable brush-holder, so that 
 one presses on each ring. The circuit between the two brushes 
 is completed once in each revolution, and the position of the 
 contact can be read off by a pointer attached to the holder on a 
 circle 13^ inches diameter, divided into 360 degrees. The two 
 points between which it is desired to measure the potential 
 difference are connected through the contact-maker to a con- 
 denser and the quadrant electrometer, as shown in fig. 2, in which. 
 
 FIG. 2. FIG. 3. 
 
 A and B are the points, C the revolving contact-maker, D the 
 reversing switch of the electrometer, E the condenser, and F the 
 quadrant electrometer. By plotting as ordinates the volts mea- 
 sured at any epoch, and as abscissae the position of the contact- 
 maker as representing time, the curve of potential is obtained. 
 The electrometer is standardised by means of a Clark cell, so that 
 the deflections on the scale can be reduced to volts : when the 
 potential difference between A and B was too great for the 
 electrometer, it was reduced in any desired ratio by two consider- 
 able non-inductive resistances introduced between A and B, as 
 shown in fig. 3. 
 
 The characteristic curve of the alternator is given in fig. 4, 
 and shows the relation between the total induction /, between 
 one pole piece and the opposing one, in terms of the line integral 
 of magnetising force due to the two windings in series on the two 
 respective magnet cores; the scale of amperes in the magnet 
 winding is also given horizontally. 
 
 H. i. 11 
 
162 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 2,000 
 
 6,000 
 
 FIG. 4. 
 
 10,OOOLine Integral of Magnetising 
 Force dae to two Magnets. 
 
 FIG. 5. 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 163 
 
 In fig. 5 the speed of the alternator experimented upon was 
 923 revolutions per minute, or a frequency of 92*3 complete 
 periods per second. For the purpose of obtaining a marked effect 
 from the current in the armature a large current was taken out of 
 the armature, and the current in the magnet winding was only 
 8 amperes. A Kelvin multicellular voltmeter placed across the 
 terminals of the machine read 190 volts on open circuit, and 
 81 volts when loaded, and a Kelvin ampere balance in the external 
 non-inductive circuit read 40 amperes. The armature bobbins 
 were coupled 6 in series 2 parallel between the brushes, the total 
 resistance of the circuit (R) was 2-52 ohms, the armature resist- 
 ance alone being '55 ohm. 
 
 Curve E is the electromotive force curve of the machine when 
 there is no current in the armature. Rx is the curve of electro- 
 motive force deduced from the potential difference taken between 
 the terminals of the alternator when supplying current through 
 non-inductive resistances. The curves E and Rx have been 
 integrated, the corresponding integral curves being A and B 
 respectively. 
 
 That the ordinary theory does not fully account for the facts 
 is easily shown. We have Rx = E(Lx). Integrate both sides 
 from any fixed epoch to any time t and we have 
 
 \* Rxdt = [ Edt- \Lx\ . 
 Jo Jo Jo 
 
 Each term of this equation consists of a constant part and of a 
 periodic part. The constant parts must be equal and also the 
 periodic parts. We have to deal only with the periodic parts. 
 The curves A and B, fig. 5, represent the periodic parts of each 
 of the first two terms ; the difference of ordinates of these curves 
 should at all times be equal to Lx. In particular, and this is the 
 only point of moment, as we do not know how L may vary, when 
 Lx vanishes JRxdt=fEdt. 
 
 If the effect of the current in the armature on the induction 
 through the armature could be represented by a term which 
 vanishes with the current in the armature, it is obvious that the 
 curves A and B would cross at the epoch when x = 0. They do 
 not. The difference of inductions as given by these curves at this 
 epoch is 25 per cent, of the induction which would then traverse 
 
 112 
 
164 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 the armature coil if the machine were running on open circuit, 
 that is to say, 25 per cent, of the ordinate at this epoch given by 
 the A curve. It it is assumed that the average effect of the arma- 
 ture current upon the induction in the magnets is such as to 
 lower this induction by 25 per cent., the ordinates of the E curve 
 would be decreased in like proportion, giving the curve E' of 
 which C is the integral. The difference at any epoch between the 
 curve C and the Rx curve is to be fully accounted for by the 
 term (Lx). 
 
 We may put it in this way. In this machine the armature 
 current at the times when it has a value affects the field at the 
 instant when the armature current is zero. The effect is pro- 
 duced by variations induced in the current in the field magnet- 
 winding and in the solid iron of the magnets by the varying 
 current in, and the varying position of, the armature. That these 
 induced currents must exist is obvious, and it is easy enough to 
 measure them in the copper coils. They have the effect of 
 causing the armature reaction to produce an average effect upon 
 the magnetism of the fields by partially annulling its periodic 
 effect. If the current in the armature did not lag behind the 
 electromotive force of the magnets E, there would be little or no 
 diminution of the average magnetism of the magnets. We may 
 correctly say that this diminution of the magnetism of the 
 magnets is due to the self-induction of the armature causing a 
 lag of current. The effect arises from the self-induction of the 
 armature modified by currents induced in the magnets. 
 
 The effect on the magnets of any current in the armature is 
 greatest when the armature bobbins are opposite the pole-faces, it 
 is nil or small when half-way between the pole-faces. We may 
 therefore represent its effect at any instant approximately as pro- 
 portional to the expression 
 
 ZtrL/T sin 27rt/T + R cos %7rt/T . 
 
 ' sm 
 
 or 
 
 TrLjT -n-L/T cos 4-Trt/T - R sin 4>irt/T 
 
 (27rL/T)* + R* (Z-n-L/T) + E 2 
 
 The constant term, causes the fall in average magnetism, the 
 periodic term causes currents in the magnets, and its effect on the 
 magnetism is partly annulled thereby. The effect will vary as the 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 165 
 
 square of the current if this is small. The effect of self-induction 
 in diminishing the apparent electromotive force of the machine 
 varies as the square of the current, so that we may expect the 
 two effects, that due to the reaction of the armature on itself and 
 that brought about by the armature inducing currents in the 
 magnets, to vary together. 
 
 The lag of phase is less than we should expect from the 
 diminution of electromotive force, or the electromotive force 
 suffers greater diminution than we should expect from the angle 
 of lag of phase. 
 
 We have tried a number of experiments for the purpose of 
 tracing the variations of current in the magnets, and also with the 
 intention of increasing or diminishing the effect we have observed. 
 It is easy enough to trace the variations in the current round the 
 magnets by measuring at points during the period the potential 
 difference between the ends of a non-inductive resistance in series 
 with the magnets. These variations are shown in figs. 6 and 7, in 
 which the armature bobbins were coupled, 4 series, 3 parallel, and 
 12 series, respectively. We see, as we should expect, that the 
 variations have a periodic time one-half the periodic time of the 
 machine. But the current round the magnet could be made 
 constant by exciting the two machines with the same current, 
 loading each to the same degree, and placing their armatures one- 
 fourth part of a period apart in phase. 
 
 The machines were run under conditions set forth in Table I., 
 and the curves are given in figs. 5, 6, 7, 8. An electromotive force, 
 curve JE, was observed with no current in the armature, and a 
 curve of potential difference was taken between the brushes with 
 the alternator loaded on a non-inductive resistance. Rx is this 
 curve with variations in the exciting current, and Rx without 
 variations, in each case corrected for the resistance of the arma- 
 ture. Figs. 6 and 7 show the curves of actual electromotive force, 
 Rx and Rx, when the current in the magnet-winding is allowed 
 to vary and when its variations are stopped. It will be seen that 
 they do not differ a great deal. What currents are stopped in the 
 magnet-winding no doubt turn up in the substance of the cores 
 themselves and have an effect not differing greatly. Curve E 
 represents electromotive forces observed. Rx represents the 
 potential difference taken between the brushes and corrected for 
 
166 ON ALTERNATE CURRENT DYNAMO -ELECTRIC MACHINES. 
 
 FIG. 6. 
 
 FIG. 7. 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 167 
 
 the resistance of the armature, with the alternator working on a 
 non-inductive resistance with variations in the exciting current, 
 Rx without such variations in each case. The induced currents 
 are in either case adequate to nearly stop the variation of induc- 
 tion. Fig. 8 shows the same thing. 
 
 FIG. 8. 
 
 An exploring coil was wound and placed on one of the magnet 
 limbs and the electromotive force in it was observed in terms of 
 the time for the various positions of the exploring coil, marked 1, 
 2, 3, 4, 5, in fig. 1. Both the amplitude and the epoch varied 
 with the position of the coil, but, in all cases, the periodic time 
 was half the periodic time of the machine. It does not seem 
 worth while to publish the curves connecting electromotive force 
 and time. 
 
 Lastly, we tried to exaggerate the effects ; for this purpose we 
 introduced plates of copper, ^ inch thick, in the form of two flat 
 rings between the pole faces and the armature. Curves 9, 10, 11, 
 12, give the results for two different currents round the magnets 
 
168 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 Frequency 72-5. 
 
 Volts on open circuit 240 
 
 Volts when loaded 92. 
 
 FIG. 9*. 
 
 With Copper Rings 
 Frequency 72-5. 
 Volts on open circuit 240. 
 Volts when loaded 99. 
 
 FlG. 10. 
 
 * In the case of figs. 9, 10, 11 and 12, the armature bobbins -were coupled all 
 in series, and the magnet-cores were separated in order to admit the copper plates, 
 the air-space being thereby increased from 1^ inches to If inches. In figs. 9 and 10 
 the resistance E was 7*67 ohms, and in figs. 11 and 12 it was 2-51 ohms. [Ed.] 
 
ON ALTERNATE CURRENT DYNAMO- ELECTRIC MACHINES. 169 
 
 with the copper plates in and the copper plates absent. A com- 
 parison shows that the copper plates do not make a great deal of 
 
 V Without Copper Rings 
 Frequency 72- 5.) 
 Volts on open circuit 117. 
 Exciting Current 3-9 Amp 
 
 FlG. 11. 
 
 difference. The principal effect is to diminish the current induced 
 in a coil on the magnet placed at position 5, fig. 1, close behind 
 the copper plate. 
 
 Volts on opeo circuit 118. 
 Exciting Current 3}98 Amp 
 
 FIG. 12. 
 
 It may be inferred that in this machine there is conductivity 
 enough in the magnet cores to have in large measure the effect 
 indicated, and that the effect cannot be greatly diminished by 
 
170 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 compelling the magnetising current to be constant in the magnet 
 coils, nor can it be greatly increased by exaggerating the currents 
 induced about the magnets by intentionally introducing additional 
 conductivities around them. The effect of each is merely to alter 
 the place where the currents occur. 
 
 Recently machines have been built, with finely -divided pole 
 pieces to the magnets by Messrs Mather and Platt and by the 
 British Thomson -Houston Company. 
 
 It was obviously desirable to obtain a verification with a 
 machine of totally different construction. For this purpose we 
 had available the first model made of the alternating machines 
 manufactured by Messrs Mather and Platt. It has an iron core in 
 the armature which projects and extends beyond the armature 
 coils. It was treated in exactly the same way as the Siemens' 
 machines but with a fairly full load. The results are shown in 
 fig. 13, from which it will be observed that the total induction 
 actually observed when the machine is loaded is about 11 per 
 cent, below the induction inferred from the electromotive force on 
 open circuit. 
 
 FIG. 13. 
 
 II. 
 
 The following experiments were primarily made lor the pur- 
 pose of determining the efficiency of the machine, but they will 
 be seen in Section III. to have an important bearing upon the 
 principal subject of this paper. 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 171 
 
 For the purpose of finding the efficiency of the alternators, 
 when running as generator and motor*, the two armatures were 
 rigidly mechanically coupled together, the leading machine being 
 generator, and were connected in series with a non-inductive resist- 
 ance r, and a Kelvin ampere balance (7, as shown in fig. 14. The 
 
 FIG. 14. 
 
 potential difference of the generator was measured at different 
 epochs by means of the Kelvin quadrant electrometer Q, and the 
 contact-maker K, the potential applied to the electrometer being 
 reduced by the non-inductive resistances r lt r 2 . For corresponding 
 epochs a curve of potential was taken across r, this gives the 
 current passing between the machines and also the difference of 
 potential difference between motor and generator. 
 
 The power difference, or loss in the combination, was supplied 
 by a shunt-motor through shafting and belts, and was determined 
 by observing the watts supplied to the motor when driving the 
 shafting, the alternator belt being removed, and then observing 
 the watts taken to drive the alternator when loaded the speed 
 being the same in each case. The difference gives the power 
 absorbed by the combination. 
 
 It was found that the watts required to drive the shafting 
 alone were 1681 ; the watts required to drive the shafting and 
 alternators when excited, but not loaded, were 2479, the difference 
 being in part due to currents induced in the metal frames of the 
 armature. 
 
 * This is the same method of test which has been applied to direct current 
 machines (see Phil. Trans., R.S., 1886, p. 331). 
 
172 ON ALTERNATE CURRENT DYNAMO- ELECTRIC MACHINES. 
 
 Tables II. and III. give for about half and full load (with 
 regard to current only) the data for getting at the watts given 
 out by generator and received by motor, and have been obtained 
 from the potential and current curves. The phase difference 
 between the armatures was ^th and yftth period respectively. 
 
 Table IV. shows how the efficiencies of generator, motor, and 
 combination have been obtained ; and also gives the allocation of 
 losses in the system. 
 
 The frequency was about 70 periods per second, and, since the 
 machines are built for 100 periods per second, the figures must be 
 taken only as illustrative of the method of test. 
 
 The alternators being connected, as shown in fig. 14, we were 
 able to vary the exciting currents of the two machines by means of 
 the adjustable resistances r 3 , r 4 . The armatures were coupled y^th 
 of a period apart in phase, and the following experiments were made. 
 
 Frequency 71;6. 
 
 Generator Excitation 1 -5 Am.) 
 
 Motor Excitation 17-5 Amp. 
 Armatures 4 series 3 parallel. 
 
 FlG. 15. 
 
 1. The alternators were equally excited with a current of 
 17*5 amperes and run at a speed of 716 revolutions per minute, 
 corresponding with a frequency of 71 6 periods per second, and 
 the following curves obtained (see fig. 15). 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 173 
 
 E G , E M are the E.M.F/S of generator and motor when running 
 on open circuit. 
 
 PD G , PD M are the potential differences of generator and motor 
 respectively when a current of 42'2 amperes (Vmean 2 ) was passing 
 through the armatures. 
 
 e G , e H are the E.M.F.'S of the respective machines when loaded, 
 that is to say, they are the curves PD G) PD M corrected for current 
 into armature resistance. 
 
 E is the E.M.F. of the combination when not loaded, that is, it 
 is the difference of the curves E G , E M . 
 
 x is the curve of current passing between the machines, and is 
 proportional to the E.M.F. (e) of the combination when loaded, the 
 connecting leads being non-inductive. This electromotive force is 
 the difference of the curves e G , e^. 
 
 2. In fig. 16* the frequency is 71, the motor is excited with 
 18*6 amperes and the generator with 7*2 amperes. In this case 
 
 Motor Excitation 18 6 Amp. 
 Armatures 4 series 3 parallel 
 
 FIG. 16. 
 
 the motor is working at higher E.M.F. on open circuit than the 
 generator. Curves corresponding to those in the Experiment 1 
 were obtained and are marked in a similar manner. 
 
 * Vide Hopkinson, Institute of Civil Engineers' Lecture delivered 1883 ; Insti- 
 tute of Civil Engineers, November, 1884; or Original Papers on Dynamo Machinery, 
 pp. 58 and 148. 
 
174 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 The potential curves in fig. 16 have been integrated, and the 
 integral curves so obtained are given in fig. 17. These give there- 
 fore the inductions in terms of the time. 
 
 40 
 
 FIG. 17. 
 
 3. In fig. 18 the frequency is 70, the generator is excited 
 with 18'6 and the motor with 1T5 amperes. The generator is 
 working with a higher E.M.F. on open circuit than the motor. 
 The potential curves have been integrated, and the integral curves 
 are given in fig. 19. 
 
 It was observed that when the exciting current of the motor 
 was decreased, that of the generator being kept fairly constant 
 (the two machines being equally excited with about 18 amperes 
 each to begin with), the current between the machines gradually 
 decreased until a critical point was reached, when a further dimi- 
 nution of the motor exciting current had the effect of increasing 
 the current between the machines*. It was also observed that 
 the watts given out by the generator did not vary in the propor- 
 tion of the currents between the machines. 
 
 Table V. gives the watts given out by generator for three 
 values of its exciting currents 18*2, 18'6, and 19 amperes, the 
 corresponding exciting currents for the motor being 18, 1T5, and 
 8*4 amperes. The current between the machines is a minimum 
 
 * This effect has been independently observed by Mr Mordey and Mr Kapp (see 
 Journal of Institute of Electrical Engineers, vol. xxn, pp. 128, 173). 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 175 
 
 Generator Exc tation 18*6 Amp 
 Motor Excitation 11-5 Amp. 
 Armatures 4 series 3 parallel. 
 
 FIG. 18. 
 
 FIG. 19. 
 
176 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 for exciting currents of 18'6 and 11 '5 in the two machines, and 
 the curves in fig. 17 have been taken under these conditions. 
 
 This is a point of practical importance in transmission of 
 power by alternate currents, since the size of the conductor 
 between motor and generator is mainly determined by the current 
 transmitted. The cause is readily explained from the curves. 
 
 Starting with the conditions as in Experiment 2, where the 
 motor is more highly excited than the generator, we see that the 
 current (x) is accelerated in phase with regard to the potential 
 difference of the machines. On increasing the exciting current of 
 the generator until the machines are equally excited as in Experi- 
 ment 1, the current (as) is still accelerated with regard to the 
 potential difference, but not to such an extent. On diminishing 
 the motor exciting current until the machines are excited as in 
 Experiment 3, the current (a?) is in phase with the potential 
 difference. For a given power transmitted this will be the point 
 of maximum efficiency with regard to the intermediate conductors. 
 Any further diminution of the motor exciting current has the 
 effect of retarding the current (x) with regard to the potential 
 difference, and consequently for the same watts transmitted and 
 the same potential difference the current must be increased. The 
 case in which the conductors between motor and generator have 
 considerable induction or capacity has not been worked out. 
 
 The losses in the system can be supplied electrically (instead 
 of by belt as in these experiments) as in the case of direct current 
 machines*. 
 
 III. 
 
 The results of the last section are valuable in relation to the 
 effects of induced currents in the magnets, the subject of Section I. 
 With a machine working as a simple generator the current lags 
 behind the electromotive force on open circuit by any amount 
 from to 90. But when a generator and motor are run rigidly 
 coupled together, the current may lead the generator electro- 
 motive force, or may lag and the motor may lag by any amount 
 from 90 to 270. Regarding the relative phases of electromotive 
 force of machines and of current, the machine is a generator when 
 
 * See Engineering, 24th March, 1893. 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 177 
 
 the current is from to 90 behind the machine ; it is a motor 
 from 90 to 270, and again a generator from 270 to 360. We 
 have already stated that we should naturally expect that the 
 induced currents in the magnets would have little or no effect 
 when E.M.F. and current were in the same phase, and that they 
 would have a maximum effect when the two were 90 apart, or at 
 quarter centres. We should expect further that, as a generator 
 can be made into a motor by reversing the current in the arma- 
 ture, wherever local currents diminish E.M.F. of a generator, they 
 would increase E.M.F. of a motor. That is, we should expect that 
 local currents would diminish E.M.F. from lead to 180, and 
 increase E.M.F. from 180 to 360. As a fact, we find this to be 
 partially verified ; it seems that local currents diminish E.M.F. from 
 a negative angle of comparatively small amount, perhaps 30, 
 to considerably more than 90, and that they increase E. M. F. from 
 180 to over 270. 
 
 Referring to the curves in fig. 14, x and E G are in phase, and 
 fe G dt would need increasing 3 per cent, to meet JE G dt, when x 
 vanishes. E M lags 216, and je M dt needs diminishing, that is the 
 currents have increased the E.M.F. In fig. 15 a very small change 
 in the observations would change the character of the results. 
 
 Cienerator Excita 
 Motor Excitation 
 Armatures' all series 
 Motor inductions 
 
 FIG. 20. 
 
 We have taken another set of curves shown in figs. 20 and 21. 
 In fig. 20, we have a very small current 3'3 amperes in the 
 generator magnets, and the current is in phase with the generator, 
 H. i. 12 
 
178 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 the motor being 264 behind the current. The generator is about 
 12 per cent, low owing to local currents, and the motor is 25 per 
 cent, of its actual value high. To obtain a better standard we 
 excited a machine with 3'3 amperes and passed the same current 
 as before through the armature and an ordinary non-inductive 
 
 Frequency 72-5. 
 
 Excitation 3-3 Amperes 
 
 Armature all series. 
 
 Fm. 21. 
 
 resistance, and found the current lagged 72, and the E.M.F. of the 
 machine was diminished 50 per cent, instead of 12 per cent. The 
 results are given in fig. 21. 
 
 In considering the applications of these results, it must be 
 remembered that the machines have been worked far outside the 
 limits of practice for the purpose of accentuating the effect. If 
 we confined ourselves to these limits we should still find these 
 effects, but smaller in amount. 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 179 
 
 
 pill 
 
 
 11 lls 
 
 J 
 
 If it!!i! 
 
 
 1||||111| 
 
 
 H WWW 
 
 Exciting current in wind- 
 ing on magnets. 
 Ampdres 
 
 Maximum 
 variation both 
 sides from 
 normal 
 
 Ol Ol rH O 
 O) Ol Ol Ol 
 
 & 
 
 OQ 
 
 III 
 
 00 C* l> C^ O O 
 
 c* 
 
 
 
 1|i? 
 
 lip 
 
 O O rH p 
 
 I ' en 05 O5 t> 
 
 rH rH rH 
 
 Amperes (Vmean 2 ) 
 ture bobbii 
 
 II 5 
 
 
 With varia- 
 tions in current 
 in magnet 
 winding 
 
 CO rH O^ CO 
 
 O W5 SQ 4t< - 00 t> 
 
 (M rH rH rH rH 
 
 * 
 
 III? 
 
 ||l| 
 
 M|,M 
 
 il !l 
 
 Pos -^ en 
 ^ CO O OJ >O 
 rH rH rH O O 
 
 a 
 1 
 
 5 ^ Ol !> 
 
 01 t- U5 05 rH 
 
 O5 O5 C5 O5 rH 
 
 # 
 
 - 
 
 5-. 
 
 
 2 
 
 
 1 
 
 
 1 
 
 
 A 
 
 
 .2 
 
 
 id 
 
 
 Z 
 
 
 o~ 
 
 
 II 
 
 
 H 
 
 
 ^3 
 
 
 ^ 
 
 
 * 
 
 
 
 1 
 
 II 
 
 03 
 
 H 
 
 ^ 
 
 
 ^ 
 
 1 
 
 <o 
 
 O 
 
 1 
 
 1 
 
 eH 
 
 P 
 
 
 I 
 
 1 
 
 5 
 
 *0 
 
 ? 
 
 
 o 
 
 
 
 II 
 
 <o 
 
 ^ 
 
 M 
 
 K) 
 
 ^3 
 
 ' I 
 
 II 
 
 ( * 
 
 3 
 
 " 
 1 
 
 2 
 
 S 
 
 *!*< , 
 
 KJ 
 
 ^^ 
 
 01 
 
 H)W 
 
 1 -^ 
 
 1 
 
 HM 
 
 <3 
 
 122 
 
180 ON ALTERNATE CUKKENT DYNAMO- ELECTRIC MACHINES. 
 
 Ill 
 
 F&fl 
 
 1 1 1 1 1 + 1 
 
 
 
 J 
 
 1 1 1 1 1 I+ + + + + + + + + 
 
 
 
 3d 
 
 I? 
 
 CO 
 
 s? 
 
 II 
 cs in a o 
 ^- g 2 S 
 
 B .|M 
 
 (N 
 
 o 
 
 & 
 
 s 
 
 la 
 
 O 
 
 jWrcJ 
 H 
 
 
 s 
 
 -2 d 
 ll 
 
 ^^ 
 
 H 
 
 1 1 1 1 1 
 
 iH 
 
 oo y5 
 
ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 181 
 
 ^ 
 
 ^ 
 
 la 
 
 l>i 
 ^'3b s 
 
 1 ++ 1 1 1 1 1 1 1 1 1 1 1 1 
 
 t*\ 
 
 -f; 
 
 iT 1 
 
 coeo 
 
 iH iH 
 
 ^ 
 <N 
 
 6i 
 
 CO 
 
 *s 
 
 *3 O 
 
 * a 
 
 -- 
 
 . . _r 
 
 + I 1 1 1 1 1 1 1 1 1 1 1 1 1 
 
 00 9 
 
 01 <M 
 
 ^1 
 
 'M 
 
 ^ 
 ^ 
 
 ?5 
 
 O 
 
 ^ 
 
 B8 1 
 
 H 
 >J 
 
 - 
 
 ^ 
 
 
 s 
 
 + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
 
 I I I + + + + + + + + + + + + 
 
 s 
 
 m 
 
 cp oil oq Tt 
 
 rH 6 CO 00 00 <N 
 
 >O CO CO O CO i I OS 
 
182 ON ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 
 
 TABLE IV. 
 
 No. 
 
 Description of Magnitude 
 
 Half load 
 
 Full load 
 
 
 Frequency in complete periods per second .... 
 
 70-3 
 
 69-2 
 
 
 Phase difference between armatures in fractions of a 
 complete period ... 
 
 i 
 
 A- 
 
 1 
 
 Watts given out by generator (see Tables II. and III.) 
 
 3493 
 
 6400 
 
 2 
 
 Watts given to motor (see Tables II. and III.) . . . 
 
 3448 
 
 6196 
 
 3 
 
 Watts dissipated in generator armature = (\/mean 2 C.) 2 
 275 ohm . 
 
 128-5 
 
 481-2 
 
 
 
 
 
 4 
 
 Watts dissipated in motor armature = (v/mean 2 C. ) 2 
 275 ohm . . 
 
 128 -5 
 
 481-2 
 
 5 
 
 Watts dissipated in generator magnet winding . . . 
 
 537 
 
 537 
 
 6 
 
 Watts dissipated in motor magnet winding .... 
 
 537 
 
 537 
 
 7 
 
 Watts dissipated in connection between machines . . 
 
 45 
 
 204 
 
 8 
 
 Watts absorbed by combination through belt .... 
 
 1848 
 
 2941 
 
 9 
 
 Total electrical power developed in generator = No. 1 
 + No. 3 
 
 3621 
 
 6881 
 
 10 
 
 Half watts absorbed by system minus half known watts 
 -{No. 8- (No. 3 + No. 4 + No. 7)} 
 
 746 
 
 889 
 
 11 
 
 Total power given to generator=No. 5+No. 9 + No. 10 
 
 4904 
 
 8307 
 
 10 
 
 
 iy-i ,n 
 
 iyy.f) 
 
 13 
 
 Percentage loss in generator armature 
 
 2-61 
 
 11 U 
 
 5-79 
 
 14 
 
 Percentage loss in generator magnet winding . . . 
 
 10-9 
 
 6-46 
 
 15 
 
 Percentage sum of all other losses in generator . . . 
 
 15-29 
 
 9-75 
 
 16 
 
 Percentage efficiency of motor 
 lnn /No. 9 + No. 10 -No. 8\ 
 
 fiQ-O 
 
 77.7 
 
 17 
 
 U V No.2 + No. 6 ) 
 
 3-22 
 
 7-14 
 
 18 
 
 Percentage loss in motor magnet winding 
 
 13-5 
 
 7-98 
 
 19 
 
 Percentage sum of all other losses in motor .... 
 
 20-1 
 
 13-18 
 
 20 
 
 Percentage efficiency of combination = (No. 12 x No. 16) 
 A* . 
 
 45 '0 
 
 55 '2 
 
 
 
 
 
OX ALTERNATE CURRENT DYNAMO-ELECTRIC MACHINES. 183 
 
 Fre 
 
 V 
 
 imo 
 
 i IOi IC"IC~ 
 
 CO CO vH CO 
 
 saiadray 
 
 + + 1 1 1 1 1 1 1 1 
 
 uoipanap 
 
 5, 
 70 
 
 ags. 18 - 0, motor 
 tor 143. Freque 
 
 nt in gen 
 ean' J volts on 
 
 C 
 
 \/ 
 
 A*q jno 
 
 I ICOOSi I 00 Ol CO rH 00 CO 
 
 of *cT of of <?f cT co" m 
 I I I I I I I I I I 
 
 sajadray 
 
 + 1 1 1 1 1 1 1 1 1 
 
 noi^oagap 
 
 O CO 
 
 s 
 
 mags. 18 '2, motor 18, 
 tor 155. Frequency 7 
 
 5 1 
 
 l> 
 
 Iff: 
 
 aocooooooco 
 
 C<ll>*OU5CiIr-lt~t I 
 
 A*q imo 
 
 + 1 1 
 
 saaadray 
 
 uoiijoagap 
 
 Sns 
 rH 
 
 pouad B jo stflOQ ui ajSoy 
 
 irsaOi-H^ 
 
 ^ rH (M <M 
 
11. 
 
 AN UNNOTICED DANGER IN CERTAIN APPARATUS 
 FOR DISTRIBUTION OF ELECTRICITY. 
 
 [From the Philosophical Magazine, September, 1885.] 
 
 MANY plans have been proposed, and several have been to a 
 greater or less extent practically used, for combining the ad- 
 vantage of economy arising from a high potential in the conductors 
 which convey the electric current from the place where it is 
 generated with the advantages of a low potential at the various 
 points where the electricity is used. A low potential is necessary 
 where the electricity is used ; partly because the lamps, whether 
 arc or incandescent, each require a low potential, and partly 
 because a high potential may easily become dangerous to life. 
 Among the plans which have been tried for locally transforming 
 a supply of high potential to a lower and safer, the most 
 promising is by the use of secondary generators or induction 
 coils. It has been proved that this method can be used with 
 great economy of electric power and with convenience; under 
 proper construction of the induction coils it may also be perfectly 
 safe. It is, however, easy and very natural so to construct them 
 that they shall be good in all other respects but that of safety 
 to life that they shall introduce an unexpected risk to those 
 using the supply. 
 
 In a distribution of electricity by secondary generators, an 
 alternating current is led in succession through the primary coils 
 of a series of induction coils, one for each group or system of 
 lamps. The lamps connect the two terminals of the secondary 
 
AN UNNOTICED DANGER. 185 
 
 coil of the induction coils. It is easy to so construct the 
 induction coils that the difference of potential between the 
 terminals of the secondary coils may be any suitable number 
 of volts, such as 50 or 100 ; while the potential of the primary 
 circuit, as measured between the terminals of the dynamo 
 machine, may be very great, e.g., 2,000 or 3,000 volts. If the 
 electromagnetic action between the primary and secondary coils, 
 on which the useful effect of the arrangement depends, were the 
 only action, the supply would be perfectly safe to the user so long 
 as apparatus with which he could not interfere was in proper 
 order. But the electromagnetic action is not the only one. 
 Theoretically speaking, every induction coil is also a condenser, 
 and the primary coil acts electrostatically as well as electro- 
 magnetically upon the secondary coil. This electrostatic action 
 may easily become dangerous if the secondary generator is so 
 constructed that its electrostatic capacity, regarded as a con- 
 denser, is other than a very small quantity. 
 
 Imagine an alternate current dynamo machine, A, tig. 1, 
 its terminals, B, C, connected by a continuous conductor, BDC, 
 
 FIG. 1. 
 
 on which may be resistances, self-induction coils, secondary 
 generators, or any other appliances : at any point is a condenser, 
 E, one coating of which is connected to the conductor, or may 
 indeed be part of it ; the other is connected to earth through a 
 resistance, R. Let K be the capacity of the condenser, V the 
 potential at time t of the earth coating of the condenser, U the 
 potential of the other coating, x the current in resistance R to 
 the condenser from the earth, being taken as positive, and the 
 earth potential as zero. We have 
 
 V 
 
186 AN UNNOTICED DANGER IN CERTAIN 
 
 and 
 
 K(U- F) = tf; 
 whence, since 
 
 U= A si 
 
 where A is a constant depending on the circumstances of the 
 dynamo circuit as well as the electromotive force of the machine, 
 and n is the reciprocal of the periodic time of the machine, 
 we have 
 
 KRx + x fan KA cos 
 
 x = g - - { 27ra KR sin 2imt + cos 
 
 mean square of cc = , . mean square of A. 
 
 Let us now consider the actual values likely to occur in 
 practice. Let the condenser E be a secondary generator ; let the 
 resistance R be that of some person touching some part of the 
 secondary circuit, and also making contact to earth with some 
 other part of the body; n may be anything from 100 to 250, 
 say 150; K will depend on the construction of the secondary 
 generator it may be as high as 0'3 microfarad or even more, but 
 there would be no difficulty even in large instruments in keeping 
 it down to one hundredth of this or less. The mean square of A 
 will depend on the circumstances of other parts of the circuit ; 
 it might very easily be as great, or very nearly as great, as the 
 mean difference of potential between the terminals of the machine 
 if the primary circuit were to earth at G. Suppose, however, that 
 the circuit BDC is symmetrical, that E is at one end, and that 
 another person of the same resistance as the person at E is 
 touching the secondary circuit of the secondary generator F at 
 the other end of the circuit. In that case, if 2,400 be difference 
 of potential of the machine, mean square of A will be 1,200 ; 
 in which case we have, taking R as 2,000 ohms, 
 mean square of 
 
 27T x 150 x 0-3 x 10~ 6 
 
 x . x 1,200 
 
 V(27r x 150 x 0-3 x 10- 6 x 2,00()) 2 + 1 
 
 = about 0'3 ampere. 
 
 Experiments are still wanting to show what current may be 
 considered as certain to kill a man, but it is very doubtful 
 
APPARATUS FOR DISTRIBUTION OF ELECTRICITY. 187 
 
 whether any man could stand 0*3 ampere for a sensible length 
 of time. It is probable that if the two persons both took firm 
 hold of the secondary conductors of E and F, both would be 
 killed. If the person at F be replaced by an accidental dead 
 earth on the secondary circuit of F, the person at E would 
 experience a greater current than 0*3 ampere. 
 
 It follows from the preceding consideration that secondary 
 generators of large electrostatic capacity are essentially dangerous, 
 even though the insulation of the primary circuit and of the 
 primary coils from the secondary coils is perfect. The moral is 
 for the constructor, Take care that the secondary generators have 
 not a large electrostatic capacity, say not more than 0'03 micro- 
 farad, better less than ^ microfarad ; for the inspector, Test the 
 system for safety. The test is very easy. Place a secondary 
 generator of greatest capacity at one end of the line and connect 
 its secondary circuit to earth through any instrument suitable for 
 measuring alternate currents under one ampere; put the other 
 end of the primary to earth ; the reading of the current measuring 
 instrument should not exceed such a current as it may be 
 demonstrated a man can endure with safety. 
 
12. 
 
 INDUCTION COILS OR TRANSFORMERS'. 
 
 [From the Proceedings of the Royal Society, February, 1887.] 
 
 THE transformers considered are those having a continuous 
 iron magnetic circuit of uniform section.* 
 
 Let A be area of section of the core ; 
 
 m and n the number of convolutions of the primary and 
 secondary coils, respectively ; 
 
 R, r, and p their resistances, p being the resistance of the 
 
 secondary external to the transformer ; 
 x and y currents in the two coils ; 
 a induction per square centimetre ; 
 a the magnetic force ; 
 I the length of the magnetic circuit ; 
 
 E = B sin 2?r (t/T), the difference of potentials between 
 the extremities of the primary; 
 
 T being the periodic time. 
 
 We have 
 
 (1) 
 
 (2) 
 
 Q = (r + p)y-nAa (3) 
 
 * For a discussion of transformers in which there is a considerable gap in the 
 magnetic circuit, see Ferraris, Torino, Accad. Sci. Mem., vol. xxxvu. 1885; also 
 chapter on the " Theory of Alternating Currents," in this volume. 
 
INDUCTION COILS OR TRANSFORMERS. 189 
 
 From (2) and (3), 
 
 nE = nRx m(r + p)y ................... (4) 
 
 Substituting from (1), 
 
 ......... (6) 
 
 (r + p)mE laR(r + p) . 
 
 n*R + m 2 (r + p) + 4?r In 2 ^ + m 2 (r + p)} ' 
 
 We may now advantageously make a first approximation. 
 Neglect ta in comparison with 4<7rmx, that is, assume the per- 
 meability to be very large; we have 
 
 _ ij (r + p)mflcos(2/r) 
 
 For practical purposes these equations are really sufficient. 
 
 We see first that the transformer transforms the potential in 
 the ratio njm, and adds to the external resistance of the secondary 
 circuit p a resistance (ri*R/m?) + r. This at once gives us the 
 variation of potential caused by varying the number of lamps 
 used. The phase of the secondary current is exactly opposite to 
 that of the primary. 
 
 In designing a transformer it is particularly necessary to 
 take note of equation (9), for the assumption is that a is 
 limited so that la may be neglected. The greatest value of 
 a is B/{(27r/T)mA} t and this must not exceed a chosen value. 
 We observe that B varies as the number of reversals of the 
 primary current per unit of time. 
 
 But this first approximation, though enough for practical 
 work, gives no account of what happens when transformers are 
 worked so that the iron is nearly saturated, or how energy is 
 wasted in the iron core by the continual reversal of its magnetism. 
 The amount of such waste is easily estimated from Swing's results 
 when the extreme value of a is known, but it is more instructive 
 to proceed to a second approximation, and see how the magnetic 
 properties of the iron affect the value and phase of x and y. We 
 
190 
 
 INDUCTION COILS OR TRANSFORMERS. 
 
 shall, as a second approximation, substitute in equations (5), (6), 
 (7) values of a deduced from the value of a furnished by the first 
 approximation in equation (9). 
 
 In the accompanying diagram, fig. 1, Ox represents a, Oy 
 represents a, and Oz the time t. 
 
 FIG. 1. 
 
 The curves ABGD represent the relations of a and a. EFG 
 the induction a as a function of the time, and HIK the deduced 
 relation between a and t. We may substitute the values of a 
 obtained from this curve in equations (5) and (6), and so obtain 
 the values of x and y to a higher degree of approximation. If the 
 values of a were expressed by Fourier's theorem in terms of the 
 time, we should find that the action of the iron core introduced 
 into the expression for x and y, in addition to a term in 
 cos (27r/jT) which would occur if a and a were proportional, terms 
 in sin (^irtfT) and terms in sines and cosines of multiples of 
 %7rt/T. It is through the term in sin (Zirt/T) that the loss of 
 energy by hysteresis comes in. 
 
 A particular case, in which to stay at a first approximation 
 would be very misleading, is worthy of note. Let an attempt be 
 made to ascertain the highest possible values of a by using upon 
 a transformer a very large primary current and measuring the 
 consequent mean square of potential in the secondary circuit 
 by means of an electrometer, by the heating of a conductor, 
 or other such device. The value of a will be related to the time 
 
INDUCTION COILS OR TRANSFORMERS. 
 
 191 
 
 somewhat as indicated by ABCDEFG in fig. 2 ; for simplicity 
 assume it to be as in fig. 3 ; the resulting relations of potential 
 in the secondary and the time will be indicated by the dotted 
 
 FIG. 2. 
 
 line HIJKOLMNPQ. The mean square observed will be pro- 
 portional to ML . \JLP ; but ML . LP is proportional to EL, hence 
 the potential observed will vary inversely as *JLP, even though 
 the maximum induction remain constant. If, then, the maximum 
 
 FIG. 3. 
 
 induction be deduced on the assumption that the induction is 
 a simple harmonic function of the time, results may readily be 
 obtained vastly in excess of the truth. 
 
13. 
 
 REPORT TO THE WESTINGHOUSE COMPANY OF 
 THE TEST OF TWO 6,500-WATT WESTINGHOUSE 
 TRANSFORMERS. May 31, 1892. 
 
 BEFORE giving any of the results of the tests I have made 
 with your transformers, it will be well to explain the methods of 
 experiment adopted. The instantaneous value at any epoch in 
 the period of the difference of potential between any two points 
 of a circuit in which the potential difference is varied periodically 
 is made effective on the measuring instrument by means of a 
 rotating contact maker attached to the shaft of the alternate 
 current generator. This contact maker was constructed for the 
 King's College laboratory by Messrs Siemens Brothers. It makes 
 contact once in each revolution for a period of about three- 
 quarters of a degree, and breaks it for the rest of the revolution. 
 It is entirely insulated, and so can be connected to any part 
 of the circuit. The position of the contact can be varied, and the 
 variation be read off on a graduated circle of 13 J inches diameter 
 divided into degrees, and by estimation the variation can be read 
 to one-tenth of a degree. The two points between which it is 
 desired to measure a potential difference are connected through 
 the contact maker to a condenser and a quadrant electrometer, 
 as shown in fig. 1, in which A and B are the points, the 
 potential difference of which at a stated epoch is to be measured, 
 (7 the revolving contact maker, D the reversing switch of the 
 electrometer, E the condenser, of which the capacity can be 
 varied, F the quadrant electrometer. It is evident that the 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 193 
 
 quadrant electrometer will give a reading proportional to the 
 potential difference of A and B, when C makes contact. If there 
 were no leakage, it would at once give this potential. It is to 
 obviate the effect of leakage that the condenser is introduced, 
 and the amount of the effect was determined by varying the 
 
 condenser thus: When the condenser had capacity 1, 0*5, and 
 0'2 microfarads, the readings of the electrometer for a given 
 potential difference of an alternating current at the position in 
 the period of maximum electromotive force were 138, 136, and 
 132, respectively. The rate of loss of potential will be pro- 
 portional to the reciprocal of the capacity, whence we infer that 
 the true reading, if insulation were perfect, would be 139^, and 
 hence the readings are always corrected by adding one per cent. 
 When the potential difference was too great for the electrometer 
 it was reduced in any desired ratio by two considerable resistances 
 introduced between the points to be measured in the usual way 
 (fig. 2). . The potential difference may, of course, be measured 
 
 e 
 
 FIG. 2. 
 
 in other ways. An ordinary voltmeter may be placed between 
 A and B, in which case it must be standardized with the contact 
 breaker in circuit ; and it will depend for its constant on the 
 duration of the contact, which may vary. Further, it gives, not 
 the difference of potential at any definite epoch, but the mean 
 difference for the whole time of the contact. The condenser may 
 be used and its potential be measured by discharge through a 
 galvanometer: this is open to the objection that if there be any 
 leakage, the result will depend on the time at which the contact 
 is broken by the condenser key in relation to the time at which it 
 was made by the revolving contact maker. Lastly, a Clark cell 
 H. i. 13 
 
194 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 may be used, by a method which Major Cardew pointed out 
 to me (fig. 3), the resistance being adjusted till there is no 
 deflection. This is open to the same objection as the first, 
 
 CELL 
 
 FIG. 3. 
 
 namely, that it gives the mean of the potential differences which 
 occur during the contact. By making use of the first-mentioned 
 method we have the means of measuring accurately any potential 
 difference at any epoch of the period, and of knowing the epoch. 
 
 For these experiments two transformers intended to be 
 identical were available, each transforming between 2,400 and 
 100 volts. It was most convenient on account of the resistance 
 available to couple these transformers up from 100 to 2,400 in the 
 first or No. 1 transformer, then down from 2,400 to 100 in the 
 second or No. 2 transformer, and to take up the energy from the 
 second in a non-inductive resistance. The arrangement is shown 
 in fig. 4. 
 
 FROM TERMINALS S^ <.^> JO NON-INDUCTIVE 
 
 OF MACHINE. S> ><^ RESISTANCE. 
 
 TRANSFORMER No.1. TRANSFORMER No.2. 
 FIG. 4. 
 
 The obvious way in returning the efficiency of the combination 
 would be to measure, at various epochs of half a period, the 
 potential differences of the terminals of the machine and the 
 current passing in the No. 1 transformer; in like manner, at 
 the same epochs, to measure either the potential differences or 
 the current passing to the non-inductive resistance, thence to 
 deduce the power supplied to the first transformer and taken 
 from the second. This would be open to certain objections; we 
 are comparing two nearly equal magnitudes and desire their 
 ratio ; the ratio will be affected with the full error arising from an 
 error in the determination of either magnitude, and such errors 
 may be material, as the observations are not simultaneous, 
 and conditions may change between one series of observations 
 and another. 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 195 
 
 These objections are avoided by the method adopted. The 
 current from No. 2 is observed at certain epochs, the difference of 
 current between No. 2 and No. 1, and the difference of potential 
 difference of No. 2 and No. 1 at the same epochs. These give the 
 currents and potentials of No. 1 at the same epochs as the 
 corresponding determinations of No. 2, and the difference will 
 only be affected with the proportion of error of those differences. 
 For example, suppose the efficiency of the combination were 
 90 per cent., and the possible error of determination of power 
 1 per cent., our result might be anything from 88 per cent, to 
 92 per cent, if made in the obvious way, but if made by differences 
 the maximum loss would be 10*1 per cent., and the possible least 
 determination of the efficiency would be 89'8 per cent. The 
 method is essentially similar to the method I described* and 
 
 TO NON-INDUCTIV^ 
 RESISTANCE,, 
 
 No.1, No,2,| 
 
 TO REVOLVING CONTACT MAKER. 
 
 FIG. 5. 
 
 subsequently used for testing dynamos. The measurements for 
 difference of potential differences are made as in fig. 5 and for 
 current differences as in fig. 6, where G is a known small non- 
 
 TO NON'-INDUCTIVE 
 RESISTANCE. 
 
 TO REVOLVING CONTACT MAKER. 
 FIG. 6. 
 
 inductive resistance. The two currents will, of course, slightly 
 disturb each other, but this is readily allowed for in the calcu- 
 lations. 
 
 No.1, 
 
 _!_ 
 
 TO NON-INDUCTIVE 
 RESISTANCE. 
 
 TO REVOLVING CONTACT MAKER. 
 
 FIG. 7. 
 
 Another method would be to couple them as in fig. 7, G^ 
 and 6r 2 being equal non-inductive resistances. This arrangement 
 
 * Phil Trans., 1886, page 347. 
 
 132 
 
196 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 is quite free from disturbance, but requires two resistances 
 adjusted to exact equality. A single transformer can be tested in 
 the same way, though in this case reliance must be placed upon 
 resistances to reduce the current of the low potential coil, and to 
 reduce the potential of the high potential coil in the ratio of the 
 number of windings in the two coils. 
 
 The current was throughout generated by a Siemens alternator 
 with 12 magnets, run at a speed between 830 and 840 revolutions 
 per minute, which gives a frequency of 5,000 per minute, or 83 to 
 84 per second. 
 
 The first experiment tried* was with the two transformers 
 coupled, but with No. 2 transformer on open circuit, or on nearly 
 open circuit, for a high resistance for purposes of measurement 
 was interposed between the terminals of the low resistance coil of 
 No. 2 transformer. The actual results are given in Table I. 
 
 TABLE I. 
 
 
 
 Potential No. 2. 
 
 Potential No. 1. 
 
 
 
 
 Current 
 
 Thick Coils 
 
 Thick Coils 
 
 
 
 Leads of 
 Exploring 
 Brush on 
 Divided 
 Circle 
 
 No. 1. 
 Thick 
 
 Coils 
 
 Amperes 
 
 
 
 Square of 
 Volts 
 
 Watts 
 supplied 
 to No. 1 
 
 Volts 
 
 Square of 
 Volts 
 
 P. D. 
 
 See Nos. 
 1 and 2 
 
 Volts 
 
 <v/mean 2 
 = 101-9 
 
 \/mean' 2 
 
 
 
 
 = 101-1 
 
 Volts 
 
 
 
 
 267 
 
 -2-2 
 
 + 25-4 
 
 645 
 
 + 0-9 
 
 + 26-3 
 
 692 
 
 - 57-9 
 
 270 
 
 -0-3 
 
 + 70-2 
 
 4,928 
 
 + 1-2 
 
 + 71-4 
 
 5,098 
 
 - 21-4 
 
 273 
 
 + 1-1 
 
 + 95-3 
 
 9,082 
 
 + 1-1 
 
 + 96-4 
 
 9,292 
 
 + 106-0 
 
 276 
 
 + 2-1 
 
 + 120-4 
 
 14,496 
 
 + 1-1 
 
 + 121-5 
 
 14,761 
 
 + 255-1 
 
 279 
 
 + 2-8 
 
 + 147-7 
 
 21,816 
 
 + 1-1 
 
 + 148-8 
 
 22,140 
 
 + 416-6 
 
 282 
 
 + 3-2 
 
 + 147-2 
 
 21,668 
 
 + 0-9 
 
 + 148-1 
 
 21,935 
 
 + 473-9 
 
 285 
 
 + 3-4 
 
 + 119-8 
 
 14,351 
 
 + 0-7 
 
 + 120-5 
 
 14,520 
 
 + 409-7 
 
 288 
 
 + 3-5 
 
 + 97-8 
 
 9,565 
 
 + 0-6 
 
 + 98-4 
 
 9,683 
 
 + 344-4 
 
 291 
 
 + 3-7 
 
 + 71-3 
 
 5,084 
 
 + 0-4 
 
 + 71-7 
 
 5,140 
 
 + 260-3 
 
 294 
 
 + 3-5 
 
 + 26-0 
 
 676 
 
 + 0-3 
 
 + 25-97 
 
 674 
 
 + 90-9 
 
 
 
 
 102,311 
 
 
 
 103,935 
 
 2,282-6 
 
 * So far as I know, the first discussion of endless magnetic circuit transformers, 
 based on the actual properties of the material, is in a note by myself (Proc. Roy. 
 Soc. vol. XLII., and The Electrician, vol. xvm. p. 421). Definite results were 
 obtained by methods generally similar to those now used by Prof. Ryan (The 
 Electrical World, Dec. 28, 1889). The theory of transformers is well set forth by 
 Prof. Fleming (The Electrician, April 22 and 29, 1892). 
 
TEST OF WESTIXGHOUSE TRANSFORMERS. 
 
 197 
 
 and are expressed in fig. 8. Tables II., III., and IV. give the 
 results for half power, nearly full power, and full power, and the 
 sets of curves of figs. 9, 10 and 11 give the results of the table. 
 In these tables the first column gives the position of the contact 
 brush in degrees, so that 60 on this scale corresponds with a 
 
 FIG. 9. 
 
 of a second. 
 
 complete cycle. Three degrees are thus ^3-5 
 
 ooo X 
 
 The second column of Table I. is the current in the thick coil of 
 No. 1 transformer, as determined by the difference of potential at 
 
198 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 the two ends of a non-inductive resistance in which the current 
 passes. The third column is the potential difference of No. 2 
 transformer, a direct determination. The fourth column is solely 
 for the purpose of determining the square root of the mean of the 
 
 40- 
 
 20- 
 
 10- 
 
 200 
 
 160 
 
 100 
 
 2J4 
 
 50 n 
 
 40 
 
 30- 
 
 w 20- 
 
 o 
 
 > 10- 
 
 C 
 
 10- 
 
 P 20 
 30- 
 40- 
 
 50- 
 
 
 <D 
 O 
 
 2 ^ 
 
 4 
 
TEST OF WESTIXGHOUSE TRANSFORMERS. 199 
 
 squares of the third column. The fifth column is a direct 
 determination of the difference of potential of No. 1 and No. 2, 
 obtained in the manner explained with reference to fig. 5. 
 
 The sixth column is the deduced potential difference of the 
 terminals of the thick wire of No. 1 transformer, being the sum of 
 the third and fifth columns. The seventh column, like the fourth, 
 is merely for the purpose of determining the square root of the 
 mean of the squares of column six, while the eighth gives the 
 rate at which power is given out or received by the pair of 
 transformers. 
 
 If the transformers had been exactly equal, the potentials for 
 the two given by Table I. would have been equal, though 
 they would have differed a little in phase owing to the lines of 
 magnetic induction which pass through the non-magnetic space 
 between the two coils of the transformer*. The difference shows 
 that No. 1 transformer has a ratio of transformation slightly 
 greater than No. 2. If we correct the potential of either 
 No. 1 or No. 2, there still remains a difference between them, 
 but this difference will be greatest about when the potentials are 
 nil. This is due to the lost induction just referred to. In order 
 to check the conclusion that the two transformers are not precisely 
 equal, they were directly compared, as in fig. 12. The trans- 
 formers were coupled parallel, as in fig. 12, and the difference of 
 
 FROM MACHINE TERMINALS. 
 
 No1 
 
 /VWVWVWMM _ A/WVWWWWA 
 
 TO CONTACT MAKER & ELECTROMETER. 
 FIG. 12. 
 
 potential of the two high potential coils was measured : the value 
 of its square root of mean square was 12'5 volts, the potential 
 of the transformer being 2,400. This does not necessarily imply 
 that the potentials of the two transformers differ by one half 
 per cent. ; it may be largely due to a difference of phase between 
 the two. 
 
 * Prof. Perry has already pointed out that the effect of such an induction cannot 
 be entirely neglected, even in endless circuit transformers 
 
200 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 The current supplied to the No. 1 transformer is to be ac- 
 counted for by the currents necessary to magnetize the two 
 transformers, and by the local currents in their cores. To ascer- 
 tain the former, the curve of magnetization of one of the trans- 
 formers was determined by the ballistic galvanometer for nearly 
 the same induction as in Table I., the changes of current 
 supplied by a battery being made by a reversing switch, or by 
 suddenly introducing resistance into the primary circuit, and the 
 consequent changes of induction being measured by the galvano- 
 meter. The tardiness of change of current in the transformer due 
 to its self induction was sufficiently reduced by using many cells 
 and a considerable resistance. The results are shown in fig. 13 
 
 FIG. 13. 
 
 for a single transformer. In this curve the abscissae are the 
 currents in the thin coil of the transformer, divided by 24 to 
 reduce it to the same effect as it would have had if it had been in 
 the thick coil. The ordinates are the inductions as measured by 
 the kick on the galvanometer, but reduced to a scale to make 
 them directly comparable with the volts when the transformer is 
 used with an alternating current. These results are not given in 
 absolute units. The procedure to determine points on the curve 
 was : first, pass the maximum current corresponding to the 
 point (7; next, suddenly diminish the current by inserting suitable 
 resistance in the thin coil circuit, and observe the kick the drop 
 of ordinate from C to A corresponds to the kick, and the abscissa 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 201 
 
 of A is the current after it has been reduced ; next, reverse the 
 current, and observe the kick the kick corresponds to the further 
 drop of ordinates from A to E. In this manner a series of points 
 are determined on the curve. Fig. 14 shows the relation between 
 
 induction and magnetizing current for the pair of transformers, as 
 deduced from the experiments with alternating currents set forth 
 in Table I. The ordinates in this curve are the area of the 
 curve of potentials of fig. 8, for the ordinates of this latter 
 curve are the rates at which the induction is changing, while 
 the abscissas are the currents in the thick wire at corresponding 
 times. The points marked in fig. 15 give the remainder after 
 deducting the magnetizing current as estimated in fig. 13 from 
 the currents of fig. 14 that is to say, fig. 13 is corrected first 
 for the small difference in maximum induction ; then, correspond- 
 ing to any induction, the current is taken from the curve, it 
 is doubled, as there is only one transformer, and the result is 
 deduced from the corresponding current of fig. 14. The diffe- 
 rences are, the magnetizing current equivalent and opposite in 
 effect to the local currents in the cores. If the local currents 
 were equivalent to a current in a single secondary circuit, the 
 points of fig. 15 ought to have had the form of the full line of 
 fig. 15, drawn through the points + , in which the abscissae are 
 
202 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 proportional to the potential difference, and the ordinates to the 
 induction. Returning to Table I., we find that the fall of 
 potential difference on open circuit in the whole combination is 
 0*8 volt, and that the loss of power in magnetizing the cores 
 and in local currents is 228*26 watts, that is, a loss for each trans- 
 former of 11413 watts. The total loss of 228 watts may be 
 divided into 126 watts accounted for by hysteresis and 102 watts 
 due to local currents. 
 
 252 
 
 240> 
 
 Amperes. 
 
 270 
 
 21012 
 Amperes. 
 
 FIG. 15. 
 
 Referring now to Table III. and fig. 10, the earlier columns 
 explain themselves, but a word is necessary about the last six 
 columns. The watts supplied to No. 1 are simply the products 
 at each time of the volts at its terminals and the amperes passing 
 through, similarly to the watts given out by No. 2. We see first 
 that the efficiency of the whole combination with this load is 
 9373 per cent., and hence the efficiency of one transformer, if the 
 losses in the two are equal, may be taken as 9 6 '9 per cent. The 
 fall of potential in the whole combination is 6*1 volts, but the fall 
 with no load is 0*8 volt ; hence the variation due to the load with 
 constant potential on the thin coil of No. 1 is 5*3 volts, or, if the 
 fall of potential in the two transformers were equal, which it 
 is not, for a single transformer 2'65 volts. Assuming that the 
 transformers are equal, the power lost in resistance would be 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 203 
 
 expected to be the mean of mean current x the difference of 
 potential difference, or 215*4 watts. It is, in fact, 150 watts, 
 as given by multiplying the square of currents by resistances. 
 But the transformers are not exactly equal, and there is the 
 waste magnetic field, both of which will have a small effect on 
 the distribution of loss between the two classes of loss, viz., that 
 by hysteresis and local currents, and that by resistance, but none 
 upon the gross efficiency. 
 
 The other tables, II. and IV., are arranged in exactly the 
 same way as Table III., but the number of observations on 
 Table IV. is insufficient to bring out all the peculiarities of the 
 transformers. 
 
 It has already been stated that, if the loss of potential due to 
 load in the two transformers be equal, it will amount to 2 65 per 
 cent. The following experiment was tried to ascertain if this loss 
 was equal: The transformers were coupled in series as before. 
 The mean potential difference of the thick wire was measured by 
 Thomson's multicellular, and of the thin wire by Thomson's 
 electrostatic voltmeter. The mean of a considerable number of 
 experiments is given in the following table, the load being the 
 same as in Table III., and the results being corrected to the same 
 potential of the thin wire : 
 
 
 Full 
 
 Load 
 
 Open 
 
 Circuit 
 
 Number 
 
 Thomson's 
 Electrostatic 
 
 Thomson's 
 Multicellular 
 
 Thomson's 
 Electrostatic 
 
 Thomson's 
 Multicellular 
 
 1 
 2 
 
 2,380 
 2,380 
 
 99 '-8 
 94-2 
 
 2,380 
 2,380 
 
 97-0 
 96-2 
 
 This shows that of a total drop of 4'8 volts, 2 - 8 volts occurred 
 in No. 1, and 2 volts in No. 2. There is no doubt of the fact that 
 the drop is greater in No. 1 than in No. 2, which is connected with 
 the waste field between the two coils. Of course these trans- 
 formers are intended to work exactly as No. 2 is working, in which 
 case the drop from no load to nearly full load, as shown by this 
 experiment, is 2'0 volts. The way in which this waste field causes 
 inequality of drop of potential in the two transformers, coupled 
 
204 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 as in my experiments, is well worthy of careful consideration. 
 The waste field is proportional to the current in the transformers, 
 or, better, to the mean of the two currents in ampere turns. The 
 electromotive force due to this waste field will be proportional to 
 the rate of change of the current. If the current were expressed 
 by a simple harmonic curve, the electromotive force due to the 
 waste field would also be a simple harmonic curve differing in 
 
 7T 
 
 phase by ^ The curve of potentials is roughly in the same 
 
 phase as the curve of current. Let a be the amplitude of potential 
 difference of No. 2 transformer, b be the amplitude of difference 
 between the potential difference in No. 2, and the potential diffe- 
 rence of the thin wire divided by 24. 26 will be very nearly the 
 amplitude of difference between the thick wires of Nos. 1 and 2. 
 The ratios of potentials in No. 1 and No. 2 will then be 
 
 and 
 
 ^ , _ 
 
 or 1 H and 1 + 
 
 2a z 
 
 or the drop in the first from this cause is three times as great 
 as in the second transformer. We shall return to the waste field 
 immediately. Putting aside harmonic curves, and returning to 
 the facts as they are, the following table gives : first, half the 
 
 Half Difference of 
 Potential Difference 
 
 Volts of High Potential 
 Coil Divided by 24 
 
 Squares of Volts 
 
 15-6 
 
 -5-0 
 
 25-0 
 
 14-8 
 
 41-3 
 
 1,706-0 
 
 11-3 
 
 74-3 
 
 5,520-0 
 
 10-8 
 
 102-6 
 
 10,530-0 
 
 11-1 
 
 131-3 
 
 17,240-0 
 
 5-5 
 
 147-1 
 
 21,640-0 
 
 - 1-1 
 
 137-0 
 
 18,770-0 
 
 - 3-1 
 
 119-3 
 
 14,230-0 
 
 - 5-9 
 
 95-1 
 
 9,040-0 
 
 -12-1 
 
 53-4 
 
 2,850-0 
 
 Square root of mean square =100*8 
 
 difference of potential difference taken from Table III., that is, at 
 each instant the drop of potential in No. 2 ; secondly, the volts of 
 
TEST OF WESTING HOUSE TRANSFORMERS. 205 
 
 the thin wire of No. 2 reduced for number of convolutions this is 
 of course the mean of potential difference between 1 and 2 ; lastly, 
 the squares of these volts. From this we see a mean square 100*8 
 showing the drop in No. 2 to be 2*6 volts out of a total drop 
 of 6*1, and the remainder 3*5, the drop in No. 1. Diminishing 
 these results by 0*4, the half of 0'8, the fall observed with no 
 load, the actual losses from no load to nearly full load will be 2*2 
 and 3-1. 
 
 Turn now to the last column of Table III. This gives the 
 difference of potential differences corrected for the loss of volts 
 by resistance. It is shown dotted on fig. 10; this curve presents 
 one or two peculiar features. It should be possible to infer the 
 form of this curve from the curve of current. The rates at which 
 the mean current is changing are as follows : 
 
 27H 
 30-7 24-2 19-2 18-5 13'9 1*7 -9'3 -12'7 -21-7 -28'1 
 
 which happens to come to a scale which can be at once plotted. 
 The points marked are the points of the curve corresponding 
 with the above rates. The agreement of the points with the 
 curve is remarkably close. This exhibits very completely the 
 effect of waste magnetic field in this transformer. 
 
 For half power, as taken from Table II., the rates are as 
 follows : 
 
 27H 274 277 260^ 
 14-6 11-5 9-4 10-6 4-4 -4-6 -7-2 -7-5 -13-6 -17-6 
 
 and in the same way in fig. 9 the dotted curve represents the 
 difference of electromotive force corrected for resistance, and the 
 points correspond with the above rates. 
 
 Fig. 16 gives the efficiencies for the combined transformers in 
 terms of the load. This curve is the hyperbola : 
 
 X - (A + BX + CX*) 
 Efficiency = 100 . - , 
 
 where A = 228, the loss by hysteresis ; 
 
 B = 0*005, and mainly depends upon the waste field ; 
 C = 0*0000035, and is mainly the loss by resistance ; 
 X = load in watts. 
 
206 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 To sum up, I find that the efficiency of the transformer at full 
 load would be 96'9 per cent. ; at half load, 96 per cent. ; and at 
 quarter load, over 92 per cent. The magnetizing current of the 
 transformer amounts to 114 watts, or 175 per cent. The drop 
 of potential from no load to full load is between 2 per cent, and 
 2'2 per cent. 
 
 ^ 80 
 
 X 
 
 i"*"," 
 
 
 
 
 
 / 
 u / 
 
 * 60 7 
 
 / 
 
 
 
 
 
 
 *S J 
 
 01 / 
 
 w / 
 
 m 40 1_/ 
 
 
 
 
 
 
 
 IJ/ 
 
 
 
 
 
 
 
 0. ZU / 
 
 
 
 
 
 
 
 01234567 
 Load in io 3 watts. 
 
 FIG. 16. 
 
 In conclusion, I wish to express my thanks to Mr Wilson, of 
 King's College ; this gentleman carried out the experiments under 
 my direction, and made nearly all the numerical calculations and 
 drew most of the curves for me. 
 
TEST OF WESTIXGHOUSE TRANSFORMERS. 
 
 207 
 
 "3.* 
 
 I* 
 
 r 
 
 r-( ii d i-H i-H 
 
 i- 
 
 s o 
 
 s 
 
 t-g 
 s; 3 
 
 i 
 
 E 
 
 < 
 
 1 
 
 + + 1 
 
 1 1 1 
 
 ppppoptNO^p 
 
 iH H rH <M (M o5 &5 
 
 O <M O 03 O 00 t- 
 
 * ' * 00 O C4 ^ CQ 
 
 rH iH O? 7Q (N (M 
 
 C 
 
 
 
 S 
 
 00 O O 
 C ^ 00 
 
 co 
 
 OJ 
 
 o-^^ P 
 
 "a. S > S 
 
208 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 -II 
 
 jli 
 
 + -H + + + + I 1 1 
 
 O SD >O O 00 rH 
 
 a?TH(>Joq>o 
 oo<M<X)TH-t< 
 
 CO -^ "** CO CO iH 
 
 1 1 
 
 Loss by Eesistance 
 and probably Waste 
 Field 
 
 sin 
 
 S e iT S 
 
 + + + + 
 
 C i I i I C^ CO 
 
 QC 00 CO t*" 00 
 
 (M <N (M <N 
 
 + I I I I 
 
 I s 
 
 s? S J 
 
 ^ > 
 
 '5b- 
 
 1 
 
 CD 
 
 i 
 
 CO __o 
 | 
 
 00 ^ 
 
 
 -S 8* 
 
 " 
 
 
 >H (M <M rH i-H 
 
 fi* 
 
 q 
 
 "81 
 
 ' 
 
 ODlO ' 
 CDO5OJ 
 
 + + + + + + 1 ! 1 
 
 posooooopo 
 
 OOOOC5?O> ICOOOC<I 
 
 p$ f 9 A Q IP t 1> (5 2 
 
 CO (M rH rH W i-H <M 
 
 'g 
 oa > i 
 PH |3 .2 V^ 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 209 
 
 A*q 
 
 rH <M CO CO CO CO rH 
 + 1 I + + + + + + + 
 
 
 pa^unoooun sasso^j 
 
 + + + 1 1 1 1 
 
 
 
 -o^ <n paijddns S^BAY 
 
 S I!0 ^PNX '& P n 
 -[ -sovj ni iBi^na^oj jo 
 
 ntial Diff 
 No 1. 
 Thick Co 
 
 r-l<N 
 
 + + + + + + 1 1 1 1 
 
 " , 
 
 
 
 (M-<^CO(MO 
 il i 1 i 1 i 1 r 1 
 
 g ptre j -sox ui 
 
 u-eaj^ 
 
 rO 
 
 
 sai^dray 
 
 +++++++++ 
 
 saiadtay -g pu 
 
 aouaiajgtQ; 
 
 1 1 +++++++ 
 
 n0 
 
 'OK 
 
 1 +++++++++ 
 
 no 
 
 H. I. 
 
 jo 
 
 
 TJI 
 
 U 
 
210 
 
 TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 
 "o 
 
 o, 05 
 
 ^ <M O O CO O5 
 
 
 1- 
 
 li 
 
 C rH 1O 00 Ci 00 
 ^ 10 OS -rt* 00 <N 
 
 <5 o 
 
 n [>, 
 
 S || 
 
 CO CO CO CO rH 
 
 ^2 
 
 m 
 
 > 
 
 
 1 
 
 o 
 
 
 s 
 
 rH O O CO (N 
 C<1 00 CO rH CO 
 
 PH 
 
 
 > 
 
 rH rH 
 
 
 'o "c . -^ 
 
 9 
 
 3 
 
 TH ^ ^ 00 <N 
 
 
 g g S, 
 
 3 
 
 M 
 
 CO rH CO 
 rH CO O OS IO 
 
 
 So a C3- 
 
 1 
 
 + + + + + 
 
 
 ' rt i 
 
 H 
 
 
 
 i 
 
 i 
 I 
 
 CO 05 CO <N 00 
 
 
 1 
 
 i 
 
 (M rH rH (M <M 
 
 rH CO O O5 1C 
 
 
 1 
 
 | 
 
 
 
 <: 
 
 | 
 
 + + + + + 
 
 
 
 S 
 
 t** O5 CO Oi O^ 
 
 6 
 
 | 
 
 1 
 
 rH <N <M CO 
 
 1 + + + + 
 
 2 
 
 6 
 
 << 
 
 
 1 
 
 
 
 rH rH O5 t rH 
 
 ^ 
 
 H<* 
 
 'o 
 
 **^^ 
 
 (M rH O? CO * 
 + 1 1 1 1 
 
 
 
 ^2 
 
 
 
 K 
 
 * 
 
 
 
 Current 
 
 3nt Differen 
 Nos. 1 
 
 Corrected 
 Deflection 
 
 o o * oo o 
 
 rH rH rH (M 
 
 
 g 
 
 n3 S 
 
 
 
 
 
 O> O 
 
 
 
 o 
 
 
 
 
 
 S-i o 
 
 t* l> C- 00 rH 
 
 O U5 <* CO rH 
 
 
 
 SQ 
 
 rH rH rH <M 
 
 
 I ; 
 
 i 
 
 3 
 
 CO O CO CO CO 
 Tj< rH O5 O Oi 
 rH CO OS CO "* 
 
 
 
 
 11 
 
 
 
 oi 
 
 m 
 
 
 
 Oi O5 O Ci 1C 
 O C rH CO O 
 <M rl< CO <M 
 
 
 o 
 
 
 
 
 
 
 >Q 
 
 
 
 a 
 
 ^ a 
 
 
 
 lit! 
 
 li 
 
 O5 CO C~ rH C~ 
 U3 IO (N 00 O 
 <?Q Tfi CO <M 
 
 
 ifji 
 
 i 
 
 g gs j 2 
 
 
 ^I^s 
 
 
 
 
TEST OF WESTINGHOUSE TRANSFORMERS. 
 
 211 
 
 
 o-S 2 
 
 Il^s 
 Jill 
 
 -8 i5 
 
 -^ US O) <N t- 
 
 cc OQ o is t- 
 
 CO (N i-H 
 
 + + + i 1 
 
 
 
 
 03 < m 
 
 >"S a 3 
 
 2 
 .2^ g 
 
 rrj g 
 ^ffii^ 
 
 ,H 00 p CO ^ 
 
 b o oo oo 
 
 O 00 i t CQ O 
 CO CO rH 
 
 1 + + + + 
 
 O 
 
 | 
 
 CO 
 
 CO 
 
 Kesistance 
 ibly Waste 
 
 * ^ 
 
 8"S .3 
 
 JlllS 
 
 ^ 8 8S 
 
 I 1 M 
 
 >O Ofl O O CO 
 
 t O CO O O 
 ^ 00 CS CO (N 
 ^ CO^ 0^ GO ^ 
 i-T iH* 1 1 
 
 + + + 1 1 
 
 9 s 
 
 rH 
 
 
 
 cc 
 <N 
 
 *! 
 
 l* 
 
 OQ r& 
 
 3 i 
 
 H 
 
 -i a, 
 
 v. r 
 
 00 00 O CO CO 
 
 b c<i OQ <N o 
 
 -^< 00 H O5 
 r-t CO CO 
 
 W 
 
 co 
 <* 
 
 C5 
 
 
 
 a,* * 
 
 |gl 
 
 s s a s 
 
 t- 
 
 3 
 
 
 
 *-j? 
 
 "* <M CO 
 1 1 1 1 
 
 II 
 
 co 5- 
 
 a 
 
 rH 
 
 
 si" 
 
 1-3.5 
 
 > A 25 
 ^5 
 
 *O O O O CO 
 C^ CO Wt) t* CO 
 
 O M3 O rH O5 
 
 CD* ^ o" ^r 
 
 1-1 1-1 
 
 o 
 
 s 8 
 
 CO 
 CO 
 
 
 
 ^-s^a 
 !119 
 
 is^a 
 
 So ^ 
 PW^H 
 
 CO rH (M C9 US 
 
 00 CO t- CO Oi 
 CO OS <M rH rtl 
 i 1 iH 
 
 
 
 
 lift* 
 
 ^ |g 
 
 5 S S S 5 
 
 g ^ C- rH CO 
 
 01 
 t- 
 
 w 
 
 
 
 i*>" 
 
 ~ H CT CM i-l 
 W i-H <N rH 
 
 CO 
 
 ^ 
 
 
 1 
 
 | 
 1 
 
 1 
 
 U5 <N CO CO 
 
 b >b * o cb 
 
 rH rH CO 
 rH rH rH 
 
 + + 1 + + 
 
 
 
 rH 
 
 
 B 
 
 IS 
 
 t l 
 
 <u ^ , 
 
 OS 00 (O 00 00 
 CO Tj< 4ji 10 U3 
 CO <M rH O? 
 
 + + + 1 1 
 
 
 
 1 
 
 
 
 IS 11 
 
 "S-2 g^g 
 ?Fl| <5 
 
 tO C* <M O5 OQ 
 <* 1O -<fl 10 O 
 CO OJ rH <M 
 
 
 
 
 1 11 
 
 1! 
 
 O O (N Oi CO 
 M5 O <* O CO 
 CO CQ rH <N 
 
 
 
 
 s.s^ 
 
 r^ gjS'C'g 
 
 3|H 3 
 
 <M 00 rjt 
 t* t* 00 00 O5 
 01 <M <N (M <M 
 
 
 
 > 
 
 1 
 M 
 
 142 
 
14. 
 
 PRESIDENTIAL ADDRESS TO THE INSTITUTION OF 
 ELECTRICAL ENGINEERS, JANUARY 9, 1890. 
 
 ; MAGNETISM. 
 
 As old as any part of electrical science is the knowledge that 
 a needle or bar of steel which has been touched with a loadstone 
 will point to the North. Long before the first experiments of 
 Galvani and Volta the general properties of steel magnets had 
 been observed how like poles repelled each other, and unlike 
 attracted each other ; how the parts of a broken magnet were each 
 complete magnets with a pair of poles. The general character of 
 the earth's magnetism has long been known that the earth 
 behaves with regard to magnets as though it had two magnetic 
 poles respectively near the rotative poles, and that the direction of 
 the needle has a slow secular motion. For many years the earth's 
 magnetism has been the subject of careful study by the most 
 powerful minds. Gauss organised a staff of voluntary observers, 
 and applied his unsurpassed powers of mathematical analysis to 
 obtaining from their results all that could be learned. 
 
 The magnetism of iron ships is of so much importance in 
 navigation that a good deal of the time of men of great power has 
 been devoted to its study. It was the scientific study of Archibald 
 Smith; and Airy and Thomson have added not a little to our 
 practical knowledge of the disturbance of the compass by the iron 
 of the ship. Sir W. Thomson, in addition to much valuable prac- 
 tical work on the compass, and experimental work on magnetism, 
 has given the most complete and elegant mathematical theory of 
 
MAGNETISM. 213 
 
 the subject*. Of late years the development of the dynamo 
 machine has directed attention to the magnetisation of iron from 
 a different point of view, and a very great deal has been done by 
 many workers to ascertain the facts regarding the magnetic pro- 
 perties of iron. The upshot of these many years of study by 
 practical men interested in the mariner's compass, or in dynamo 
 machines by theoretical men interested in looking into the 
 nature of things, is, that although we know a great many facts 
 about magnetism, and a great deal about the relation of these 
 facts to each other, we are as ignorant as ever we were as to any 
 reason why the earth is a magnet, as to why its magnetic poles 
 are in slow motion in relation to its substance, or as to why iron, 
 nickel, and cobalt are magnetic, and nothing else, so far as we 
 know, is to any practical extent. In most branches of science the 
 more facts we know the more fully we recognise a continuity in 
 virtue of which we see the same property running through all the 
 various forms of matter. It is not so in magnetism ; here the 
 more we know the more remarkably exceptional does the property 
 appear, the less chance does there seem to be of resolving it into 
 anything else. It seems to me that I cannot better occupy the 
 present occasion than by recalling your attention to, and inviting 
 discussion of, some of those salient properties of magnetism as 
 exhibited by iron, nickel, and cobalt properties most of them 
 very familiar, but properties which any theory of magnetism 
 must reckon with and explain. We shall not touch on the 
 great subject of the earth as a magnet though much has been 
 recently done, particularly by Rticker and Thorpe but deal 
 simply with magnetism as a property of these three bodies, 
 and consider its natural history, and how it varies with the 
 varying condition of the material. 
 
 To fix our ideas, let us consider, then, a ring of uniform 
 section of any convenient area and diameter. Let us suppose 
 this ring to be wound with copper wire, the convolutions being 
 insulated. Over the copper wire let us suppose that a second 
 wire is wound, also insulated, the coils of each wire being 
 arranged as are the coils of any ordinary modern transformer. 
 Let us suppose that the ends of the inner coil, which we will 
 call the secondary coil, are connected to a ballistic galvanometer ; 
 
 * Papers on Electrostatics and Magnetism, p. 340 et seq. 
 
214 MAGNETISM. 
 
 and that the ends of the outer coil, called the primary, are 
 connected, through a key for reversing the current, with a battery. 
 If the current in the primary coil is reversed, the galvanometer 
 needle is observed to receive a sudden or impulsive deflection, 
 indicating that for a short time an electromotive force has been 
 acting on the secondary coil. If the resistance of the secondary 
 circuit is varied, the sudden deflection of the galvanometer needle 
 varies inversely as the resistance. With constant resistance of the 
 secondary circuit the deflection varies as the number of convolu- 
 tions in the secondary circuit. If the ring upon which the coils of 
 copper wire are wound is made of wood or glass or, indeed, of 99 
 out of every 100 substances which could be proposed we should 
 find that for a given current in the primary coil the deflection of 
 the galvanometer in the secondary circuit is substantially the 
 same. The ring may be of copper, of gold, of wood, or glass, it 
 may be solid or it may be hollow, it makes no difference in the 
 deflection of the galvanometer. We find, further, that with the 
 vast majority of substances the deflection of the galvanometer in 
 the secondary circuit is proportional to the current in the primary 
 circuit. If, however, the ring be of soft iron, we find that the 
 conditions are enormously different. In the first place, the deflec- 
 tions of the galvanometer are very many times as great as if the 
 ring were made of glass, or copper, or wood. In the second place, 
 the deflections on the galvanometer in the secondary circuit are 
 not proportional to the current in the primary circuit ; but as the 
 current in the primary circuit is step by step increased we find 
 that the galvanometer deflections increase somewhat as is illus- 
 trated in the accompanying curve (Fig. 1), in which the abscissae 
 are proportional to the primary current, and the ordinates are 
 proportional to the galvanometer deflections. You observe that 
 as the primary current is increased the galvanometer deflection 
 increases at first at a certain rate ; as the primary current attains 
 a certain value the rate at which the deflection increases there- 
 with is rapidly increased, as shown in the upward turn in the 
 curve. This rate of increase is maintained for a time, but only 
 for a time. When the primary current attains a certain value 
 the curve bends downward, indicating that the deflections of 
 the galvanometer are now increasing less rapidly as the primary 
 current is increased ; if the primary current be still continually 
 increased, the galvanometer deflections increase less and less rapidly. 
 
MAGNETISM. 
 
 215 
 
 Now what I want to particularly impress upon you is the 
 enormous difference which exists between soft iron on the one 
 hand, and ordinary substances on the other. On this diagram 
 I have taken the galvanometer deflections to the same scale for 
 iron, and for such substances as glass or wood. You see that the 
 deflections in the case of glass or wood, to the same scale, are so 
 
 15,000- 
 
 50 100 
 
 Induction in Non-magnetic substances. 
 
 FIG. 1. 
 
 small as to be absolutely inappreciable, whilst the deflection for 
 iron at one point of the curve is something like 2000 times as 
 great as for non-magnetic substances. This extraordinary property 
 is possessed by only two other substances besides iron cobalt and 
 nickel. On the same figure are curves showing on the same scale 
 what would be the deflections for cobalt and nickel, taken from 
 Professor Rowland's paper*. You observe that they show the 
 same general characteristics as iron, but in a rather less degree. 
 Still, it is obvious that these substances may be broadly classed 
 with iron in contradistinction to the great mass of other bodies. 
 On the other hand, diamagnetic bodies belong distinctly to the 
 other class. If the deflection with a non- magnetic ring be unity, 
 that with iron, as already stated, may be as much as 2000 ; that 
 with bismuth, the most powerful diamagnetic known, is 0'999825 
 a quantity differing very little from unity. Note, then, the first 
 fact which any theory of magnetism has to explain is: Iron, 
 
 * Phil. Mag., Nov. 1874. 
 
216 MAGNETISM. 
 
 nickel, and cobalt, all enormously magnetic ; other substances 
 practically non-magnetic. A second fact is: With most bodies 
 the action of the primary current on the secondary circuit is 
 strictly proportional to the primary current ; with magnetic bodies 
 it is by no means so. 
 
 You will observe that the ordinates in these curves, which are 
 proportional to the kicks or elongations of the galvanometer, are 
 called induction, and that the abscissae are called magnetising 
 force. Let us see a little more precisely what we mean by the 
 terms, and what are the units of measurement taken. The elonga- 
 tion of the galvanometer measures an impulsive electromotive 
 force an electromotive force acting for a very short time. Charge 
 a condenser to a known potential, and discharge it through the 
 galvanometer : the needle of the galvanometer will swing aside 
 through a number of divisions proportional to the quantity of 
 electricity in the condenser that is, to the capacity and the 
 potential. From this we may calculate the quantity of electricity 
 required to give a unit elongation. Multiply this by the actual 
 resistance of the secondary circuit and we have the impulsive 
 electromotive force in volts and seconds, which will, in the 
 particular secondary circuit, give a unit elongation. We must 
 multiply this by 10 8 to have it in absolute C.G.S. units. Now 
 the induction is the impulsive electromotive force in absolute 
 C.G.S. units divided by the number of secondary coils and by 
 the area of section of the ring in square centimetres. The line 
 integral of magnetising force is the current in the primary in 
 absolute C.G.S. units that is, one-tenth of the current in amperes 
 multiplied by 4?r and by the number of convolutions in the 
 primary coil. The magnetising force is the line integral divided 
 by the length of the line over which that line integral is dis- 
 tributed. This is, in truth, not exactly the same for all points of 
 the section of the ring an imperfection so far as it goes in the 
 ring method of experiment. The absolute electro-magnetic C.G.S. 
 units have been so chosen that if the ring be perfectly non- 
 magnetic the induction is equal to the magnetising force. We 
 may refer later to the permeability, as Sir W. Thomson calls it ; it 
 is the ratio of the induction to the magnetising force causing it, 
 and is usually denoted by /JL. 
 
 There is a further difference between the limited class of 
 magnetic bodies arid the great class which are non-magnetic. 
 
MAGNETISM. 217 
 
 To show this, we may suppose our experiment with the ring to 
 be varied in one or other of two or three different ways. To fix 
 our ideas, let us suppose that the secondary coil is collected in 
 one part of the ring, which, provided that the number of turns 
 in the secondary is maintained the same, will make no difference 
 in the result in the galvanometer. Let us suppose, further, that 
 the ring is divided so that its parts may be plucked from 
 together, and the secondary coil entirely withdrawn from the 
 ring. If now the primary current have a certain value, and if 
 the ring be plucked apart and the secondary coil withdrawn, we 
 shall find that, whatever be the substance of which the ring is 
 composed, the galvanometer deflection is one-half of what it 
 would have been if the primary current had been reversed. I 
 should perhaps say approximately one-half, as it is not quite 
 strictly the case in some samples of steel, although, broadly 
 speaking, it is one-half. This is natural enough, for the exciting 
 cause is reduced from let us call it a positive value, to nothing 
 when the secondary coil is withdrawn ; it is changed from a 
 positive value to an equal and opposite negative value when the 
 primary current is reversed. Now comes the third characteristic 
 difference between the magnetic bodies and the non-magnetic. 
 Suppose that, instead of plucking the ring apart when the current 
 had a certain value, the current was raised to this value and then 
 gradually diminished to nothing, and that then the ring was 
 plucked apart and the secondary coil withdrawn. If the ring be 
 non-magnetic, we find that there is no deflection of the galvano- 
 meter ; but, on the other hand, if the ring be of iron, we find a 
 very large deflection, amounting, it may be, to 80 or 90 per cent, 
 of the deflection caused by the withdrawal of the coil when the 
 current had its full value. Whatever be the property that the 
 passing of the primary current has imparted to the iron, it is 
 clear that the iron retains a large part of this property after the 
 current has ceased. We may push the experiment a stage 
 further. Suppose that the current in the primary is raised to a 
 great value, and is then slowly diminished to a smaller value, 
 and that the ring is opened and the secondary coil withdrawn. 
 With most substances we find that the galvanometer deflection is 
 precisely the same as if the current had been simply raised to its 
 final value. It is not so with iron: the galvanometer deflection 
 depends not alone upon the current at the moment of withdrawal, 
 
218 
 
 MAGNETISM. 
 
 but on the current to which the ring has been previously sub- 
 jected. We may then draw another curve (Fig. 2) representing 
 the galvanometer deflections produced when the current has been 
 
 10 7 000 
 
 Wrought 
 
 ron. 
 
 A o 
 
 10 
 
 Magnetizing Force. 
 
 FIG. 2. 
 
 20 
 
 raised to a high value and has been subsequently reduced to a 
 value indicated by the abscissae. This curve may be properly 
 called a descending curve. In the case of ordinary bodies this 
 curve is a straight line coincident with the straight line of the 
 ascending curve, but for iron is a curve such as is represented in 
 the drawing. You observe that this curve descends to nothing 
 like zero when the current is reduced to zero; and that when 
 the current is not only diminished to zero, but is reversed, the 
 galvanometer deflection only becomes zero when the reversed 
 current has a substantial value. This property possessed by 
 magnetic bodies of retaining that which is impressed upon them 
 by the primary current has been called by Professor Ewing 
 "hysteresis*," or, as similar properties have been observed in 
 quite other connections, "magnetic hysteresis." The name is a 
 good one, and has been adopted. Broadly speaking, the induction 
 as measured by the galvanometer deflection is independent of the 
 time during which the successive currents have acted, and depends 
 only upon their magnitude and order of succession. Some recent 
 experiments of Professor Ewing, however, seem to show a well- 
 
 * Phil. Trans. R. S., 1885, Part n. p. 526. 
 
MAGNETISM. 219 
 
 marked time effect*. There are curious features in these experi- 
 ments which require more elucidation. 
 
 It has been pointed out by Warburg, and subsequently by 
 Ewingf, that the area of curve 2 is a measure of the quantity of 
 energy expended in changing the magnetism of the mass of iron 
 from that produced by the current in one direction to that 
 produced by the current in the opposite direction and back again. 
 The energy expended with varying amplitude of magnetising 
 forces has been determined for iron, and also for large magnetising 
 forces for a considerable variety of samples of steel J. Different 
 sorts of iron and steel differ from each other very greatly in this 
 respect. For example, the energy lost in a complete cycle of 
 reversals in a sample of Whit worth's mild steel was about 10,000 
 ergs per cubic centimetre ; in oil-hardened hard steel it was near 
 100,000 ; and in tungsten steel it was near 200,000 a range of 
 variation of 20 to 1. It is, of course, of the greatest possible v 
 importance to keep this quantity low in the case of armatures \ 
 of dynamos, and in that of the cores of transformers. If the 
 armature of a dynamo machine be made of good iron, the loss 
 from hysteresis may easily be less than 1 per cent. ; if, however, to 
 take an extreme case, it were made of tungsten steel, it would 
 readily amount to 20 per cent. In the case of transformers and 
 alternate-current dynamo machines, where the number of reversals 
 per second is great, the loss of power by hysteresis of the iron, 
 and the consequent heating, become very important. The loss of 
 power by hysteresis increases more rapidly than does the induc- 
 tion. Hence it is not well in such machines to work the iron to 
 anything like the same intensity of induction as is desirable in 
 ordinary continuous-current machines. The quantity OA when 
 measured in proper units, as already explained that is to say, the 
 reversed magnetic force, which just suffices to reduce the induction 
 as measured by the kick on the galvanometer to nothing after the 
 material has been submitted to a very great magnetising force 
 is called the " coercive force," giving a definite meaning to a term 
 which has long been used in a somewhat indefinite sense. The 
 quantity is really the important one in judging the magnetism of 
 
 * Paper by Professor Ewing, "On Hysteresis in the Relation of Strain to 
 Stress," read before the British Association, Sept. 1889. 
 t Report Brit. Assoc. 1883. 
 J Hopkinson, Phil. Trans. 1885, Part n. 
 
220 
 
 MAGNETISM. 
 
 short permanent magnets. The residual magnetism, OB, is then 
 practically of no interest at all ; the magnetic moment depends 
 almost entirely upon the coercive force. The range of magnitude 
 is somewhat greater than in the case of the energy dissipated in a 
 complete reversal. For very soft iron the coercive force is 1*6 
 c. G.s. units; for tungsten steel, the most suitable material for 
 magnets, it is 51 in the same units. A very good guess may be 
 made of the amount of coercive force in a sample of iron or steel 
 by the form of the ascending curve, determined as I described at 
 first. This is readily seen by inspection of Fig. 3, which shows 
 
 FIG. 3. 
 
 the curves in the cases of wrought-iron, and steel containing 0'9 per 
 cent, of carbon. With the wrought-iron a rapid ascent of the 
 ascending curve is made, when the magnetising force is small and 
 the coercive force is small ; in the case of the hard steel the ascent 
 of the curve is made with a larger magnetising current, and the 
 coercive force is large. There is one curious feature shown in the 
 curve for hard steel which may, so far as I know, be observed in 
 all magrietisable substances: the ascending curve twice cuts the 
 continuation of the descending curve, as at M and N. This 
 peculiarity was, so far as I know, first observed by Professor 
 G. Wiedemann. 
 
 I have already called emphatic attention to the fact that 
 magnetic substances are enormously magnetic, and that non- 
 
MAGNETISM. 221 
 
 magnetic substances are hardly at all magnetic ; there is between 
 the two classes no intermediate class. The magnetic property of 
 iron is exceedingly easily destroyed. If iron be alloyed with 12 
 per cent, of manganese, the kick on the galvanometer which the 
 material will give, if made into a ring, is only about 25 per cent, 
 greater than is the case with the most completely non-magnetic 
 material, instead of being some hundreds of times as great, as 
 would be the case with iron*. Further, with this manganese 
 steel, the kick on the galvanometer is strictly proportional to the 
 magnetising current in the primary, and the material shows no 
 sign of hysteresis. In short, all its properties would be fully 
 accounted for if we supposed that manganese steel consisted of a 
 perfectly non-magnetic material, with a small percentage of 
 metallic iron mechanically admixed therewith. Thus the property 
 of non-magnetisability of manganese steel is an excellent proof of 
 the fact which is also shown by the non-magnetic properties of 
 most compounds of iron that the property appertains to the 
 molecule, and not to the atom ; or to put it in another way, 
 suppose that we were to imagine manganese steel broken up 
 into small particles, as these particles became smaller there would 
 at length arrive a point at which the iron and the manganese 
 would be entirely separated from each other : when this point is 
 reached the particles of iron are non-magnetic. By the magnetic 
 molecule of the substance we mean the smallest part which has 
 all the magnetic properties of the mass. The magnetic molecule 
 must be big enough to contain its proportion of manganese. In 
 iron, then, we must have a collection of particles of such magni- 
 tude that it would be possible for the manganese to enter into 
 each of them, to constitute an element of the magnet. Manganese 
 is, so far as I know, a non-magnetic element. Smaller proportions 
 of manganese reduce the magnetic property in a somewhat less 
 degree, the reduction being greater as the quantity of manganese 
 is greater. It appeared very possible that the non- magnetic 
 property of manganese steel was due to the coercive force being 
 very great that, in fact, in all experiments we were still on that 
 part of the magnetisation curve below the rapid rise, and that if 
 the steel were submitted to greater forces it would presently prove 
 to be magnetic, like other kinds of steel. Professor Ewing, 
 however, has submitted manganese steel to very great forces 
 
 * Hopkinson, Phil. Trans. 1885, Part H. p. 462. 
 
222 
 
 MAGNETISM. 
 
 indeed, and finds that its magnetism is always proportional to the 
 magnetising force. 
 
 No single body is known having the property of capacity for 
 magnetism in a degree which is neither very great nor very small, 
 but intermediate between the two extremes. We can, however, 
 mix magnetic and non-magnetic substances to form bodies appa- 
 rently intermediate. It is, therefore, interesting to consider what 
 the properties might be of such a mixture. It depends quite as 
 much on the way in which the magnetic part is arranged in the 
 mass, as on its actual quantity. Suppose, for example, it is 
 arranged as in Fig. 4 in threads or plates having a very long 
 
 HSfe 
 
 FIG. 4. 
 
 axis in the direction of the magnetising force we may at once 
 determine the curve of magnetisation of the mixture from that of 
 the magnetic substance by dividing the induction for any given 
 force in the ratio of the whole volume to the volume of magnetic 
 substance. If, on the other hand, it is as in Fig. 5 with a very 
 short axis in the direction of the force, and a long axis perpendi- 
 cular thereto we can equally construct the curve of magnetisation. 
 This is done in Fig. 6, which shows the curve when nine-tenths of 
 the material is highly magnetic iron arranged as in fig. o, whilst 
 the other curve of the same figure is that when only one-tenth is 
 
MAGNETISM. 
 
 223 
 
 maguetic, but arranged as in Fig. 4. You observe how very 
 different is the character of the curve a difference which is 
 
 FIG. 5. 
 
 reduced by the much less proportion of magnetic material in the 
 mixture in the one case than in the other. One peculiarity of 
 
 15,000 
 
 10,000 
 
 5,000 
 
 Magnetizing Force. 
 FIG. 6. 
 
 these arrangements of the two materials in relation to each 
 other is, that the resulting material is not isotropic; that is, 
 
224 
 
 MAGNETISM. 
 
 its properties are not the same in all directions, but depend 
 upon the direction of the magnetising force in the material. 
 Of course, this is not at all a probable arrangement, but it is 
 instructive in showing the character of the result as depending 
 upon the construction of the material. Let us, however, consider 
 the simplest isotropic arrangement; let us suppose that one 
 material is in the form of spheres bedded in a matrix of the 
 other : if the spheres are placed at random this is clearly an 
 isotropic arrangement. The result is very different according as 
 the matrix or the spheres are of the magnetic material. Suppose 
 that the volume of the spheres is one-half of the whole volume. 
 In Fig. 7 we have approximately the curve for iron, for a mixture 
 
 15,000-- 
 
 .210,000 
 
 5,000-- 
 
 Magnetizing Force. 
 FIG. 7. 
 
 of equal quantities of iron and a non-magnetic material; the 
 spheres being non-magnetic and the matrix iron, and for a 
 mixture, the spheres being iron, and the matrix non-magnetic. 
 Observe the great difference. When the spheres are iron, the 
 induction is near four times the force for all values of the force. 
 When the matrix is iron, the induction is near f ths of the induction 
 when the material is iron only. 
 
 In speaking of the properties of bodies which, like manganese 
 steel, are slightly magnetic, it may be well here to enter a 
 caution. But little that is instructive is to be learned by testing 
 filings, or the like, with magnets, as these show but little difference 
 
MAGNETISM. 225 
 
 between bodies which are slightly magnetic and those which are 
 strongly magnetic. Suppose the filings to be spheres, in the 
 following table are given comparative values of the forces they 
 would experience in terms of /Lt, if placed in a magnetic field of 
 given value, fi having its ordinary signification that is, being the 
 ratio of the kick on the galvanometer when a ring is tried made of 
 the material of the filing to the kick if the ring is made of a 
 perfectly non-magnetic material : 
 
 p. Attraction. 
 
 1 Non-magnetic body. 
 
 1-47 018 Manganese steel with 12 %. 
 
 3-6 1-2 Manganese steel with 9 % 
 
 5 1-5 
 
 10 2-1 
 
 100 2-8 
 
 1,000 2-98. 
 
 Now bodies in which (JL is so small as 3*6 belong distinctly to the 
 non-magnetic class; but the test with the magnet would very 
 markedly distinguish them from manganese steel with 12 per 
 cent, of manganese. The distinction, however, between /z, = 3*6 
 and fjb = 1,000 is comparatively small ; whereas, under the condi- 
 tions of experiment, /z- is much more than 1,000 for most bodies 
 of which iron is the principal constituent. 
 
 The effect of stress on the magnetic properties of iron and 
 nickel have been studied by Sir W. Thomson*. A fact interesting 
 from a broad and general point of view is that the effects of stress 
 are different in kind in the case of iron and nickel. In the case 
 of iron, for small magnetising forces in the direction of the tension, 
 tension increases the magnetisation ; for large forces, diminishes 
 it. In the case of nickel the effect is always to diminish the 
 magnetisation. 
 
 When one considers that the magnetic property is peculiar 
 to three substances, that it is easily destroyed by the admixture 
 of some foreign body, as manganese, one would naturally expect 
 that its existence would depend also on the temperature of the 
 body. This is found to be the case. It has long been known 
 that iron remains magnetic to a red heat, and that then it some- 
 
 * Mathematical and Physical Papers, vol. n. p. 332. 
 H. I. 15 
 
226 MAGNETISM. 
 
 what suddenly ceases to be magnetic, and remains at a higher 
 temperature non-magnetic. It has long been known that the 
 same thing happens with cobalt, the temperature of change, 
 however, being higher ; and with nickel, the temperature being 
 lower. The magnetic characteristics of iron at a high temperature 
 are interesting*. Let us return to our ring, and let us suppose 
 that the coils are insulated with a refractory material, such as 
 asbestos paper, and that the ring is made of the best soft iron. 
 We are now in a position to heat the ring to a high temperature, 
 and to experiment upon it at high temperatures in exactly the 
 same way as before. The temperature can be approximately 
 determined by the resistance of one of the copper coils. Suppose, 
 first, that the current in the primary circuit which we use for 
 magnetising the ring is small; that from time to time, as the 
 ring is heated and the temperature rises, an experiment is made 
 by reversing the current in the primary circuit and observing the 
 deflection of the galvanometer needle. At the ordinary tempera- 
 ture of the air the deflection is comparatively small ; as the 
 temperature increases the deflection also increases, but slowly at 
 first; when the temperature, however, reaches something like 
 600 C., the galvanometer deflection begins very rapidly to increase, 
 until, with a temperature of 770 C., it attains a value of no less 
 than 11,000 times as great as the deflection would be if the ring 
 had been made of glass or copper, and the same exciting current 
 had been used. Of course a direct comparison of 11,000 to 1 
 cannot be made: to make it we must introduce resistance into 
 the secondary circuit when the iron is used ; and we must, in fact, 
 make use of larger currents when copper is used. However, the 
 ratio of the induction in the case of iron to that in the case of 
 copper, at 770 C., for small forces is no less than 11,000 to 1. 
 Now mark what happens. The temperature rises another 15 C. : 
 the deflection of the needle suddenly drops to a value which we 
 must regard as infinitesimal in comparison to that which it had at 
 a temperature of 770 C. ; in fact, at the higher temperature of 
 785 C. the deflection of the galvanometer with iron is to that 
 with copper in a ratio not exceeding that of 1/14 to 1. Here, 
 then, we have a most remarkable fact : at a temperature of 770 C. 
 the magnetisation of iron 11,000 times as great as that of a non- 
 magnetic substance ; at a temperature of 785 C. iron practically 
 * Hopkinson, Phil. Trans. 1889. 
 
MAGNETISM. 
 
 227 
 
 non-magnetic. These changes are shown in Fig. 8. Suppose now 
 that the current in the primary circuit which serves to magnetise 
 
 11,000 
 
 10,000 
 
 i 9,000 
 
 f 8,000 
 
 M 
 
 ' 7,000 
 
 Wrought Iron. 
 Magnetizing Force 0-3. 
 
 g 5,000 
 
 | 4,000 
 
 c 
 
 S 3,000 
 
 
 2,000 
 
 1,000 
 
 100 200 300 400 500 600 700 785 800 C 
 
 FIG. 8. 
 
 the iron had been great instead of very small. In this case we 
 find a very different order of phenomena. As the temperature 
 rises the deflection on the galvanometer diminishes very slowly 
 till a high temperature is attained ; then the rate of decrease 
 is accelerated until, as the temperature at which the sudden 
 change occurred for small forces is reached, the rate of diminution 
 becomes very rapid indeed, until, finally, the magnetism of the 
 iron disappears at the same time as for small forces. Instead of 
 following the magnetisation with constant forces for varying tem- 
 peratures, we may trace the curve of magnetisation for varying 
 forces with any temperature we please. Such curves are given in 
 Diagrams 9 and 10. In the one diagram, for the purpose of 
 bringing out different points in the curve, the scale of abscissae 
 is 20 times as great as in the other. You will observe that the 
 effect of rise of temperature is to diminish the maximum magneti- 
 sation of which the body is capable, slowly at first, and rapidly at 
 the end. It is also very greatly to diminish the coercive force, 
 and to increase the facility with which the body is magnetised*. 
 To give an idea of the magnetising forces in question, the force 
 
 * Vide Wiedemann, Elektricitat, vol. in. p. 769. 
 
 152 
 
228 
 
 MAGNETISM. 
 
 for Fig. 8 was 0'3 ; and as you see from Figs. 9 and 10, the force 
 ranges as high as 60. Now the earth's force in these latitudes is 
 0'43, and the horizontal component of the earth's force is 0*18. In 
 
 10 
 
 20 
 
 50 
 
 60 
 
 70 
 
 30 40 
 
 Magnetizing Force. 
 
 Fm. 9. 
 
 the field of a dynamo machine the force is often more than 7,000. 
 In addition to the general characteristics of the curve of magneti- 
 sation, a very interesting, and, as I take it, a very important, fact 
 comes out. I have already stated that if the ring be submitted to 
 a great current in one direction, which current is afterwards 
 gradually reduced to zero, the ring is not in its non-magnetic 
 
 0-5 
 
 2-5 
 
 3-0 
 
 1-0 1-5 2-0 
 
 Magnetizing Force. 
 
 Fig. 10. 
 
 condition, but that it is, in fact, strongly magnetised. Suppose 
 now we heat the ring, whilst under the influence of a strong 
 magnetising current, beyond the critical temperature at which it 
 ceases to have any magnetic properties, and that then we reduce 
 the current to zero, we may in this state try any experiment we 
 please. Reversing the current on the ring, we shall find that it is 
 in all cases non-magnetic. Suppose next that we allow the ring 
 
MAGNETISM. 
 
 229 
 
 to cool without any current in the primary, when cold we find 
 that the ring is magnetised ; in fact, it has a distinct recollection 
 of what had been done to it before it was heated to the tempera- 
 tare at which it ceased to be magnetic. When steel is tried in 
 the same way with varying temperatures, a similar sequence of 
 phenomena is observed; but for small forces the permeability 
 rises to a lower maximum, and its rise is less rapid. The critical 
 temperature at which magnetism disappears changes rapidly with 
 the composition of the steel. For very soft charcoal iron wire the 
 critical temperature is as high as 880 C. ; for hard Whitworth 
 steel it is 690 C. 
 
 The properties of an alloy of manganese and iron are curious. 
 More curious are those of an alloy of nickel and iron*. The 
 alloy of nickel and iron containing 25 per cent, of nickel is 
 non-magnetic as it is sure to come from the manufacturer; that 
 is to say, a substance compounded of two magnetic bodies is 
 non-magnetic. Cool it, however, a little below freezing, and its 
 properties change: it becomes very decidedly magnetic. This 
 is perhaps not so very remarkable : the nickel steel has a low 
 critical temperature lower than we have observed in any other 
 magnetisable body. But if now the cooled material be allowed 
 to return to the ordinary temperature it is magnetic ; if it be 
 heated it is still magnetic, and remains magnetic till a temperature 
 
 200 
 
 100 
 
 100 
 
 200 300 
 
 Temperature. 
 FIG. 11. 
 
 400 
 
 500 
 
 600 
 
 of 580 C. is attained, when it very rapidly becomes non-magnetic, 
 exactly as other magnetic bodies do when they pass their critical 
 temperature. Now cool the alloy : it is non-magnetic, and remains 
 non-magnetic till the temperature has fallen to below freezing. 
 The history of the material is shown in Fig. 11, from which it will 
 
 * Hopkinson, Proc. R. S. 1889. 
 
230 
 
 MAGNETISM. 
 
 be seen that from 20 C. to 580 C. this alloy may exist in either 
 of two states, both quite stable a magnetic and a non-magnetic 
 and that the state is determined by whether the alloy has been 
 last cooled to - 20 C. or heated to 580 C. 
 
 Sudden changes occur in other properties of iron at this very 
 critical temperature at which its magnetism disappears. For 
 example, take its electrical resistance*. On the curve, Fig. 12, 
 
 100 200 300 400 500 600 700 
 
 Fig. 12. 
 
 900 1000 1100 1200 C. 
 
 is shown the electrical resistance of iron at various temperatures, 
 and also the electrical resistance of copper or other pure metal. 
 Observe the difference. If the iron is heated, its resistance 
 increases with an accelerating velocity, until, when near the 
 critical temperature, the rate of increase is five times as much 
 as the copper; at the critical temperature the rate suddenly 
 changes, and it assumes a value which, as far as experiments 
 have gone, cannot be said to differ very materially from a pure 
 metal. The resistance of manganese steel shows no such change ; 
 its temperature coefficient constantly has the value of '0012, which 
 it has at the ordinary temperature of the air. The electrical 
 resistance of nickel varies with temperature in an exactly similar 
 manner. Again, Professor Tait has shown that the thermo-electric 
 properties of iron are very anomalous that there is a sudden 
 change at or about the temperature at which the metal becomes 
 
 * Kohlrausch, Wiedemann's Annalen, 1888; Hopkinson, Phil. Trans. R. S. 
 1889. 
 
MAGNETISM. 231 
 
 non-magnetic, and that before this temperature is reached the 
 variations of thermo-electric property are quite different from a 
 non-magnetic metal. 
 
 Professor Tomlinson has investigated how many other properties 
 of iron depend upon the temperature. But the most significant 
 phenomenon is that indicated by the property of recalescence. 
 Professor Barrett, of Dublin, observed that if a wire of hard steel 
 is heated to a very bright redness, and is then allowed to cool, the 
 wire will cool down till it hardly emits any light at all, and that 
 then it suddenly glows out quite bright again, and afterwards 
 finally cools. This phenomenon is observed with great difficulty 
 in the case of soft iron, and is not observed at all in the case 
 of manganese steel. A fairly approximate numerical measurement 
 may be made in this way*: Take a block of iron or steel on which 
 a groove is cut, and in this groove wind a coil of copper wire 
 insulated with asbestos; cover the coil with many layers of 
 asbestos; and finally cover the whole lump of iron or steel 
 with asbestos again. We have now a body which will heat and 
 cool comparatively slowly, and which will lose its heat at a rate 
 very approximately proportional to the difference of temperature 
 between it and the surrounding air. Heat the block to a bright 
 redness, and take it out of the fire and observe the resistance of 
 the copper coil as the temperature falls, due to the cooling of the 
 block. Plot a curve in which the abscissae are the times, and the 
 ordinates the logarithms, of the increase of resistance of the 
 copper coil above its resistance at the temperature of the room. 
 If the specific heat of the iron were constant, this curve would be 
 a straight line ; if at any particular temperature latent heat were 
 liberated, the curve would be horizontal so long as the heat was 
 being liberated. If now a block be made of manganese steel, it is 
 found that the curve is very nearly a straight line, showing that 
 there is no liberation of latent heat at any temperature. If it is 
 made of nickel steel with 25 per cent, of nickel, in its non- 
 magnetic state, the result is the same no sign of liberation of 
 heat. If now the block be made of hard steel, the temperature 
 diminishes at first ; then the curve (Fig. 13) which represents the 
 temperature bends round : the temperature actually rises many 
 degrees whilst the body is losing heat. The liberation of heat 
 
 * Phil. Trans. R. S. 1889, p. 463. 
 
232 
 
 MAGNETISM. 
 
 being completed, the curve finally descends as a straight line* 
 From inspection of this curve it is apparent why hard steel 
 exhibits a sudden accession of brightness as it yields up its heat. 
 In the case of soft iron the temperature does not actually rise as 
 the body loses heat, but the curve remains horizontal, or nearly 
 horizontal, for a considerable time. This, again, shows why, 
 although a considerable amount of heat is liberated at a tempera- 
 ture corresponding to the horizontal part of the curve, no marked 
 recalescence can be obtained. From curves such as these it is 
 easy to calculate the amount of heat which becomes latent. As 
 the iron passes the critical point it is found to be about 200 times 
 as much heat as is required to raise the temperature of the iron 
 1 degree centigrade. From this we get a very good idea of the 
 
 c 
 
 712' 
 
 435 
 
 245 3'0 3-15 3'30 345 4'0 4'15 
 
 Fio. 13. 
 
 importance of the phenomenon. When ice is melted and becomes 
 water, the heat absorbed is 80 times the heat required to raise the 
 temperature of the water 1 degree centigrade, and 160 times the 
 heat required to raise the temperature of the ice by the same 
 amount. The temperature of recalescence has been abundantly 
 identified with the critical temperature of magnetism*. I am 
 
 * I have only recently become acquainted with the admirable work of M. Osmond 
 (Transformation du Fer et du Garbone, 1888) on recalescence. He has examined 
 a great variety of samples of steel, and determined the temperatures at which they 
 
MAGNETISM. 233 
 
 not aware that anything corresponding with recalescence has been 
 observed in the case of nickel. Experiments have been tried*, 
 and gave a negative result, but the sample was impure ; and the 
 result may, I think, be distrusted as an indication of what it would 
 be in the case of pure nickel. The most probable explanation in 
 the case of iron, at all events, appears to be that when iron passes 
 from the magnetic to the non-magnetic state it experiences a 
 change of state of comparable importance with the change from 
 the solid to the liquid state, and that a large quantity of heat 
 is absorbed in the change. There is, then, no need to suppose 
 chemical change ; the great physical fact accompanying the 
 absorption of heat is the disappearance of the capacity for 
 magnetisation. 
 
 What explanations have been offered of the phenomena of 
 magnetism ? That the explanation must be molecular was early 
 apparent. Poisson's hypothesis was that each molecule of a 
 magnet contained two magnetic fluids, which were separated 
 from each other under the influence of magnetic force. His 
 theory explained the fact of magnetism induced by proximity to 
 magnets, but beyond this it could not go. It gave no hint that 
 there was a limit to the magnetisation of iron a point of satura- 
 tion ; but slight of hysteresis ; no hint of any connection between 
 the magnetism of iron and any other property of the substance ; 
 no hint why magnetism disappears at a high temperature. It 
 does, however, give more than a hint that the permeability of iron 
 could not exceed a limit much less than its actual value, and that 
 it should be constant for the material, and independent of the 
 force applied. Poisson gave his theory a beautiful mathematical 
 development, still useful in magnetism and in electrostatics. 
 
 give off an exceptional amount of heat. Some of his results are apparent on my 
 own curves, though I had assumed them to be mere errors of observation. For 
 example, referring to my Royal Society paper, comparing Figs. 38 and 38 A, we see 
 that the higher the heating, the lower is the point of recalescence; both features are 
 brought out by M. Osmond. The double recalescence observed by M. Osmond 
 in steel with a moderate quantity of carbon I would explain provisionally by 
 supposing this steel to be a mixture of two kinds which have different critical 
 temperatures. Although M. Osmond's method is admirable for determining the 
 temperature of recalescence, and whether it is a single point or multiple, it is not 
 adapted to determine the quantity of heat liberated, as the small sample used ia 
 enclosed in a tube of considerable mass, which cools down at the same time as the 
 sample experimented upon. 
 * * Proc. E. S. vol. XLIV. 1888, p. 319. 
 
234 MAGNETISM. 
 
 Weber's theory is a very distinct advance on Poisson's. He 
 supposed that each molecule of iron was a magnet with axes 
 arranged at random in the body; that under the influence of 
 magnetising force the axes of the little magnets were directed to 
 parallelism in a greater degree as the force was greater. Weber's 
 theory thoroughly explains the limiting value of magnetisation, 
 since nothing more can be done than to direct all the molecular 
 axes in the same direction. As modified by Maxwell, or with 
 some similar modification, it gives an account of hysteresis, and 
 of the general form of the ascending curve of magnetisation. It 
 is also very convenient for stating some of the facts. For example, 
 what we know regarding the effect of temperature may be ex- 
 pressed by saying that the magnetic moment of the molecule 
 diminishes as the temperature rises, hence that the limiting 
 moment of a magnet will also diminish; but that the facility 
 with which the molecules follow the magnetising force is also 
 increased, hence the great increase of //, for small forces, and its 
 almost instantaneous extinction as the temperature rises. Again, 
 in terms of Weber's theory, we can state that rise of temperature 
 enough to render iron non-magnetic will not clear it of residual 
 magnetism. The axes of the molecules are brought to parallelism 
 by the force which is impressed before and during the time that 
 the magnetic property is disappearing ; they remain parallel 
 when the force ceases, though, being now non-magnetic, their 
 effect is nil. When, the temperature falling, they become again 
 magnetic, the effect of the direction of their axes is apparent. 
 But Weber's theory does not touch the root of the matter by 
 connecting the magnetic property with any other property of 
 iron, nor does it give any hint as to why the moment of the 
 molecule disappears so rapidly at a certain temperature. 
 
 Ampere's theory may be said to be a development of Weber's : 
 it purports to state in what the magnetism of the molecule 
 consists. Associated with each molecule is a closed electric 
 current in a circuit of no resistance ; each such molecule, with its 
 current, constitutes Weber's magnetic molecule, and all that it 
 can do they can do. But the great merit of the theory and a 
 very great one it is is that it brings magnetism in as a branch of 
 electricity ; it explains why a current makes a magnetisable body 
 magnetic. It also gives, as extended by Weber, an explanation 
 of diamagnetism. It, however, gives no hint of connecting the 
 
MAGNETISM. 235 
 
 magnetic properties of iron with any other property. Another 
 difficulty is this : When iron ceases to be magnetisable, we must 
 assume that the molecular currents cease. These currents repre- 
 sent energy. We should therefore expect that, when iron ceased 
 to be magnetic by rise of temperature, heat would be liberated ; 
 the reverse is the fact. 
 
 So far as I know, nothing that has ever been proposed even 
 attempts to explain the fundamental anomaly, Why do iron, 
 nickel, and cobalt possess a property which we have found 
 nowhere else in nature ? It may be that at lower temperatures 
 other metals would be magnetic, but of this we have at present 
 no indication. It may be that, as has been found to be the case 
 with the permanent gases, we only require a greater degree of 
 cold to extend the rule to cover the exception*. For the present, 
 the magnetic properties of iron, nickel, and cobalt stand as 
 exceptional as a breach of that continuity which we are in the 
 habit of regarding as a well-proved law of nature. 
 
 * Faraday was strongly of opinion that other metals must be magnetisable at 
 a low temperature : vide Experimental Researches, vol. n. p. 217 et seq., and vol. m. 
 p. 444. 
 
15. 
 
 INAUGURAL ADDRESS. INSTITUTION OF ELEC- 
 TRICAL ENGINEERS, 16TH JANUARY, 1896. 
 
 WHEN it was suddenly proposed to me that I should a second 
 time be your President, I felt considerable reluctance to accept 
 the duty. This reluctance arose from two causes. Of the first I 
 am ashamed pure laziness and of it the less I say the better. 
 The second was a bond fide doubt as to whether I was specially 
 suitable for the post. But it soon struck me that that was a 
 matter for which those who proposed me were responsible, and not 
 I who accepted, but had not sought the office. But, if I felt a 
 temporary reluctance, do not suppose that I for a moment failed 
 to appreciate the honour which had been done me. To be called 
 by his fellow professional men to fill the chair which has been 
 occupied by men of such distinction as Kelvin, Siemens, Abel, 
 Crookes, not to mention others, is an honour of which anyone 
 may confess himself proud. After once having occupied this 
 chair, to be called to it a second time is a greater honour, for it 
 shows that one's efforts, however imperfect, have been generously 
 appreciated by those for whom they were made. I thank you for 
 the honour, and assure you I will do my best to verify, if I can, 
 the judgment of those who proposed and you who elected me, 
 rather than my own misgivings. 
 
 The century which is now just drawing to a close has been a 
 time remarkable above all other times for the extraordinary 
 development of our knowledge of the physical sciences, and in 
 particular of experimental physics and chemistry, and for the 
 extent of the practical application of this knowledge to useful 
 
INAUGURAL ADDRESS. 237 
 
 purposes. The century has seen the discovery of the mechanical 
 nature of heat, of the spectroscope, and of the whole of the science 
 of organic chemistry; it has seen the enormous development of 
 the application of the steam-engine, the construction of our rail- 
 way system, and the supersession of sailing vessels by steamboats. 
 But perhaps the most remarkable illustration of this develop- 
 ment is to be found in the science, and its application, with which 
 this Institution has to deal. Consider what was known of the 
 sciences of electricity and magnetism at the end of the last 
 century. The two sciences were then quite unconnected. In 
 magnetism the properties of permanent magnets were known 
 that is to say, it was known that steel needles could be rendered 
 magnetic by nibbing with a loadstone, and that when so rendered 
 magnetic they would tend to remain in that condition; it was 
 known that, if a magnet were broken in parts, each part would 
 exhibit North and South poles like the magnet from which it was 
 broken ; it was also known that the earth exhibited properties of 
 magnetism, inasmuch as a magnetic needle free to move would 
 point, on the whole, to the North ; broadly speaking, what we 
 know to-day about permanent magnets was known, and that was 
 about all. The practical applications were limited to the use of a 
 magnetic needle in the mariner's compass. The knowledge of 
 electricity was confined to what is now known as electrostatics. 
 That certain bodies when rubbed exhibited peculiar properties, 
 attracting and repelling each other, had long been observed ; and 
 the facts expressed by the hypothesis of positive and negative 
 electricity were known namely, that two pieces of amber which 
 had been rubbed repelled each other, two pieces of glass which 
 had been rubbed repelled each other, but a piece of rubbed glass 
 and a piece of rubbed amber attracted each other. In a general 
 way the properties of conductors, as distinguished from insulators, 
 were also known in their relation to charges of frictional electricity. 
 Cavendish had made elaborate investigations into the capacity of 
 condensers, the condensers being usually of glass, and being 
 charged by the old-fashioned frictional means. Franklin had 
 proved the identity of the cause of lightning r with the cause of 
 the sparks produced by frictional electricity. Just one hundred 
 years ago Galvani had made his celebrated experiments showing 
 that the muscles of the limb of a frog were disturbed by contact 
 with a piece of copper and a piece of zinc which touched each 
 
238 INAUGURAL ADDRESS. 
 
 other ; and that was the only fact which up to that time had ever 
 been observed in the enormous group of facts which now constitute 
 our knowledge of the production of electricity by chemical action. 
 Shortly stated, that was the extent of our theoretical and experi- 
 mental knowledge of electricity. The practical applications of 
 this knowledge were almost nil. I can recall nothing excepting 
 the provision of lightning conductors as a protection to buildings. 
 
 It is worth insisting that the additions to our knowledge of 
 the properties of permanent magnets and of frictional electricity 
 during the century have not been of great importance, and the 
 practical applications of these limited branches of knowledge have 
 been few. If one is asked what uses can be made of our knowledge 
 of frictional electricity apart from the phenomena of currents, it is 
 hard to name anything of importance. In like manner, in regard 
 to our knowledge of permanent magnets, it may almost be said 
 that the advances in practical applications have been confined to 
 improvements in the use of the mariner's compass, which, most 
 important although they are, have had comparatively little share 
 in the changes in our conditions which the last hundred years 
 have witnessed. Almost everything in the way of practical 
 applications of electrical science has been the outcome of subse- 
 quent discoveries the voltaic cell, discovered by Volta in the 
 year 1800 ; Davy's discoveries in electrolysis ; Oersted's discovery 
 of the action of currents upon magnets; Ampere's discoveries of 
 the mechanical action of currents upon currents; and Faraday's 
 discoveries in electro-magnetism ; not to mention the names of 
 eminent men still living. Now the remarkable thing is that none 
 of these phenomena had ever been witnessed by mortal man. It 
 was not that they were constantly occurring around us, and that 
 the explanation had not been seen ; it is the fact that the 
 phenomena had never been experienced. It would seem that the 
 phenomena of electric currents as Volta discovered them do not 
 occur in nature on any substantial scale. Electro-magnets may 
 be regarded as purely a creation of the human mind ; so far as 
 we know at present, no example of an electro-magnet is found in 
 the natural world. The great currents produced by the action 
 of electro-magnets have, so far as we know, no counterpart in 
 nature not only no counterpart in degree, but none in kind. In 
 this respect our science differs much from many others. In 
 mechanics and in heat we may find the phenomenon of which 
 
INAUGURAL ADDRESS. 239 
 
 we make use occurring without our aid on an enormously greater 
 scale than we are accustomed to use; changes are constantly 
 occurring around us, and it is conceivable that we might have 
 obtained much of our present knowledge by the aid of observation 
 without experiments. But it is not so with electricity and 
 magnetism. We should be puzzled even now to adequately 
 illustrate the facts we know by observation alone without ex- 
 periment. 
 
 Let us consider for a moment the practical applications which 
 have been made of electrical knowledge during the last 60 years. 
 The first, of course, is the telegraph. What are the scientific 
 facts which have been used in the development of telegraphy? 
 The currents are generated either by chemical means or electro- 
 magnetic means. The receiving instruments either depend for 
 their action on the action of currents upon magnets, or, in a 
 limited number of cases, on electro-chemical decomposition. We 
 might put it broadly thus that, with the exception of the distinc- 
 tion between conductors and non-conductors and certain properties 
 of condensers, the telegraph could do without anything that was 
 known up to the end of the last century, and that it wholly 
 depends upon more recent discoveries. Much the same may be 
 said with regard to the more recent applications: the electric 
 light, electric transmission of power, and the rapidly growing 
 department of electro-chemistry may all be said to be quite 
 independent of any facts which were known before the year 
 1800, and entirely based upon discoveries made since. Suppose 
 it were a fact that electricity could not be produced by friction, 
 that we knew nothing concerning the attraction which oppositely 
 electrified bodies have for each other, that permanent magnets 
 did not exist or, in other words, that iron had no hysteresis 
 would it make any material difference, so far as we know, in the 
 practical applications of electrical science to telegraphy, telephony, 
 electric light, electric transmission of power, or electro-chemistry ? 
 The permanent magnets, which are practically used only in instru- 
 ments, would be at once replaced by electro-magnets, and the 
 apparatus would work just as it does now. 
 
 Enough has been said, I think, to show that the knowledge 
 of electricity and magnetism which was possessed by men at the 
 end of the last century, intensely interesting though it was, has 
 
240 INAUGURAL ADDRESS. 
 
 not been the parent of the great applications of later days ; that 
 the knowledge of the last century has not grown in any great 
 degree upon the lines which existed at its commencement, but 
 that our advances in science, as in practice, were the result of the 
 discoveries which were made since the beginning of the present 
 century. 
 
 It has been a frequent practice with presidents of societies 
 devoted to promoting some department of science, theoretic or 
 applied, to deal with the history of the science in their presiden- 
 tial addresses, to show how one idea has led up to another, 
 and how marked have been the advances made. This evening 
 I propose to adopt a different course. What I wish to consider is, 
 how would the theory of electricity have been arranged if the 
 order of discovery of the facts of the science had been other than 
 it has been ? Here I owe you some words of apology. You are a 
 practical body more immediately interested in the application of 
 science to the service of man than in the promotion of abstract 
 knowledge. The justification I would offer for my subject is that 
 the science of electricity, whether viewed from the practical or 
 theoretical side, is in a state of extraordinarily rapid advance. 
 The rules of practice of yesterday are of little use to-day, hence 
 more discussion is needed, more publication is needed, than in 
 departments which are in a more stable state. Furthermore, 
 there is no department of applied science in which the connection 
 with theory is so close and intimate. The practical electrical 
 engineer reads eagerly the results of those who, careless whether 
 their work finds application or not, labour to advance knowledge ; 
 he attacks these results whether they be expressed in the ordinary 
 speech of men or in mathematical symbols. On the other hand, 
 much of our knowledge of electricity, viewed from the scientific 
 side, has come from those who are concerned with practical 
 application. Nowhere else do we find a closer interdependence of 
 pure science and practice. In what I have to say there will be 
 much that is trite and obvious to the merest tyro in electricity. 
 What I wish to do is to show how the facts of electrostatics can be 
 explained by the facts of current-electricity without hypothesis; 
 and it is necessary to rehearse elementary principles. In a 
 complicated subject like electricity, in which the appeals to 
 our senses are indirect, there are open to us many ways of 
 arranging our ideas, any one of which will give us a consistent 
 
INAUGURAL ADDRESS. 241 
 
 account of that which we observe. We may take as our funda- 
 mental basis one or other of various groups of facts, and deduce 
 others therefrom. The actual arrangement of ideas on the subject 
 depends in a measure upon the accident of the historical order of 
 discovery. Thus, the fact that actions at a distance between 
 electrified bodies were known many years before the phenomena 
 of current-electricity and electro-magnetism is the reason why 
 that part of the science which treats of such actions is to-day 
 treated first and made the basis of the rest. The time has, I 
 think, come when we may with advantage reconsider our position, 
 and see whether or not our ideas may be more conveniently 
 arranged. The arrangement which is most convenient may no 
 doubt depend upon the phenomena which occupy the most pro- 
 minent place in the practical use we wish to make of the science. 
 Those facts are best treated as fundamental which are most 
 frequently used, provided they are sufficiently simple. To the 
 practical electrician, are the facts of current-electricity, or of the 
 attractions and repulsions of electrified bodies, more familiar? 
 Surely the transference of energy by current is the agent by 
 which almost every operation he purposes is effected, whilst the 
 phenomena of electrostatics touch him only at points in the 
 theory of electrometers and so forth. I propose, then, this evening 
 to sketch out very briefly, ab initio, how we may base the science 
 of electrostatics upon the theory of current-electricity taken as 
 fundamental. We might, if we pleased, drop the word " current " 
 altogether and substitute another. It seems hardly worth while, 
 but I shall ask you to bear in mind that, if used to-night, it does 
 not connote the idea of anything flowing along the conductor. It 
 is a name for a directed magnitude, and nothing more. I shall 
 have occasion to refer to some elementary experiments, but you 
 will bear with me, I trust, for we are concerned with arranging 
 the subject on as small a basis of facts as is consistent with rigid 
 deduction. Please, then, to banish from your minds all theory 
 on the subject, and let us imagine that the facts of current- 
 electricity are first discovered, and that it is only when these are 
 well developed that electrostatic attractions and repulsions are 
 found out. 
 
 In a vessel of dilute sulphuric acid is placed a piece of pure 
 zinc, or of zinc carefully amalgamated, and also a piece of copper, 
 platinum, silver, or carbon, the two plates not being in contact 
 H. i. 16 
 
242 INAUGURAL ADDRESS. 
 
 with each other. It is observed that no change takes place ; the 
 acid does not attack either plate. The two plates are now 
 touched with the two ends of a wire of copper or other metal ; 
 immediately the zinc begins to dissolve in the sulphuric acid, 
 and gas which, if collected, proves to be hydrogen is found 
 on the copper or platinum plate. If the plates are large and 
 near together, and the wire is not too long or thick, it becomes 
 very sensibly heated. On separating the wire from either plate, 
 the chemical reaction and the heating of the wire cease. When 
 the wire touches both plates there is then development of chemical 
 energy in the vessel of acid ; but a part of this energy appears as 
 heat, not where it is developed, but in the wire connecting the 
 plates. Whether this energy goes across the space of air between 
 the zinc plate and the wire, or whether it goes along the wire, 
 we do not know; but that the two plates should be rendered 
 continuous with each other by a wire or some equivalent is a 
 condition precedent to the chemical reaction and to the heating of 
 the wire. 
 
 Let two such vessels of dilute acid, with plates of zinc and 
 copper, be provided, and let the copper in one vessel be connected 
 metallically to the zinc in the other : nothing happens until the 
 copper in the second vessel is connected to the zinc of the first ; 
 then both zincs are dissolved, hydrogen is liberated on both copper 
 plates, and the connecting wires are more or less heated. 
 
 Again, varying the experiment, let the coppers in the two 
 vessels be connected together and the zincs be connected together : 
 no reaction or heating occurs. 
 
 The combination of a piece of zinc and a piece of copper 
 dipping separately into a vessel of dilute acid is called a " galvanic 
 cell," or element ; a series of elements connected together copper 
 to zinc is called a "galvanic battery." Galvanic elements and 
 batteries take a multitude of forms: the zinc may be replaced 
 by another metal for example, cadmium and the copper by 
 platinum ; many other liquids than dilute sulphuric acid may 
 be used ; but all galvanic batteries have this in common to cause 
 them to work, the chain or circuit must be completed by a wire 
 touching the zinc at one end of the series and the copper at the 
 other, and then chemical reactions occur in the cells, and heat is 
 liberated in the metal connections. The zinc and copper plates, 
 
INAUGURAL ADDRESS. 243 
 
 or their equivalents, at the ends of a galvanic battery are called 
 " poles." 
 
 Let two plates of platinum dip into dilute sulphuric acid ; 
 connect one plate by means of a wire to the zinc pole of a battery, 
 the other plate to the copper pole. So soon as the connections 
 are made, chemical reactions occur in the cells of the battery, the 
 connecting wires are more or less heated, and, further, a reaction 
 occurs in the vessel in which the platinum plates dip, the water 
 is decomposed, gases are liberated on the two plates ; if these are 
 collected, it is found that the gas from the plate connected to 
 the zinc pole is hydrogen, that from the plate connected to the 
 copper is oxygen. The effects cease on detaching either wire 
 from the platinum plate or the pole of the battery, or otherwise 
 interrupting the continuity of the circuit. In this experiment 
 is seen a chemical reaction liberating energy in the cells of the 
 battery, and another chemical reaction absorbing energy in the 
 vessel containing the platinum plates; how the energy passes 
 from one vessel to the other we do not know. 
 
 The experiment may be varied. Let two plates of zinc or other 
 metal dip into a solution of salt of zinc or other metal, and let the 
 plates be connected to the poles of a galvanic battery for a time. 
 If the plates be weighed before and after the operation, it is found 
 that the plate which was connected to the zinc pole has gained in 
 weight, and that the plate which has been connected to the copper 
 has lost an equal amount. By weighing such plates, and noting 
 the time the experiment was allowed to continue, it is practicable 
 to examine quantitatively the phenomena of a galvanic circuit. 
 Such pair of plates and solution of salt is called a " voltameter." 
 
 Suppose now a series of voltameters, having in each the same 
 metal, are connected together in a chain, a plate of one to a plate 
 of the next, and the two ends of the chain connected to the two 
 poles of a battery, it is found that, no matter what be the size and 
 form of the voltameters, their position, or the arrangement of the 
 connecting wires, there is the same gain and loss of weight of 
 the plates in all the voltameters ; it is further found that, if the 
 zincs of the cells of the battery are weighed before and after 
 the experiment, and if the metal used in the voltameter be zinc, the 
 quantity of zinc dissolved is the same in all the cells, and is the 
 same as that transferred in each voltameter. The rate of dissolu- 
 
 162 
 
244 INAUGURAL ADDRESS. 
 
 tion and deposit is the same in the several voltameters and cells. 
 In a closed galvanic circuit we have, then, a measurable something 
 the same for all cross- sections of the circuit, measurable by the 
 quantity of zinc or other selected metal which is transferred from 
 one plate to the other of a voltameter is a unit of time. This 
 something has direction as well as magnitude, and as the 
 magnitude may be represented in terms of any unit chosen by a 
 numerical quantity G, so the direction may be represented by the 
 sign + or . It is arbitrarily chosen to take as -f the direction 
 from the plate which loses weight to that which gains weight 
 through the liquid in the voltameter. The quantity G taken, with 
 its sign, is called the galvanic or electric current round the circuit, 
 but it must not be supposed that it is known that there is any- 
 thing flowing round the circuit. 
 
 Suppose that, instead of a simple galvanic circuit, the circuit 
 divides or branches as indicated in the sketch, in which A, B, C, 
 are voltameters, FED the battery. It is found that the quantity 
 of zinc moved in B, together with the quantity of zinc moved in 
 (7, is equal to the quantity moved in A. This gives us the idea of 
 current in the branch B or G, and we may say that the current in 
 A is the algebraic sum of the currents in B and G. 
 
 Not all bodies are competent to complete a galvanic circuit. 
 Thus, if the copper wires which serve to connect the poles of the 
 cells of the batteries and the voltameter are any of them replaced 
 by thread, the phenomena of galvanism do not occur ; if one of 
 the wires be severed and a piece of paraffined paper interposed, 
 the phenomena do not occur. 
 
 Thus we have a distinction of substances into those which are 
 capable of forming continuously part of a galvanic circuit and 
 those which are not; the former are called "conductors," the 
 
INAUGURAL ADDRESS. 245 
 
 latter " non-coDductors." The distinction will be found to be 
 really one of degree. 
 
 Consider a wire forming part of the galvanic circuit : after a 
 short time no change occurs in the wire; it is heated by the 
 current, and it loses heat by heat conduction, convection, or 
 radiation. It is possible by the methods of calorimetry to 
 measure the total quantity of energy leaving the wire as heat by 
 these agencies; it must be equal to the quantity of energy 
 brought into the wire by galvanic agency. 
 
 Again, consider the battery itself. A certain chemical reaction 
 is going on ; zinc is being oxidised, and other reactions are occur- 
 ring. Of the net amount of energy liberated per second by these, 
 some goes to heat the battery, but some also appears in parts of 
 the circuit external to the battery that is, leaves the battery by 
 galvanic agency. Thus a galvanic current is an instrument which 
 takes energy from certain parts of the circuit and takes it into 
 other parts of the circuit ; and when the current is steady the 
 Algebraic sum of the quantity of energy taken into all parts of the 
 circuit is nil. Denote by EG the quantity of energy per unit of 
 time taken into any section, A, B, of the galvanic circuit, the 
 positive direction of the current being from A to B. If the whole 
 of the circuit be broken into sections, the algebraical sum of the 
 values of EC is nil, but the value of C is the same for all sections ; 
 hence the algebraic sum of the values of E is nil. Let there be 
 any quantity, V a , referred to each point of the circuit, such that 
 V a V b = E, the condition that the sums of the values of E shall 
 be nil is fulfilled. E is therefore properly described as the differ- 
 ence of two quantities, one peculiar to A, the other to B; it 
 is called the difference of potential between A and B, and V a is 
 called the potential at A, though it is only with differences of 
 potential that we are concerned. 
 
 Suppose now the circuit divides at A into two or more 
 branches, joining again at B, by our definition the difference of 
 potential between A and B is the sum of the energies taken per 
 unit of time into the conductors A, B, divided by the sum of the 
 currents in the conductors A, B. We have now to show that 
 the energy taken into each of the conductors A, B, is equal to the 
 difference of potential between A and B multiplied by the current 
 in that conductor. This is by no means obvious, but depends on 
 
246 INAUGURAL ADDKESS. 
 
 an assumption of an experimental truth, viz., that in a given 
 conductor the energy taken into it by the current is a function of 
 the current only, and is independent of other conditions external 
 to the conductor. Granted this, it easily follows that, if two or 
 more conductors be joined at A and B, the potential difference 
 between A and B deduced from each will be the same. 
 
 As we have defined difference of potential by means of work 
 done in a conductor when a given current exists in it, the laws 
 of resistance must have the same basis. In the case of a homo- 
 geneous metallic conductor under given constant physical condi- 
 tions of temperature, stress, and magnetic field carrying a constant 
 galvanic current C, Joule found that the heat liberated per unit of 
 time varies as the square of CRC 2 when R is a constant relative 
 to G for the conductor. Whence follows that E = RC.R is called 
 the electrical resistance of the conductor. For metallic conductors 
 R is constant, but the constant R does not exist for all conductors ; 
 for the electric arc, for example, the heat generated varies more 
 nearly as C than as C 2 , and therefore E is more nearly constant 
 than varying as C. 
 
 We have now gained two fundamental ideas that of galvanic 
 current, and difference of potential. In terms of what units are 
 we to measure them ? We have only one unit to choose, because 
 EC must be expressed in terms of our mechanical unit of power. 
 If a unit were to be fixed at this stage, it would be natural to 
 define either a unit of current or of resistance the ratio of 
 
 TJ1 
 
 -~ ; for example, we might say the unit of current shall be that 
 
 current whereby a unit weight of distilled water is decomposed 
 per second ; or we might say, let the resistance of a piece of wire 
 of defined shape and material at a definite temperature be the 
 unit of resistance. The units in general use have an electro- 
 magnetic basis, but be it observed that all rational systems 
 must be such that EG is expressed in some ordinary mechanical 
 units. 
 
 We have supposed that galvanic effects are measured by 
 chemical change, and that the rate of galvanic effect or, as it is 
 generally called, the electric current is measured by the rate of 
 chemical change. From a theoretical point of view it would be 
 possible to thus measure electric currents ; but for practical 
 
INAUGURAL ADDRESS. 247 
 
 purposes other means are adopted electrometers, galvanometers, 
 electro-dynamometers, and the like. With a description of such 
 instruments and their methods of use I have not the time to 
 concern myself this evening. We must assume that we have the 
 means of measuring C, the galvanic or electric current so called, 
 at any instant, and E, the difference of potential, whether these 
 be great or small, and with any desired accuracy. 
 
 We should now be in a position to give a detailed account of 
 galvanic batteries and of electrolysis, and the theory of the 
 distribution of currents in systems of conductors of any form, and 
 we are in a position to place the theory of thermo-electricity upon 
 a thermo-dynamic basis without the introduction of any fresh 
 idea. These, however, I leave on one side, and hasten to consider 
 how the phenomena of electrostatics can be based upon what we 
 have been discussing. There is a broad group of facts very 
 familiar to the practical electrician engaged in laying telegraphic 
 cables of which I have as yet given no account: I refer to the 
 phenomena of capacity. Let us examine a little more closely the 
 statement that I made that if a slip of paraffined paper were 
 interposed between the two parts of a conductor no electrical 
 action would occur. Suppose that, instead of paraffined paper 
 interposed between the ends of a wire, we have a very large num- 
 ber of sheets of tinfoil separated from each other by paraffined 
 paper in such wise that we have a great area of tinfoil connected 
 together, and separated from another great area of tinfoil by 
 nothing more than the paraffined paper. If now these two areas 
 of tinfoil are suddenly connected to the poles of a galvanic battery, 
 we find that it is by no means true that no galvanic effect will 
 ensue ; we find that a galvanic current exists, but that, whilst it 
 begins with a large quantity, this quantity goes on diminishing 
 until, barring the slight imperfection of insulation of the paraffined 
 paper, it becomes nil. We find, then, that it is not true to state 
 that paraffined paper cannot form a part of a galvanic circuit; 
 it can form a part of a galvanic circuit, but it does so under 
 completely different laws to the metallic conductor. With the 
 metallic conductor the difference of potential at its two ends 
 depends only on the current which then exists in that conductor, 
 and not at all upon the currents which have previously existed; 
 with paraffined paper, on the other hand, the difference of potential 
 between the sheets of tinfoil depends not at all upon the then 
 
248 INAUGURAL ADDRESS. 
 
 current, but entirely upon the currents which have existed since 
 its two coatings were connected together, and the times for which 
 they have existed. A galvanic current may be measured by the 
 rate of electrolysis ; being measured by a rate, its time integral 
 will have a perfectly definite meaning, and will be measured by 
 the total quantity of substance which would be decomposed in a 
 voltameter in the circuit. We find that the difference of potential 
 between the two coatings of the paraffin condenser is proportional 
 to the time integral of the current since the time at which the 
 coatings were connected together last. The constant ratio of this 
 time integral of current to the difference of potential is called the 
 "capacity" of the condenser. Suppose now that the condenser has 
 been connected to a galvanic battery and the time integral of the 
 current has been measured ; let now the coatings of the condenser 
 be disconnected from the battery and be connected together 
 through any instrument for measuring the time integral of 
 current : if this is accomplished with sufficient rapidity for loss 
 by imperfect insulation to be negligible, we find that the time 
 integral in the second case is equal and opposite to that which 
 it was in the first. Here, again, is a difference of conduction in 
 the ordinary sense. If a conductor in which a current has existed 
 be disconnected from the source of current and be connected to 
 any measuring instrument, no return current will be observed. 
 Here, then, we have a new order of facts presented in an extreme 
 case, but, in fact, applicable to all kinds of insulators. Suppose 
 we diminish the area of surface of the paraffined paper, we 
 diminish pro rata the capacity of the condenser ; but even when 
 the paraffined paper is merely interposed between the ends of two 
 copper wires it still will be a condenser having a definite capacity. 
 There is no need to use paraffined paper to form a condenser. 
 Two metallic plates may be insulated and placed parallel to each 
 other : if they be connected one to one pole of a battery, the other 
 to the other, a current will exist for a finite time ; if they are now 
 disconnected from the battery and connected to each other 
 through a suitable instrument for measuring the time integral 
 of current, a return current exists for a finite time. Consider 
 now a condenser consisting of two parallel plates of very large 
 area placed near to each other : its capacity varies as the area 
 of the plates, and it also varies inversely as the distance between 
 them laws precisely analogous to those of conductors. It also, as 
 
INAUGURAL ADDRESS. 249 
 
 might be expected, depends upon the material interposed between 
 the two plates. Since the capacity of the condenser varies as the 
 area, and inversely as the distance, whatever be the substance 
 between the plates, there is a constant for every substance analo- 
 gous to the specific conductivity of the material ; this constant is 
 called the " specific inductive capacity " of the material. 
 
 That the magnetic effects of the transient galvanic currents 
 in insulators are the same as of corresponding currents in con- 
 ductors, is a fundamental law at the basis of Maxwell's theory of 
 electro-magnetism ; it was, I believe, first definitely propounded 
 by Maxwell, and it is one over which some of the most eminent 
 minds have since contended. You will notice how, if the subject 
 be arranged in the unhistorical, but not unnatural, way I have 
 adopted this evening, this law drops so easily into its place, 
 that its assumption would be almost unnoticed. Why should 
 we assume that the magnetic effects of electric currents in 
 insulators and in conductors are different ? By far the most 
 natural assumption is that they are the same. 
 
 Maxwell's electro-magnetic theory of light one of the great 
 generalisations of the century is directly based upon this law. 
 What is this theory? It is simple enough in its character, 
 broadly stated. Suppose you have an electrical disturbance, a 
 transient galvanic current, in any dielectric, this disturbance 
 assuming the magnetic effects of currents in dielectrics to be the 
 same as in conductors will be propagated as a wave in directions 
 perpendicular to the direction of the currents. The velocity of 
 the wave can be calculated from purely electrical experimental 
 knowledge ; it is 3 x 10 10 , if the dielectric be a vacuum. The 
 velocity of light is 3 x 10 10 . We know nothing of what light is ; 
 we do know that it is a wave, and that the disturbance is perpen- 
 dicular to the direction of transmission of the light ; but what is 
 the ultimate nature of that disturbance we have no idea from the 
 standpoint of the science of light. Is it not infinitely probable 
 that the waves of light are none other than the electrical waves 
 which we know must exist, and must be propagated with the 
 observed velocity of light ? And, mark, this theory demands no 
 ether ; it merely identifies the phenomenon of light with known 
 phenomena of electricity and magnetism ; it demands no know- 
 ledge of the fundamental nature of these phenomena, it demands 
 
250 INAUGURAL ADDRESS. 
 
 only a knowledge of their laws. Surely Maxwell's generalisation 
 is similar both in kind and in magnitude with the discovery of 
 universal gravitation. Newton showed that the force which caused 
 any body an apple, if you like to fall on our earth was the same 
 as the force which kept the planets in their courses. He gave no 
 theory of how that force was transmitted, nor of what, in its 
 inmost nature, it was. He merely identified the two forces as 
 one. So now Maxwell's theory may be shorn of all reference to an 
 ether ; it identifies as one the forces whereby light is transmitted 
 and the forces with which we are familiar in our dynamo machines, 
 and shows that they are measurably the same. It does not 
 pretend to say what electricity and magnetism are, or what, if 
 any, is the medium whereby the disturbances on which both 
 depend are transmitted. Whether the postulate of an all-per- 
 vading ether be, or be not, a metaphysical necessity, surely it 
 is well for the practical man and the physicist to leave the 
 question to the metaphysician. My point, however, is that the 
 hypothesis of two electric fluids and the ethereal theory of light 
 have rather delayed than accelerated the acceptance of a great 
 generalisation. Let us now return to elementary matters. 
 
 I have just stated that the capacity of two large plates near 
 and parallel to each other varies as their area, and inversely as 
 their distance. In what units are we to measure capacity ? If 
 we have already chosen a unit of resistance, a unit of capacity 
 must follow from that through the units of potential and current. 
 It would be the capacity of that condenser which, if brought to 
 unit difference of potential, would discharge a galvanic current 
 whose time integral was unit current for unit time. It would be 
 quite natural to define as a unit of resistance the resistance 
 between opposite faces of a cube of a defined substance at a 
 defined temperature, in which case the dimensions of resistance 
 would be the reciprocal of a length. Or, again, we might lay by a 
 piece of wire and carefully preserve it, and say, let that be our 
 unit of resistance. Then resistance would have no dimensions in 
 terms of mass, length, and time it would be a fundamental unit. 
 In either case we should introduce physical constants into our 
 formulae for electrostatic and electromagnetic phenomena, depend- 
 ing in the one case on the physical properties of the substance 
 chosen, in the other on its actual dimensions. If the history of 
 electrical discovery had followed the course adopted in this 
 
INAUGURAL ADDRESS. 251 
 
 discourse, and it had become necessary to fix upon a unit of 
 capacity at the point we have now reached, it would have been 
 very natural to have taken the capacity per square centimetre of 
 two plates at unit distance, the insulating medium being vacuum. 
 We shall see shortly what is the actual electrostatic unit which 
 has been chosen, but the fact is there is nothing specially natural, 
 nothing specially absolute in the choice. 
 
 It is a matter of very great interest to know the capacities of 
 condensers of various forms. Let us take, for example, the case of 
 a sphere enclosed concentrically within another sphere. If r lt r 2 , 
 be the radii of the two spheres, the result is that the capacity 
 
 varies as - ^ ; if ?* 2 be very great in comparison with r l} the 
 
 capacity varies as r x . The electrostatic unit of capacity ordinarily 
 adopted as absolute is the capacity of a sphere of unit radius 
 enclosed concentrically in a very great sphere, with vacuum as 
 insulator. From this, remembering that the product of a differ- 
 ence of potential and a galvanic current shall be power in ordinary 
 mechanical units, all other units will follow. Thus time integral 
 of current divided by difference of potential or capacity is a line ; 
 therefore conductivity is a velocity, and resistance the reciprocal of 
 a velocity. Difference of potential multiplied by current is power, 
 and has dimensions ML*/T 3 , but potential divided by current has 
 dimensions T/L ; therefore current squared has dimensions ML 3 /T 4 , 
 and current M^L^/T 2 , and so on. 
 
 Again, the capacity of two plates, area A, distance x, can be 
 deduced from that of two concentric spheres at a small distance 
 apart : it is A/^TTX in these units. 
 
 We may now prove that mechanical forces must exist between 
 the plates of a charged condenser. Let a condenser be formed of 
 two parallel plates of area A at a distance x from each other, the 
 distance x being capable of variation ; let the condenser be 
 charged to a given difference of potential, and then insulated, and 
 the position of the plates in relation to each other varied. If the 
 condenser be then discharged, it is found, first of all, that the total 
 discharge is the same however the position of the plates be varied. 
 Suppose now that the condenser be charged to a difference of 
 potential E, and a quantity, or time integral, of current Q, the 
 work done in so charging the condenser will be ^EQ. Let now 
 
252 INAUGURAL ADDRESS. 
 
 the condenser be insulated, and the distance of the plates 
 increased to x + Sx : the capacity of the condenser will be 
 diminished in the ratio x\(x + #) ; and therefore, since the 
 quantity remains the same, the difference of potential will have 
 increased to E(x+x)jx. Now discharge the condenser. The 
 work done by the discharge will be \EQ (x + &)/#, or an amount 
 of work ^EQ Sxjx greater than was done in charging the condenser. 
 This work must come from somewhere. The only way in which it 
 can be introduced is by the work done in separating the plates 
 from each other. To increase the distance between the two plates 
 by an amount So; therefore requires that we shall do mechanical 
 work ^EQSxjx upon the plates. This mechanical work is done 
 through a distance Sx, therefore a force must be exerted in sepa- 
 rating equal to ^EQjx ; hence it follows, as a matter of necessary 
 consequence from the laws of the capacity of conducting surfaces 
 in the presence of each other, that those surfaces shall when 
 charged act mechanically upon each other; and the amount of 
 mechanical force is determined. 
 
 T? A 
 
 Now - is equal to Q, hence the force between the plates is 
 
 ^-j . Let us now suppose that matter is laid upon each plate 
 
 of density r , and that the matter on one plate attracts that on 
 
 the other plate with a force varying as the inverse square of the 
 distance : the resultant attractive force between the plates is 
 
 exactly - . ; hence we should accurately express the facts of 
 A. 
 
 attraction of two plates if we said there is on each plate a charge 
 of electric substance, and every particle of substance on the one 
 plate attracts every particle on the other with a force varying 
 inversely as the square of the distance. But that the facts can 
 be so expressed is no evidence that any such electric substance 
 exists. 
 
 I do not propose to touch on electro-magnetic and magnetic 
 phenomena ; I would only point out this : Just as electrostatics 
 has been based on action at a distance between hypothetical 
 electric fluids, so magnetism has been based on the action at a 
 distance of hypothetical magnetic fluids. There can be no doubt 
 that the science could be easily rearranged, and that the 
 
INAUGURAL ADDRESS. 253 
 
 phenomena of electro-magnetism could be made fundamental, 
 and that the facts concerning permanent magnets could be made 
 subsidiary thereto, exactly as we have deduced this evening the 
 facts of electric attraction from the phenomena of current- 
 electricity. I believe that in the future this is the way the 
 science must be arranged for practical men. They are but 
 little concerned with the attractions between charged spheres 
 and the like, and very much concerned with the laws of currents 
 and differences of potential and capacities. The theory of per- 
 manent magnets has for the modern electrical engineer only a 
 general interest, but the laws of magnetic circuits and induction 
 therein are all-important. It would seem that the subject needs 
 rearranging, and that that which is most important should be 
 put most prominently forward. I even venture to think that this 
 would be no loss to pure science ; we should see with increased 
 clearness how little we know what electrical phenomena really are, 
 and how much we know of how electrical laws work. We should 
 see how much there is that is arbitrary and conventional, and by 
 no means absolute, in the system of units we have adopted. The 
 science of electricity is so essential to the practical electrical 
 engineer that it should be arranged so that he can learn in logical 
 order what he most wants to know. In what I have briefly 
 indicated there will be something which is trite to all, and 
 something perhaps not easy to comprehend when stated too 
 shortly. My aim has been rather to excite in your minds dis- 
 content with the way in which the science of electricity is usually 
 arranged, in the hope that such discontent may take an articulate 
 form, and become a demand for something more convenient for 
 your particular purpose. When the demand becomes clear it will 
 not be long before it is supplied*. 
 
 * I am informed by Professor S. P. Thompson that he has for some time past 
 in his lectures begun the subject of electricity with the consideration of currents. 
 My attention has also been called to Professor Ayrton's excellent book on Practical 
 Electricity (1886), and to Dr Walmsley's book on The Electric Current (1894), with 
 the contents of which I ought to have been, but was not, acquainted, in which 
 a similar arrangement of the subject has been adopted. J. H. Jan. 22nd. 
 
16. 
 
 PRESIDENTIAL ADDRESS TO THE JUNIOR ENGI- 
 NEERING SOCIETY, 4TH Nov., 1892, ON THE COST 
 OF ELECTRIC SUPPLY. 
 
 [From the Transactions of the Junior Engineering Society, 
 Vol. in., Part I., pp. 114.] 
 
 THE interests of an Engineer are many sided. If he is to 
 successfully use the forces of nature for the service of man he 
 must understand how those forces work ; he must in fact be 
 scientific. It may be that his ideas are arranged differently 
 from the ideas of those who study science for its own sake, and 
 without regard to practical applications, but if he is to succeed 
 they must be so arranged that he can deduce from knowledge 
 already acquired, knowledge which is applicable to new cases 
 which have not as yet come under his observation. The Engineer 
 who can only do that which he has seen done before may be a 
 practical man, but he will always belong to a lower grade of his 
 profession. The scientific Engineer is one who by his knowledge 
 of nature is able to deal with new engineering problems and 
 provide useful solutions of those problems. But a practical man 
 must be something more than a man of science, or rather he must 
 look at matters from a different point of view. He cannot choose 
 some feature of a problem, concentrate all his attention upon that, 
 and leave other matters out of consideration, which is the process 
 by which most scientific advance has been made; but he must 
 
ON THE COST OF ELECTRIC SUPPLY. 255 
 
 always deal with the whole matter before him and leave no 
 relevant question out. But an Engineer may be scientific inas- 
 much as he has knowledge of nature and the power of applying 
 that knowledge in new cases ; he may be practical in the sense 
 that the means he devises to attain his ends may be complete 
 at all points, and not break down from trifling defects, and yet 
 may find that there are other subjects which he has to consider. 
 Our complete Engineer must give his attention to commercial 
 matters as well ; he must know if, when he has devised the means 
 to attain the ends in view, those ends when attained will result in 
 a profit. He must recognise the conditions which render an 
 undertaking economical to work, and which secure that it shall 
 bring in a large return. When it has been my lot to address 
 Engineers I have usually directed attention to some scientific 
 point which I thought would be of interest to them. This 
 evening I should like to go to the other extreme and deal with a 
 purely commercial question, with a matter into which no science 
 enters, and which relates entirely to pounds, shillings, and pence. 
 
 You are all of you familiar with the fact that the expenses of 
 an undertaking may be broadly divided into two classes. On the 
 one hand there are expenses which are quite independent of the 
 extent to which the undertaking is used, and on the other, 
 expenses which are absent unless the undertaking is used and 
 which increase in proportion to the use. For example, the 
 charges for interest on the construction of a bridge are the same 
 whether that bridge is used much or little or at all, and the cost 
 of maintaining the bridge is also practically independent of its 
 user. The same is true in a large measure of a harbour or a dock. 
 Such undertakings lie at one extreme of the scale. It is less easy 
 to find good examples at the present day of the other extreme, as 
 nearly all undertakings with which Engineers have to deal 
 require the employment of some capital, and there will be a fixed 
 charge for the use of that capital and for maintaining against the 
 assaults of time the things in which the capital is embodied. But 
 we can readily see for example in the case of a cotton mill that, if 
 on the one hand there are expenses for interest and dilapidation 
 which are independent of the amount of yarn actually manu- 
 factured in a given factory, there are other expenses for material 
 and labour, and even for actual wear of machinery which will be 
 very nearly proportional to the output. Undertakings vary 
 
256 ON THE COST OF ELECTRIC SUPPLY. 
 
 enormously in the proportion of these two classes of expenses, in 
 some the expense is quite independent of the extent of the user, 
 in others it is for the greater part proportional to the user. 
 
 But undertakings differ from each other in another respect. 
 In some cases the service which the undertaking is designed to 
 render can be performed at a time selected by the undertakers ; 
 in others at a time selected by him to whom the service is 
 rendered. In the case of most manufactures it matters not if the 
 thing made is made to-day or to-morrow, in the morning or the 
 evening, for it will not be used for a month hence perhaps ; the 
 thing can in fact be extensively stored and kept till it is wanted. 
 Other services must be rendered at the moment the person served 
 desires. For example, the Metropolitan District Railway must be 
 prepared to bring in its thousands of passengers to the City at 
 the beginning of the day and to take them back in the evening, 
 and for the rest of the day it must be content to be comparatively 
 idle. In this case the services cannot be stored. The line must 
 be of a carrying capacity equal to the greatest demand, and if this 
 be great for a very short time the total return for the day must 
 be small in comparison with the expense of rendering the service. 
 In such a case it would not be inappropriate to charge more for 
 carrying a person in the busy time than in the slack time, for it 
 really costs more to carry him. 
 
 Let us see how these considerations apply to the supply of 
 electricity for lighting. Electrical Engineers now realise that 
 they have to provide the same plant and no more to give a steady 
 supply day and night as to give a supply for one hour out of the 
 twenty-four. They also now realise that if they are to be ready 
 to give a supply at any moment, they must burn much coal and 
 pay much wages for however short a time the supply is actually 
 taken. Indeed, the term " load factor " proposed by Mr Crompton 
 is as constantly in the mouths of those who are interested in the 
 supply of electricity, as volt or ampere or horse-power. The 
 importance of the time during which a supply of electricity is 
 used was so strongly impressed on my mind years ago that in 
 1883 I had introduced into the Provisional Orders with which 
 I had to do, a special method of charge intended to secure 
 some approach to proportionality of charge to cost of supply. 
 Unfortunately the orders of that day all came to nought. 
 
ON THE COST OF ELECTRIC SUPPLY. 257 
 
 A supply of electricity must be delivered at the very 
 moment when the consumer chooses to use it, and as long as 
 and no longer than he pleases to use it ; it cannot be very 
 readily or cheaply stored, and much of the cost of production 
 is the fixed charge for plant and conductors. Furthermore the 
 provisional orders require that the supply shall be available at 
 all hours ; hence coal must be consumed and workmen must 
 attend, though but few consumers are drawing a supply. The 
 service of supplying electricity has from an economic point of 
 view a great deal of similarity to the service of providing a 
 breakwater for a harbour. A great deal of the expense is inde- 
 pendent of the number of hours in the day during which the 
 supply is used. To put it in another way, the cost of supply- 
 ing electricity for 1,000 lamps for ten hours is very much less 
 than ten times the cost of supplying the same 1,000 lamps for 
 one hour, particularly if it is incumbent on the undertaker to 
 be ready with a supply at any moment that it is required. 
 
 The actual importance of considerations of this kind can 
 only be realised by examining figures. The figures may as 
 well be estimated figures, because the circumstances vary from 
 one neighbourhood to another. No criticism of the details of 
 the figures will affect the general character of the conclusion. 
 Let us then imagine a station capable of supplying 40,000 
 sixteen-candle lamps at one time, with mains and spare 
 machinery enough to ensure that the supply shall not fail, and 
 let us see what the charge for running such a station will be ; 
 firstly on the hypothesis that it is always to be ready to supply 
 the 40,000 lights at half-an-hour's notice day or night but that 
 the lights are hardly ever actually required; secondly on the 
 hypothesis that the 40,000 lights are steadily and continuously 
 supplied day and night. These are the two extreme cases 
 possible. In the former, the load factor is nil ; in the latter it is 
 100 per cent. If the charge is by meter at 8d. per unit in the 
 former case, the revenue will be nil; in the latter it will be 
 730,000 a year. 
 
 We are going to divide the cost of supplying electricity into 
 
 two parts ; a part which is independent of the hours the supply is 
 
 used, and a part which is directly proportional thereto ; and we are 
 
 going to estimate the amount of each element. It is for the 
 
 H. i. 17 
 
258 ON THE COST OF ELECTRIC SUPPLY. 
 
 purpose of ascertaining these elements that we consider two quite 
 hypothetical cases; cases which can themselves never actually 
 occur. 
 
 We must first have an idea of the capital outlay required. 
 To provide the maximum of 40,000 lamps we need to deliver 
 2,500 units per hour, and we may estimate the capital outlay as 
 
 follows : 
 
 
 
 Land 25,000 
 
 Buildings 15,000 
 
 Boilers and Pipes 14,000 
 
 Engines 24,000 
 
 Dynamos 15,000 
 
 Switchboard and Instruments 2,000 
 
 Feeders and Mains 50000 
 
 145,000 
 
 Let us deal with the annual charge for each item of capital 
 separately on the two hypotheses. The charge for land and for 
 buildings including repairs is clearly the same in the two cases, 
 say at 4 per cent. 1,000 for the land, and at 10 per cent. 1,500 
 for the buildings. The boilers, engines, and dynamos will have a 
 charge for interest, and a charge for writing off or amortization 
 as the French call it, that is, for writing off the value of the plant 
 before the time at which it becomes antiquated, exactly the 
 same in the two cases. The boilers too will require exactly the 
 same repairs whether they are merely keeping steam or whether 
 they are generating steam continuously; but the machinery will 
 certainly require more for repairs and renewals if it is all running 
 than if a part only is running without load and the rest is 
 standing ready for a load if required. I take 4 per cent, as the 
 charge for interest; 3 per cent, for amortization ; 8 per cent, for 
 repairs and maintenance. Of the repairs of engines and dynamos 
 I assume that 2 per cent, will be applicable if the plant runs 
 light, the remaining 6 per cent., if it is fully and continuously 
 loaded. The expenses connected with conductors and switchboard, 
 etc., will be exactly the same whether the current is passing or 
 not ; these I take at 15 per cent. The rates I put down at 500 
 
ON THE COST OF ELECTRIC SUPPLY. 259 
 
 a year. The account then for the fixed charges already enumerated 
 
 would stand as follows : 
 
 Running Light. Fully Loaded. 
 
 
 
 Land 1,000 1,000 
 
 Buildings 1,500 1,500 
 
 Rates 500 500 
 
 Boilers 2,100 2,100 
 
 Switchboard and Conductors 7,800 7,800 
 
 Engines 2,160 3,600 
 
 Dynamos 1,350 2,250 
 
 16,410 18,750 
 
 We now come to a most important item in the account, the 
 coal. There is no doubt that with uniform and continuous load 
 a unit of electric energy 1J horse-power for one hour can be 
 produced for less than 3 Ibs. of coal ; it is also pretty much 
 admitted that with a load factor of about 12 per cent., but 
 continuous maintenance of pressure, the consumption of coal in 
 good practice is something like 7 Ibs. That is to say, to keep the 
 boilers warm, turn round the machinery for 24 hours, and deliver 
 full current for 24 hours, will require 72 Ibs. of coal per kilowatt ; 
 whereas to keep the boilers warm, turn round the machinery, and 
 deliver current for 3 hours, will require 21 Ibs. of coal. The 
 boilers being kept warm, it will take ol Ibs. of coal to generate 
 steam enough to give a unit per hour for 21 hours ; 58 Ibs. to give 
 a unit per hour for 24 hours ; subtracting this from 72 Ibs., the 
 amount required both to generate steam and keep the boiler 
 warm, we may infer that to keep the boiler warm and merely 
 turn the machinery in readiness to meet a demand will take about 
 14 Ibs. of coal per day for every unit per hour the plant is capable 
 of producing. In 1889, for the Society of Arts, tests were made 
 of a Paxman compound engine, from which it appears that a 
 boiler which when fully loaded consumed 40 Ibs. of coal per hour, 
 required 4 Ibs. per hour to keep steam up to normal pressure when 
 the engine was standing : that is, 10 per cent, of the coal used was 
 used to maintain the steam pressure. Remembering that in 
 addition we keep some of our machinery moving, this may be 
 said to confirm the figures adopted. Thus if the plant runs light 
 
 172 
 
260 ON THE COST OF ELECTRIC SUPPLY. 
 
 all the year round 12,775,000 Ibs., or let us say 6,000 tons of coal 
 will be consumed. If the plant runs fully loaded 65,700,000 Ibs., 
 or let us say 30,000 tons would be consumed. If we suppose the 
 coal to be best smokeless it might cost 205. per ton. Next we 
 have water, oil and petty stores ; say 600 and 3,000 in the two 
 cases. Wages will be a little less if we run light than if we run 
 fully loaded, and of course will largely depend on local circum- 
 stances ; let us say 5,000 and 7,500 in the two cases. This 
 gives us substantially all the expenses which have to be met and 
 our account will then stand thus : 
 
 Fixed Charges 
 
 Running Light. 
 
 
 16410 
 
 Fully Loaded. 
 
 
 18,750 
 
 Coal 
 
 6000 
 
 30000 
 
 Stores 
 
 . . 600 
 
 3000 
 
 Wages 
 
 5000 
 
 7 500 
 
 
 
 
 28,010 59,250 
 
 Thus the cost of merely being ready to supply 2,500 units per 
 hour at any moment throughout the year will be 28,010, and the 
 cost of actually supplying 2,500 units per hour for every minute 
 in the year will be 59,250. The undertaker therefore who incurs 
 the liability to supply, ought to receive 11 per annum per unit 
 per hour from those on whose behalf he incurs the liability, and if 
 he receives the 11 he need not charge more than Jd per unit for 
 what he actually supplies, to cover his expenses. That these 
 figures are fair approximations can be seen as follows : according 
 to this calculation the cost of supplying 2,500 units for one hour 
 per day is 28,010 + 2,500 x 365 x jd. = 29,277, and the charge 
 for the service at Sd. a unit would be 30,417 ; it is doubtful if 
 such a supply would pay. On the other hand an indicated horse- 
 power on such a scale could certainly be supplied continuously for 
 from 12 to 14 per annum, and according to this calculation an 
 electrical horse-power will cost just under 18 per annum. No 
 account is taken of expenses peculiar to companies, such as 
 directors' fees and the cost of forming the company. It will also 
 be noted that it is assumed that accumulators are not used. 
 
 The charge for a service rendered should bear some relation to 
 the cost of rendering it. If it is a matter of open competition the 
 
ON THE COST OF ELECTRIC SUPPLY. 261 
 
 matter will settle itself, for no one will for long be able to supply 
 some customers at a loss, and recoup himself by exorbitant profits 
 from others. If the matter be a case more or less of monopoly, 
 the adjustment is less certain ; thus the Post Office charges %d. 
 postage for a printed circular and Id. for a written letter, the two 
 costing the Post Office exactly the same. What a boon to the 
 public it would be if the Post Office would charge more for 
 printed trade circulars, which in nine cases out of ten are a 
 nuisance to those who receive them. The supply of electricity is 
 not quite a monopoly ; companies compete with each other, and 
 there is always the competition with other methods of illumination 
 such as gas and paraffin. It is clearly to the advantage of the 
 undertaker to secure all those customers whom it pays best to 
 supply, and as far as may be, to compel those who are unre- 
 in unerative to adopt these other methods. The ideal method of 
 charge then is a fixed charge per quarter proportioned to the 
 greatest rate of supply the consumer will ever take, and a charge 
 by meter for the actual consumption. Such a method I urged in 
 1883, and obtained the introduction into certain Provisional Orders 
 of a clause sanctioning " a charge which is calculated partly by 
 the quantity of energy contained in the supply and partly by a 
 yearly or other rental depending upon the maximum strength of 
 the current required to be supplied." In fixing the rates of fixed 
 charge it must not be forgotten that it is improbable that all 
 consumers will demand the maximum supply at the same 
 moment and consequently the fixed charge named might be 
 reduced or some profit be obtained from it. There is no object 
 in reducing the cost of electricity for lighting in the case of any 
 customer much below the cost of equivalent lighting by gas, 
 unless there are competitors in the field willing to do it, hence the 
 current charge proportioned to the power supplied may safely be 
 increased. In certain recent cases in which I am acting as 
 engineer, the Board of Trade have sanctioned on my application, 
 "for each unit per hour in the maximum power demanded, a 
 charge not exceeding 3 per quarter, and in addition for each unit 
 supplied, a charge not exceeding two pence." It is sometimes 
 said as an objection to this method of charge, the public will 
 object to pay a fixed charge whether they make use of their 
 lights or not, and that in fact they will not pay it. The best 
 answer that can be made is to give everyone the choice of 
 
262 ON THE COST OF ELECTRIC SUPPLY. 
 
 being charged the maximum simple rate provided by the 
 Order, or by the compound rate, as they prefer. What is 
 wanted is not so much an increased charge for those consumers 
 whose lights are used for a short time, as such a special reduced 
 charge for those whose lights are used long as will induce them 
 to use the supply. 
 
 It is instructive to compare the cost to different classes of 
 consumers of electricity and gas for lighting with 16-candle gas. 
 Flat flame burners must be large and of first- rate quality to give 
 more than two candles per cubic foot of gas per hour ; the large 
 majority of burners give much less than this even at their best, 
 and as a rule the pressure of the gas is not regulated and much 
 gas is wasted as far as the production of light is concerned. In- 
 candescent lamps give about one-quarter of a candle per watt; 
 hence a Board of Trade unit is equivalent to 125 cubic feet of gas. 
 Thus we readily arrive at the following comparative table, the 
 charge being at the rates recently sanctioned by the Board of 
 Trade : 
 
 Price of Gas at which 
 
 Hours of use cost of lighting by 
 
 per annum. Load Factor ' electricity and J 
 
 16-candle gas are equal. 
 
 480 5-5 5*. 4d. 
 
 960 10-9 3s. U. 
 
 1,440 16-4 2s. 8d. 
 
 1,920 21-9 25. U. 
 
 2,880 32-9 2s. Od. 
 
 3,840 43-8 1*. IQd. 
 
 7,680 87-6 1*. 7d. 
 
 In the accompanying curves are shown the cost of production, 
 arid the charge per unit at the compound and simple rate. The 
 ordinates represent pence and the abscissae the number of hours 
 per annum the supply is used. 
 
 It is obvious that those whose user is long will find the 
 electric light economical to themselves and that it will be pro- 
 fitable to the undertaker. With a cheap light which is free from 
 the products of combustion there will be extensions for the hours 
 of use. Shops may find it worth while to continue the light after 
 closing, as an advertisement. 
 
ON THE COST OF ELECTRIC SUPPLY. 
 
 263 
 
 We have so far assumed that the supply of electricity is 
 carried on without the aid of accumulators. Let us first compare 
 the cost of an electric accumulator with the cost of a gas-holder 
 containing the same possibility of producing light. A gas-holder 
 is at present being put up in Manchester to hold 7,000,000 cubic 
 feet of gas and is to cost complete with its tank 60,000. With 
 16-candle gas seven million cubic feet are equivalent to 56,000 
 Board of Trade units. Accumulators, capable of storing a ten 
 hours' supply, cost about 50 per unit. The equivalent accumu- 
 lator will therefore cost about 280,000. But this is not all; the 
 gas-holder is comparatively permanent ; the accumulators require 
 
 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 
 Hours 
 
 frequent renewals and repairs; the gas-holder gives back all the 
 energy pat into it : the accumulators waste at least 20 per cent. ; 
 the gas-holder may be emptied as fast as you please ; the accu- 
 mulators, not faster than a certain rate without diminishing their 
 capacity. Taking all into consideration, the cost of storing energy 
 by the aid of accumulators and storing it in a gas-holder are 
 quantities of a different order of magnitude. If no gas-holders 
 were used, and all the gas had to be made just as it was wanted, 
 its cost for lighting would be several fold what it now is, even if 
 gas-producers could be found capable of instantly varying the 
 supply as the demand varies. The gas-producing plant would 
 have to be enormously increased; so would the size of the mains, 
 and so would the wages of labour. If electric power could be 
 stored as cheaply as gas, there would soon be little hope that the 
 gas companies would maintain their dividends. 
 
264 ON THE COST OF ELECTRIC SUPPLY. 
 
 Let us see from a financial point of view whether accumulators 
 can be used economically for storing up electrical power con- 
 tinuously produced during the 24 hours, and used rapidly for a 
 short time. 
 
 Assume that the whole of the plant with the accumulators is 
 capable of supplying 40,000 lights for ten hours continuously, and 
 that during that time half the power is supplied from the 
 accumulators. Ten hours in the twenty-four hours is not an 
 unreasonable allowance, for we have melancholy experience in 
 London of continuous fog for days, and this would tax the plant 
 we are considering to the utmost. We are to be ready then at 
 any time on short notice to supply 40,000 lights, and to continue 
 to supply them for 10 hours. Compare the cost firstly of main- 
 taining this state of readiness with the accumulators and with a 
 plant without accumulators. We shall require a battery capable 
 of giving 1,250 units for ten hours ; such a battery costs not less 
 than 50 per unit, or in all 62,500. To maintain it, will cost 
 from 10 to 15 per cent, on the cost; there will also be interest on 
 the outlay and amortization, say in all 20 per cent, or 12,500 a 
 year. If we assume that the batteries are distributed at the 
 various points of the system of conductors, we may also assume 
 that the charges for land and buildings will be much the same as 
 for the plant without accumulators. The boilers, engines, and 
 dynamos will be just one-half. The switchboard and instruments 
 will be much the same. But the conductors will be reduced, 
 smaller or shorter feeders being necessary, probably 40,000 will 
 go as far with accumulators as 50,000 without. The coal bill 
 may be dispensed with entirely, as we may assume that steam 
 could always be got up during the time in which the demand 
 increased from nothing to one-half of the maximum, and that 
 therefore all the coal burned can be assumed to be burned for 
 producing current. That is to say, we assume the quantity of 
 coal burned is proportional to the quantity of electric energy, and 
 that therefore when no electricity is actually used, no coal will be 
 burned. The wages may be reduced, for we have only to be ready 
 to run half the plant, and a small wage will suffice for attendance 
 on the accumulators. The wages of linesmen and the like will 
 remain the same. Assume the total wages to be 3,500 instead 
 of 5,000. The account will then stand thus : 
 
ON THE COST OF ELECTRIC SUPPLY. 265 
 
 
 
 Land 1,000 
 
 Buildings 1,500 
 
 Rates 500 
 
 Accumulators 12,500 
 
 Boilers 1,050 
 
 Engines 1,080 
 
 Dynamos 675 
 
 Switchboard 300 
 
 Conductors 6,000 
 
 Wages 3,500 
 
 28,105 
 practically the same result as we obtained before. 
 
 Now consider another hypothetical case, which of course can 
 never occur in practice. We are to supply 40,000 lamps for ten 
 hours every day with the plant just described, charging the 
 accumulators during twelve and a half of the fourteen hours 
 during which the light is not required, twelve and a half hours' 
 charging giving ten hours' discharge of the same energy. The 
 coal would cost the half of 30,000 if the machinery had to run 
 the whole of the 24 hours. It has to run 22J hours, but the 
 boilers have to be kept warm the whole time, hence the coal will 
 cost the half of 6,000 for keeping the boilers warm, and 22* of 
 the half of 24,000 for generating steam. The wages may fairly 
 be taken as 4,750, and the account will stand : 
 
 
 
 Land 1,000 
 
 Buildings 1,500 
 
 Rates 500 
 
 Accumulators 12,500 
 
 Boilers 1,050 
 
 Engines 1,800 
 
 Dynamos 1,125 
 
 Switchboard 300 
 
 Conductors 6,000 
 
 Wages 4,750 
 
 Coal 14,250 
 
 Stores L425 
 
 46,200 
 
266 ON THE COST OF ELECTRIC SUPPLY. 
 
 The cost of supply for the same ten hours without accumu- 
 lators would be as follows : 
 
 
 
 Land 1,000 
 
 Buildings 1,500 
 
 Rates 500 
 
 Boilers 2,100 
 
 Switchboard and Conductors 7,800 
 
 Engines 2,760 
 
 Dynamos 1,725 
 
 Coal 16,000 
 
 Stores 1,600 
 
 Wages 6,000 
 
 40,985 
 
 a cost of about 11 per cent, less than where accumulators are 
 used. 
 
 Putting it another way, the cost of being ready to supply and 
 to continue to supply, is about the same whether accumulators 
 are used or not ; the additional cost of actually supplying current 
 is about 40 per cent, more where accumulators are used than 
 where they are not used. It may be safely inferred that the use 
 of accumulators does not seriously alter the conclusions I have 
 drawn as to the proper method of charging consumers for a supply 
 of electricity. 
 
 The question of whether the great cost of a supply for short 
 hours can be removed by the use of accumulators may be looked 
 at in another way. Will it pay a consumer to put in his own 
 accumulators and charge them from the station supply ? We may 
 reasonably suppose the undertaker will remit the fixed charge in 
 consideration of the consumer only taking his current at slack 
 times. His accumulators if they are to be of capacity to maintain 
 his supply through a foggy day will cost him 50 per unit per 
 hour (or per kilowatt) and the annual charge in respect of them 
 will be 10 per year, to which if we add a rent for the space the 
 battery occupies, gives us a charge not differing materially from 
 the fixed charge made or suitable to be made by the undertaker. 
 But in order to obtain 2d. worth of electricity he must purchase 
 
 . worth for charging his battery. 
 
ON THE COST OF ELECTRIC SUPPLY. 267 
 
 A word or two more about the use of accumulators. These 
 have certainly improved, and they will continue to improve. 
 They will become more durable and more economical of power in 
 working, and their first cost will become less. An inspection of 
 my tables of cost shows that a very little improvement would 
 render them valuable even in very large stations for the mere 
 purpose of diminishing the machinery required, by storing the 
 energy developed at slack times to be used in busy times. The 
 certainty of improvements in accumulators, and the possibility 
 that the improvement may be considerable, is a strong argument 
 for the use of the direct current wherever it is not precluded by 
 the distance of transmission being too great. 
 
 It will be noted that I have assumed a very large station. 
 Accumulators have another use which greatly increases their 
 advantage in smaller stations. There are many hours in the 
 twenty-four when it is absolutely certain that the demand will be 
 small. If accumulators are used, the attendance of the staff may 
 be dispensed with during those hours, and a considerable sum in 
 wages will be saved. The proportion of wages to the whole of the 
 charges is much greater in small stations than in large. In most 
 small stations giving continuous supply, accumulators ought to be 
 used notwithstanding their expenses and defects, and I believe the 
 day is not far distant when they ought to be used in connection 
 with most large stations also. 
 
 If instead of a continuous current, an alternating current with 
 transformers is used, the modification in the account will be that 
 the cost of conductors will be diminished, but the cost of trans- 
 formers will have to be added. If the distances are small, the 
 increased cost of transformers will exceed the saving in the con- 
 ductors ; if the distances are considerable, the cost of transformers 
 will be less than the saving of conductors. In both cases the 
 general character of the result will be the same as before, the cost 
 of being prepared to give a supply will be considerable, and the 
 cost of actually giving the supply will be much smaller than is 
 generally supposed. Indeed with the alternating current this 
 peculiarity will be even more marked, for the machinery has not 
 only to be kept in motion however small the consumption may 
 be, but a certain current must be maintained in every transformer. 
 With the best transformers, this current may only have an energy 
 
268 ON THE COST OF ELECTKIC SUPPLY. 
 
 1J per cent, of the energy of the current when the transformer is 
 fully loaded. This would increase the coal bill in the case 
 considered by about 500 per year whether the supply was 
 used or not. 
 
 It is possible, indeed probable, that some of my assumed 
 figures may be shown to be too high or too low for the generality 
 of cases. It is of no moment ; let each one take any figures he 
 pleases within reason ; let him assume that the supply of electricity 
 is made by any system he pleases ; he will arrive at a result 
 broadly similar to mine. To be ready to supply a customer with 
 electricity at any moment he wants it will cost those giving 
 the supply not much less than 11 per annum for every kilo- 
 watt, that is for every unit per hour, which the customer can 
 take, if he wishes, and afterwards to actually give the supply, will 
 not cost very much more than ^d. per unit. This is the point I 
 have been labouring to impress, for I take it, it is essential to the 
 commercial success of Electric Supply. It is hopeless for elec- 
 tricity to compete with gas in this country all along the line, if 
 price is the only consideration. But with selected customers, 
 electricity is cheaper than gas. Surely it is the interest of those 
 who supply electricity to secure such customers by charging them 
 a rate having some sort of relation to the cost of supplying them. 
 
17. 
 
 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 [From the Proceedings of the Institution of Civil Engineers, 
 Vol. cxvm. Session 189394. Part IV.] 
 
 MATHEMATICS has been described in this room as a good 
 servant but a bad master. It will be my duty this evening to 
 prove by suitable illustration the first half of the proposition, and 
 to show the service mathematics has rendered and can render to 
 engineers and engineering. 
 
 In our Charter the Institution of Civil Engineers is defined as 
 " A society for the general advancement of Mechanical Science, 
 and more particularly for promoting the acquisition of that species 
 of knowledge which constitutes the profession of a Civil Engineer, 
 being the art of directing the great sources of power in Nature for 
 the use and convenience of man, as the means of production and 
 of traffic in states both for external and internal trade, as applied 
 in the construction of roads, bridges, aqueducts, canals, river 
 navigation and docks, for internal intercourse and exchange, and 
 in the construction of ports, harbours, moles, breakwaters and 
 lighthouses, and in the art of navigation by artificial power for the 
 purposes of commerce, and in the construction and adaptation of 
 machinery, and in the drainage of cities and towns." No better 
 definition can, I think, be found for our profession than that it is 
 the art of directing the great sources of power in Nature for the 
 use and convenience of man. It covers all that the widest view 
 of our work can include, and it excludes those applied sciences, 
 such as medicine, which deal with organized beings. Mathe- 
 
270 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 matics has to deal with all questions into which measurement of 
 relative magnitude enters, with all questions of position in space, 
 and of accurate determination of shape. Engineering is a mathe- 
 matical science in a peculiar sense. Medicine, the other great 
 profession of applied science, has but little to do with questions of 
 measurement of magnitudes, or of geometry ; but the engineer 
 finds them enter into everything with which he has to deal, and 
 enter in the most diverse ways. The thing he has to determine 
 is that the means he employs is enough and not unnecessarily 
 more than enough to attain the end in view. For this he must 
 numerically measure the end and the means and see that they 
 are justly proportioned to each other. It is useless this evening 
 to waste time proving, what all will admit, that no one can be 
 even the humblest engineer without a knowledge of arithmetic and 
 enough of geometry to enable him to read a drawing, that some 
 trigonometry, some rational mechanics and a knowledge of pro- 
 jections, is a very useful part of the mental equipment of a 
 draughtsman. It is hardly necessary to call attention to the 
 great economy in the labour of calculations effected by the use of 
 logarithms, a mathematical instrument for which we are indebted 
 to Napier. We may with more profit examine what use the 
 higher mathematics can be to the practical engineer, and what has 
 been done in the past for engineering by its aid. 
 
 Judging from etymology, mathematics must have been begun 
 by engineers ; for surely geometry is the work of the earth 
 measurer or land surveyor. But since the prehistoric times when 
 geometry was initiated, engineers have not added much that 
 is new to mathematics. They have rather sought amidst the 
 stores of the mathematician and selected the handiest mathe- 
 matical tool they could find for the particular purpose of the 
 moment, but have done little or nothing in return in the way of 
 improving the tools which they borrow. In this respect the 
 relation of engineering to mathematics differs much from its 
 relation to experimental physics. In electricity, magnetism and 
 heat, engineers have from their practical experience repeatedly 
 corrected the ideas of the theorists, and have started the science 
 on more accurate lines. If our subject to-night had been the use 
 of the practical applied science of engineering in promoting the 
 development of pure mathematics, we should speedily find that 
 there was hardly any material for discussion. The account being 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 271 
 
 all on one side, let us see to what the debt of the engineer to the 
 mathematician amounts. 
 
 There is no department of practical engineering in which the 
 application of mathematics is more familiar than in that which 
 relates to the calculation of the strength and rigidity of structures 
 of various kinds. It is impossible to take up any book dealing 
 with the subject without finding that it is crammed either with 
 mathematical formulae, or with geometrical figures. The question 
 is not whether mathematics is necessary to an adequate compre- 
 hension of the subject, but whether analytical or purely geo- 
 metrical methods are more convenient. Of course one might 
 occupy many lectures in discussing the practical application of 
 mathematics to the question of bridge building, roofs, guns, 
 shafting, and the like. Our object must be to illustrate by 
 various examples rather than to attempt anything like a complete 
 discussion. 
 
 Consider the case of a long strut, so long that its transverse 
 dimensions can be regarded as insignificant in comparison with its 
 length. Whilst the strut remains perfectly symmetrical about its 
 middle line, its strength will depend only upon the resistance of 
 the material to crushing. Everyone knows that this would be an 
 inadequate conclusion ; we have to consider another element, 
 namely, its stability, that is, we must examine what will happen 
 to the strut if from any cause it is displaced somewhat from the 
 direct line between its extremities. A mathematical discussion 
 of the question results in a differential equation of the second 
 order with one independent variable. Upon consideration of this 
 we are enabled to see that if the thrust upon the strut be less 
 than a certain critical value, a slightly bent strut will tend to 
 return to its straight condition ; but that if the thrust upon the 
 strut be greater than this critical value the displacement will tend 
 to increase, and the strut will give way. Further, that the 
 critical value will depend upon whether one or both of the two 
 extremities of the strut are held free, or whether they are rigidly 
 attached by flanges or otherwise, so that the direction of the axis 
 of the strut at this point must remain unaltered. Again, we infer 
 that if the ends are held rigidly fixed, the length of the strut may 
 be twice as great for a given critical value of the thrust as if the 
 two ends are free to turn. We can also infer what the critical 
 
272 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 value will be for struts of various lengths arid of varying cross 
 sections. This critical value depends not upon the resistance of 
 the material to crushing, but upon its rigidity. 
 
 Another example, having a certain degree of similarity with 
 the case of struts, is that of a shaft running at a high number of 
 revolutions per minute, and with a substantial distance between 
 its bearings; for simplicity, we will suppose that there are no 
 additional weights such as pulleys upon the shaft. How will the 
 shaft behave itself in regard to centrifugal force as the speed 
 increases ? In this case, so long as the shaft remains absolutely 
 straight it will not tend to be in any way affected by the centri- 
 fugal force, but suppose the shaft becomes slightly bent, it is 
 obvious to anyone that if the speed be enormously high this 
 bending will increase, and go on increasing until the shaft breaks. 
 In this case also we may use mathematical treatment ; we find 
 that the condition of the shaft is expressed by a differential 
 equation of the fourth order, and from consideration of the 
 solution of this equation we can say that if the speed of any 
 particular shaft be less than a certain critical speed, the shaft will 
 tend to straighten itself if it be momentarily bent, but that, on 
 the other hand, if the speed exceeds this critical value, the 
 bending will tend to increase with the probable destruction of the 
 shaft. I do not know that either of these two questions can be 
 properly understood without some knowledge of differential 
 equations. 
 
 A problem having a certain analogy to those to which I have 
 just referred is that of hollow cylinders under compression from 
 without, such as boiler tubes. Whether the tubes be thick or 
 thin, so long as they are perfect circular cylinders, they should 
 stand until the material was crushed. But if the tubes are thin, 
 what will happen if the tube from any cause deviate ever so little 
 from the cylindrical form ? The solution cannot be obtained 
 without a substantial quantity of mathematics. 
 
 The next illustration shows how a mathematical conclusion, 
 correct within the limits to which it applies, may mislead if 
 applied beyond those limits, and how a more thorough mathe- 
 matical discussion will give a correct result. Considering a case 
 of shafting in torsion it was shown by Coulomb that the stiffness 
 and strength of a shaft having the form of a complete circular 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 273 
 
 cylinder could be readily calculated if the transverse elasticity of 
 the material and its resistance to shearing were known. From 
 the complete symmetry about the axis it is evident that points 
 which lie in a plane perpendicular to the axis before twisting will 
 still be in that plane when the shaft is twisted ; it is also clear 
 that the angle through which all points in the same plane move 
 will be the same ; hence the problem was as simple as problem 
 could be. But many who had occasion to make use of Coulomb's 
 results gave them an application which was wholly unwarranted. 
 They assumed that they were equally applicable to other cases 
 than complete circular cylinders ; they assumed in fact that every 
 point of the material which lay in a plane perpendicular to the 
 axis would remain in that plane when the shaft was twisted, 
 whether the shaft was symmetrical about its axis or not, and they 
 consequently arrived at very erroneous results. That the assump- 
 tion was erroneous is obvious enough from a consideration of an 
 extreme case. In Fig. 1 is shown in cross-section a hollow cylin- 
 drical shaft, which is not complete, but divided by a plane passing 
 
 FIG. 1. 
 
 FIG. 2. 
 
 through its axis. In this case the shaft when twisted will be as 
 illustrated in the side elevation ; two points, A and B, were in one 
 plane perpendicular to the axis when the shaft was free from 
 twist ; they cease to be in one plane when the shaft is twisted. 
 St Venant* in 1855 investigated the question of shafts without 
 making incorrect assumptions ; he expressed the condition of the 
 
 * Memoires des Savants Strangers, 1855 ; and Thomson and Tait, Treatise on 
 Natural Philosophy. 
 
 H. I. 18 
 
274 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 material by a partial differential equation of the second order, and 
 gave suitable surface conditions. A general solution of the 
 problem for all forms of shafts has not been obtained, but St 
 Venant gives a number of solutions for particular forms, and he 
 obtains some general results of interest. In all cases the stiffness 
 of the shaft is less than would be inferred from an erroneous 
 application of Coulomb's theory. Fig. 2 shows diagrammatically 
 the strain in a shaft of triangular section ; the full lines indicate 
 that the parts of the shaft which lay in one plane before twisting 
 when twisted rise above the plane ; the dotted lines indicate that 
 they lie behind the plane of the paper. The shearing stress is 
 least at the angles of the triangle, and is greatest at the middles 
 of the sides. At this point then the shaft will begin to break 
 under torsion. The fact is probably well known to men of 
 practical experience, but it is directly contradictory to the con- 
 clusion at which one would arrive by a careless use of Coulomb's 
 theory beyond the narrow limits within which it is applicable. 
 The longitudinal ribs which one often sees on old cast-iron 
 shafts are useful enough to give stiffness to the shafts against 
 bending, but are good for very little if torsional stiffness or 
 torsional strength is desired. 
 
 Another application of mathematical theory which has been 
 carried somewhat further than the premises warrant is found in 
 the case of girders. It is almost invariably customary to treat a 
 girder as though the sections retain when the girder is bent the 
 form and size which they had before bending. Making this 
 assumption, it is very easy to calculate the strength and stiffness 
 of a girder of any section. Unfortunately, the assumption is 
 untrue ; but, fortunately, it is approximately true in the case of 
 most girders with which engineers in practice have to deal. 
 That it is untrue can be readily seen from consideration of a 
 girder of exaggerated form, the section of which is shown in 
 Fig. 3. Any practical man would at once see that the outer 
 parts of the flanges would add little to the strength of the girder, 
 but according to the usual mathematical theory the outer parts of 
 this flange should be as useful as the parts which are nearer to 
 the web. This problem St Venant also deals with in a rigid 
 mathematical manner. Amongst other things, he showed that a 
 girder of rectangular section, such as shown in Fig. 4, would, 
 when bent, take the form shown by the curved lines in the same 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 275 
 
 figure. The last two examples show how a little knowledge may 
 be a dangerous thing, and how easy it is for anyone who attempts 
 to apply mathematics without adequate mathematical knowledge 
 to be misled. 
 
 FIG. 3. 
 
 FIG. 4. 
 
 The theory of thick cylinders under bursting stress from within 
 has many important practical applications to hydraulic presses 
 and to guns. It has been discussed more than once in this room. 
 As usual in considering these cases we are immediately led to 
 differential equations, which here are fortunately solved without 
 serious difficulty, and the solution tells us the whole story. We 
 learn that doubling the thickness by no means doubles the 
 strength of the cylinder. And as a converse, that doubling the 
 strength of the material will permit the thickness to be diminished 
 to much less than one-half. Twenty-five years ago hydraulic 
 presses were mostly made of cast-iron. Many people were not a 
 little astonished at the great reduction in thickness and weight 
 which became possible when steel was substituted for the weaker 
 material. In the case of guns it is well known that greater 
 strength can be obtained if the outer hoops are shrunk on to the 
 inner ones*. Mathematical theory tells us what amount of shrink- 
 age should give the best results. It may possibly not be worth 
 while to follow the results of theory precisely, but without the 
 guidance of theory it would not be unnatural to give so great a 
 shrinkage that the gun would be weaker than if no shrinkage 
 were used. 
 
 The rolling of ships in a sea-way gives an illustration of a 
 principle which has very varied application in many branches of 
 physics. Suppose a body is capable of oscillating in a certain 
 periodic time, and that it is submitted to a disturbing force of 
 
 * Lam6, Lemons sur la Theorie Mathematique de V Elasticity des corps solides. 
 14th Le<?on. 
 
 182 
 
276 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 given period, the equation of motion easily shows that the resulting 
 disturbance will be great if the two periods are equal or nearly 
 equal. We meet with the principle in acoustics as resonance. If 
 two tuning-forks are tuned to the same pitch, and one is sounded 
 in the neighbourhood of the other, that other will presently be 
 thrown into vibration by the waves transmitted through the air 
 from the first. You may try a similar experiment at any time on 
 any piano. Strike the higher G in the treble, the sound ceases on 
 raising the finger. Now hold down the middle C, and again strike 
 G, the C string at once takes up the note sounded, and can be 
 heard after the exciting string has been silenced by damping. 
 The same fundamental idea is found in the lunar theory in the 
 term in the equation known as the evection, and again in the 
 theory of Jupiter's satellites. The reason why the metals present 
 in the solar atmosphere give black lines in the spectrum by 
 absorption, corresponding in position with the bright lines in 
 the spectrum which the same metals give when incandescent, 
 is again the same. Gas will absorb or take in from the ether 
 waves of the exact period which it is capable of giving to the 
 ether. The general explanation of all these phenomena is easy. 
 Imagine a pendulum, and suppose it experiences a periodic dis- 
 turbing force, the first impulse of the disturbing force gives the 
 pendulum a slight swing, the effect of the second impulse 
 depends entirely on when it occurs, it may occur so as to 
 neutralize the effect of the first, or it may occur so as to increase 
 it. If the period of the force is the same as the natural period 
 of the pendulum, the effect of the second, third, and later im- 
 pulses will be added to the effect of the first, and the final 
 disturbance will be great even though the individual impulses 
 be minute. But the mathematical theory tells us much more 
 than any general explanation can do. It tells us exactly what 
 the character of the effect will be, and its amount if the 
 periods are nearly but not exactly the same. It tells us, too, 
 exactly how friction affects the results. And the beauty of it 
 is that the mathematical theory is much the same in all cases, 
 so that having learned to deal with one case we are enlightened 
 as to a host of others. The oscillating body may be an ironclad, 
 or it may be an atom of hydrogen, the disturbing periodic force 
 may be the waves of the Atlantic, or it may be the waves in 
 the ether occurring five hundred millions of millions of times 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 277 
 
 in a second; it is all one to the mathematician, the treatment 
 is substantially the same. 
 
 The question of the speed of ships and the power to propel 
 them is probably more effectually treated by experiment on 
 models, as was done by the late Mr Froude, than by mathematics 
 alone ; but in order to learn from the experiments all they are 
 capable of teaching a mathematical understanding is needed. 
 Given that we know by experiment all about a given model, that 
 we know what force is needed to propel it at every speed, we want 
 to know from these experiments how a great ship, 100 times as 
 big but similar in form in every respect, will behave, and here 
 mathematics come in to aid us in making the inference. 
 
 The construction of ships at once leads us on to the methods 
 of navigating them. In navigation I should find much material 
 for my purpose, but navigation is not usually included in engi- 
 neering, but many of the implements of navigation undoubtedly 
 are. The mariners' compass has for ages been the mainstay of 
 the navigator, and a simple enough instrument it was till it was 
 disturbed by the iron of which ships came to be built. The 
 disturbance of the compass by the iron of the ship was first 
 seriously attacked by two senior wranglers, Sir G. Airy and Mr 
 Archibald Smith. The disturbance may be divided into two 
 parts, the first due to the permanent magnetism of the ship, the 
 second to the temporary magnetism induced by the earth's induc- 
 tive action on the iron of the ship the first causes the semi- 
 circular, the second the quadrantal, error. One has only to open 
 the " Admiralty Manual of Deviations of the Compass " to see 
 how the mathematics of Archibald Smith have accomplished a 
 proper understanding of the subject. The errors of the compass 
 are dealt with in two ways : they are compensated by soft iron 
 correctors, and by permanent magnets so placed as to have an 
 etfect equal and opposite to the effect of the temporary and 
 permanent magnetism of the ship. Or they are dealt with by 
 formulae of correction which enable the error to be calculated 
 when the course of the ship and the conditions of the earth's 
 magnetism are given, or a combination of the two methods is 
 used. Either method is based on Archibald Smith's theory. It 
 is not possible to leave the subject of the mariners' compass with- 
 out referring to the great improvements of Lord Kelvin. The 
 
278 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 improvements relate to every part of the instrument, and I venture 
 to say that none of them could have been made by anyone but a 
 mathematician. In order to get his card steady he knew that its 
 period must be different to any possible period of the waves, or he 
 would have the resonance to which I have just referred coming in, 
 so he gave his card a considerable moment of inertia ; but this was 
 managed with a light card so that small needles could be used. 
 If the needles are small the correction by soft iron masses and 
 by permanent magnets is easier and more accurate. Then the 
 bowl of the compass had to be suitably carried so that it would 
 not be unduly disturbed by shock, and provision had to be made 
 for damping by fluid friction the oscillations of the bowl if they 
 occurred. Lastly, a most beautiful method of correcting the 
 compass, without taking a sight, was discovered. In every 
 detailed improvement one can detect that the inventing mind 
 was that of a most able and trained mathematician. 
 
 An essential of safe navigation is an efficient system of 
 lighthouses. The optical problem of the lighthouse engineer 
 is to construct apparatus which shall usefully direct all the 
 light produced. The present forms of apparatus are in their 
 leading features due to Fresnel, the able mathematician, who 
 established on an absolutely firm foundation the undulatory 
 theory of light. To properly design an optical apparatus formulae 
 must be used, and the advantage is great if the designer can 
 with ease manufacture the formulae he requires. 
 
 Submarine telegraphy yields some interesting examples of 
 the application of the higher mathematics. When a cable across 
 the Atlantic was first seriously entertained, the first point to be 
 settled was, how many words a minute could be sent through such 
 a cable. This was the most practical question possible. Upon 
 the answer depended the prospect of the cable paying commercially 
 if successfully laid. The matter was dealt with by Professor 
 Thomson*, of Glasgow, now Lord Kelvin. He showed that the 
 propagation of an electric disturbance in a cable could be expressed 
 by a partial differential equation, and that the solution of this 
 equation under certain conditions applicable to practice could be 
 expressed either by a definite integral or by an infinite series. The 
 values of these were calculated, and hence before an Atlantic cable 
 
 * Mathematical and Physical Papers, vol. n. p. 61. Sir W. Thomson. 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 279 
 
 was laid at all it was known how long it would take a signal to 
 reach the opposite shore, and how much its intensity would be 
 diminished in transmission. Referring to Fig. 5, abscissae repre- 
 
 \ 
 
 FIG. 5. 
 
 sent time, reckoned from the time of making contact at the 
 sending end of the cable, ordinates the currents at the receiving 
 end, curve (I) gives these currents when the contact at the 
 receiving end, after being made, is continuously maintained. 
 It will be observed that for a time a there is hardly any current 
 at the receiving end, and then the current rapidly increases, and 
 attains to half its final value after a time equal to about oa. 
 
 Curves (1) (7) show the currents at the receiving ends when 
 
 the contact is made at the sending end maintained for times a, 2a 
 
 7a respectively, and then broken. Looking at curve (I) one 
 
 sees how small is the amount of current and how long it lasts 
 compared with the time during which contact is made. The 
 time a depends on the length and character of the cable ; it is 
 equal to kcl 2 log e f/vr 2 , where k is the resistance per unit length, 
 c the capacity per unit length, and I the length of the cable. The 
 knowledge of what is the commercial value of a cable depends on 
 a knowledge of the value of a, and this cannot be obtained without 
 
 knowing the differential equation ck -j- = -7-^*, to which I have 
 
 * v is the potential, t the time, and x the distance from the sending end of the 
 cable. 
 
280 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 referred, and its by no means simple solution either as a definite 
 integral or as an infinite series. So far as I know, this piece of 
 higher mathematics cannot be evaded by any mere elementary 
 treatment. The transmission of disturbance in a cable is quite 
 different from the transmission of sound waves in air, which move 
 with constant velocity. If the cable be doubled in length, it 
 takes four times as long for the signal to pass through it instead 
 of just twice as long, as would be the case if it were a proper wave 
 motion. In fact the time of passage between the making of 
 contact at the sending end of the cable and the beginning of the 
 resulting disturbance at the receiving end, varies as the square of 
 the length of the cable. The mathematical theory is exactly the 
 same as that of the transmission of heat in a plate, one surface of 
 which is suddenly exposed to a temperature different to the tem- 
 perature of the plate. This is constantly occurring in the applica- 
 tion of mathematics one piece of mathematical work serves for 
 many physical problems having apparently little in common. 
 Fourier long ago discussed the heat problem, little dreaming 
 that his analysis would be just what was wanted for ascer- 
 taining how fast signals could be sent across the Atlantic by 
 a system of telegraphy which in his days had not even been 
 projected in its simplest form. The same differential equation 
 also gives the theory of the transmission of telephonic messages 
 through cables ; but the solution is then easier, and tells us 
 exactly why it is so much more difficult to speak through 
 100 miles of cable than through 1,000 miles of overhead line. 
 As I have just stated, the differential equation of the disturbance 
 
 in the cable is ck -y = - 7 . A musical note of period T spoken 
 dt dx 2 
 
 into the cable through a telephone is properly represented by 
 A sin -- ; the disturbance in the cable will be 
 
 as may be easily verified by differentiating. This equation tells 
 us everything. It tells us the rate at which the waves diminish 
 with the distance. This rate increases with the resistance, with 
 the capacity, and with the frequency. If the capacity is at all 
 considerable the diminution is rapid. The velocity of the waves 
 is not the same for all frequencies, as is the case with waves in 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 281 
 
 air, but varies as the square root of the period, so that if two notes 
 were sounded the high note would arrive after the low note, and 
 the resultant effect would be entirely destroyed. Here, again, it 
 is difficult to see how the differential equation and its solution 
 can be evaded. 
 
 Though the history of the telegraph dates only from a little 
 more than fifty years ago, it is ancient in comparison with the 
 other great applications of electrical science, which have received 
 their development during the last fifteen years. Here again 
 mathematics which are not quite elementary have played their 
 part. In the theory of transformers we find another illustration 
 of the need of knowing how formulae are obtained if they are to 
 be correctly applied. The early transformers were made with 
 unclosed magnetic circuits ; there was an iron core, but the lines of 
 magnetic force passed through air for a considerable part of their 
 path. In this case a complete mathematical theory was not very 
 difficult. But speedily closed magnetic circuits were found to be 
 better, and the relation of magnetic induction and magnetic force 
 became all important. If anyone were to apply mathematical 
 formulae, which were true for the earlier transformers, to the later 
 ones, his results would be inaccurate. Indeed a wholly different 
 method of attack on the problem was needed, taking account of 
 the facts as they are, and not applying results which were true of 
 older apparatus to cases essentially distinct*. 
 
 The employment of alternating currents has brought into use, 
 as a necessity for understanding the actually observed phenomena, 
 a great deal of mathematics. Why is the apparent resistance 
 of a conductor greater for an alternating current than for a 
 direct current ? And by resistance I do not mean the quasi- 
 resistance due to self-induction f. The mathematical electrical 
 theory is ready with an answer ; it is ready, too, to tell us how the 
 difference depends upon the frequency of the current and on 
 the size of the conductor. In the case of a cylindrical con- 
 ductor the solution involves a knowledge of Bessel's functions. 
 We learn that if the current has a high frequency, or if the 
 conductor be large, there will be very little current in the 
 centre of the cylinder, and that therefore for any practical 
 
 * Proceedings of Royal Society, February 17th, 1887. 
 t Lord Rayleigh, Phil. Mag. vol. xxi. p. 381. 
 
282 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 purpose the centre of the cylinder might just as well not be 
 there ; the current is largely confined to the part of the con- 
 ductor near to its surface. The currents at different depths in 
 the conductor attain to their maximum values at different 
 times ; those near the surface of the cylinder occur before those 
 at some distance from the surface. The mathematical conditions 
 are expressed by the same equation as is used to express the 
 disposition of heat in a cylinder the surface of which is sub- 
 mitted to a periodic variation of temperature. Anyone who had 
 thoroughly mastered the heat problem would be quite prepared 
 to deal with the problem of currents in a conductor. It cannot be 
 too often repeated, any piece of pure mathematics which finds one 
 application to a physical problem is almost sure to find, in exactly 
 the same form, applications to other problems which superficially 
 are absolutely distinct. The differential equation in this case is 
 
 kc -j- = f-j- a + - -T- j , the similarity of physical condition to the 
 problem of linear propagation of heat is close, but the mathe- 
 matics differs materially owing to the presence of the term - -y- 
 
 in the equation. Mathematics deals with the relation of quantities 
 to each other without troubling as to what the physical meaning 
 of the quantities may be. Hence it is that the mathematical 
 treatment of two such problems as the distribution of currents in 
 a cylindrical conductor and of heat in a cylinder is identical, 
 whereas the treatment of the distribution of heat in a cylinder is 
 quite distinct from the treatment of the distribution of heat in a 
 sphere or in a solid bounded by two parallel planes. 
 
 A curious phenomenon was observed in the large alternate- 
 current machines at Deptford when connected to the long cables 
 intended to take the current to London. The pressure at the 
 machines when connected to the conductors was, under certain 
 conditions, actually greater than when not so connected. The 
 phenomenon is one of resonance very analogous to the heavy 
 rolling of ships when the natural period of roll is about the same 
 as the period of the waves*. The period of the alternating current 
 corresponds to the period of the waves, the self-induction of the 
 machine to the moment of inertia of the ship, the reciprocal of the 
 capacity to the stiffness of the ship, and the electrical resistance 
 
 * Institution of Electrical Engineers, November 13th, 1884. 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 283 
 
 of the conductors to the frictional resistance to rolling. The mathe- 
 matics in the two cases is then the same. The effect was predicted 
 long before it was observed in a form calculated to cause trouble. 
 
 A problem which is still agitating electrical engineers is that of 
 running more than one alternate-circuit dynamo machine con- 
 nected to the same system of mains. Before the matter became 
 one of practical concern, it was considered in this room, and it 
 was shown mathematically, that it was possible to run inde- 
 pendently-driven alternators in parallel but impossible to run 
 them in series. That is to say, that if two alternators were con- 
 nected to the same mains they would tend to adjust themselves in 
 relation to each other so that their currents could be added, but 
 that if an attempt were made to couple them, so that their 
 pressures should be added, they would adjust themselves so that 
 their effects would be opposed*. 
 
 Perhaps of all engineering problems which have received their 
 solution in the last hundred years that of the greatest practical 
 importance is the conversion of the energy of heat into the energy 
 of visible mechanical motion. The science of thermodynamics 
 has advanced along with the practical improvement of the steam- 
 engine. By its aid, particularly by the aid of the so-called second 
 law, we know what is possible of attainment by the engineer 
 under given conditions of temperature. I must not trench on the 
 subject of one of my successors, but I may point out that our 
 knowledge of the second law of thermodynamics was first 
 developed by means of mathematics, and that to-day its neatest 
 expression is by means of partial differential coefficients. The 
 two most notable names in connection with the development of 
 the second law of thermodynamics in harmony with the first are 
 those of Kelvin and Clausius ; both dealt with the subject in a 
 mathematical form not comprehensible to those who have not had 
 substantial mathematical training. 
 
 Illustrations such as these might be multiplied almost indefi- 
 nitely. They show that the advancement of the Science of 
 Engineering has been aided in no inconsiderable measure by the 
 labours of mathematicians directly applying the higher mathe- 
 matical methods to engineering problems. They show, too, one 
 
 * Minutes of Proceedings Inst. C.E., April 5th, 1883 ; Institution of Electrical 
 Engineers, November 13th, 1884. 
 
284 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 way in which respect for a formula may be dangerous, one way in 
 which it is true that mathematics may be a bad master. In St 
 Venant's problems we have an example in which the use of older 
 results of limited application in cases where the assumptions on 
 which they rest are not true will mislead. The examples show the 
 proper remedy ; it is a more complete application of mathematical 
 methods. The error is just one which a man will make who 
 has the power to use a formula without a ready understanding of 
 how it is arrived at. A practical man, ignoring mathematical 
 results, might or might not escape the error of supposing that a 
 triangular shaft would break at the angles under torsion ; the half- 
 educated mathematician would certainly fall into the snare from 
 which complete mathematical knowledge would deliver him. 
 You can only secure the services of that good servant, mathe- 
 matics, and escape the tyranny of a bad ma,ster by thoroughly 
 mastering the branches of mathematics you use. The mistake 
 caused by the wrong application of mathematical formulae is only 
 to be cured by a more abundant supply of more powerful mathe- 
 matics. 
 
 There is another drawback to the use of results, taken, it may 
 be, out of an engineering pocket-book by those who are not 
 prepared to understand how they are reached and on what 
 foundations they rest. The educational advantage is lost. The 
 close observations which enabled the earlier engineers to propor- 
 tion their means to the end to be attained was no doubt very 
 laborious, and the results could not be applied to cases much 
 different from those which had been previously seen, but the 
 effect on the character of the engineer was great. In like 
 manner, to thoroughly understand the theory of au engineering 
 problem makes a man able to understand other problems, and 
 in addition to this precisely the same mathematical reasoning 
 applies to many cases. The mere unintelligent use of a formula 
 loses all this ; it leaves the mind of the user unimproved, and it 
 gives no help in dealing with questions similar in form though 
 different in substance. 
 
 But even the use of mathematics by competent mathematicians 
 is not without drawbacks. Mathematical treatment of any prob- 
 lem is always analytical analytical, I mean, in this sense that 
 attention is concentrated on certain facts, and other facts are 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 285 
 
 neglected for the moment. For example, in dealing with the 
 thermodynamics of a steam-engine, one dismisses from considera- 
 tion very vital points essential to the successful working of the 
 engine, questions of strength of parts, lubrication, convenience 
 for repairs. But if an engineer is to succeed he must not fail to 
 consider every element necessary to success ; he must have a 
 practical instinct which will tell him whether the instrument as 
 a whole will succeed. His mind must not be only analytical, or 
 he will be in danger of solving bits of the problems which his 
 work presents, and of falling into fatal mistakes on points which 
 he has omitted to consider, and which the plainest, intelligent, 
 practical man would avoid almost without knowing it. 
 
 Again, the powers of the strongest mathematician being limited, 
 there is a constant temptation to fit the facts to suit the mathe- 
 matics, and to assume that the conclusions will have greater 
 accuracy than the premises from which they are deduced. This is 
 a trouble one meets with in other applications of mathematics to 
 experimental science. In order to make the subject amenable to 
 treatment, one finds, for example, in the science of magnetism, that 
 it is boldly assumed that the magnetization of magnetizable 
 material is proportional to the magnetizing force, and the ratio 
 has a name given to it and conclusions are drawn from the 
 assumption, but the fact is, no such proportionality exists, and all 
 conclusions resulting from the assumption are so far invalid. 
 Wherever possible, mathematical deductions should be frequently 
 verified by reference to observation or experiment, for the very 
 simple reason that they are only deductions, and the premises from 
 which the deductions are made may be inaccurate or may be in- 
 complete. We must always remember that we cannot get more 
 out of the mathematical mill than we put into it, though we may 
 get it in a form infinitely more useful for our purpose. 
 
 Engineers no doubt regard their profession from very different 
 points of view; some think it a mere means of making money, 
 some regard it as an instrumentality for benefiting the race, 
 whilst otheis again delight in it as an interest in itself, and 
 delight in it most of all when new knowledge is added to that 
 which we know already. It is just the same with the medical 
 profession ; some attend patients for the guineas they receive, 
 some give a very high place to motives of benevolence, whilst 
 
286 THE RELATION OF MATHEMATICS TO ENGINEERING. 
 
 others love it as a field where new knowledge may be found and 
 the delight of discovery enjoyed. In regard to the first class of 
 engineers, I have no doubt a little skill in managing a board of 
 directors or impressing a committee of Parliament will be much 
 more useful to the engineer than a great deal of mathematics. 
 Let him manage his board and buy his mathematician, and it is 
 very probable he will make much more money than the mathe- 
 matician or any other person of skill whom he may employ. But 
 we cannot all of us make money in this way. In the future it is 
 likely that educated men will have to work harder and receive 
 less, and it is a great thing if their work can be made itself a joy, 
 and surely this can best be by a thorough understanding of the 
 reason of all they do, by the feeling that they have full competence 
 to form their own judgments without depending much on the 
 authority of others. This can only be, in the words of Sir John 
 Herschel, by a " sound and sufficient knowledge of mathematics, 
 the great instrument of all exact inquiry, without which no man 
 can ever make such advances in any of the higher departments of 
 science as can entitle him to form an independent opinion on any 
 subject of discussion within their range." 
 
 After all, in any department of applied or pure science the 
 highest satisfaction comes from accomplishing that which no one 
 has done before, from disclosing what no one hitherto has known. 
 If a department of the Arts or Sciences ceases to advance and 
 becomes simply the application in known ways of known prin- 
 ciples to obtain known ends, that department has lost its charm 
 till the time comes for a fresh advent of change and development. 
 To effect such advances it is easy to show that mathematics is a 
 most necessary instrument. Here it is no drawback that the mind 
 of the discoverer is too analytical ; he may deal at his pleasure with 
 one aspect of a problem, and it does not detract in any way from 
 the value of his solution that he does not touch on incidental 
 matters. Some of you who love the interest of continual advance 
 in our science and practice, may look forward with a shade of sad- 
 ness to a possible time when all is done or known which can be 
 done or known, and the work of the engineer shall be merely 
 applying principles discovered by his predecessors. In such a 
 state, when the experience of the older generations shall control 
 the practice of to-day, the free use of mathematical methods may 
 be effectually superseded by the application according to rule of 
 
THE RELATION OF MATHEMATICS TO ENGINEERING. 287 
 
 mathematical formulae. But it would be a much less interesting 
 condition than the constant change of to-day, when the practical 
 experience of ten years ago is in many departments rendered 
 worthless by later discoveries. But we need not fear that such a 
 time of petrifaction will come so long as, whilst reverencing the 
 discoverers who have added to our knowledge, we endeavour to 
 replace their methods by better, and expect that those who come 
 after us will, in their time, improve upon ours. Our knowledge 
 must always be limited, but the knowable is limitless. The 
 greater the sphere of our knowledge the greater the surface of 
 contact with our infinite ignorance. 
 
 Mr ALFRED GILES, President, said, to those cognizant with the 
 higher branches of mathematical science, the lecture of Dr 
 Hopkinson would be an intellectual treat. To those not so con- 
 versant with that subject, the lecture would, he hoped, have the 
 effect of spurring theni, particularly the younger members of the 
 profession, to further exertions to follow the brilliant example set 
 them by Dr John Hopkinson. He was sure all present would 
 join in offering to the lecturer their most cordial thanks for his 
 brilliant lecture. Dr Hopkinson had taken immense pains in 
 assembling and presenting the questions that he had brought 
 forward. There was one subject specially mentioned, of which 
 Mr Giles had some practical knowledge, and to which he was 
 glad to refer he alluded to the excellent compass invented by 
 their Honorary Member, Lord Kelvin, better known in that con- 
 nection as Sir William Thomson. He could assure the Meeting 
 that from an intimate acquaintance with many seafaring men he 
 had only heard one opinion as to the excellence and superiority of 
 Sir William Thomson's compass. He was glad to have the oppor- 
 tunity of expressing his thanks to Lord Kelvin personally for the 
 advantage he had conferred in that respect upon navigators. 
 
 In asking the meeting to thank the lecturer, he might observe 
 that it was not very often that they had the opportunity of 
 receiving good advice from a senior wrangler as on the present 
 occasion. What had fallen from Dr Hopkin son's lips would, it 
 might be hoped, induce the younger members of the engineering 
 profession to exert themselves in the directions indicated. He 
 called upon all present to join him in according most hearty 
 thanks to Dr Hopkinson for the lecture. 
 
288 THE KELATION OF MATHEMATICS TO ENGINEERING. 
 
 The Resolution was carried by acclamation. 
 
 Dr JOHN HOPKINSON, in acknowledging the Resolution, con- 
 fessed that when he undertook the lecture, he had no idea how 
 difficult a subject it would be to deal with ; and he very much 
 feared he might have completely failed to make it at all interest- 
 ing to many present. However, the members might be sure of 
 this, that the exceedingly kind way in which they had received 
 the attempt he had made to place the subject before them was 
 ample reward for any trouble it had cost him. 
 
APPENDIX. 
 
 [Extract from paper on Magnetisation of Iron. Roy. Soc. Trans. 
 
 1885.] 
 
 LET be the magnetic force at any point, 33 the magnetic induction, 
 and 3 the magnetisation (vide Thomson, reprint, Maxwell, vol. ii., 
 Electricity and Magnetism)^ then 23 = Jp + 47r3. We may therefore 
 express any results obtained as a relation between any two of these 
 three vectors; the most natural to select are the induction and the 
 magnetic force, as it is these which are directly observed. 25 is subject 
 to the solenoidal condition, and consequently it is often possible to 
 infer approximately its value at all points, from a knowledge of its 
 value at one, by guessing the form of the tubes of induction. is a 
 force having a potential, and its line integral around any closed curve 
 must be zero if no electric currents pass through such closed curve, but 
 is equal to 4?rc if c be the total current passing through the closed 
 curve. In arranging the apparatus for my experiments, I had other 
 objects in view than attaining to a very small probable error in 
 individual results. I wished to apply with ordinary means very 
 considerable magnetising forces ; also to use samples in a form easily 
 obtained; but above all to be able to measure not only changes of 
 induction but the actual induction at any time. The general arrange- 
 ment of the experiments is shown in fig. 1, and the apparatus in which 
 the samples are placed in fig. 2. In the latter fig. AA is a block of 
 annealed wrought iron 457 millims. long, 165 wide, and 51 deep. A 
 rectangular space is cut out for the magnetising coils BB. The test 
 samples consist of two bars CC\ 12'65 millims. in diameter; these are 
 carefully turned, and slide in holes bored in the block, an accurate but 
 loose fit ; the ends which come in contact are faced true and square ; 
 a space is left between the magnetising coils BB for the exploring 
 coil Z>, which is wound upon an ivory bobbin, through the eye of 
 which one of the rods to be tested passes. The coil D is connected to 
 
 H. i. 19 
 
290 
 
 APPENDIX. 
 
 FIG. 1. 
 
 FIG. 2. 
 
APPENDIX. 
 
 291 
 
 Wrought Iron N^L 
 
 FIG. 3. 
 
 10.00C 
 
 A A 
 
 FIG. 4. 
 
292 APPENDIX. 
 
 the ballistic galvanometer, and is pulled upwards by an india-rubber 
 spring, so that when the rod C is suddenly pulled back it leaps 
 entirely out of the field. Each of the magnetising coils B is wound 
 with twelve layers of wire, 1'13 mm. diameter, the first four layers 
 being separate from the outer eight, the two outer sets of eight layers 
 are coupled parallel, and the two inner sets of four layers are in series 
 with these and with each other. The magnetising current therefore 
 divides between the outer and less efficient convolutions, but joins 
 again to pass through the convolutions of smaller diameter. The 
 effective number of convolutions in the two spools together is 2008. 
 Referring to fig. 1, the magnetising current is generated by a battery 
 of eight Grove cells E, its value is adjusted by a liquid rheostat F, it 
 then passes through a reverser G, and through a contact-breaker ff, 
 where the circuit can be broken either before or at the same instant as 
 the bar C is withdrawn ; from H the current passes round the magne- 
 tising coils, and thence back through the reverser to the galvanometer 
 K. The galvanometer K was one of those supplied by Sir W. Thomson 
 for electric-light work, and known as the graded galvanometer, but it 
 was fitted with a special coil to suit the work in hand. The exploring 
 coil D was connected through a suitable key with the ballistic 
 galvanometer L. Additional resistances M could be introduced into 
 the circuit at pleasure, and also a shunt resistance N. With this 
 arrangement it was possible to submit the sample to any series of 
 magnetising forces, and at the end of the series to measure its 
 magnetic state ; for example, the current could be passed in the 
 positive direction in the coils J3, and gradually increased to a known 
 maximum ; it could then be gradually diminished by the rheostat F to 
 a known positive value, or it could be reduced to zero ; or, further, it 
 could be reduced to zero, reversed by the reverser 6', and then increased 
 to any known negative value. At the end of the series of changes of 
 magnetising current, the circuit is broken at H (unless the current 
 was zero at the end of the series), and the bar C is simultaneously 
 pulled outwards. Three successive elongations of the galvanometer L 
 are observed. From the readings of the galvanometer K, the known 
 number of convolutions of the coils B, and an assumed length for the 
 sample bars, the intensity of the magnetising force is calculated. 
 The exploring coil D had 350 convolutions. From its resistance, 
 together with that of the galvanometer with shunts, the sensibility of 
 the galvanometer, its time of oscillation, and its logarithmic decrement, 
 a constant is calculated which gives the intensity of induction in the 
 iron from the mean observed elongation of the galvanometer. The 
 resistances have been corrected in the calculation for the error of the 
 
APPENDIX. 293 
 
 B. A. unit, and both galvanometers were standardised on the assump- 
 tion that a certain Clark's cell had an electromotive force of 
 1-434 x 10 8 C.G.S. units. This Clark's cell had been compared to 
 and found identical with those tested by Lord Rayleigh. 
 
 Let the mean length of the lines of induction in the sample be I, 
 and a- the section of the sample ; let I' be the length of lines of induc- 
 tion in the block, and </ their section, 93 the intensity of induction in 
 the sample, 93' in the block, then o-S3 = <r'93' = / ; let 
 
 and 
 then 
 
 or 
 
 II II' 
 
 ft(7 /ACT 
 
 where n is the number of convolutions of the magnetising coils. Now 
 in the instrument used cr' is large, and // is as large as can be obtained, 
 
 II' 
 
 hence the term - T -, is small comparatively. My first intention was 
 /x<r 
 
 to correct the magnetising force by deducting this small correction, 
 but finally I did not do so, because in the more interesting results the 
 magnetism of the block is dependent in part upon previous magnetising 
 forces, the effect of which cannot be allowed for with certainty. We 
 know then that in all the curves the magnetising force indicated is 
 actually too great by a small but sensible amount, which does not 
 affect the general character of the results or their application to any 
 practical purpose. The magnetising force then at any point of the 
 
 sample is - - = -- a small correction which we deliberately neglect. 
 
 There is another source of uncertainty in the magnetising force : the 
 length / is certainly greater than the space within the wrought-iron 
 block, but it is not possible to say precisely how much greater. If the 
 sample bars and the block were a single piece, the results of Lord 
 Rayleigh for the resistance of a wire soldered into a block would be 
 fairly applicable; but it is essential that there should be sufficient 
 freedom for the bar to slide in the hole ; the minute difference between 
 the diameters of the sample and the hole will increase the value which 
 should be assigned to L Throughout, I is assumed to be 32 centims., 
 and it is not likely that this value is incorrect so much as half the 
 
294 APPENDIX. 
 
 radius of the bar, or 1 per cent. The magnetising forces ranged up to 
 240 c.G.s. units when both bars were of the same material. In some 
 cases a single bar only was available for experiment ; the plan then 
 was to use it as the bar which enters into the exploring coil, and for 
 the other to use a known bar of soft iron. We have then to deduct 
 from 4?mc the magnetising force required to magnetise the bar of soft 
 iron to the state observed, and to distribute the remainder over the 
 shorter length of sample examined. The results obtained in this way 
 are subject to a greater error, because some lines of induction un- 
 doubtedly make their way across from the end of the soft-iron bar to 
 the body of the block. A small correction is required, important in 
 the case of bodies but slightly magnetic, for the fact that the area of 
 the exploring coil is greater than the area of the bars tested. Thus 
 the induction measured by the exploring coil is not only that in the 
 sample, but something also in the air around the sample. The amount 
 of this was tested by substituting for a sample of iron or steel a bar of 
 copper, and afterwards a rod of wood, and it was found in both cases 
 that the induction 23 was 370 when the force $ was 230. The 
 correction is in all cases small, but it has been applied in the column 
 giving the maximum induction, as it materially affects the result when 
 the sample contains much manganese, and is consequently very little 
 magnetic. 
 
 CAMBRIDGE : PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. 
 
RETURN TO the circulation desk of any 
 University of California Library 
 or to the 
 
 NORTHERN REGIONAL LIBRARY FACILITY 
 Bldg. 400, Richmond Field Station 
 University of California 
 Richmond, CA 94804-4698 
 
 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 
 2-month loans may be renewed by calling 
 
 (415) 642-6753 
 1-year loans may be recharged by bringing books 
 
 to NRLF 
 Renewals and recharges may be made 4 days 
 
 prior to due date 
 
 DUE AS STAMPED BELOW 
 
 FEB 2 1991 
 
 APR 12 
 
 M1B 1ISC OCT 1 6 1991 
 
U.C. BERKELEY LIBRARIES