Cambridge Papers

by W. W. Rouse Ball

The regulations of 1827 definitely prescribed that all the papers should be printed. They are also noticeable as being the last which gave the examiners power to ask vivâ voce questions, though such questions “were restricted to asking about propositions contained in the mathematical works commonly in use at the University, or examples and explanations of such propositions.” It was further recommended that no paper should contain more questions than well-prepared students could be expected to answer within the time allowed for it, but that if any candidate, before the end of the time, had answered all the questions in the paper, the examiners might propose additional questions vivâ voce. The power of granting honorary optime degrees now ceased; it had already fallen into abeyance. Henceforth the examination was conducted under definite rules, and I no longer concern myself with its traditions.

In the same year as these changes became effective the examination for the poll degree was separated from the tripos with different sets of papers and a different schedule of subjects^[69]. It was, however, still nominally considered as forming part of the senate-house examination, and until 1858 those [297] ]who obtained a poll degree were arranged in four classes, described as fourth, fifth, sixth, and seventh, as if in continuation of the junior optimes or third class of the tripos.

In the course henceforth ordained for the poll or ordinary degree, the examination, later known as “the General,” represents that part of the old senate-house examination which was intended for the poll-men, but gradually it was moved to an earlier period in the normal course taken by the men. In 1851 admission to the classical tripos^[70] was allowed to others than those who passed the mathematical tripos, and this provided another avenue to a degree entirely independent of the old senate-house examination. In 1852 another set of examinations, at first called “the Professor’s Examinations,” and now somewhat modified and known as “the Specials,” was instituted for all poll-men to take before they could qualify for a degree.

In 1858 the fiction that the poll examinations were part of the senate-house examination was abandoned, and subsequently they have been treated as providing an independent method of obtaining the degree: thus now the mathematical tripos is the sole representative of the old senate-house examination. Since 1858 numerous other [298] ]ways of obtaining a degree in arts have been established, and it is now possible to graduate by showing proficiency in very special, or even technical subjects.

Further changes in the mathematical tripos were introduced in 1833^[71]. The duration of the examination, before the issue of the brackets, was extended to five days, and the number of hours of examination on each day was fixed at five and a half: seven and a half hours were assigned to problems. The examination on the first day was confined to subjects that did not require the differential calculus, and only the simplest applications of the calculus were permitted on the second and third days. During the first four days of the examination the same papers were set to all the candidates alike, but on the fifth day the examination was conducted according to classes. No reference was made to vivâ voce questions, though permission was reserved to re-examine candidates if it were found necessary: this right remained in force till 1848, but in fact was never used. In December 1834, a few unimportant details were amended.

Mr Earnshaw, the senior moderator in 1836, informed me that he believed that the tripos of that year was the earliest one in which all the papers were marked, and that in previous years the [299] ]examiners had partly relied on their impression of the answers given.

New regulations came into force^[72] in 1839. The examination now lasted for six days, and continued as before for five hours and a half each day: eight and a half hours were assigned to problems. Throughout the whole examination the same papers were set to all candidates, and no reference was made to any preliminary classes. It was no doubt in accordance with the spirit of these changes that the acts in the schools should be abolished, but they were discontinued by the moderators of 1839 without the authority of the senate. The examination was for the future confined^[73] to mathematics.

In the same year in which the new scheme came into force a proposal to reopen the subject was rejected on 6 March 1839.

The difficulty of bringing professorial lectures into relation with the needs of students has more than once been before the University. The desirability of it was emphasized by a syndicate in February 1843, which recommended conferences at stated intervals between the mathematical professors [300] ]and examiners. This report, which foreshadowed the creation of a Mathematical Board, was rejected by the senate on 31 March.

A few years later the scheme of the examination was again reconstructed by regulations^[74] which came into effect in 1848. The duration of the examination was extended to eight days. The examination lasted in all forty-four and a half hours, twelve of which were devoted to problems. The first three days were assigned to specified elementary subjects; in the papers set on these days riders were to be set as well as bookwork, but the methods of analytical geometry and the calculus were excluded. After the first three days there was a short interval, at the end of which the examiners issued a list of those who had so acquitted themselves as to deserve mathematical honours. Only those whose names were contained in this list were admitted to the last five days of the examination, which was devoted to the higher parts of mathematics. After the conclusion of the examination the examiners, taking into account the whole eight days, brought out the list arranged in order of merit. No provision was made for any rearrangement of this list corresponding to the examination of the brackets. The arrangements of 1848 remained in force till 1873.