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

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.'

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.

Please convey thanks to the Society for the Diffusion of Useful Knowledge for its star maps. Finds them preferable to [Johann] Bode's maps, 'which are full of egregious errors.'

Will be a great reception for JH when he returns. Is working on a theory of probabilities. Francis Baily is the man for mapping the entire heavens. G. B. Airy is to test JH's topsy-turvy observations of Orion.

Possible to purchase 12 postage covers for 11d in the Strand. Points out an apparent error in one of JH's books on sound. How does an open pipe vibrate? Regarding the private character of J. L. Lagrange.

Thanks AD for a correction in one of JH's writings; tries to explain the partial echo that occurs when blowing across the end of an open pipe.

Regarding JH's telescope. Includes a rhyme on it.

Thanks AD for his theorems; comments on the value of such abstract speculations.

Points out an error JH has made concerning J. E. Bode's law. What is the proper notation for the satellites?

Thanks AD for the corrections to JH's writing on astronomy; congratulates AD on his book on differential calculus.

Thanks for the gift of the book. Thomas Longman is now the editor of Lardner's Cyclopaedia. Latitude of the pole star incorrect in Charles Knight's publications. Regarding truth.