[301]
]In the same year as these regulations came into force, a Board of Mathematical Studies (consisting of the mathematical professors, with the moderators and examiners for the current year and the two preceding years) was constituted[75] by the senate. From that time forward their minutes supply a permanent record of the changes gradually introduced into the tripos. I do not allude to subsequent changes which only concern unimportant details of the examination.
In May 1849, the board issued a report in which, after giving a review of the past and existing state of the mathematical studies in the University, they recommended that the mathematical theories of electricity, magnetism, and heat should not be admitted as subjects of examination. In the following year they issued a second report, in which they recommended the omission of elliptic integrals, Laplace’s coefficients, capillary attraction, and the figure of the earth considered as heterogeneous, as well as a definite limitation of the questions in the lunar and planetary theories. In making these recommendations the board were only recognizing what had become the practice in the examination.
I may, in passing, mention a curious attempt which was made in 1853 and 1854 to assist candidates to estimate the relative difficulty of the [302] ]questions asked. This was effected by giving to the candidates, at the same time as the examination paper, a slip of paper on which the marks assigned for the bookwork
and rider for each question were printed. I mention the fact merely because these things are rapidly forgotten and not because it is of any intrinsic value. I possess a complete set of slips which came to me from Todhunter.
In 1856 there was an amusing difference of opinion between the vice-chancellor and the moderators. The vice-chancellor issued a notice to say that for the convenience of the University he had directed the tripos lists to be published at 8.0 a.m. as well as at 9.0 a.m., but when members of the senate arrived at 8.0 the moderators said that the list should not be read until 9.0.
Considerable changes in the scheme of examination were introduced in 1873. On 5 December 1865, the board had recommended the addition of Laplace’s coefficients and the figure of the earth considered as heterogeneous as subjects of the examination; the report does not seem to have been brought before the senate, but attention was called to the fact that certain departments of mathematics and mathematical physics found no place in the tripos schedules, and were neglected by most students. Accordingly, a syndicate was appointed on 6 June 1867, to consider the matter, and a scheme drawn [303] ]up by them was approved in 1868[76] and came into effect in 1873.
The new scheme of examination was framed on the same lines as that of 1848. The subjects in the first three days were left unchanged, but an extra day was added, devoted to the elements of mathematical physics. The essence of the modification was the greatly extended range of subjects introduced into the schedule of subjects for the last five days, and their arrangement in divisions; the total marks awarded to the questions in each of the five divisions being approximately in a proportion to the total marks assigned to the questions in the first three days as 2, 1, 1, 1, 2/3 to 1 respectively. Under these regulations the number of examiners was increased from four to five.
The assignment of marks to groups of subjects was made under the impression that the best candidates would concentrate their abilities on a selection of subjects from the various divisions. But 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: while the wide range of subjects rendered it practically impossible to [304] ]cover all the ground thoroughly in the time allowed. The failure was so pronounced that in 1877 another syndicate was appointed to consider the mathematical studies and examinations of the University. They presented an elaborate scheme, but on 13 May 1878, some of the most important parts of it were rejected; their subsequent proposals, accepted on 21 November 1878 (by 62 to 49), represented a compromise which pleased few members of the senate[77].
Under the new scheme which came into force in 1882 the tripos was divided into two portions: the first portion was taken at the end of the third year of residence, the range of subjects being practically the same as in the regulations of 1848, and the result brought out in the customary order of merit. The second portion was held in the following January, and was open only to those who had been wranglers in the preceding June. This portion was confined to higher mathematics and appealed chiefly to specialists: the result was brought out in three classes, each arranged in alphabetical order. The moderators and examiners conducted the whole examination without any extraneous aid.
In the next year or two further amendments [305] ]were made[78], the second part of the examination being moved to the June of the fourth year, and thrown open to all men who had graduated in the tripos of the previous June. At the same time the conduct of the examination in part II was transferred to four examiners nominated by the board: this put it largely under the control of the professors. The range of subjects of part II was also greatly extended, and candidates were encouraged to select only a few of them. It was further arranged that part I might be taken at the end of a man’s second year of residence, though in that case it would not qualify for a degree. A student who availed himself of this leave could take part II at the end either of his third or of his fourth year as he pleased.