"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.