Has been trying his hand at functions; quotes some. Hopes to visit him at Torquay. Push on with the supplement.
Is grateful for JH's assistance regarding the Persepolitan writing. G. C. Renouard's communication appears to be conclusive. Hopes he can convey the information to the Royal Society of Göttingen. Would like a copy of the whole inscription if this is not imposing too much.
Is glad to hear he will be visiting Torquay. Regarding mathematical functions.
No summary available.
Regrets delay in answering letter, but is setting to work and hopes to send part of his manuscript on curves in a few days. Has spoken to Smith (the printer). [Richard?] Harraden is immovable.
Encloses paper by DeWitt Clinton for "Linnean Transactions" [unknown], with plants and seeds to follow. Appends an addition to his paper on "the Carolina fungus" in case it is published. Has sent a box of books.
Sending Professor [Josef August] Schultes' new botanical publication, [presumably "Osterreichs Flora"], by request of the author.
Family news, and the sad state of current poetry.
Sends one mathematical article on isoperimetrical problems and asks to write the article on variations as well.
No summary available.
Regarding the calculus of derivations.
[Francis] Boott unexpectedly returning to England. He has invited Boott to work on his "Flora of New England"; as yet they are novices in the science and have much to gain from Smith's advice; similarities and differences of New England and European floras. State of science in USA "rapidly progressive" but not yet advanced enough to support the "luxuries of science", such as coloured engravings of American plants; he is making the experiment in his "Medical Botany", sends plates via Boott. Sends pencilled sketch of an 'Orchis grandiflora', close to 'O. fimbriata'. Corrêa is Portugeuse Minister Plenipotentiary at Washington. Requests that the plants he sent Smith for determination be reserved for his and Boott's flora; some have since been published in Elliott's; further query on the two 'Rubus'.
Discusses plans for an edition of the mathematical writings of the late William Spence, to be edited by JH.
Gave "5 lights" to the Great Mogul melon Smith sent seeds of from Shuckburgh, [Warwickshire], and thinks that those who admire this fruit do not know the small orange cantaloupe or Green Egyptian melons.
His garden: abundant mushrooms from mushroom house he built last spring; like most others has no peaches or nectarines on open walls this year so is now building a 43 feet long peach house; began mowing 8 July but much of the hay still out and is as black as the corn is green.
Undertook tour of England in June, travelling 654 miles: London, where the temperature was 84°F, to Wincanton, [Somerset]; Stourhead and Longleat, [Wiltshire]; Bath, [Somerset]; Rodborough, [Gloucestershire]; Cheltenham, [Gloucestershire]; Warwick and its Castle, [Warwickshire]; and Northampton, [Northamptonshire], before joining north road at Wansford, [Cambridgeshire]. Encloses plant specimen collected between Andover, [Hampshire], and Amesbury, [Wiltshire]; Smith has annotated "'Sonchus oleraceus' the prickly var[iet]y". His son failed to find local 'Burbaumia' in Tunbridge Wells, [Kent], but [James] Dickson has sent both kinds though he only requested 'B. foliosa'.