Requests the return of his manuscript paper on double stars so that he may prepare his presentation to the next meeting of the Astronomical Society.

Comments about AD's work in mathematical functions, and then refers to JH's reductions and other astronomical matters, including the need for reform of stellar nomenclature.

Thanks AD for having pointed out an error in one of JH's papers.

Returns manuscript and corrected proofs of one of JH's papers on double stars, with the rest of the paper going to Francis Baily.

Wants to make a new musical instrument on the principle of resonance; JH also suggests some improvements in the construction of the organ.

Decimal Association will not publish answers to questions by Lord Overstone [S. J. Loyd] until next session. Seeks consent of JH and other members to publish these sooner.

Raises a question regarding the size of an infinitely small quantity. Argues that 1850 is the last year of the first half of the nineteenth century.

Asks a whole series of silly riddles, and JH complains of not having heard from AD.

Has received a copy of JH's paper on double stars, but is confined to bed by a severe attack of rheumatism, so is not sure when he can finish the corrections.

Asks what AD knows about the Andersonian Institution in Glasgow, which JH's son Alexander is considering as a place of employment. JH then deals with a problem in probability theory, and concludes the letter with a riddle.

His paper on double stars is required for press so would be grateful if it could be sent along. The society is short of papers for reading so any JH can produce would be very welcome.

Encloses the proof of the first part of his paper, with queries. Regarding the seal used. Volume of the memoirs have been published. There are important matters for the next Astronomical Council.

Returns his paper and would be glad to receive an abstract. JH has been removed from the Council of the R.A.S. in deference to his wishes. King of Denmark has offered a gold medal for the discovery of a comet.

Has sent off his observations by the coach. Account of the Oxford meeting is in Tilloch's Magazine, now amalgamated with David Brewster's Edinburgh Journal. Will be able to include the new catalogue of stars in the forthcoming volume if JH desires it.

Hopes to have JH's catalogue for the first meeting of the R.A.S. Anything about the comet would be welcome. Regarding one of Franciscus Vièta's mathematical theories.

Has received the catalogue and it will be sent to the press. Is grateful for JH's offers. Does he know anything of Bullialdi's (Ismael Boulliau) Astronomica philolaica? Refers to Franciscus Vièta's Harmonicum coeleste. 25 copies of JH's latest paper has been forwarded.

Arrangements related to JH's going to the Cape.

Thanks for his paper on nebulae. Scarlet fever has been very prevalent this season. R.S.L. in financial straits. Paper on John Flamsteed has caused friction between James Ivory and the R.A.S. Government has promised financial aid to Edinburgh Observatory.

Sending a letter by Francis Baily. Anniversary of the R.A.S. takes place on Friday. Capt. [Walter?] Forman has had a rise in the world. Observations of Henry Foster fills volume VII of the memoirs.

Sending him the Calculus of Functions, which he may retain, and also some maps of the stars published by Society for the Diffusion of Useful Knowledge. The R.A.S. is preparing a picture of Francis Baily and has added JH's name to the subscription list. Supposes he has fixed a date for his return. Regarding 'Warren's jet blacking.'