Jebb’s statement about the number of wranglers and senior optimes is only approximate.
It may be added that it was now frankly recognized that the examination was competitive[45]. Also that though it was open to any member of the senate to take part in it, yet the determination of the relative merit of the students was entirely in the [271] ]hands of the moderators[46]. Although the examination did not occupy more than three days it must have been a severe physical trial to anyone who was delicate. It was held in winter and in the senate-house: that building was then noted for its draughts, and was not warmed in any way; and, according to tradition, on one occasion the candidates on entering in the morning found the ink frozen in the pots on their desks.
The University was not altogether satisfied[47] with the regulations, and in 1779[48] the scheme of examination was amended in various respects. In particular the examination was extended to four days, a third day being given up entirely to natural religion, moral philosophy, and Locke’s Essay. It was further announced[49] that a candidate would not receive credit for advanced subjects unless he had satisfied the examiners in Euclid’s Elements and elementary natural philosophy.
A system of brackets or “classes quam minimae” was now introduced. Under this system the examiners issued on the morning of the fourth day a provisional list of men who had obtained honours, with the names of those of about equal merit bracketed, and that day was devoted to arranging [272] ]the names in each bracket in order of merit: the examiners being given explicit authority to invite the assistance of others in this work. Whether at this time a candidate could request to be re-examined with the view of being moved from one bracket to another is uncertain, but later this also was allowed.
The number of examiners was also increased to four, the moderators of one year becoming, as a matter of course, the examiners of the next. Thus of the four examiners in each year, two had taken part in the examination of the previous year, and the continuity of the system of examination was maintained. The names of the moderators appear on the tripos lists, but the names of the examiners were not printed on the lists till some years later.
The right of any master of arts to take part in the examination was not affected, though henceforth it was exercised more sparingly, and I believe was not insisted on after 1785. But it became a regular custom for the moderators to invite particular residents to examine and compare specified candidates: Milner, of Queens’, was constantly asked to assist in this way.
It was not long before it became an established custom that a candidate, who was dissatisfied with the class in which he had been placed as the result [273] ]of his disputations, might challenge it before the examination began. This power seems to have been used but rarely; it was, however, a recognition of the fact that a place in the tripos list was to be determined by the senate-house examination alone, and the examiners soon acquired the habit of settling the preliminary classes without exclusive reference to the previous disputations.
The earliest extant paper actually set in the senate-house, to which we can with certainty refer, is a problem paper set in 1785 or 1786 by W. Hodson, of Trinity, then a proctor. The autograph copy from which he gave out the questions was luckily preserved, and is in the library[50] of Trinity College. It must be almost the last problem paper which was dictated, instead of being printed and given as a whole to the candidates. The paper is as follows:
1. To determine the velocity with which a Body must be thrown, in a direction parallel to the Horizon, so as to become a secondary planet to the Earth; as also to describe a parabola, and never return.
2. To demonstrate, supposing the force to vary as 1 / D² how far a body must fall both within and without the Circle to acquire the Velocity with which a body revolves in a Circle.
[274]
]3. Suppose a body to be turned (sic) upwards with the Velocity with which it revolves in an Ellipse, how high will it ascend? The same is asked supposing it to move in a parabola.4. Suppose a force varying first as 1 / D³, secondly in a greater ratio than 1 / D² but less than 1 / D³, and thirdly in a less ratio than 1 / D², in each of these Cases to determine whether at all, and where the body parting from the higher Apsid will come to the lower.
5. To determine in what situation of the moon’s Apsid they go most forwards, and in what situation of her Nodes the Nodes go most backwards, and why?
6. In the cubic equation x³ + qx + r = 0 which wants the second term; supposing x = a + b and 3ab = −q, to determine the value of x. (sic.)
7. To find the fluxion of xr × (yn + zm)1/q.
8. To find the fluent of aẋ / (a + x).
9. To find the fluxion of the mth power of the Logarithm of x.
10. Of right-angled Triangles containing a given Area to find that whereof the sum of the two legs AB + BC shall be the least possible. [This and the two following questions are illustrated by diagrams. The angle at B is the right angle.]
11. To find the Surface of the Cone ABC. [The cone is a right one on a circular base.]
12. To rectify the arc DB of the semicircle DBV.
In cases of equality in the senate-house examination, the acts were still taken into account in settling [275] ]the tripos order: and in 1786, when the second, third, and fourth wranglers came out equal in the examination, a memorandum was published that the second place was given to that candidate who dialectis magis est versatus, and the third place to that one who in scholis sophistarum melius disputavit.