"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).