NA rURE 



{Dec. 30, 1886 



and this led to a great waste of examining power, many 

 questions having to be constructed each >ear upon sub- 

 jects which none of the candidates had studied. The 

 Board accordingly formed a schedule in which all the 

 subjects of pure and applied mathematics were included 

 — none being intentionally omitted. These were divided 

 into eight divisions, the first four relating to pure mathe- 

 matics, and the last four to applied mathematics. To 

 avoid the waste of questions that would ensue from the 

 examiners having to represent all the subjects in the 

 papers in each year, they proposed that before the first day 

 of December preceding the examination the names of the 

 candidates and of the divisions and subjects in which 

 they desired to be examined should be forwarded to the 

 Registrary of the University. The examiners would 

 thus be made acquainted with the subjects which the 

 candidates had studied, and would be able to frame their 

 questions accordingly. Changes were also proposed with 

 respect to the candidates who were admissible, and to 

 the form of the final list. By the existing regulations 

 only wranglers were allowed to present themselves for 

 examination in Part II., and the list was arranged in 

 three divisions ; there was no separation into classes, 

 because, as only wranglers were admissible, it was con- 

 sidered that all the candidates were first-class men from 

 the beginning. The new proposals were, that the restric- 

 tion which admits only wranglers should be removed, and 

 that the candidates should be divided into three classes, 

 each class being subdivided into as many divisions as the 

 examiners in each year thought proper. In previous 

 schemes the endeavour of the Board had been to frame 

 regulations that would tempt the students to specialise 

 their reading. A few years had made so great a differ- 

 ence that, with a view to prevent undue specialisation, 

 the Board now inserted a regulation to the effect that 

 proficiency in subjects taken from more than one of the 

 divisions should be requisite in order that a candidate 

 might be placed in the first class. 



The Report containing these proposals was confirmed 

 by the Senate on May 27, and it is noteworthy that both 

 this Report and its predecessor, in which the nomination 

 of examiners was placed in the hands of the Board, were 

 sanctioned without opposition of any kind. The latter of 

 these Reports also made a few minor changes, the most 

 important of which was the omission of the problem 

 paper which had been still retained, from the old five days, 

 in the scheme of 1882.' The examination in Part II. 

 had assumed such a character, that the kind of questions 

 to which one would usually apply the name of problems 

 was no longer in keeping with the contents of the other 

 papers." 



Under the new scheme, in which all the examiners 

 were to be appointed by the Board with special reference 

 to their collective fitness for conducting the examination 

 in Part II., there was no further need for an Additional 

 Examiner, and this office w'as, accordingly, discontinued.^ 



Thus has the Mathematical Tripos been divided into 

 two parts ; and thus has surely arisen in the University 



• Although the Board were unable to make any recommendation upon the 

 subject, I may mention that the principle of prefi.xing to the final three days 

 a preliminary day, i-i which the subjects of examin.'Xtion should be those 

 parts of higher pure mathematics which are needed in mathematical physics, 

 found a considerable amount of favour on the Board. The proposal, how- 

 ever, was found to be more difficult in execution than was anticipated (partly 

 00 account of the impossibility of forming a perfectly satisfactory scliedule 

 of su jects for this day), and was ultimately abandoned by most of its 

 original supporters. 



^ In the first examination in Part III., in 1883, the examiners set, as one 

 of the question papers, a paper of essays ; and their example was followed 

 by the examiners in 1884, 1885, and 1886. These essay papers were intro- 

 duced merely on the authority of the examiners, and not m consequence of 

 any new regulation. Experience seems to show that the essay paper affords 

 very little additional assistance in ascertaining the relative merits of the 

 candidates. The essays were, perhaps, more useful at first, when they were 

 a novelty. 



3 Unless the office should be revived at some future time, there will there- 

 ore have been only one Additional Examiner for the final part of the ex- 

 amination, viz. in 1886, the last occasion of the examination taking place in 

 January. 



a mathematical examination of a higher type than has 

 been known before, or could have existed under any 

 system in which all the candidates for mathematical 

 honours were required to be examined by the same 

 papers throughout. For those who study mathematics 

 for the sake of exact knowledge or mental discipline, and 

 who propose to go forth into the world to follow pro- 

 fessional or other careers, the first part secures all the 

 old stimulus to industry, and gives to those who are suc- 

 cessful the same stamp of intellectual distinction as 

 before : such students are released at the end of their 

 third year to enter upon the active duties of their lives, 

 equipped with a sound understanding of the principles of 

 the exact sciences, and with minds well trained to 

 accurate habits in reasoning and in the acquisition of 

 knowledge. To those whose attachment to our science 

 lies deeper, and whose studies have carried them beyond 

 its threshold, the second part, at the end of their fourth 

 year, affords an opportunity of distinction of a higher kind, 

 and one more suited to their tastes ; no longer is the wise 

 and thoughtful student hopelessly distanced in the Tripos 

 race by his quick and ready rival. 



The wants of the candidate whose mathematical career 

 closes with the last paper in Part I., and of the candidate 

 whose mathematical life only begins from this moment, 

 are equally provided for by the new scheme. The order 

 of merit relates to an examination that can bear it. All 

 the subjects included in Part I. are such as ought to be 

 the common property of every one who has received a 

 sound mathematical education ; and by the results of an 

 examination in subjects which all the candidates should 

 have read a list in order of merit can properly be formed. 

 The specialist for the first lime is set free to follow his 

 own tastes, and give his whole heart and time to the 

 branches of mathematics by which he is attracted. The 

 University permits him to select any subjects he pleases 

 from the whole range of pure and applied mathematics, 

 and undertakes to examine him in them and award to 

 him the credit he deserves for his attainments. A per- 

 fectly free choice is given to him, subject only to the one 

 condition that, in order to ciualify himself for admission 

 to the first class, he must not select all his subjects from 

 a single division.' 



But what to us as mathematicians is more than all, as 

 bearing on the future of our science, is that now for the 

 first time will it be possible in Cambridge for an able and 

 earnest worker and teacher to interest and engage his 

 pupils in his work, and found a school such as we are so 

 familiar with in foreign Universities, where the presence 

 of a great professor has been almost invariably marked 

 by a succession of illustrious pupils — pupils worthy of 

 their master, and w-orthy to carry on his work. Think 

 of the school of arithmeticians founded by Gauss at 

 Gottingen, and how impossible such a result would have 

 been at Cambridge, dominated as she has been by the 

 competition for places in the Tripos ! Great as has been 

 the value to the University of the order of merit — as a 

 stimulus to industry, an encouragement to thoroughness 

 in mathematical study, and a paramount influence in 

 regulating elections to Fellowships at colleges where no 

 independent examination existed — it has yet been in 

 recent years a deadly enemy to the spread of research 

 and the advance of our science. Throughout his whole 

 career the student has had to devote himself unremittingly 

 to the work for his Tripos, taking up a fresh subject each 

 term, and often having to read two in one term. He 

 could never pursue any subject far enough to reach the 

 really interesting portions of it, or obtain complete 



^ This condition would be complied with by the candidate's showing pro- 

 ficiency in one subject taken from one division and in one other subject taken 

 from one other division. The intention of the Board was to discourage 

 students from specialising too narrowly at too early a period Some of the 

 divisions (as, for example, the fourth, which contains only projective geo- 

 metry and analytical geometry of curves and surfaces) are so restricted that 

 it was considered undesirable that students should be allowed to confine 

 themselves entirely to subjects chosen from a single division. 



