Dec. 



iSS6j 



NA TURE 



199 



liarly good omen for progress in the study of nebulii; 

 that a mode of record at once so fluctuating and so 

 laborious as that of hand-drawing should be replaced (as 

 it will no doubt soon wholly be) by automatic impressions 

 which, with some points of inferiority, at least leave no 

 room for " individualism." 



M. Tempel's description of the Merope nebula (dis- 

 covered by himself in 1S59), and his remarks on the great 

 elliptical mass in the girdle of Andromeda, derive parti- 

 cular interest from recent events. His observational 

 faculty, and the high quality of his telescope, are illus- 

 trated in the disclosure to him, by Amici I., of nearly 900 

 stars in the Pleiades, all of them comprised within the 

 field of view of a 4-inch Steinheil bearing a magnifying- 

 power of 24. With the former instrument he detected 

 independently on September 30, J 875, a few days before 

 reading Bond's description of them, the strange obscure 

 channels in the Andromeda nebula ; and has since with 

 soxe difficulty made out similar markings in some small 

 nebulfe of the same class. They would accordingly 

 appear to be a more or less characteristic feature of 

 " ova! " nebuke, and might perhaps be assimilated to the 

 symptoms of partial duplication in Messier I. 



In respect to the nature of nebulaj, our author's experi- 

 ence leads him decidedly to adopt the view of their close 

 connection with stars. He shows, indeed, for spectro- 

 scopic evidence a disregard that is neither philosophic nor 

 just ; yet his contention that purely gaseous nebute do 

 not exist, is probably well founded. No aggregation of 

 celestial mist, at any rate, has ever been observed by him 

 in which his li-inch failed to reveal the pricking light of 

 minute stars, marking some knot or nucleus, and thereby 

 evincing structural relations of a most intimate kind. 



THE MATHEMATICAL TRIPOS^ 

 III. 

 ■VXrHEN the interval between the earlier portion of the 

 ' • examination and Part III. had been extended to a 

 year, it became evident that some substantial relief must 

 be afl'orded to the examiners. By the existing regulations a 

 person who accepted the office of Moderator would have 

 to take part in the examination in three consecutive years, 

 and in his second year of office he w'ould have to e.xamine 

 the candidates of one year in Part III. simultaneously 

 with those of the year below in Parts I. and II. This led 

 to the consideration of the whole question of the appoint- 

 ment of examiners. The two Moderators in each year 

 are nominated by two colleges, according to a prescribed 

 cycle of fifty years. This nomination by colleges, though 

 theoretically not very defensible, had worked very fairly so 

 long as the examination only included subjects with which 

 any high wrangler might be expected to be acquainted ; 

 but it was clearly unsuitable for Part III. In any case the 

 nomination of the four examiners by four independent 

 bodies might easily bring about the result that among 

 the various subjects included there would be some which 

 had not been made the object of special study by any 

 of the examiners : indeed there was nothing to prevent 

 the four examiners bemg all pure mathematicians or all 

 physicists. .Accordingly, with a unanimity almost unique 

 in matters relating to the Tripos, the Board recommended 

 in a Report dated June 15, 1885, that the examiners for 

 Part III. should be quite distinct from those for Parts I. 

 and II., and that all four should be nominated by the 

 Board. It was also proposed that they should hold 

 office for only one year. This Report was sanctioned by 

 tlie Senate on October 29, 18S6. In future, therefore, the 

 Moderators will not take part in the highest portion of 

 the examination. The appointment of Moderators dates 

 from 1680. Previously the Proctors had themselves pre- 



' Address delivered before the London Mathematical Society by the 

 President, Mr. J. W. L. Glaisher, M.A., F.R.S., on vacating the chair, 

 November 11, 1886. Continued from p. 157. 



sided in the schools, but in that year the duty of conduct- 

 ing the disputations was transferred to the Moderators, 

 who were specially appointed to perform this office. The 

 Moderators have always been, and still remain, high 

 University officers, ranking next to the Proctors.' Not 

 only were they the earliest examiners in the University, 

 but it is to them that we owe the origin of the examina- 

 tion system. Their severance from a portion — and that 

 the highest portion — of the examination is therefore a 

 notable event in the history of the Tripos. Neither the 

 Board nor the University would have agreed lightly to 

 such a break in the traditions of the Senate House 

 examination, had it been possible to retain the Mode- 

 rators as examiners for the final part without altering the 

 system of nomination by colleges. The complete separa- 

 tion of Part III. from the earlier parts of the examination 

 was, however, inevitable. Many members of the Uni- 

 versity who would discharge most admirably the duty of 

 examining for Parts I. and II. would shrink from Part 

 III. ; and the professors and specialists who were best 

 fitted to examine in Part III. would generally be reluctant 

 to undertake the heavy burden of examining all the 

 candidates for Parts I. and II., especially in two consecu- 

 tive years. 



Thus, by the irresistible pressure of events, it has come 

 to pass, in the last few years, that not only the titles of 

 wranglers, senior optimes, and junior optimes have lost 

 their old significance and refer only to the earlier examina- 

 tion, but that even the more ancient title and office of 

 Moderator has undergone a similar restriction. The final 

 part of the examination has indeed made rapid progress : 

 within three years of its first coming into existence it 

 has emancipated itself from union with the earlier parts, 

 and become an independent examination. 



Besides these important innovations, the Senate sanc- 

 tioned at the same time a slight change in the nomencla- 

 ture of the Tripos, the earlier portion of the examination, 

 previously called Parts I. and II., upon which the list in 

 order of merit depended, being designated Part I., and 

 Part III. being henceforth designated Part II. This 

 change was made in order to bring the nomenclature of the 

 Mathematical Tripos into harmony with that of the Clas- 

 sical and other divided Triposes. 



As soon as Part II., to adopt its new name, became 

 an independent examination, the Board directed its 

 attention to the schedule of subjects relating to it. 

 The existing schedule contained only those subjects 

 which had been included in the schedule which 

 came into operation in 1873, when the results of the 

 whole examination were still expressed by one final 

 list, arranged in order of merit. Now that Part II. was 

 a separate examination, and that there was no order of 

 merit, the reasons for the limitation of the subjects had 

 been entirely reinoved. Although the theory of elliptic 

 functions, which dates only from the publication of 

 Jacobi's " Fundamenta Nova" in 1829, was included, the 

 theory of numbers, which had its origin in Gauss's 

 " Disquisitiones Arithmeticse" of 1801, was still excluded. 

 .Abelian functions, the theory of functions of a complex 

 variable, projective geometry, and quaternions were not 

 formally included by name, and questions on these sub- 

 jects could only be set, if at all, by straining the meaning 

 of the title of some other subject. Besides the total 

 exclusion of certain branches of pure mathematics, a 

 further reason for revising the existing schedule was 

 afforded by the fact that the four groups A, B, C, D were 

 very unequal both in magnitude and popularity among 

 the students. According to the existing regulations the 

 four groups had to be equally represented by questions, 



I It is still the custom for the list of wranglers, senior optimes. and 

 junior optimes to be shown to the senior Proctor on the evening of the day 

 before it is read in the Senate House. This is doubtless a rehc of the fact 

 that the Moderators were originally the substitutes of the Proctors. It has 

 been already mentioned that the Proctors, as well as the Vice-Chancellor, used 

 to have the right to insert a certain number of names where they pleased in 

 the Tripos list. 



