Dec. 1 6, 1886] 



NA TURE 



155 



have felt themselves bound to follow the precedent of 

 their predecessors, so that no new subjects were intro- 

 duced. One would suppose from an examination of the 

 papers set that those of the last five days must have been 

 framed in accordance with a schedule as precise and 

 detailed as that which governed the first three. 



In 1865 the Board recommended that after 1866 La- 

 place's coefficients and the figure of the earth considered as 

 heterogeneous should be included in the examination, but 

 this appears to be the only extension of the range of sub- 

 jects recommended by the Board during the time that 

 the regulations of 184S remained in force. 



The period that followed the constitution of the Mathe- 

 matical Board was one of activity in the whole University. 

 The first examinations of the Moral Sciences Tripos and 

 of the Natural Sciences Tripos were held in 1851. In 

 1850 a Royal Commission was issued to inquire into the 

 University and Colleges, and in 1S52 their Report was 

 presented to Parliament. Inconsequence of this Report, 

 a Bill was introduced into Parliament, which received 

 the Royal assent in 1856 ; and, under its powers new 

 statutes were fram.ed, both for the University and the 

 Colleges. Amid all these changes the Mathematical 

 Board, though not very active, was not idle. The subjects 

 w-hich chiefly occupied its attention were the alteration 

 of the date of the first three days from January to the 

 previous June (as by recent changes the poll-men were 

 examined in June, and so received their degrees seven 

 months before the mathematical honour men), and the 

 introduction of the I'iva voce element into the examina- 

 tion. Neither of these innovations, though frequently 

 discussed and finally recommended by the Board, was 

 received with much favour in the University. With re- 

 gard to the latter, the opinion seems now to have become 

 general that an admixture of the viva voce element, how- 

 ever valuable it may be in the lecture-room, is useless, or 

 even worse, in testing the proficiency of candidates with 

 the view to arranging them in strict order of merit. The 

 change of time from January to June was at length 

 eftected, as will be seen, by the regulations which came 

 into operation in 18S2. 



In 1866 the attention of the Board was directed to the 

 exclusion of certain important branches of mathematics 

 from the studies of the University, owing to the fact that 

 they were not represented in the Tripos examination. 

 The rewards attending a high place in the Tripos were 

 so great that the reading of most of the best men was 

 directed almost w-holly to this end ; it was therefore prac- 

 tically impossible to introduce new mathematical subjects 

 into the University w-ithout assigning to them some place 

 in the Tripos. Now, although the recommendations of 

 1849-50 had curtailed the range of subjects, the course 

 had nevertheless extended itself in some directions — 

 where the name of the subject permitted of such exten- 

 sion — and especially in analytical geometry and higher 

 algebra. The fact of this extension taking place in cer- 

 tain subjects, while others were wholly omitted, alone 

 sufficed to show the need of some revision of the limita- 

 tions imposed upon the subjects that might be set. The 

 Board, after careful consideration, came to the conclusion 

 that the time had come when it was desirable to allow the 

 candidates a certain option with respect to the higher 

 branches of mathematics, and that this could be effected 

 by increasing the nuinber of subjects and arranging them 

 in several divisions over which the marks were distributed 

 in a known proportion. Each candidate would be at 

 liberty to devote himself to such of the divisions as he 

 thought most advantageous, there being nothing to pre- 

 vent his taking up all the divisions, if it were possible for 

 him to do so. In a Report dated May 8, 1867, the 

 Board gave expression to these views, and recommended 

 a scheme for the five days, according to which the sub- 

 jects of examination were arranged in five divisions, with 

 an approximately determinate number of marks assigned 



to each division. The subjects included in the five divi- 

 sions were thirty-five in number, and included elliptic 

 integrals, elastic solids, heat, electricity, and magnetism. 

 On June 3, 1S67, a syndicate was appointed by the Senate 

 to consider the proposals of the Board ; and the regulations 

 recommended by this syndicate were approved by the 

 Senate on June 2, 186S, and came into operation in 

 January 1873. 



In this new scheme of examination the three days were 

 left unchanged, and the schedule of subjects for the five 

 days, and their arrangement in divisions as proposed by 

 the Board, were adopted with very slight modifications, 

 the marks awarded to the five divisions being to those 

 awarded to the three days in the proportion of 2, i, i, i, 

 ^ to I respectively.' 



The new regulations also made two other changes of, 

 importance : they added an extra day to the examination 

 and increased the number of the examiners from four to 

 five. The extra day was the day immediately following the 

 three days, and it was devoted to easy questions upon the 

 subjects in the five days' schedule. Although the papers 

 set on this fourth day were put before all the candidates, 

 they were taken into account along with the five-day 

 papers, and not with the three-day papers ; so that this 

 day had no effect upon the alphabetical list of those who 

 deserved mathematical honours ; which, as before, was 

 dependent upon the three days' marks only. 



The Additional Examiner was appointed on the 

 nomination of the i\Iathematical Board, and held office 

 for one year only ; and, to render his duties as little irk- 

 some as possible, he was not required to take part in the 

 first three days — the most laborious part of the examina- 

 tion as far as the looking over the papers is concerned, on 

 account of the quantity of work sent in. It was thought 

 that in introducing the new subjects of electricity and 

 magnetism into the examination, certain non-resident 

 Cambridge mathematicians whose names were closely 

 connected with great recent advances in these subjects 

 might be willing to give the University the benefit of their 

 assistance, and that the influence of eminent non-resident 

 mathematicians upon the examination, and therefore also 

 upon the course of studies in the University, would be 

 of the greatest value. These hopes were abundantly 

 justified. 



The general working of the new system soon disclosed 

 the fact that the desired effect of inducing the best 

 candidates to make a selection from the higher sub- 

 jects, and concentrate their reading, had not been 

 attained. It was found that, unless the questions were 

 made extremely difficult, more marks could be obtained 

 by reading superficially all the subjects in the five 

 divisions than by attaining real proficiency in a few of the 

 higher ones ; and the best men of the year were tempted, 

 not to say compelled, to extend their reading as widely as 

 possible over the book-work of the whole range of sub- 

 jects. Thus, with respect to the main object which the 

 framers of the scheme had in view, it was a complete 

 failure. 



Accordingly, on May 17, 1S77, a syndicate was appointed 

 by the Senate to consider the higher mathematical studies 

 and examinations of the University. This syndicate con- 

 sisted of eighteen members representing nearly all phases 

 of mathematical research and study in Cambridge ; they 

 met every week during the whole academical year, and 

 the thoro'ugh examination and discussion that the subject 

 received, both on the syndicate and in the University 

 at large, brought out in the strongest light how great 

 were the intrinsic difficulties connected with the re- 

 tention of the order of merit, and how wide w-as the 

 diversity of opinion — so much so, that at one time it 

 seemed almost hopeless to attempt to devise a scheme 



1 The regulation assigning the proportion of marks to be awarded to the 

 different di\'isions was one which was found in practice very diflicult to carry 

 out, even appro.\imateIy. 



