The (almost really) Complete Works of Lewis Carroll

To be Submitted to Congregation on Oct. 27, 1885

If, as will be generally admitted, the Proctorship is a dignity coveted by many members of this University, it is surely axiomatic that one’s chance of attaining to it should depend on personal fitness for it—not on the mere accidental circumstance of belonging to a large or small College. Yet the proposed scheme would actually make one’s chance vary inversly as the size of the College! For example, Keble College, with 120 members of Convocation and 5 of Congregation, is to have as many turns as Exeter with 471 members of Convocation and 22 of Congregation, so that each member of the smaller College will have four times as good a chance of being made Proctor as a member of the larger would have!

The obvious way to avoid this anomaly is to give to each College turns, in electing a Proctor, which shall be in proportion to its size. The now rejected Cycle was made on that principle: and, because in some details it was open to objection, it is proposed to abandon its principle, and to substitute one as crude, and as absurd in its results, as could well be imagined.

The chief objection, brought against the rejected Cycle, seems to be that it takes account of the number of Undergraduates in a College—which is considered to be an irrelevant matter. This seems to be a fair objection: but surely we need not reject, on its account, the whole well-established principle on which a Cycle should be calculated. The number of turns, assigned to a College, should clearly be proportioned to the number of its members who are eligible as Proctors. And I think no great injustice will be done if we assume this number to vary as the number of its members who are members of Convocation.

In the following 30-year Cycle, this principle has been adopted, and the reader can see for himself, by inspecting the table which follows it, that turns assigned are, as nearly as possible, proportional to the number of members of Convocation. The number of turns, assigned by the Cycle of 1859, are added in parentheses.

The foregoing Cycle has not been arranged at random, but the claims of the various Colleges have been estimated for each year, allowing a claim to be stronger in proportion to the number of turns the College is to have in the Cycle, and also in proportion to the number of years it has been waiting for a turn.

Though I am not offering this scheme for a Cycle with any idea of its being proposed for adoption in its present form, yet I hope that what I have said may induce many members of Congregation to pause before they assent to the adoption of a Cycle so utterly unjust and unreasonable as the one to be considered next Tuesday.

Postscript

Addressed to Mathematicians Only

It will, I think, be satisfactory to mathematical readers to know the details of the process by which I calculated the foregoing Cycle.

First, I divided 5473, the total number of members of Convocation, by 60, the total number of “turns” in a 30-year Cycle, which gave 91 as quotient. It seemed reasonable, then, that each College should have one turn assigned to it for every 91 members of Convocation it possessed. So I divided these numbers by 91. The quotients are as follows:—

The number of turns assigned is, in all but 4 cases, the nearest integer to the quotient so obtained. The excepted cases are:—

Here the integer, assigned to Ch. Ch., is 2 less than it should be; while the other 3 integers are 1 too great. But they are so similar that, if one be lowered, all must be; and, though we could then give Ch. Ch. its proper integer, 8, we should have an extra turn to dispose of, which could not be anywhere assigned without injustice. Moreover, I think Ch. Ch. has so exceptional a number of members of Convocation on its books that it is reasonable to ignore much of this excess, and it may well be content to have one turn more than any other College.

Having settled the number of turns each College should have, I calculated, for each College, and for each year in the Cycle, a “claiming number,” and assigned “turns” to the two Colleges whose “claiming numbers” stood highest for the year. In calculating them, I assumed that, where two Colleges have the same number of “turns” assigned to them, that one, which has been longer without a turn, has the higher claim; and that, where two Colleges have been waiting equally long, that one, which has the greater number of turns assigned to it, has the higher claim. Hence, since both these elements are variable, I took their product as the claiming number. It was of course necessary, in commencing the Cycle, to assign fictious periods of waiting to Keble and the Non-Collegiates, who have not as yet had turns at all. For this purpose I took the average of all the other periods of waiting.

In most of the years I found two of the “claiming numbers” greater than all the rest, so that it was clear which Colleges ought to have the turns. The excepted cases were as follows:—

In 1896, Ch. Ch. stood first with “30,” while B. N. C. and S. John’s came next with “28” each. I could not settle the question, of which to take, by actual numbers of members of Convocation, as these are exactly equal: so I took into account the fact that, at the beginning of the Cycle, S. John’s had been waiting one year longer than B. N. C. But, to be quite fair to B. N. C., I reckoned as claim, in subsequent years, as if it had been waiting since 1896, instead of 1897.

In 1905, Licoln and Merton stood equal for the second place, with “26” each. Here I gave Merton the preference, as having more members of Convocation. I observed the same principle in 1914 and 1916.

Lastly, in 1918, I assigned a turn to Jesus College, with a “claiming number” 30, rather than to either B. N. C. or S. John’s, with “32” each: this was simply because it had not yet had a turn at all, while all the other Colleges had had their proper numbers.

If the calculation were carried on into 1919, B. N. C. and S. John’s would have the two turns, as they have in 1889. Thus the Cycle would begin again.

It might be found necessary, in order to make due allowance for the variying numbers of members in Colleges, to make a fresh calculation at less intervals than 30 years, e. g. every five years.