“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 (L14 for a part of the Vacation, and L14 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.