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ADDRESSES 
 
 OBUVEREO ON THE OCCASION Of THE PRESENTATION OF A 
 PORTRAIT TO 
 
 PROFESSOR N. F. DUPUIS. 
 
 APBIL 30TR, 1901. 
 
 The preaantation of the portrait wm made at OonTooation, 
 on TneKlay afternoon, April aoth, 1901, Cbanoellor Fleming 
 in the chair. Prof. James Bosa, of Montreal, being called 
 npon, spoke as follows: 
 
 Mr. Chancellor, Memberg of Convocation, iS^udenta of Queen' g, 
 Ladiea and OaUlemen: 
 
 Who is the greatest among the children of men? This 
 question is an old one; the answer has oh»nged with the ages, 
 and it still varies according to the character and ideals of the 
 man who gives it. The warrior chief wrecking nations, the con- 
 scienceless statesman robbing them under forms of law, the 
 graphic story-teller charming snccessiTe generations, the dis- 
 coverer of the secrets of Nature have each had his day. In the 
 century into which we are entering with such hopefulness and 
 enthusiasm, I venture to think that the educator will icceive 
 his just meed of praise and be crowned chief among his fellowe. 
 The secrets of nature are wonderful, but the hidden ih'xugn c»f 
 the human soul are more marvellous and wore valnaliU* Ntill; 
 and he who can so handle the faotH of nature and of mind an to 
 draw the soul out of the mists which at first surround it, and 
 make it conscious of its own great powers and of the wondrr^is 
 possibilities of its surroundings, is our chief benefactor. The 
 discoverer of a new star deservis recognition, but the discov- 
 erer of a thoroughly original and creative intellect deserves a 
 crown. We have more stars now than we know what to do 
 with, but we cannot have too many men. 
 
 Those master minda who have attained eminence in the 
 intellectual world are almost a unit in ascribing the awakening 
 of their mental life to the teachers who had a genius for mak- 
 
ing tnith AttrMtiTe Mid of m opening new departmenU of it m 
 to ■timnUte enthaiiatm and thrill the whole inner n«tiue 
 with jojr. In a lense every nun mnet edoMte himself. Books, 
 instruments, trsvel, teachers, are bat helps in the prooess. 
 It may be done in ezoeptiooal oases withor' Ay of them. Bat 
 among the agencies belpfal in mental training, \,y far the most 
 inflnential, is the livinK soal which plays with its mighty 
 forots apon the spirit of the learner. No environment oan 
 mould a man like a truly powerful and versatile mind which 
 understands him, sympathises with him, and which moves up- 
 on him like the Spirit ot the Eternal upon the primal abyss, 
 quickening its chaotic i. jutialities into the order and beaaty 
 of life. 
 
 What are the influences which have made this University 
 a power in our young country and which have given her na 
 ever enlarging constituency where even those who loved her 
 could once see only limitations and lessening prestige? What 
 strange magnetism is it that has grappled the hearts of her 
 sons to her as if with hooks of steel and bound them into a 
 brotherhood whose solidarity and joyous enthusiasm are the 
 wonder of those less highly favoured? Smething is doubt, 
 less due to the character of the men whom she has drawn to 
 her class-rooms, but the central secret of her power has been 
 tht genins of the teaohors who drew them. How varieo have 
 tlieii gifts been! Who could delineate their excellencies or 
 fu}!y describe the debt which we owe them* 
 
 Some of them were not very remarkable for teaching pow- 
 er, their strength lay elsew'aere. Many of us oan recall one 
 who seldom succeeded in an experiment i nd whose peregrin- 
 ations OP the blackboard could be followed by only a chosen 
 few. Yet the moral fibre of his soul had the power of aroas- 
 ing a universal and ardent love that followed him to the grave, 
 and no man's memory is greener in the hearts of the Alumni of 
 Queen's. To his simple-hearted goodness, his untir.^g efTorts 
 to promote the welfare of the humblest student, his enthus- 
 iasm for learning, all who knew him • -ill offer an unstinted 
 tribute of praise. 
 
 It is our gladsome privilege, to-day, to do homage to one 
 of the fathers who remain with us, to one whose power of un- 
 folding truth would have given distinction to any seat of leam< 
 ing, to one whose influence on the life of this University for 
 
 ; » 
 
 u J 
 
mot. tlun thirty yean hu been lik« ths forMi of natnra. 
 wideipread, powerful, and iiervMive. and yet 40 even and 
 noiieleH that, like them, it is apt to be orerlooked. foryotten. 
 or eaaily aatnmed aa a n.^. >r of oonrse. 
 
 [Here the portrait was nnveiled by Mr. J. B. Lavell.] 
 
 Profe'«M>r Dnpai*. in the name of the Graduates of Queen'* 
 who hare enjoyed the Insneflt of your teaching, we beg yon to 
 do them the honour of aoceiiting from them this portrait of 
 yonrsclf as a slight recognition of their appreciation of your 
 many and multifarious Ibbnurs for the welfare of this institu- 
 tion and for the fuller mental and physical equipment of its 
 students. 
 
 It may have seemed to you, when you contemplated our 
 Scottish reticence and th limitations amid which you have 
 been long suffered to Ubour, that you have toiled in vaii and 
 spent your strength foi naught. We assure you, that, while 
 we have nndoubteuly torgotten many of the formulas you have 
 Unght, we all carry in our hearts, grateful recollections of the 
 mental stimulus, the spiritual inspiration, derived from your 
 instruction; and we regard with wonder, and hbld ;n the verv 
 highest esteem, your unwearying diligence in the service of 
 our Alma Mater. 
 
 We find it diihcult in your presentx. to express our esti- 
 mate of the share you have had in her attainment of a position 
 BO gratifying to ns, all of which is only the prediction of what 
 is to be. The experience of matnrer years and long familiar- 
 i*r with the difficulty of thoroughly awakening the human soul 
 ha\«» deepened our early conviction of the wisdom of your 
 methv>ds. We remember with admiration the simplicity and 
 direct! ess of your prelections, you wise economy of explan- 
 ation, aid especially your singular accuracy and precision in 
 experiment, wherein you have so unvaryingly honoured na- 
 ture thai she has honoured you with a success which has be- 
 come provcA-bial. The most conclusive proof that this world is 
 rational, that it has been built up by a far-seeing intelligence, 
 is to behold a mind analyzing the -trocesses of the Creator, 
 predicting the exact results to be retched by the experiment 
 and then displaying the elements falling into their places with 
 the exactitude of the Infinite Reason. 
 
Wa Imt* ofton wondared mt jour app«reniijr anlimitMl 
 ▼flrMtility. The number of thinga yon ran do haa flUed tu 
 with amaMinent and taaght na humility. We hare apeoial- 
 iied BO much, in order to gat the Tery beat derelopment of 
 one amall part ot man, that we are in danger of degrading hu- 
 man natnra. Indeed, oiTiliution hai already arrested the 
 deyelopment of manhood by leaying oat of aooonnt erery part 
 of the man, except the fraction required to make the head or 
 the point of a pin, or rather, to auperintend the machine that 
 makea it. A comic artist haa pictured the men of forty cent* 
 uriea hence, as little more than animated brains with soma 
 feeble, attenuated fragments of a body attached, just enough 
 > ^ roll the big head into a ilat bowl of soup that it may absorb 
 some nourishment. But a true education is not the cultiration 
 of one or two organs, it is the quickening of the whole oomplez 
 soul. Oifts of brain to think, to originate, of eye to perceive 
 and judge of proportion of beauty, of ear to interpret harmony 
 of sounds, of hand to give artistic and permanent embodiment 
 to thought, are all necessary to complete manhood. Now, the 
 limitationa under which you have always had to carry on the 
 education of thoae committed to your tutelage, are deeply re- 
 gretted by all the friends of this University, and we trust that 
 your facilities may soon be enlarged. 
 
 But these limitations have not been an unmixed evil, they 
 have called forth, in an eminent degree, the qualities of which 
 I have spoken. The man is alway greater than machines. 
 
 I have heard of a atudent of Queen's, who came down to 
 McOill, and saw all the fine testing and assaying appliancea 
 that we have there. Tour Principal was afraid that he would 
 be dissatisfied with the equipment of Queen's, and would re- 
 gret that he had resolved to take his course here. He waa 
 much comforted when be heard that the student in question 
 had said, he waa glad he had gone to Queen's because Profess- 
 or Dupuis taught his men to make their own kit, to be large- 
 ly independent of expensive laboratories, to construct, out of 
 the materials within their reach, wherever they may happen 
 to or, the means of conquering Nature and wrenching her se- 
 crets from her breast. This is the highest kind of education. 
 It shows the soul how to triumph over barriers which impede 
 its progress, and to transform them into stepping stones to 
 wider usefulness and greater power. 
 
Thii iwrtrait may MrT« to pnuatrt th« featiire* <ato which 
 raoo«MiT« genentioni of ■tudent*' b«v« looked with profovml 
 respaot. The painter h.ji ■kilfnlly eaaghi the riffht expren- 
 ■ion and hia work in rery oreuitable to (Canadian art. But 
 what honour would he have trained if he ooald have depicted 
 the «oul, if he had lieen able to lay bare the working* oi ihe 
 Rpirit which penetrates to the heart of truth, oalU forth the 
 highest iiowem of other mindfi, and reigna a king over thinga 
 not made of olay. 
 
 We truat that you may )>e yet long afiared to .Hpire the 
 atndenta of to-day and to-morrow where you have tanght 
 ao long, to aet before the world further treannrea from your 
 garnered wiadom, and to confer additional luatre ni>cn the 
 Univeraity yon have helped to build We hope that in the 
 evening of life'a well-apent day you r . rejoice in the brilliant 
 aobievementa of the men whom you have clothed with |iower, 
 and that you may aee your work here paaaing over into the 
 very beat handa. 
 
 Mr. J. R. Lavell, B.A.. M.P, of Smith Falla, then apoke 
 on behalf of Prof. Dupnia' old atndenta, teatifying to their 
 aifeotionate regard, and to their appreciation of the Profea- 
 Bor'a teaching and training. 
 
 'Prof. Dupnia, in accepting the portrait, apoke aa folio wa: 
 
 In connection with an epiaode in the life of Carlyle, 
 Leigh Hunt wrote a little poem, the laat atanza of which I 
 ■ball repeat to you: 
 
 Say I'm lorrT, say I'm sad. 
 
 Say that health and wealth have mitied ne. 
 
 Say I'm Krowing old, but add, 
 
 Jenny kissed me. 
 
 I do not quote thia beautiful little poem, becanae I ever 
 had a aweetheart, or even a particular friend of the name 
 of Jenny, but because in it the poet aeema to me to have 
 moat happily expressed the forgetting of those thinga which 
 we are aoouatomed to look upon aa the miseries of life, 
 sorrow, sadness, ill-health, poverty, and old age, forgetting 
 all on a memorable occasion, and in a moment of joyous 
 satisfaction. 
 
I am somewhat in tluit position to-day. I look busk with 
 s sort of contempt upon the difBonltiea of the past, the straggle 
 against adverse oironmstanoes, the burning of the midnight 
 oil, the anxiety, the work and stndy which frequently became 
 a weariness to both mind and flesh. I relegate these to the 
 distant background, in presence of this graceful act of my old 
 students on whose behalf the efforts were made and the diffi- 
 culties overcome. 
 
 It is not that I have any particular regard for the gift as 
 being a portrait of myself. I never was a dude; I never parted 
 my hair in the middle or admired my countenance in the glass; 
 and now that I have no longer any hair to part, and my face is 
 becoming careworn and marked with the lines of age, I do not 
 see any reason for admiring that face when transferred to a bit 
 of canvass. But I must always admire tho geniality and the 
 skill of the artist, and still more the sacrificing spirit of the 
 graduates which has been the means of calling forth the art- 
 ist's efforts. 
 
 I feel that Byron did not include all the sweet things of 
 life in his celebrated stanzas in "Don Juan," for it is cer- 
 tainly sweet to be reminded th»t your work in life has not been 
 in vain, but that it has been useful to some one, and that it 
 has been appreciated by those for whom it was performed. 
 
 And standing here to-day, from the fullness of my heart, 
 I thank every one of my old students for the part which he 
 has contributed to the pleasure of this moment, which must be 
 to me an ever memorable occasion, and a long-drawn out sweet- 
 ness to sooth the evening years of life. 
 
 Incidents like the present are enough to inspire any man 
 to try and make greater efforts in the future than he did in 
 the past. But to those who have done practically their best, 
 and are drawing near to that stage whith is symbolized by the 
 sere and yellow leaf, the inspiration can have little effect, for 
 it is too much to hope that they will be able to any extent, 
 either to increase the output of their labours, or to improve 
 upon their general character. 
 
 And now I ask your indulgence for a little, while I make 
 a few remarks upon my life and work in this University. In 
 doing so I can assure you I am not moved by any vain feeling 
 of egotism, for I think that my friends will not charge me with 
 being immodest in spirit, but a foolish sense of modesty would 
 
— 7- 
 
 in this OMe, prevent the ntterance of some of the very things 
 I wish to say. I hare tried to do well, bnt I see many cases 
 in which I might have done better if I had been wiser. My 
 life here has been somewhat unique, and not along the lines 
 of the life of any other professor in the institution, in that I 
 am not now teaching, any one of the five subjects which en- 
 gaged my attention during the first thirteen years of my la- 
 bours as a teacher here. 
 
 When I first came on the staff, Wordsworth's littte poem, 
 "We Are Seven," was not applicable to the Senate, unless 
 you counted in the janitor, faithful John Cormack, for we were 
 only six. One of these now lives in Scotland, one in Montreal, 
 three sleep in Gataraqni, and like Job's servant, "I only am 
 left alone to tell thee" of those early days of Queen's College. 
 
 I had to teach the subjects now taught by six men, name- 
 ly. Chemistry, Mineralogy, Botany, Animal Biology and Geo- 
 logy. Gl course I did not do the work of six men, but I made 
 the work of one man go as far as I could. 
 
 These were days of Irath scientific and financial poverty in 
 Queen's, and although the scientific condition has somewhat 
 improved, the financial state has very much the appearance of 
 having become chronic. Such a thing as a laboratory with- 
 in the College precincts was unknown. In a dimly-lighted 
 room in the basement of the building, now occupied by Prin- 
 cipal Qrant as a residence, was a heterogeneous collection of 
 glass tubes and bottles and chemicals done up in paper par- 
 cels, and minerals and fossils and geological specimens, with- 
 out order or arrangement. Much of this was the debris from 
 a quasi chemical department attached to the Medical College 
 but belonging to Queen's, and which had not been successful 
 in introducing its subject into the Arts course. 
 
 The first year of my incumbency, and the most weary ses- 
 sion I ever put in at Queen's, was very largely lost iu lecturing 
 on Chemistry without any means of putting life into the lec- 
 tures by experimentation. However, after some time a room 
 was found and this chaos was brought into some sort of order. 
 But the appliances were extremely meagre and the supply lim- 
 ited, and no means were forthcoming to remedy the defects. 
 
 How could any man, whatever his powers, be successful 
 in teaching an experimental subject under such cdnditions, 
 
-8- 
 
 for tbe flrst ehemiMl Iftboratory of Qncen's mme into exiat- 
 enoe only two years before I oeased to teaoh the subject. 
 
 But the ingennity with which Nature endowed me, and a 
 mechanically trained hand and eye were of singular advantage 
 to me, and more than one piece of apparatus which under the 
 stress of necessity I constructed in those days, is still serving a 
 purpose in the science department, and bids fair to outlast its 
 maker. In the face of these diflSonlties I gave many lectures, 
 and got the reputation, justly or unjustly, of being a brilliant ex- 
 perimenter; and that my teaching was not altogether unsuccess- 
 ful I infer from the fact that many of the graduates who have 
 contributed to this occasion, sat in my class-room in those 
 days, and among whom I count by no means least, those two 
 friends who have so gracefullj presented the picture. 
 
 It was the necessities of this pioneer work that led me to 
 form the high opinion which I hold of the value of manual 
 training of a superior kind to every person who proposes to 
 follow a pursuit in which delicate lipparatus is employed. No 
 man is properly prepared to deal with an experimental subject 
 who has not had such a training, and were it more common, 
 there would be less experimenters with fingers which are all 
 thumbs. 
 
 But I must not weary you with too many minute details. 
 My first intimate aoquaintuioe with Queen's goes back thirty- 
 seven years, and she was in the midst of her most perilous 
 times only a year or so later. What with the Wier-George 
 turmoil in the University, separating even the students into 
 hostile factions, and the Stewart-Dickson embroglio, which 
 culminated in the separation of the medical faculty and its 
 formation into an independent institution, bearing the very 
 pretentious name of the Royal College of Physicians and Sur- 
 geons, and both capped with the withdrawal of that little but 
 important pittance of help known as the Government grant; 
 it was a question whether Queen's would survive or not. And 
 at a meeting to consider ways and means I distinctly remem- 
 ber one of the medical professors proposing to place the uni- 
 versity under the wing of the Medical College, for medical 
 students were more numerous than arts, thus reversing the 
 ordinary state of affairs. Little did he dream, at the time, 
 of the difficulties which the near future had in store for his 
 own institution. 
 
i 
 
 — 9— 
 
 A fully attended meeting of the old kirk ministers and eld- 
 ers was held in St. Andrew's Church in this city, to discusss 
 as to whether an effort shouid made to keep up the University, 
 or whether it should be abandoned. After much deliberation 
 the wiser course prevailed, and we see to-day how wise it was. 
 This was the origin of the first endowment fund. 
 
 From this onward Queen's was for a number of years very 
 poor in both money and students, but she was hopeful. I lec- 
 tured on a certain part of my work for a whole session to only 
 two students, and they both survived it and are liviui; men 
 to-day. And my late colleague. Professor Mowat, did still bet- 
 ter, for he and a solitary student discussed Hebrew verbs 
 throughout a session, sitting on opposite sides of the stove, 
 and the sneering cry went abroad, " what is a college without 
 students." 
 
 For about thirteen years I lectured to both arts and medi- 
 cate not conjointly as is done to-day, but in separate classes. 
 The arts classes occupied the buildings known as the resi- 
 dences, and the medical classes, the building which was ex- 
 pressly built for them and which they occupy now. 
 
 Matters then went on quietly for a few years until the uni- 
 versity authorities discovered, quite suddenly, that they were 
 in need of residences for a few professors, and that by taking 
 over the medical building for university purposes, the build- 
 ings then occupied might be transformed into residences. 
 And so the medical building was seized upon, and with short 
 notice the Boyal College of Physicians was hustled into the 
 street, whether to live or die was quite a matter of indifference 
 to the authors of the act. I thought then, and I have always 
 thought that a more unfriendly and uncharitable act could not 
 have been perpetrated upon a sister institution, and especially 
 in the face of the fact that the residences were not a crying 
 necessity of the time. 
 
 But the trustees little knew of what sturdy stuff the Pro- 
 fessors of the Royal College were made. They refused to suc- 
 cumb to the frigid coldness of a sister's charity, and forthwith 
 engaged for a single session, a building about two miles from 
 here on the Montreal road, and now used as the House of In- 
 dustry. For all of us, but for me in particular, that was a ses- 
 sion of especially hard work. 
 
—10- 
 
 For after oompletiog my day's work at the UniTeraity I 
 had to walk two miles through sun and storm, fair weather or 
 foal, for iive eTenings in the week, carry in my hands anoh 
 means of illnstration as I oonid, leotnre an hoar, and then walk 
 two miles to my home again. It required some conrage to 
 stick to a cause which appeared to be so near a collapse as the 
 Boyal then was, but we determined, one and all, to work for it 
 and support it as long as we had students, for we felt that if 
 it went down there could never be another Medical College in 
 Kingston. And for some inscrutable reason we had students 
 and a considerable number of them. And from that number I 
 count some of my oldest au<I best friends among the Medical 
 men of the country to-day. 
 
 In the following and subsequent sessions the Royal Col- 
 lege had its home in a building near the foot of Princess Street, 
 once occupied by the Commercial Bank, and there it remained 
 until it removed to its present, which was also its first 
 quarters. ' 
 
 Buch is a brief sketch of the experience of the Medical 
 College during the early days of my conncoHcn with it. 
 
 The people of Kingston and the University have to-day 
 cause to be thankful that men were found willing to champion 
 and support with their best efforts an institution surrounded 
 with difficulties as the Boyal College then was. And it I could 
 in any way exclude myself, I would be inclined to say all hon- 
 or to the men who stood by it in the time of trial, for they car- 
 ried it through the valley of the shadow of death, and brought 
 it forth a living energetic thing of action to become as it is to- 
 day a new and yet an old faculty of Queen's having in it all the 
 elements necessary to a vigorous and continuous growth. 
 
 When through the efforts of Principal Orant and the liber- 
 ality of friends this building was erected, a small room in the 
 corner of the building was set apart as a chemical laboratory, 
 and I took some pains in arranging it and in designing special 
 conveniences in the class room, and expected to settle down 
 into some kind of a fixed and quiet course of life. This was 
 not to be, however, and within two years I was consulted as to 
 my willingness to be transferred to the chair of Mathematics. 
 
 It might be pertinent to ask why the authorities wished to 
 change me from the department of Chemistry, where my ex- 
 perimental and constructive abilities were of the highest value 
 
-11— 
 
 to A subject like mathematios vhere saoh qnalifications are 
 praotioally in no demand. I cannot answer the question; but 
 I ofcn answer the somewhat cognate question as to why I was 
 willing to make the change. It was for three reasons:— First, 
 I was willing to do whatever was thought to be for the best in- 
 terests of the University; second, Mathematics was my first 
 love among subjects of study, and I am certain it will be my 
 Ust; third, I had and I still have a higher idea of Mathematics 
 than I have of Chemistry as an educational subject, and I do 
 not say this with the intention of disparaging the latter sub- 
 ject in the least, but because I believe that although an exper- 
 imental subject may be of the highest interest and value in 
 many ways and for many purposes, yet as a means of mental 
 training it is not equal to those subjects which deal more with 
 the abstract and draw more fully upon the powers of the mind 
 in itself. 
 
 To those who know no better, and who have not had ex- 
 perience in the matter, it may appear as a very simple thing 
 for a teacher in middle life to change from one subject to anoth- 
 er quite inoognate; in reality it is anjrthing but simple, it is a 
 serious loss. Of course everything is not lost. The experience 
 which you have gained in teaching largely remains with you; 
 but years of work spent in bringing your subject to that high 
 state of form and efficiency which may be most profitable and 
 acceptable to your students, all that is lost, and to some extent 
 your professional life has to begin anew. 
 
 Having made the change I did not come into a very good- 
 ly heritage, for Mathematics from the modern point of view 
 was at a low ebb in the College, and it has never been, as far 
 as I know, a white-headed boy with the authorities which con- 
 trol the University. Hard and unceasing work offered the 
 only hope for a better state of things. 
 
 For years I had to do this alone; then with a temporary 
 assistant from year to year; and more recently with a perman- 
 ent one, which has given me great relief, but for which I have 
 to do a considerable amount of work outside of my own depart- 
 ment. But I am glad to be able to say that the labour has not 
 been in vain. A goodly number of young men and women who 
 find their way to Queen's to make a special study of Mathem. 
 atics are to be found in the honour classes, and wherever our 
 higher graduates come into contact with those from other insti- 
 
-la— 
 
 tntiona, ai »l Johns Hopkins and Clark UniTersities, we have 
 no reason to be ashamed of them. I say this not in a spirit of 
 boastfnlness, for I am not given to boasting, bat in one of 
 thankfnlness. And I do not believe that there is a better, 
 more thorough, or more modern undergraduate course in Math- 
 ematics to be found in any College in America, if in the world, 
 than in Queen's. And if I did believe so I would try to in- 
 spire my students to rise to the higher ideal. 
 
 I may be permitted to say that my relations with my stu- 
 dents have always been of the pleasantest kind. I have tried 
 to treat them as gentlemen, in recent years as ladies and gent- 
 lemen, and they have given me, in retuvn, all the respect that 
 any person has any right to ask for. Whatever their failings, 
 I have never discouraged them by comparing their brains to 
 those of a hen or any other fowl, and I never rose to the occa- 
 sion to call one of them a fool. This may have been a weakness 
 on my part, but it has worked well. And standing here to-day 
 I thank all the studenta individually and collectively, who have 
 attended my classes for the past third of a century, for assisting 
 to make my life a series of pleasant sessions and happy memor- 
 ies, instead of a succession of disagreeable labours burdened by 
 unpleasant associations. 
 
 But I have said enough and possibly too much about my- 
 self. I must now asi your indulgence for a few minutes while 
 I say something about my special subject. Mathematics. 
 
 I have spoken from this platform a great many times, on 
 various subjecta, but never upon Mathematics. My beloved is 
 getting jealous, and urges me to say a few words about her. I 
 am not going Uj call it the queen of the sciences, or say it is the 
 only science, or tell you that it is the one subject worthy of 
 study or that it will make kings of men, or anything so bigot- 
 ed and sil'.y. But the subject has certain features which are 
 characteristic and to be found in no other subject of study. 
 
 The Spiritualist holds that the mediumistj ^ property is due 
 to a new sense which, although potential in every person, has 
 in only a few received a sufficient degree of development to 
 make it a distinctive powtir. 
 
 Somewhat in the same way the great Evolutionist, Dr. 
 Alfred S. Wallace, believes that them athematical faculty is the 
 most recent development of the great faculties of the mind. If 
 this be so, and there are many things in favour of the view, the 
 
r 
 
 iiuithemftticUn mnat b« Bomewluit further adTMioed tluui his 
 non-mathemstioal brother, in the great proeese of evolntionMry 
 development. Be this as it may, however, many things about 
 the subject stand out in bold relief. 
 
 Mathematics is one of the oldest of subjects, as we have a 
 written treatise ni>on it coming down from 8,700 years before 
 Christ, and in the oldest known remains of civilisation, going 
 back some 7,000 years B.C., there are ample evidences of the 
 applications of elementary mathematical principles. And yet 
 if '• < except a few subjects which were born in the nineteenth 
 century, no other great subject of human study has made as 
 much progress as mathematics during the past hundred years. 
 And the progress has been, not only in the volume of the mat- 
 ter and results attained, but also in new processes and new 
 views, so that a great mathematician like Newton or Euler, 
 would quite fail at first to recognize the fullness and complete- 
 ness of the subject could he come upon the scene of human 
 action to-day. 
 
 This was noted by Lord Kelvin at the British Association 
 Meeting in Toronto, a few years ago, when he said that when 
 be was a young man, " Fourier's theorem was thought to be- 
 long to the higher mathematics, but aov it was found quite 
 common in text books." Tb- same remark would apply to 
 many other theorems, and there are more good mathematicians 
 in the world now than ever before, although, of course, the old 
 adage applies, there is still room at the top. 
 
 In some ways mathematics is a unique subject and stands 
 in marked contrast to others. Thus every man is an econom- 
 ist, and a politician, and a philosopher, and a theologian in his 
 own wsy. But every man is not a mathematician, and does 
 not proless to be so. 
 
 The student of practical science requires a work shop, and 
 a paraphernalia of tools and appliances of various kinds, and 
 can do little without them. 
 
 The mathematician needs no laboratory but his brain, and 
 no tools except a pencil and paper and the instruments of his 
 own thoughts. 
 
 The philosopher is concerned about the existence or non- 
 existence of an external world. The mathematician, as far as 
 bis subject is concerned, does not care two straws whether 
 there be an external world or not. His higher life is spent in 
 
—14— 
 proiimity to the imtffiiuries »nd the infinities, and hie hisfa- 
 eet thoaghte rad oonoeptions find no oorreepondent in the ex- 
 ternal world. 
 
 It i> jnit here that the philosopher fails to understand the 
 mathematioian. or to enter into his realm of thought; and he 
 must always do so unless he becomes a mathematioian. Thus 
 the philosopher denies the possibUity of a four^imensional 
 space, and thinks the mathematioian an idiot who speaks of such 
 a thing. But space finds its mathematical relations in Euclidian 
 Geometry, and only those analytic ideas which are intorpret- 
 able in Geometry can have any relation to space as we know it. 
 But the mathematicun deals with analytic concepts which 
 transcend Geometry, and therefore transcend the known world 
 of reality; and as an analytic idea space of four dimensions is 
 just as reasonable as space of any other number of dimensions, 
 for It 18 merely the eztonsion ri symbols from a lower plane of 
 thought to a higher. 
 
 A conception of the last century known as the doctrine of 
 the imaginary is of such a nature that that called the imagin- 
 ary cannot possibly be imagined. The philosopher and the 
 man of common sense may say that such a concept cannot 
 serre any trustworthy purpose. The mathematioian knows bet- 
 ter. He knows th„t the doctrine of the imaginary has nearly 
 doubled his mathematical knowledge, that it has harmonized 
 resulte and simplified methods, that it has given him a pecul- 
 iar power over analytic operations, and that it has so complet- 
 ed his Algebraic concepts that nothing mathematical can pos- 
 sibly exist outside of them. 
 
 And tuese results, this generalizing and harmoniziiig, are 
 due to the labours of successive generations of mathematical 
 thmkers, extending over a period of fully five thousand years 
 from the ancient Egyptian Ahmes, down through Greek, and 
 Indian, and Arab, and Moor, and European to Klein and Poin- 
 carre, and Hermite, and a host of workers to-day. 
 
 And yet we hear people, who would stick on the pona a»- 
 tnorum,or if not on that on some bridge a litMe furthar on, s*y 
 that mathematics are dry and uninteresting and unprofiitable 
 To them it may be even worse than the f-ibled sour grapes; but 
 surely a man should be modest in the presence of great things 
 which he can never know or understand. 
 
« ♦?*"!. "■**"\" *° ^ • *•""'•' imP'eMion tbroad tiwt tit* 
 m«th.m.ti«»n know, nothing bnt n»th«in.tic., that h« is i^ 
 fl«dbl..nd nnin,pre..ion.ble, di.pi,ing : fratur. .nd ..nti- 
 
 r* > f *!!?",* **'*" ''"'' indiirewnee. Thi. impr«i.ion >. 
 not deduce.ble from the f«5t«. It i. true that he U not an ei' 
 pert .t.en«tiou.li«m like the norelirt. wd he doe. not m.r 
 .TT T «*^*»»"*"y qnotiiig from Greek or L*tin .uth- 
 or.. like the olM.ioi.t. but he i. not .noh • .tick after all 
 Many of them enjoy all the higher literature to their full oapi 
 •oity, and no capacity can be more than filled. Many of then 
 ike Leibnitz «d De. Carte., have written oxtenaiyeTy on .u" 
 jeot.out.ide their .peoialty; .ome of them, like Paacal have 
 been noted theologian, and controTer.iali.t.; other., like New- 
 oomb have written acceptably on economic; Mme have been 
 pa..ib.y good poet., and a goodly number have occupied their 
 hour, of reoreaUon with mu.io or ari 
 
 ul. and theologun. to have been wrwiglers at Cambiidge 
 But a very different tradition prevail, at Queen'., the higher 
 mathematic being confined quit^ exduaively to non-thA«logi. 
 
 of thi. difference, but it i. ju.t po..ibl8 that too familiar con 
 l^^Jn •-ubject which i. positive, ei«,t. demonetrable 
 and non-controversial, might not be the be.t suited for thow 
 who pro,K>.e to follow a more or less dogmatic rnd controver.. 
 lal profes.ion. 
 
 However, no inducement of any kind, a. far a. I know 
 
 mathematics And ye. there is no dearth of .tudent. in the 
 honour clasM.. Love and admiration for the .uLject, coupled 
 with the poBMssion of a mathematical taste, have m> far been 
 quite .ufflcient And I pre.ume that as long .. the subject is 
 properly taught there will alway. be a .ulBoient number « 
 young men and women interested in the pursuit of the "be- 
 witching Boionoe" to keep the teachers from growing rusty or 
 the subject from falling into de.uetude. k "« »y or 
 
 But what i. Mathematics? Different perK>n. would give 
 different answers to the question. Tiie business and oomm3r- 
 cial man would say that it consisted in arithmetic and book- 
 keeping, and general commercial and business mathematics 
 The surveyor, that it oomprUed the knowledge of Geometry' 
 
—16- 
 
 Algabn end TrigonMaetry, m applied to tb« prineiplM and 
 proMuea of all kiada of anrTaying. The astronomer would 
 •xtend it to the meaanring and weighing of worlds, and the 
 ealonUtion of the orbita and plaoea of the membera of the aolar 
 ayatem, eto. 
 
 All theae thinga would be oorreot in their way, for 
 matheuMtioa is many aidnd and inoludea all exact relation. 
 But all of theae do not conatitnte Mathematica. 
 
 Many people appear to think that the anbjeot eziata for the 
 aole pnrpoae of working ont theorema and deviaing formnlas 
 which may find their application in effecting the aolntiona of 
 the Tariona problema which occur in the prosecution of the ex- 
 perimental aoiences. For the theoriea of Heat, of Light, of 
 Electricity, Astronomy and Physical Chemiatry, all are math- 
 ematical, and would be nothing without Mathematics. 
 
 And it ia true that these subjects form a large body o- 
 Mathematica, and that in them the science finds its great field 
 of practical utility. But to aay that these form the whole of 
 Mathematics is just as reaaonable i» to say that the whole of the 
 arable land in the world constitutea the who^e of the earth's 
 surface. There are arid wilda and mountain fastnesses which 
 delight the explorer and the pioneer, but which will never be 
 cultivated, and there are mountain heights that have never 
 been climbed. The true mathematician pursues Mathematica 
 for ita own sake, regardless of any practical application which 
 the results of his labours may hav And it is through him 
 and him alone, that the subject has reached that unique beauty 
 of form and completeness of g(.>neralization which character- 
 ixea it. 
 
 But I must not detain you too long, so I will close after 
 quoting from a recent writer: 
 
 "In the minds of eighteenth century mathematicians their 
 science existed for the sake of its applications. Forgetfulness 
 of this was, in their eyes, reprehensible, or even immoral. The 
 question was, what would a given piece of mathematics do? 
 They liked smooth running and elegant machinery— there was 
 economy in this; but they were not sedulous that it should 
 have aymmetry; idle admiration of its beauty they hardly ap- 
 proved. If it was excessively complicated and intricate, that 
 was regarded rather as a feature to be proud of than as a blem- 
 ish. Were the complete revolution that the nineteenth cent- 
 
-17- 
 
 ury wrought upon the iil««l of HatheuMtien not notoriona, on« 
 could soon oouviuoe hima«lf of it by looking oyer almoat any 
 modern trestiie, lay 8«lmnn on • Hitfb«r Plane Ourrea.' That 
 Tolume, for example, would be found replete with theorems, 
 hardly any of which hold good for any cnrrea that could really 
 
 "*■* Modern Mathematioaii highly t**»iitio. Aiim- 
 
 pie theme ia ohoeen, aome conoeption pretty ai- charming in 
 itself. Then it ia ahown that by aimply holding this idea up 
 to one's eye and looking through it, a whole forest that before 
 seemed a thick and tangled jungle of bushes and briars is seen 
 to he in reality an orderly garden. The word genenHxatiun 
 really cannot be fully understood without studying modem 
 Mathematics: nor can the beauty of generalization be in any 
 other way so well appreciated. 
 
 "There is no need here of throwing out extreme cases. 
 Far from that; it is precisely in the extreme oases that the 
 power and beauty of the magic eyeglass is mo^t rpparent and 
 most marrellouc. Let me take back the word ' magic ' though ; 
 foi- the reasonableness of it is just ita crowning charm, I mnat 
 not be led away from my iwint to expatiate on the repoaeful- 
 
 neaa of the new Mathematics Buffloe to say 
 
 that it is so reasonable, so simple, so easy t< read, when the 
 right view has once been attained, that the student may easily 
 forget what arduous labours were expended in constructing 
 the first pathway to that lofty summit, what mastery of intrica- 
 cies far beyond the reach of the first century masters." 
 
 " It must not be supitosed', said Jaoobi, one of the great 
 simplifying pioneers, esr)ecially in the field of elliptic func- 
 tion, ' that it is not to any gift of nature that I owe such math- 
 ematical powers as I possess; no, it has come by hard work, 
 hard work; not mere industry, but brain-splitting thinking,' 
 hard work ; work that has often endangered my health. ' And if 
 Mathematics can be called great, as it certainly can, such wnre 
 the men who made it great. 
 
 And to Jaoobi's testimony, I can only add that nothing 
 in this life comes to a man, that is really worth having, except 
 through hard work. For it is work, good, honest, faithful 
 work that can lift a man out of the blues and make "the wheels 
 of life gae down hill scrieven." 
 
-It- 
 
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