In 1819 Peacock, who was again moderator, induced his colleague to adopt the new notation. It was employed in the next year by Whewell, and in the following year by Peacock again. Henceforth [292] ]the calculus in its modern language and analytical methods were freely used, new subjects were introduced, and for many years the examination provided a mathematical training fairly abreast of the times.
By this time the disputations had ceased to have any immediate effect on a man’s place in the tripos. Thus Whewell[64], writing about his duties as moderator in 1820, said:
You would get very exaggerated ideas of the importance attached to it [an Act] if you were to trust Cumberland; I believe it was formerly more thought of than it is now. It does not, at least immediately, produce any effect on a man’s place in the tripos, and is therefore considerably less attended to than used to be the case, and in most years is not very interesting after the five or six best men: so that I look for a considerable exercise of, or rather demand for, patience on my part. The other part of my duty in the Senate House consists in manufacturing wranglers, senior optimes, etc. and is, while it lasts, very laborious.
Of the examination itself in this year he wrote as follows[65]:
The examination in the Senate House begins to-morrow, and is rather close work while it lasts. We are employed from seven in the morning till five in the evening in giving out questions and receiving written answers to them; and when that is over, we have to read over all the papers which [293] ]we have received in the course of the day, to determine who have done best, which is a business that in numerous years has often kept the examiners up the half of every night; but this year is not particularly numerous. In addition to all this, the examination is conducted in a building which happens to be a very beautiful one, with a marble floor and a highly ornamented ceiling; and as it is on the model of a Grecian temple, and as temples had no chimneys, and as a stove or a fire of any kind might disfigure the building, we are obliged to take the weather as it happens to be, and when it is cold we have the full benefit of it—which is likely to be the case this year. However, it is only a few days, and we have done with it.
A sketch of the examination in the previous year from the point of view of an examinee was given by J. M. F. Wright[66], but there is nothing of special interest in it.
Sir George B. Airy[67] gave the following sketch of his recollections of the reading and studies of undergraduates of his time and of the tripos of 1823, in which he had been senior wrangler:
At length arrived the Monday morning on which the examination for the B.A. degree was to begin.... We were all marched in a body to the Senate-House and placed in the hands of the Moderators. How the “candidates for honours” were separated from the οἱ πολλοί I do not know, I presume that the Acts and the Opponencies had something to do with it. The honour candidates were divided into [294] ]six groups: and of these Nos. 1 and 2 (united), Nos. 3 and 4 (united), and Nos. 5 and 6 (united), received the questions of one Moderator. No. 1, Nos. 2 and 3 (united), Nos. 4 and 5 (united), and No. 6, received those of the other Moderator. The Moderators were reversed on alternate days. There were no printed question-papers: each examiner had his bound manuscript of questions, and he read out his first question; each of the examinees who thought himself able proceeded to write out his answer, and then orally called out “Done.” The Moderator, as soon as he thought proper, proceeded with another question. I think there was only one course of questions on each day (terminating before 3 o’clock, for the Hall dinner). The examination continued to Friday mid-day. On Saturday morning, about 8 o’clock, the list of honours (manuscript) was nailed on the door of the Senate House.
It must be remembered that for students pursuing the normal course the senate-house examination still provided the only avenue to a degree. That examination involved a knowledge of the elements of moral philosophy and theology, an acquaintance with the rules of formal logic, and the power of reading and writing scholastic Latin, but mathematics was the predominant subject, and this led to a certain one-sidedness in education. The evil of this was generally recognized, and in 1822 various reforms were introduced in the university curriculum; in particular the Previous Examination was established for students in their second year, the subjects being prescribed Greek and Latin works, [295] ]a Gospel, and Paley’s Evidences. Set classical books were introduced in the final examination of poll-men; and another honour or tripos examination was established for classical students. These alterations came into effect in 1824; and henceforth the senate-house examination, so far as it related to mathematical students, was known as the Mathematical Tripos.
In 1827 the scheme of examination in the mathematical tripos was revised. By regulations[68] which came into operation in January 1828, four days, exclusive of the day of arranging the brackets, were devoted to the examination; the number of hours of examination was twenty-three, of which seven were assigned to problems. On the first two days all the candidates had the same questions proposed to them, inclusive of the evening problems, and the examination on those days excluded the higher and more difficult parts of mathematics, in order, in the words of the report, “that the candidates for honours may not be induced to pursue the more abstruse and profound mathematics, to the neglect of more elementary knowledge.” Accordingly, only such questions as could be solved without the aid of the differential calculus were set on the first day, and those set on the second day involved only its elementary applications. The classes were reduced [296] ]to four, determined as before by the exercises in the schools.