Jan. 7, 1886] 



NATURE 



223 



during a lifetime of integrity and public usefulness, I 

 might address the words familiarly applied to one dear to 

 all Wykehamists : — 



" Qui condis Iseva, qui condis collegia dextra, 

 Nemo tuaium unam vicit utraque manii." 



The chair which I have the honour to occupy in this 

 University is made illustrious by the names and labours 

 of its munificent and enlightened founder, Sir Henry 

 Saville ; of Thomas Briggs, the second inventor of 

 logarithms ; of Dr. Wallis, who, like Leibnitz, drove 

 three abreast to the temple of fame— being eminent as a 

 theologian, and as a philologer, in addition to being illus- 

 trious as the discoverer of the theorem connected with the 

 quadrature of the circle named after him, with which every 

 schoolboy is supposed to be familiar, and as the author of 

 the " Arithmetica Infinitoru'ii,'' the precursor of Newton's 

 " Fluxions" ; of Edmund Halley, the trusted friend and 

 counsellor of Newton, whose work marks an epoch in the 

 history of astronomy, the reviver of the study of Greek 

 geometry and discoverer of the proper motions of the so- 

 called fixed stars ; and by one in later times not unworthy 

 to be mentioned in connection with these great names, 

 my immediate predecessor, the mere allusion to whom 

 wdl, I know, send a sympathetic thrill through the hearts 

 of all here present, to whom he was no less endeared by 

 his lovable nature than an object of admiration for his 

 vast and varied intellectual requirements, whose untimely 

 removal, at the ver\- moment when his.fame was beginning 

 to culminate, cannot but be regarded as a loss, not only 

 to his friends and to the University for which he laboured 

 so strenuously, but to science and the whole world of 

 letters. 



As I have mentioned, the first to occupy this chair was 

 that remarkable man Thomas Briggs, concerning whose 

 relation to the great Napier of Merchiston, the fertile 

 nursery of heroes of the pen and the sword, an anecdote, 

 taken from the Life of Lilly, the astrologer, has lately 

 fallen under my eyes, which, with your permission, I will 

 venture to repeat : — 



" I will acquaint you (says Lilly) with one memorable 

 story related unto me by John Marr, an excellent mathe- 

 matician and geometrician, whom I conceive you re- 

 member. He was servant to King James and Charles 

 the First. At first, when the lord Napier, or Alarchiston, 

 made public his logarithms, Mr. Briggs, then reader of 

 the astronomy lectures at Gresham College, in London, 

 was so surprised with admiration of them, that he could 

 have no quietness in himself until he had seen that noble 

 person the lord Marchiston, whose only invention they 

 were : he acquaints John Marr herewith, who went into 

 Scotland before Mr. Briggs. purposely to be there when 

 those two so learned persons should meet. J\Ir. Briggs 

 appoints a certain day when to meet at Edinburgh ; but 

 failing thereof, the lord Napier was doubtful he would 

 not come. It happened one day as John Marr and the 

 lord Napier were spei'-cing of Mr. Briggs : ' Ah John 

 (said Marchiston), Mr. Briggs will not now come.' At 

 the very moment one knocks at the gate ; John Marr 

 hastens down, and it proved Mr. Briggs to his great 

 contentment. He brings Mr. Briggs up into my lord's 

 chamber, where almost one quarter of an hour tuas spent, 

 each beholding other almost with admiration before 

 one word -was spoke. At last Mr. Briggs began : ' My 

 lord, I have undertaken this long journey purposely to 

 see your person, and to know by what engine of wit or 

 ingenuity you came first to think of this most excellent 

 help into astronomy, viz. the logarithms ; but, my lord, 

 being by you found out, I wonder nobody else found it out 

 before, when now known it is so easy.' He was nobly 

 entertained by the lord Napier ; and every summer after 

 that, during the lord's being alive, this venerable man 

 Mr. Briggs went purposely into Scotland to visit him." ' 



A ver>- similar story is told of the meeting of Leopardi and Niebuhr in 

 Rome. What Briggs said of logarithms may be said almost in the same 



Some apology may be needed, and many valid reasons 

 might be assigned, for the departure, in my case, from the 

 usual course, which is that every professor on his ap- 

 pointment should deliver an inaugural lecture before 

 commencing his regular work of teaching in the Uni- 

 versity. I hope that my remis-ness, in this respect, may 

 be condoned if it shall eventually be recognised that I have 

 waited, before addressing a public audience, until I felt 

 prompted to do so by the spirit within me craving to find 

 utterance, and by the consciousness of having something 

 of real and more than ordinary weight to impart, so that 

 those who are qualified by a moderate amount of mathe- 

 matical culture to comprehend the drift of my discourse, 

 may go away with the satisfactory feeling that their mental 

 vision has been e.xtended and their eyes opened, like my 

 own, to the perception of a world of intellectual beauty, 

 of whose existence they were previously unaware. 



This is not the first occasion on which I have appeared 

 before a general mathematical audience, as the messenger 

 of good tidings, to announce some important discovery. 

 In the year 1S59 I gave a course of seven or eight lectures 

 at King's College, London, at each of which I was honoured 

 by the attendance of my lamented predecessor, on the 

 subject of " The Partitions of Numbers and the Solution 

 of Simultaneous Equations in Integers," in which it fell 

 to my lot to show how the difficulties might be overcome 

 which had previously baffled the efforts of mathemati- 

 cians, and especially of one bearing no less venerable a 

 name than that of Leonard Euler, and also laid the basis 

 of a method which has since been carried out to a much 

 greater extent in my " Constructive Theory of Partitions," 

 published in the American Journal of Mathematics, in 

 writing which I received much valuable co operation and 

 material contributions from many of my own pupils in the 

 Johns Hopkins University.' Several years later, in the 

 same place, I delivered a lecture on the well-known 

 theorem of Newton, which fills a chapter in the " Arith- 

 metica L^niversalis," where it was stated without proof, 

 and of which many celebrated mathematicians, including 

 again the name of Euler, had sought for a proof in vain. 

 In that lecture I supplied the missing demonstration, and 

 owed my success, I believe, chiefly to merging the theorem 

 to be proved, in one of greater scope and generality. In 

 mathematical research, reversing the axiom of Euclid, 

 and converting the proposition of Hesiod, it is a con- 

 tinual matter of experience, as I have found myself over 

 and over again, that the whole is less than its part. On 

 a later occasion, taking my stand on the wonderful dis- 

 covery of Peaucellier, in which he had realised that exact 

 parallel motion which James Watt had believed to be 

 impossible, and exhausted himself in contrivances to find 

 an imperfect substitute for, in the steam-engine, I think I 

 may venture to say that I brought into being a new 

 branch of mechanico-geometrical science, which has 

 been, since then, carried to a much higher point by the 

 brilliant inventions of Messrs. Kempe and Hart. I re- 

 member that my late lamented friend, the Lord Almoner's 

 Reader of Arabic in this University, subsequently editor of 

 the Times, Mr. Chenery, who was present on that occasion 

 in an unofficial capacity, remarked to me after the lecture, 

 which was delivered before a crowded auditory at the 

 Ro)al Institution, that when they saw two suspended 



words of the subject of this lecture :— " This most e.\-cellent help to geometry 

 which, being found out, one wonders nobody else found it out before ; when, 

 now known, it is so easy." I quite entered into Brigg's feelings at his inter- 

 view with Napier when I recently paid a ^■isit to Poincar^_ in his airy perch 

 in the Rue Gay-Lussac in Paris (will our grandchildren live to see an Alex- 

 ander Williamson Street in the north-west quarter of London, or an Arthur 

 Cayley Court in Lincoln's Inn, where he once abode?) In the presence of 

 that mighty reservoir of pent-up intellectual force my tongue at first refused 

 it.s office, my eyes wandered, and it was not until I had taken some time 

 (it may be two or three minutes) to peruse and absorb as it were the 

 idea of his e.\ternal youthful lineaments that I found myself in a condition 



I In one of those lectures, two hundred copies of the mtes for which were 

 printed off and distributed among my auditors, I founded and developed to 

 a considerable extent the subject since rediscovered by M. Halphen under 

 the name of the Theory of Aspects. 



