“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 b squared(d squaredy/dx squared)=(d squaredy/dt squared), 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,