"On Feb. 11th I gave Mr Peac.o.c.k a paper on the alteration of the focal length of a telescope as directed with or against the Earth's...o...b..tal motion (on the theory of emissions) which was written out for reading to the Cambridge Philosophical Society on Feb. 24th and 25th. [This Society I think was then about a year old.] On Feb. 1 my MS. on Precession, Solar Inequality, and Nutation, was made complete.

"The important examination for Scholarships was now approaching. As I have said, this one opportunity only was given to Sizars (Pensioners having always two opportunities and sometimes three), and it is necessary to be a Scholar in order to be competent to be a candidate for a Fellowship. On Apr. 10th I addressed my formal Latin letter to the Seniors. There were 13 vacancies and 37 candidates. The election took place on Apr. 18th, 1822. I was by much the first (which I hardly expected) and was complimented by the Master and others. Wrote the formal letter of thanks as usual. I was now ent.i.tled to claim better rooms, and I took the rooms on the ground floor on the East side of the Queen's Gate of the Great Court. Even now I think of my quiet residence in the little rooms above the staircase in Neville's Court with great pleasure. I took possession of my new rooms on May 27th.

"The Annual Examination began on May 30th. The Cla.s.ses were published on June 5th, when my name was separated from the rest by two lines. It was understood that the second man was Drinkwater, and that my number of marks was very nearly double of his. Having at this time been disappointed of a proposed walking excursion into Derbyshire with a college friend, who failed me at the last moment, I walked to Bury and spent a short holiday there and at Playford.

"I returned to Cambridge on July 12th, 1822. I was steadily busy during this Long Vacation, but by no means oppressively so: indeed my time pa.s.sed very happily. The Scholars' Table is the only one in College at which the regular possessors of the table are sure never to see a stranger, and thus a sort of family intimacy grows up among the Scholars. Moreover the Scholars feel themselves to be a privileged cla.s.s 'on the foundation,' and this feeling gives them a sort of conceited happiness. It was the duty of Scholars by turns to read Grace after the Fellows' dinner and supper, and at this time (1848) I know it by heart. They also read the Lessons in Chapel on week days: but as there was no daily chapel-service during the summer vacation, I had not much of this. In the intimacy of which I speak I became much acquainted with Drinkwater, Buckle, Rothman, and Sutcliffe: and we formed a knot at the table (first the Undergraduate Scholars' table, and afterwards the Bachelor Scholars' table) for several years. During this Vacation I had for pupils Buckle and Gibson.

"I wrote my daily Latin as usual, beginning with the retranslation of Cicero's Epistles, but I interrupted it from Sept. 27th to Feb. 8th. I believe it was in this Vacation, or in the October term, that I began every evening to read Thucydides very carefully, as my notes are marked 1822 and 1823. On August 27 I find that I was reading Ovid's Fasti.

"In Mathematics I find the equation x + y = a, x^q + y^q = b, Caustics, Calculus of Variations, Partial Differentials, Aberration of Light, Motions of Comets, various Optical constructions computed with spherical aberrations, Particular Solutions, Mechanics of Solid Bodies, Attractions of Sh.e.l.ls, Chances, Ivory's attraction-theorem, Lunar Theory (algebraical), Degrees across meridian, theoretical refraction, Newton's 3rd Book, Investigation of the tides in a shallow equatoreal ca.n.a.l, from which I found that there would be low-water under the moon, metacentres, rotation of a solid body round three axes, Attractions of Spheroids of variable density, finite differences, and complete Figure of the Earth. There is also a good deal of investigation of a mathematical nature not connected with College studies, as musical chords, organ-pipes, sketch for a computing machine (suggested by the publications relating to Babbage's), sketch of machine for solving equations. In August there is a plan of a MS. on the Differential Calculus, which it appears I wrote then: one on the Figure of the Earth written about August 15th; one on Tides, Sept. 25th; one on Newton's Principia with algebraical additions, Nov. 1st. On Sept. 6th and 10th there are Lunar Distances observed with Rothman's s.e.xtant and completely worked out; for these I prepared a printed skeleton form, I believe my first. On December 13th there are references to books on Geology (Conybeare and Phillips, and Parkinson) which I was beginning to study. On July 27th, being the day on which I completed my 21st year, I carefully did nothing.

"Another subject partly occupied my thoughts, which, though not (with reference to practical science) very wise, yet gave me some Cambridge celebrity. In July 1819 I had (as before mentioned) sketched a plan for constructing reflecting telescopes with silvered gla.s.s, and had shewn it afterwards to Mr Peac.o.c.k. I now completed the theory of this construction by correcting the aberrations, spherical as well as chromatic. On July 13th, 1822, I drew up a paper about it for Mr Peac.o.c.k. He approved it much, and in some way communicated it to Mr (afterwards Sir John) Herschel. I was soon after introduced to Herschel at a breakfast with Mr Peac.o.c.k: and he approved of the scheme generally. On August 5th I drew up a complete mathematical paper for the Cambridge Philosophical Society, which I entrusted to Mr Peac.o.c.k. The aberrations, both spherical and chromatic, are here worked out very well. On Nov. 25th it was read at the meeting of the Philosophical Society, and was afterwards printed in their Transactions: this was my first printed Memoir. Before this time however I had arranged to try the scheme practically. Mr Peac.o.c.k had engaged to bear the expense, but I had no occasion to ask him. Partly (I think) through Drinkwater, I communicated with an optician named Bancks, in the Strand, who constructed the optical part. I subsequently tried my telescope, but it would not do. The fault, as I had not and have not the smallest doubt, depends in some way on the crystallization of the mercury silvering. It must have been about this time that I was introduced to Mr (afterwards Sir James) South, at a party at Mr Peac.o.c.k's rooms. He advised me to write to Tulley, a well-known practical optician, who made me some new reflectors, &c. (so that I had two specimens, one Gregorian, the other Ca.s.segrainian). However the thing failed practically, and I was too busy ever after to try it again.

"During the October term I had no pupils. I kept my second Act on Nov. 6 (opponents Hamilton, Rusby, Field), and an Opponency against Jeffries on Nov. 7. I attended the Questionists' Examinations. I seem to have lived a very comfortable idle life. The Commemoration Day was Dec. 18th, when I received a Prize, and the next day I walked to Bury. On Jan. 4th, 1823, I returned to Cambridge, and until the B.A. Examination I read novels and played cards more than at any other time in College.

"On Thursday, Jan. 9th, 1823, the preliminary cla.s.ses, for arrangement of details of the B.A. Examination, were published. The first cla.s.s, Airy, Drinkwater, Jeffries, Mason. As far as I remember, the rule was then, that on certain days the cla.s.ses were grouped (in regard to ident.i.ty of questions given to each group) thus: 1st, {2nd/3rd}, {4th/5th} &c., and on certain other days thus: {1st/2nd}, {3rd/4th}, &c. On Sat.u.r.day, Jan. 11th, I paid fees. On Monday, Jan. 13th, the proceedings of examination began by a breakfast in the Combination Room. After this, Gibson gave me breakfast every day, and Buckle gave me and some others a gla.s.s of wine after dinner. The hours were sharp, the season a cold one, and no fire was allowed in the Senate House where the Examination was carried on (my place was in the East gallery), and altogether it was a severe time.

"The course of Examination was as follows:

"Monday, Jan. 13th. 8 to 9, printed paper of questions by Mr Hind (moderator); half-past 9 to 11, questions given orally; 1 to 3, ditto; 6 to 9, paper of problems at Mr Higman's rooms.

"Tuesday, Jan. 14th. 8 to 9, Higman's paper; half-past 9 to 11, questions given orally; 1 to 3, ditto; 6 to 9, paper of problems in Sidney College Hall.

"Wednesday, Jan. 15th. Questions given orally 8 to 9 and 1 to 3, with paper of questions on Paley and Locke (one question only in each was answered).

"Thursday, Jan. 16th. We went in at 9 and 1, but there seems to have been little serious examination.

"Friday, Jan. 17. On this day the brackets or cla.s.ses as resulting from the examination were published, 1st bracket Airy, 2nd bracket Jeffries, 3rd bracket Drinkwater, Fisher, Foley, Mason, Myers.

"On Sat.u.r.day, Jan. 18th, the degrees were conferred in the usual way. It had been arranged that my brother and sister should come to see me take my degree of B.A., and I had asked Gibson to conduct them to the Senate House Gallery: but Mr Hawkes (a Trinity Fellow) found them and stationed them at the upper end of the Senate House. After the preliminary arrangements of papers at the Vice-Chancellor's table, I, as Senior Wrangler, was led up first to receive the degree, and rarely has the Senate House rung with such applause as then filled it. For many minutes, after I was brought in front of the Vice-Chancellor, it was impossible to proceed with the ceremony on account of the uproar. I gave notice to the Smith's Prize Electors of my intention to 'sit' for that prize, and dined at Rothman's rooms with Drinkwater, Buckle, and others. On Monday, Jan. 20th, I was examined by Professor Woodhouse, for Smith's Prize, from 10 to 1. I think that the only compet.i.tor was Jeffries. On Tuesday I was examined by Prof. Turton, 10 to 1, and on Wednesday by Prof. Lax, 10 to 1. On Thursday, Jan. 23rd, I went to Bury by coach, on one of the coldest evenings that I ever felt.

"Mr Peac.o.c.k had once recommended me to sit for the Chancellor's medal (Cla.s.sical Prize). But he now seemed to be cool in his advice, and I laid aside all thought of it."

It seems not out of place to insert here a copy of some "Cambridge Reminiscences" written by Airy, which will serve to explain the Acts and Opponencies referred to in the previous narrative, and other matters.

THE ACTS.

The examination for B.A. degrees was preceded, in my time, by keeping two Acts, in the Schools under the University Library: the second of them in the October term immediately before the examination; the first (I think) in the October term of the preceding year.

These Acts were reliques of the Disputations of the Middle Ages, which probably held a very important place in the discipline of the University. (There seems to be something like them in some of the Continental Universities.) The presiding authority was one of the Moderators. I apprehend that the word "Moderator" signified "President," in which sense it is still used in the Kirk of Scotland; and that it was peculiarly applied to the Presidency of the Disputations, the most important educational arrangement in the University. The Moderator sent a summons to the "Respondent" to submit three subjects for argument, and to prepare to defend them on a given day: he also named three Opponents. This and all the following proceedings were conducted in Latin. For my Act of 1822, Nov. 6, I submitted the following subjects:

"Recte statuit Newtonus in Principiis suis Mathematicis, libro primo, sectione undecima."

"Recte statuit Woodius de Iride."

"Recte statuit Paleius de Obligationibus."

The Opponents named to attack these a.s.sertions were Hamilton of St John's, Rusby of St Catharine's, Field of Trinity. It was customary for the Opponents to meet at tea at the rooms of the Senior Opponent, in order to discuss and arrange their arguments; the Respondent was also invited, but he was warned that he must depart as soon as tea would be finished: then the three Opponents proceeded with their occupation. As I have acted in both capacities, I am able to say that the matter was transacted in an earnest and business-like way. Indeed in the time preceding my own (I know not whether in my own time) the a.s.sistance of a private tutor was frequently engaged, and I remember hearing a senior M.A. remark that my College Tutor (James D. Hustler) was the best crammer for an Act in the University.

At the appointed time, the parties met in the Schools: the Respondent first read a Latin Thesis on any subject (I think I took some metaphysical subject), but n.o.body paid any attention to it: then the Respondent read his first Dogma, and the first Opponent produced an argument against it, in Latin. After this there were repeated replies and rejoinders, all in viva voce Latin, the Moderator sometimes interposing a remark in Latin. When he considered that one argument was disposed of, he called for another by the words "Probes aliter."

The arguments were sometimes shaped with considerable ingenuity, and required a clear head in the Respondent. When all was finished, the Moderator made a complimentary remark to the Respondent and one to the first Opponent (I forget whether to the second and third). In my Respondency of 1822, November 6, the compliment was, "Quaestiones tuas summo ingenio et ac.u.mine defendisti, et in rebus mathematicis scientiam plane mirabilem ostendisti." In an Opponency (I forget when) the compliment was, "Magno ingenio argumenta tua et construxisti et defendisti."

The Acts of the high men excited much interest among the students. At my Acts the room was crowded with undergraduates.

I imagine that, at a time somewhat distant, the maintenance of the Acts was the only regulation by which the University acted on the studies of the place. When the Acts had been properly kept, license was given to the Father of the College to present the undergraduate to the Vice-Chancellor, who then solemnly admitted him "ad respondendum Quaestioni." There is no appearance of collective examination before this presentation: what the "Quaestio" might be, I do not know. Still the undergraduate was not B.A. The Quaestio however was finished and approved before the day of a certain Congregation, and then the undergraduate was declared to be "actualiter in artibus Baccalaureum."

Probably these regulations were found to be insufficient for the control of education, and the January examination was inst.i.tuted. I conjecture this to have been at or shortly before the date of the earliest Triposes recorded in the Cambridge Calendar, 1748.

The increasing importance of the January examination naturally diminished the value of the Acts in the eyes of the undergraduates; and, a few years after my M.A. degree, it was found that the Opponents met, not for the purpose of concealing their arguments from the Respondent, but for the purpose of revealing them to him. This led to the entire suppression of the system. The most active man in this suppression was Mr Whewell: its date must have been near to 1830.

The shape in which the arguments were delivered by an Opponent, reading from a written paper, was, "Si (quoting something from the Respondent's challenge), &c., &c. Cadit Quaestio; Sed (citing something else bearing on the subject of discussion), Valet Consequentia; Ergo (combining these to prove some inaccuracy in the Respondent's challenge), Valent Consequentia et Argumentum." n.o.body pretended to understand these mystical terminations.

Apparently the original idea was that several Acts should be kept by each undergraduate; for, to keep up the number (as it seemed), each student had to gabble through a ridiculous form "Si quaestiones tuae falsae sint, Cadit Quaestio:--sed quaestiones tuae falsae sunt, Ergo valent Consequentia et Argumentum." I have forgotten time and place when this was uttered.

THE SENATE-HOUSE EXAMINATION.

The Questionists, as the undergraduates preparing for B.A. were called in the October term, were considered as a separate body; collected at a separate table in Hall, attending no lectures, but invited to attend a system of trial examinations conducted by one of the Tutors or a.s.sistant-Tutors.

From the Acts, from the annual College examinations, and (I suppose) from enquiries in the separate Colleges, the Moderators acquired a general idea of the relative merits of the candidates for honours. Guided by this, the candidates were divided into six cla.s.ses. The Moderators and a.s.sistant Examiners were provided each with a set of questions in ma.n.u.script (no printed papers were used for Honours in the Senate House; in regard to the [Greek: hoi polloi] I cannot say). On the Monday on which the examination began, the Father of the College received all the Questionists (I believe), at any rate all the candidates for honours, at breakfast in the Combination Room at 8 o'clock, and marched them to the Senate House. My place with other honour-men was in the East Gallery. There one Examiner took charge of the 1st and 2nd cla.s.ses united, another Examiner took the 3rd and 4th cla.s.ses united, and a third took the 5th and 6th united. On Tuesday, one Examiner took the 1st cla.s.s alone, a second took the 2nd and 3rd cla.s.ses united, a third took the 4th and 5th cla.s.ses united, and a fourth took the 6th cla.s.s alone. On Wednesday, Thursday, and Friday the changes were similar. And, in all, the questioning was thus conducted. The Examiner read from his ma.n.u.script the first question. Those who could answer it proceeded to write out their answers, and as soon as one had finished he gave the word "Done"; then the Examiner read out his second question, repeating it when necessary for the understanding by those who took it up more lately. And so on. I think that the same process was repeated in the afternoon; but I do not remember precisely. In this manner the Examination was conducted through five days (Monday to Friday) with no interruption except on Friday afternoon. It was princ.i.p.ally, perhaps entirely, bookwork.

But on two _evenings_ there were printed papers of problems: and the examination in these was conducted just as in the printed papers of the present day: but in the private College Rooms of the Moderators. And there, wine and other refreshments were offered to the Examinees. How this singular custom began, I know not.

The order of merit was worked out on Friday afternoon and evening, and was in some measure known through the University late in the evening. I remember Mr Peac.o.c.k coming to a party of Examinees and giving information on several places. I do not remember his mentioning mine (though undoubtedly he did) but I distinctly remember his giving the Wooden Spoon. On the Sat.u.r.day morning at 8 o'clock the ma.n.u.script list was nailed to the door of the Senate-House. The form of further proceedings in the presentation for degree (ad respondendum quaestioni) I imagine has not been much altered. The kneeling before the Vice-Chancellor and placing hands in the Vice-Chancellor's hands were those of the old form of doing homage.

The form of examination which I have described was complicated and perhaps troublesome, but I believe that it was very efficient, possibly more so than the modern form (established I suppose at the same time as the abolition of the Acts). The proportion of questions now answered to the whole number set is ridiculously small, and no accurate idea of relative merit can be formed from them.

THE COLLEGE HALL.

When I went up in 1819, and for several years later, the dinner was at 1/4 past 3. There was no supplementary dinner for special demands. Boat-clubs I think were not invented, even in a plain social way, till about 1824 or 1825; and not in connection with the College till some years later. Some of the senior Fellows spoke of the time when dinner was at 2, and regretted the change.

There was supper in Hall at 9 o'clock: I have known it to be attended by a few undergraduates when tired by examinations or by evening walks; and there were always some seniors at the upper table: I have occasionally joined them, and have had some very interesting conversations. The supper was cold, but hot additions were made when required.

One little arrangement amused me, as shewing the ecclesiastical character of the College. The Fasts of the Church were to be strictly kept, and there was to be no dinner in Hall. It was thus arranged. The evening chapel service, which was usually at 5-1/2 (I think), was held at 3; and at 4 the ordinary full meal was served in Hall, but as it followed the chapel attendance it was held to be supper; and there was no subsequent meal.

There were no chairs whatever in Hall, except the single chair of the vice-master at the head of the table on the dais and that of the senior dean at the table next the East wall. All others sat on benches. And I have heard allusions to a ludicrous difficulty which occurred when some princesses (of the Royal Family) dined in the Hall, and it was a great puzzle how to get them to the right side of the benches.

The Sizars dined after all the rest; their dinner usually began soon after 4. For the non-foundationists a separate dinner was provided, as for pensioners. But for the foundationists, the remains of the Fellows' dinner were brought down; and I think that this provision was generally preferred to the other.

The dishes at all the tables of undergraduates were of pewter, till a certain day when they were changed for porcelain. I cannot remember whether this was at the time when they became Questionists (in the October Term), or at the time when they were declared "actualiter esse in artibus Baccalaureos" (in the Lent Term).

Up to the Questionist time the undergraduate Scholars had no mixture whatever; they were the only pure table in the Hall: and I looked on this as a matter very valuable for the ultimate state of the College society. But in the October term, those who were to proceed to B.A. were drafted into the mixed body of Questionists: and they greatly disliked the change. They continued so till the Lent Term, when they were formally invited by the Bachelor Scholars to join the upper table.

MATHEMATICAL SUBJECTS OF STUDY AND EXAMINATION.