Was elected yesterday to the Registrarship of London University, and thanks JH for his support.

At the recent A.G.M. of the R.A.S. Club, JH was elected an Honorary Life Member. Hopes he will attend many more meetings.

Returned late on Thursday. Is gratified by JH's praise of his drawings of Saturn. Includes some further drawings and comments on JH's queries.

Made some observations of Jupiter after his last letter. Thought JH might be interested in seeing them. Would be grateful for any comments, which he will incorporate into his final drawing.

Wishing him well for the new year. Hears JH has visited the East India College. Sends a theorem. H. P. Brougham (Baron Brougham and Vaux) amuses himself by finding the laws of central force for curves. Has been finding information on a nephew of Isaac Newton. George Stanhope (6th Earl of Chesterfield) and T. A. W. Parker (9th Earl of Macclesfield) were pupils of Abraham De Moivre.

Has not heard from him for a long time. Thought that the Government was going to turn the R.A.S. out of Somerset House. There is someone to come to the rescue of Richard Sheepshanks. Has not seen Charles Babbage for many years. Their views are incompatible. C. P. Smyth is off to Teneriffe so now is the time for JH to make suggestions. Has set up a committee to make by-laws.

Is glad to hear his account of facts. Always thought he would recover his health. Gives one of his own mathematical formulae. Has no idea how the Decimal Coinage Commission is progressing.

Would he answer some of his queries when he has leisure? Queries on the law of beats for unison sounds. Met JH's daughter on Monday, who gave a fair account of JH and his recent work.

Has long held the view that a pipe underneath the strings of a piano would increase the resonance. Had not conceived such an instrument as JH suggested. Why are 3rds and 6ths more agreeable to the ear than 4ths and 5ths?

Sending a pamphlet, which may give JH some amusement.

JH's last letter was written in a good strong hand. Recommends suitable drink for hot weather. Gives his views about the possible marriage of Isaac Newton's niece. Has had a letter from a Mr. Wither on mathematical books.

Many thanks for his invitation, but he does not intend going to Eastbourne. Further remarks on his own theory regarding the marriage of Isaac Newton's niece.

Has fallen from a ladder in his library and dislocated his shoulder, which accounts for the form of his letter. Has he any recollections of Humphry Davy rubbing his hands together?

Quotes a rhyme. May have been injured even if he had been at Collingwood. Possibly [G. J.?] Stoney has not read JH on the telescope. Is thriving in health but sleeping very well.

Hopes his health is improving as his own is. Saw Henry Warburton last week. Gives one of his own theorems. Sends a lecture on the decimal coinage.

Pleased to hear his health is improving, but he should rest in the morning. Thinks it will be a long time before the decimal coinage can be introduced. Comments on cooking in the next century. Has been looking at a 10" bar of aluminum, which [Thomas?] Graham has sent him.

Inviting JH to become a candidate at Cambridge.

Hears that JH is working on the theories of color blindness and encloses some China silks that may prove useful.

[Form letter] Offers to send Commercium epistolicum J. Collins et aliorum... (1856), by J. B. Biot and Francisque Lefort, a critical edition of works by mathematician John Collins.

Heard JH not well. Offers him 'a nosegay, gathered from [JH's] own garden of the Differences of the Powers of Zero.' More notes on the self-repeating series. Developed two equations that HW may submit to Cambridge [Philosophical] Society.