Chapter 8

Latin prose, and then employed myself on the subject which I was reading for the time: usually taking mathematics at this hour. At 2 or a little sooner I went out for a long walk, usually 4 or 5 miles into the country: sometimes if I found companions I rowed on the Cam (a practice acquired rather later). A little before 4 I returned, and at 4 went to College Hall. After dinner I lounged till evening chapel time, 1/2 past 5, and returning about 6 I then had tea. Then I read quietly, usually a classical subject, till 11; and I never, even in the times when I might seem most severely pressed, sat up later.

"From this time to the close of the annual examination (beginning of June) I remained at Cambridge, stopping there through the Easter Vacation. The subjects of the mathematical lectures were ordinary algebra and trigonometry: but Mr Peacock always had some private problems of a higher class for me, and saw me I believe every day. The subjects of the Classical lectures were, the termination of Hippolytus, the book of Thucydides and the oration of Cicero. In mathematics I read Whewell's Mechanics, then just published (the first innovation made in the Cambridge system of Physical Sciences for many years): and I find in my scribbling-paper notes, integrals, central forces, Finite Differences, steam-engine constructions and powers, plans of bridges, spherical trigonometry, optical calculations relating to the achromatism of eye-pieces and achromatic object-glasses with lenses separated, mechanical problems, Transit of Venus, various problems in geometrical astronomy (I think it was at this time that Mr Peacock had given me a copy of Woodhouse's Astronomy 1st Edition), the rainbow, plans for anemometer and for a wind-pumping machine, clearing lunars, &c., with a great number of geometrical problems. I remark that my ideas on the Differential Calculus had not acquired on some important points the severe accuracy which they acquired in a few months. In Classics I read the Persae of Aeschylus, Greek and Roman history very much (Mitford, Hooke, Ferguson) and the books of Thucydides introductory to that of the lecture subject (the 3rd): and attended to Chronology. On the scribbling-paper are verse-translations from Euripides, careful prose-translations from Thucydides, maps, notes on points of grammar &c. I have also little MS. books with abundant notes on all these subjects: I usually made a little book when I pursued any subject in a regular way.

"On May 1st Mr Dobree, the head lecturer, sent for me to say that he appointed me head-lecturer's Sizar for the next year. The stipend of this office was _£10_, a sum upon which I set considerable value in my anxiety for pecuniary independence: but it was also gratifying to me as shewing the way in which I was regarded by the College authorities.

"On Wednesday, May 24th, 1820, the examination began. I was anxious about the result of the examination, but only in such a degree as to make my conduct perfectly steady and calm, and to prevent me from attempting any extraordinary exertion.

"When the Classes were published the first Class of the Freshman's Year (alphabetically arranged, as is the custom) stood thus: Airy, Boileau, Childers, Drinkwater, Field, Iliff, Malkin, Myers, Romilly, Strutt, Tate, Winning. It was soon known however that I was first of the Class. It was generally expected (and certainly by me) that, considering how great a preponderance the Classics were understood, in the known system of the College, to have in determining the order of merit, Field would be first. However the number of marks which Field obtained was about 1700, and that which I obtained about 1900. No other competitor, I believe, was near us."--In a letter to Airy from his College Tutor, Mr J. D. Hustler, there is the following passage: "It is a matter of extreme satisfaction to me that in the late examination you stood not only in the First Class but first of the first. I trust that your future exertions and success will be commensurate with this honourable beginning."

"Of the men whom I have named, Drinkwater (Bethune) was afterwards Legal Member of the Supreme Court of India, Field was afterwards Rector of Reepham, Romilly (afterwards Lord Romilly) became Solicitor-General, Strutt (afterwards Lord Belper) became M.P. for Derby and First Commissioner of Railways, Tate was afterwards master of Richmond Endowed School, Childers was the father of Childers who was subsequently First Lord of the Admiralty.

"I returned to Bury immediately. While there, some students (some of them men about to take their B.A. degree at the next January) applied to me to take them as pupils, but I declined. This year of my life enabled me to understand how I stood among men. I returned to Cambridge about July 11th. As a general rule, undergraduates are not allowed to reside in the University during the Long Vacation. I believe that before I left, after the examination, I had made out that I should be permitted to reside: or I wrote to Mr Hustler. I applied to Mr Hustler to be lodged in rooms in College: and was put, first into rooms in Bishop's Hostel, and subsequently into rooms in the Great Court.

"The first affair that I had in College was one of disappointment by no means deserving the importance which it assumed in my thoughts. I had been entered a Sizar, but as the list of Foundation Sizars was full, my dinners in Hall were paid for. Some vacancies had arisen: and as these were to be filled up in order of merit, I expected one: and in my desire for pecuniary independence I wished for it very earnestly. However, as in theory all of the first class were equal, and as there were some Sizars in it senior in entrance to me, they obtained places first: and I was not actually appointed till after the next scholarship examination (Easter 1821). However a special arrangement was made, allowing me (I forget whether others) to sit at the Foundation-Sizars' table whenever any of the number was absent: and in consequence I received practically nearly the full benefits.

"Mr Peacock, who was going out for the vacation, allowed me access to his books. I had also (by the assistance of various Fellows, who all treated me with great kindness, almost to a degree of respect) command of the University Library and Trinity Library: and spent this Long Vacation, like several others, very happily indeed.

"The only non-mathematical subjects of the next examination were The Gospel of St Luke, Paley's Evidences, and Paley's Moral and Political Philosophy. Thus my time was left more free to mathematics and to general classics than last year. I now began a custom which I maintained for some years. Generally I read mathematics in the morning, and classics for lectures in the afternoon: but invariably I began at 10 o'clock in the evening to read with the utmost severity some standard classics (unconnected with the lectures) and at 11 precisely I left off and went to bed. I continued my daily translations into Latin prose as before.

"On August 24th, 1820, Rosser, a man of my own year, engaged me as private tutor, paying at the usual rate (_£14_ for a part of the Vacation, and _£14_ for a term): and immediately afterwards his friend Bedingfield did the same. This occupied two hours every day, and I felt that I was now completely earning my own living. I never received a penny from my friends after this time.

"I find on my scribbling-paper various words which shew that in reading Poisson I was struggling with French words. There are also Finite Differences and their Calculus, Figure of the Earth (force to the center), various Attractions (some evidently referring to Maclaurin's), Integrals, Conic Sections, Kepler's Problem, Analytical Geometry, D'Alembert's Theorem, Spherical Aberration, Rotations round three axes (apparently I had been reading Euler), Floating bodies, Evolute of Ellipse, Newton's treatment of the Moon's Variation. I attempted to extract something from Vince's Astronomy on the physical explanation of Precession: but in despair of understanding it, and having made out an explanation for myself by the motion round three axes, I put together a little treatise (Sept. 10, 1820) which with some corrections and additions was afterwards printed in my Mathematical Tracts. On Sept. 14th I bought Woodhouse's Physical Astronomy, and this was quite an epoch in my mathematical knowledge. First, I was compelled by the process of "changing the independent variable" to examine severely the logic of the Differential Calculus. Secondly, I was now able to enter on the Theory of Perturbations, which for several years had been the desired land to me.

"At the Fellowship Election of Oct. 1st, Sydney Walker (among other persons) was elected Fellow. He then quitted the rooms in which he had lived (almost the worst in the College), and I immediately took them. They suited me well and I lived very happily in them till I was elected Scholar. They are small rooms above the middle staircase on the south side of Neville's Court. (Mr Peacock's rooms were on the same staircase.) I had access to the leads on the roof of the building from one of my windows. This was before the New Court was built: my best window looked upon the garden of the College butler.

"I had brought to Cambridge the telescope which I had made at Colchester, and about this time I had a stand made by a carpenter at Cambridge: and I find repeated observations of Jupiter and Saturn made in this October term.

"Other mathematical subjects on my scribbling-paper are: Geometrical Astronomy, Barometers (for elevations), Maclaurin's Figure of the Earth, Lagrange's Theorem, Integrals, Differential Equations of the second order, Particular Solutions. In general mathematics I had much discussion with Atkinson (who was Senior Wrangler, January 1821), and in Physics with Rosser, who was a friend of Sir Richard Phillips, a vain objector to gravitation. In Classics I read Aeschylus and Herodotus.

"On October 5th I received notice from the Head Lecturer to declaim in English with Winning. (This exercise consists in preparing a controversial essay, learning it by heart, and speaking it in Chapel after the Thursday evening's service.) On October 6th we agreed on the subject, "Is natural difference to be ascribed to moral or to physical causes?" I taking the latter side. I spoke the declamation (reciting it without missing a word) on October 25th. On October 26th I received notice of Latin declamation with Myers: subject agreed on, "Utrum civitati plus utilitatis an incommodi afferant leges quae ad vitas privatorum hominum ordinandas pertinent"; I took the former. The declamation was recited on November 11, when a curious circumstance occurred. My declamation was rather long: it was the first Saturday of the term on which a declamation had been spoken: and it was the day on which arrived the news of the withdrawal of the Bill of Pains and Penalties against Queen Caroline. (This trial had been going on through the summer, but I knew little about it.) In consequence the impatience of the undergraduates was very great, and there was such an uproar of coughing &c. in the Chapel as probably was never known. The Master (Dr Wordsworth, appointed in the beginning of the summer on the death of Dr Mansell, and to whom I had been indirectly introduced by Mrs Clarkson) and Tutors and Deans tried in vain to stop the hubbub. However I went on steadily to the end, not at all frightened. On the Monday the Master sent for me to make a sort of apology in the name of the authorities, and letters to the Tutors were read at the Lectures, and on the whole the transaction was nowise disagreeable to me.

"On the Commemoration Day, December 15th, I received my Prize (Mitford's Greece) as First-Class man, after dinner in the College Hall. After a short vacation spent at Bury and Playford I returned to Cambridge, walking from Bury on Jan. 22nd, 1821. During the next term I find in Mathematics Partial Differential Equations, Tides, Sound, Calculus of Variations, Composition of rotary motions, Motion in resisting medium, Lhuillier's theorem, Brightness of an object as seen through a medium with any possible law of refraction (a good investigation), star-reductions, numerical calculations connected with them, equilibrium of chain under centripetal force (geometrically treated, as an improvement upon Whewell's algebraical method), investigation of the magnitude of attractive forces of glass, &c., required to produce refraction. I forget about Mathematical Lectures; but I have an impression that I regularly attended Mr Peacock's lectures, and that he always set me some private problems.

"I attended Mr Evans's lectures on St Luke: and I find many notes about the history of the Jews, Cerinthus and various heresies, Paley's Moral Philosophy, Paley's Evidences, and Biblical Maps: also speculations about ancient pronunciations.

"For a week or more before the annual examination I was perfectly lazy. The Classes of my year (Junior Sophs) were not published till June 11. It was soon known that I was first with 2000 marks, the next being Drinkwater with 1200 marks. After a short holiday at Bury and Playford I returned to Cambridge on July 18th, 1821. My daily life went on as usual. I find that in writing Latin I began Cicero De Senectute (retranslating Melmoth's translation, and comparing). Some time in the Long Vacation the names of the Prizemen for Declamations were published: I was disappointed that not one, English or Latin, was assigned to me: but it was foolish, for my declamations were rather trumpery.

"My former pupil, Rosser, came again on August 14th. On August 29th Dr Blomfield (afterwards Bishop of London) called, to engage me as Tutor to his brother George Beecher Blomfield, and he commenced attendance on Sept. 1st. With these two pupils I finished at the end of the Long Vacation: for the next three terms I had one pupil, Gibson, a Newcastle man, recommended by Mr Peacock, I believe, as a personal friend (Mr Peacock being of Durham).

"The only classical subject appointed for the next examination was the 5th, 6th and 7th Books of the Odyssey: the mathematical subjects all the Applied Mathematics and Newton. There was to be however the Scholarship Examination (Sizars being allowed to sit for Scholarships only in their 3rd year: and the Scholarship being a kind of little Fellowship necessary to qualify for being a candidate for the real Fellowship).

"When the October term began Mr Hustler, who usually gave lectures in mathematics to his third-year pupils, said to me that it was not worth my while to attend his lectures, and he or Mr Peacock suggested that Drinkwater, Myers, and I should attend the Questionists' examinations. The Questionists are those who are to take the degree of B.A. in the next January: and it was customary, not to give them lectures, but three times a week to examine them by setting mathematical questions, as the best method of preparing for the B.A. examination. Accordingly it was arranged that we should attend the said examinations: but when we went the Questionists of that year refused to attend. They were reported to be a weak year, and we to be a strong one: and they were disposed to take offence at us on any occasion. From some of the scholars of our year who sat at table with scholars of that year I heard that they distinguished us as 'the impudent year,' 'the annus mirabilis' &c. On this occasion they pretended to believe that the plan of our attendance at the Questionists' examinations had been suggested by an undergraduate, and no explanation was of the least use. So the Tutors agreed not to press the matter on them: and instead of it, Drinkwater, Myers, and I went three times a week to Mr Peacock's rooms, and he set us questions. I think that this system was also continued during the next two terms (ending in June 1822) or part of them, but I am not certain.

"In August 1821 I copied out a M.S. on Optics, I think from Mr Whewell: on August 24th one on the Figure of the Earth and Tides; and at some other time one on the motion of a body round two centers of force; both from Mr Whewell. On my scribbling paper I find--A problem on the vibrations of a gig as depending on the horse's step (like that of a pendulum whose support is disturbed), Maclaurin's Attractions, Effect of separating the lenses of an achromatic object-glass (suggested by my old telescope), Barlow's theory of numbers, and division of the circle into 17 parts, partial differentials, theory of eye-pieces, epicycloids, Figure of the Earth, Time of body in arc of parabola, Problem of Sound, Tides, Refraction of Lens, including thickness, &c., Ivory's paper on Equations, Achromatism of microscope, Capillary Attraction, Motions of Fluids, Euler's principal axes, Spherical pendulum, Equation b²(d²y/dx²)=(d²y/dt²), barometer, Lunar Theory well worked out, ordinary differential equations, Calculus of Variations, Interpolations like Laplace's for Comets, Kepler's theorem. In September I had my old telescope mounted on a short tripod stand, and made experiments on its adjustments. I was possessed of White's Ephemeris, and I find observations of Jupiter and Saturn in October. I planned an engine for describing ellipses by the polar equation A/(1 + e cos theta) and tried to make a micrometer with silk threads converging to a point. Mr Cubitt called on Oct. 4 and Nov. 1; he was engaged in erecting a treadmill at Cambridge Gaol, and had some thoughts of sending plans for the Cambridge Observatory, the erection of which was then proposed. On Nov. 19 I find that I had received from Cubitt a Nautical Almanac, the first that I had. On Dec. 11 I made some experiments with Drinkwater: I think it was whirling a glass containing oil on water. In Classics I was chiefly engaged upon Thucydides and Homer. On October 6th I had a letter from Charles Musgrave, introducing Challis, who succeeded me in the Cambridge Observatory in 1836.

"At this time my poor afflicted father was suffering much from a severe form of rheumatism or pain in the legs which sometimes prevented him from going to bed for weeks together.

"On the Commemoration Day, Dec. 18th, I received my prize as first-class man in Hall again. The next day I walked to Bury, and passed the winter vacation there and at Playford.

"I returned to Cambridge on Jan. 24th, 1822. On Feb. 12th I kept my first Act, with great compliments from the Moderator, and with a most unusually large attendance of auditors. These disputations on mathematics, in Latin, are now discontinued. On March 20th I kept a first Opponency against Sandys. About this time I received Buckle, a Trinity man of my own year, who was generally supposed to come next after Drinkwater, as pupil. On my sheets I find integrals and differential equations of every kind, astronomical corrections (of which I prepared a book), chances, Englefield's comets, investigation of the brightness within a rainbow, proof of Clairaut's theorem in one case, metacentres, change of independent variable applied to a complicated case, generating functions, principal axes. On Apr. 8th I intended to write an account of my eye: I was then tormented with a double image, I suppose from some disease of the stomach: and on May 28th I find by a drawing of the appearance of a lamp that the disease of my eye continued.

"On Feb. 11th I gave Mr Peacock a paper on the alteration of the focal length of a telescope as directed with or against the Earth's orbital 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 entitled 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 Classes 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 passed 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 class '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 Shells, 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 canal, 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 Sextant 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 glass, and had shewn it afterwards to Mr Peacock. 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 Peacock. 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 Peacock: 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 Peacock. 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 Peacock 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 Peacock'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 Cassegrainian). 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 classes, for arrangement of details of the B.A. Examination, were published. The first class, Airy, Drinkwater, Jeffries, Mason. As far as I remember, the rule was then, that on certain days the classes were grouped (in regard to identity 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 Saturday, 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 glass 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 classes as resulting from the examination were published, 1st bracket Airy, 2nd bracket Jeffries, 3rd bracket Drinkwater, Fisher, Foley, Mason, Myers.

"On Saturday, 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 competitor 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 Peacock had once recommended me to sit for the Chancellor's medal (Classical 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 undecimâ."

"Recte statuit Woodius de Iride."

"Recte statuit Paleius de Obligationibus."

The Opponents named to attack these assertions 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 assistance 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 nobody 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 vivâ 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 acumine defendisti, et in rebus mathematicis scientiam planè 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 instituted. 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." Nobody 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 Assistant-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 classes. The Moderators and Assistant Examiners were provided each with a set of questions in manuscript (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 classes united, another Examiner took the 3rd and 4th classes united, and a third took the 5th and 6th united. On Tuesday, one Examiner took the 1st class alone, a second took the 2nd and 3rd classes united, a third took the 4th and 5th classes united, and a fourth took the 6th class alone. On Wednesday, Thursday, and Friday the changes were similar. And, in all, the questioning was thus conducted. The Examiner read from his manuscript 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 principally, 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 Peacock 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 Saturday morning at 8 o'clock the manuscript 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.

In the October Term 1819, the only books on Pure Mathematics were:--Euclid generally, Algebra by Dr Wood (formerly Tutor, but in 1819 Master, of St John's College), Vince's Fluxions and Dealtry's Fluxions, Woodhouse's and other Trigonometries. Not a whisper passed through the University generally on the subject of Differential Calculus; although some papers (subsequently much valued) on that subject had been written by Mr Woodhouse, fellow of Caius College; but their style was repulsive, and they never took hold of the University. Whewell's Mechanics (1819) contains a few and easy applications of the Differential Calculus. The books on applied Mathematics were Wood's Mechanics, Whewell's Mechanics, Wood's Optics, Vince's Hydrostatics, Vince's Astronomy, Woodhouse's Plane Astronomy (perhaps rather later), The First Book of Newton's Principia: I do not remember any others. These works were undoubtedly able; and for the great proportion of University students going into active life, I do not conceal my opinion that books constructed on the principles of those which I have cited were more useful than those exclusively founded on the more modern system. For those students who aimed at the mastery of results more difficult and (in the intellectual sense) more important, the older books were quite insufficient. More aspiring students read, and generally with much care, several parts of Newton's Principia, Book I., and also Book III. (perhaps the noblest example of geometrical form of cosmical theory that the world has seen). I remember some questions from Book III. proposed in the Senate-House Examination 1823.

In the October term 1819, I went up to the University. The works of Wood and Vince, which I have mentioned, still occupied the lecture-rooms. But a great change was in preparation for the University Course of Mathematics. During the great Continental war, the intercourse between men of science in England and in France had been most insignificant. But in the autumn of 1819, three members of the Senate (John Herschel, George Peacock, and Charles Babbage) had entered into the mathematical society of Paris, and brought away some of the works on Pure Mathematics (especially those of Lacroix) and on Mechanics (principally Poisson's). In 1820 they made a translation of Lacroix's Differential Calculus; and they prepared a volume of Examples of the Differential and Integral Calculus. These were extensively studied: but the form of the College Examinations or the University Examinations was not, I think, influenced by them in the winter 1820-1821 or the two following terms. But in the winter 1821-1822 Peacock was one of the Moderators; and in the Senate-House Examination, January 1822, he boldly proposed a Paper of important questions entirely in the Differential Calculus. This was considered as establishing the new system in the University. In January 1823, I think the two systems were mingled. Though I was myself subject to that examination, I grieve to say that I have forgotten much of the details, except that I well remember that some of the questions referred to Newton, Book III. on the Lunar Theory. To these I have already alluded.

No other work occurs to me as worthy of mention, except Woodhouse's Lunar Theory, entirely founded on the Differential Calculus. The style of this book was not attractive, and it was very little read.