"On Feb. 4th I have investigations of the density of light near a caustic (on the theory of emissions). On Feb. 5th I finished a Paper about the defect in my eye, which was communicated to the Cambridge Philosophical Society on Feb. 21st. Mr Peacock or Mr Whewell had some time previously applied to me to write a Paper on Trigonometry for the Encyclopaedia Metropolitana, and I had been collecting some materials (especially in regard to its history) at every visit to London, where I read sometimes at the British Museum: also in the Cambridge libraries. I began this Paper (roughly) on Feb. 8th, and finished it on Mar. 3rd. The history of which I speak, by some odd management of the Editors of the Encyclopaedia, was never published. The MS. is now amongst the MSS. of the Royal Observatory, Greenwich. Other subjects on my quires are: Theory of musical concords, many things relating to trigonometry and trigonometrical tables, achromatic eye-pieces, equation to the surface bounding the rays that enter my left eye, experiments on percussion. Also notes on Cumberland and Wales (I had already proposed to myself to take a party of pupils in the Long Vacation to Keswick), and notes on history and geology.
"I had been in correspondence with Dr Malkin (master of Bury School), who on Feb. 8th sent a certificate for my brother William, whom I entered at Trinity on Peacock's side. On Mar. 25th I changed my rooms, quitting those on the ground-floor east side of Queen Mary's Gate for first-floor rooms in Neville's Court, south side, the easternmost rooms. In this term my lectures lasted from Apr. 18th to May 14th. Apparently I had only the Senior Sophs, 19 in number, and the same four pupils (Turner, Dobbs, Cooper, Hovenden) as in the preceding term. The only scientific subjects on which I find notes are, a Paper on the forms of the Teeth of Wheels, communicated to the Philosophical Society on May 2nd; some notes about Musical Concords, and some examination of a strange piece of Iceland Spar. On Apr. 29th I was elected to the Northern Institution (of Inverness); the first compliment that I received from an extraneous body.
"On May 14th I have a most careful examination of my money accounts, to see whether I can make an expedition with my sister into Wales. My sister came to Cambridge, and on Monday, May 23rd, 1825, we started for Wales, equipped in the lightest way for a walking expedition. We went by Birmingham to Shrewsbury: then to the Pontycyssylte Aqueduct and by various places to Bala, and thence by Llanrwst to Conway. Here the suspension bridge was under construction: the mole was made and the piers, but nothing else. Then on to Bangor, where nine chains of the suspension bridge were in place, and so to Holyhead. Then by Carnarvon to Bethgelert, ascending Snowdon by the way, and in succession by Festiniog, Dolgelly, and Aberystwyth to Hereford (the first time that I had visited it since my father left it). From thence we went by coach to London, and I went on to Cambridge on the 23rd of June.
"I had arranged to take a party of pupils to Keswick, and to take my brother there. Mr Clarkson had provided me with introductions to Mr Southey and Mr Wordsworth. On Wednesday, June 29th, 1825, we started, and went by Leicester, Sheffield, Leeds, and Kendal, to Keswick, calling at Edensor on the way. My pupils were Cleasby, Marshman, Clinton, Wigram, Tottenham, and M. Smith. At Keswick I passed three months very happily. I saw Mr Southey's family frequently, and Mr Wordsworth's occasionally. By continual excursions in the neighbourhood, and by a few excursions to places as distant as Bowness, Calder Bridge, &c. (always climbing the intermediate mountains), I became well acquainted with almost the whole of that beautiful country, excepting some of the S. W. dales. A geological hammer and a mountain barometer were very interesting companions. I had plenty of work with my pupils: I worked a little Lunar Theory, a little of Laplace's Equations, something of the Figure of the Earth, and I wrote out very carefully my Trigonometry for the Encyclopaedia Metropolitana. I read a little of Machiavelli, and various books which I borrowed of Mr Southey. On Friday, Sept. 30th, my brother and I left for Kendal, and after a stay of a few days at Edensor, arrived at Cambridge on Oct. 11th.
"On Oct. 21st my Lectures to the Junior Sophs began, 39 names, lasting to Dec. 13th. Those to the Senior Sophs, 16 names, Oct 29th to Dec. 10th. I also examined Questionists as last year. I have notes about a Paper on the connection of impact and pressure, read at the Philosophical Society on Nov. 14th, but not printed, dipping-needle problems, curve described round three centres of force, barometer observations, theory of the Figure of the Earth with variable density, and effect on the Moon, correction to the Madras pendulum, wedge with friction, spots seen in my eyes, density of rays near a caustic. In this term I accomplished the preparation of a volume of Mathematical Tracts on subjects which, either from their absolute deficiency in the University or from the unreadable form in which they had been presented, appeared to be wanted. The subjects of my Tracts were, Lunar Theory (begun Oct. 26th, finished Nov. 1st), Figure of the Earth (1st part finished Nov. 18th), Precession and Nutation (my old MS. put in order), and the Calculus of Variations. I applied, as is frequently done, to the Syndicate of the University Press for assistance in publishing the work; and they agreed to give me paper and printing for 500 copies. This notice was received from Professor Turton on Nov. 29th, 1825. It was probably also in this year that I drew up an imperfect 'Review' of Coddington's Optics, a work which deserved severe censure: my review was never finished.
"In the Long Vacation at Keswick I had six pupils at £42 each. In the October term I had Marshman and Ogilby at £105 for three terms, and Dobbs at £75 for three terms. I had, at Mr Peacock's suggestion, raised my rate from 60 to 100 guineas for three terms: this prevented some from applying to me, and induced some to withdraw who had been connected with me: but it did me no real hurt, for engrossment by pupils is the worst of all things that can happen to a man who hopes to distinguish himself. On Dec. 17th I went to Bury, and returned to Cambridge on Jan. 30th, 1826.
"I have the attendance-bills of my Lectures to Senior Sophs (16) from Feb. 3rd to Feb. 23rd, and to Freshmen (40) from Feb. 27th to Mar. 15. It would appear that I gave but one college-lecture per day (my belief was that I always had two). The tutor's stipend per term was £50. On my quires I find, Investigations for the ellipticity of a heterogeneous spheroid when the density is expressed by sin qc/qc (the remarkable properties of which I believe I discovered entirely myself, although they had been discovered by other persons), Theoretical Numbers for precession, nutation, &c., some investigations using Laplace's Y, hard work on the Figure of the Earth to the 2nd order,'Woodhouse's remaining apparatus,' Notes about Lambton's and Kater's errors, Depolarization, Notes of Papers on depolarization in the Phil. Trans., Magnetic Investigations for Lieut. Foster, Isochronous Oscillations in a resisting medium, Observations on a strange piece of Iceland Spar. On Mar. 7th forwarded Preface and Title Page for my Mathematical Tracts.
"Some time in this term I began to think of the possibility of observing the diminution of gravity in a deep mine, and communicated with Whewell, who was disposed to join in experiments. My first notion was simply to try the rate of a clock, and the Ecton mine was first thought of. I made enquiries about the Ecton mine through Mr Smith (of Edensor), and visited the mine, but in the meantime Whewell had made enquiries in London and found (principally from Dr Paris) that the mine of Dolcoath near Camborne in Cornwall would be a better place for the experiment. Dr Paris wrote to me repeatedly, and ultimately we resolved on trying it there. In my papers on Mar. 21st are various investigations about attractions in both mines. On Apr. 3rd I went to London, principally to arrange about Dolcoath, and during April and May I was engaged in correspondence with Sir H. Davy (President of the Royal Society), Mr Herschel, and Dr Young (Secretary of the Board of Longitude) about the loan of instruments and pendulums. On Apr. 23rd I was practising pendulum-observations (by coincidence); and about this time repeatedly practised transits with a small instrument lent by Mr Sheepshanks (with whom my acquaintance must have begun no long time before) which was erected under a tent in the Fellows' Walks. On my quires I find various schemes for graduating thermometers for pendulum experiments.
"I find also Notes of examination of my brother William, who had come to College last October; and a great deal of correspondence with my mother and sister and Mr Case, a lawyer, about a troublesome business with Mr Cropley, an old friend of G. Biddell, to whom my father had lent £500 and whose affairs were in Chancery.
"My lectures in this term were to the Junior Sophs from Apr. 10th to May 13th: they were six in number and not very regular. On Apr. 28th I sent to Mawman the copy of my Trigonometry for the Encyclopaedia Metropolitana, for which I received £42. I received notice from the Press Syndicate that the price of my Mathematical Tracts was fixed at 6s. 6d.: I sold the edition to Deighton for £70, and it was immediately published. About this time I have letters from Mr Herschel and Sir H. Davy about a Paper to be presented to the Royal Society—I suppose about the Figure of the Earth to the 2nd order of ellipticity, which was read to the Royal Society on June 15th.