Sends on part of letter for CB to complete and forward.

About the mathematical formulation for the summation of any series.

Giving equations.

Regarding equational problems.

Finding it difficult to finish his memoir. Gives some integral equations for his comments. Hopes to see him at Slough soon.

[Addressed to WN as 'Editor of the Journal of Natural Philosophy, Chemistry, and the Arts from 'A Lover of Modern Analysis' [JH], this letter] derives by a new method various analytical formulae for the tangent and cotangent.

[Addressed to WN as 'Editor of the Journal of Natural Philosophy, Chemistry, and the Arts from 'A Lover of Modern Analysis' [JH], this letter] derives by a new method various analytical formulae for the sine and cosine.

Has been quite ill; talks about one journey.

Talks about JH becoming a churchman.

Is coming to visit JH at Slough.

About JG's travels to Edinburgh.

Congratulates JH on having completed examinations; JG will be admitted to the bar soon.

Note to accompany several copies of JG's thesis.

Describes his experiences in court; talks about their mutual friend J. W. Whittaker [letter completed 1812-8-11].

Philosophizes about life [letter completed 1812-9-11].

About the lady JG intends to marry; also JG's law practice.

Experienced a mild winter with primroses in full flower on 30 January, though March was severe. His apricot trees which he protected with copper plate printers' canvas, recommended by Sir Joseph Banks, [Thomas] A[ndew] Knight [(1759-1838)], and [James] Dickson as being superior to Buntine, have many flowers.

Unconvinced by some authors claims that ivy is injurious to trees as it dies if separated from the root; plants of his cut three months ago are showing no sign of decay and neglect of ivy in his gardens has caused much injury but they are now attacking it on trees and transferring it to walls. Mr Knight's peas are not worth cultivating, they produced inferior quantity of seed over two seasons which is now all saved for a third crop. Knight's method for obtaining large onions failed twice as they always run to seed in second year.

Smith's 'Conferva urceolata' is [William] Hudson's 'nigrescens' but could not find it in his drawings as [Lewis Weston] Dillwyn [(1778-1855)] still has them, complains he has had them too long and requests Smith's assistance in recovering them.

Encloses note [extant] from Mr [James] Hoy dated Gordon Castle, [Scotland], 18 Dec 1811, thanking Frankland for specimen of 'Scheuzeria' and detailing the extent of the [Alexander Gordon, 4th] Duke of Gordon's [(1743-1827)] estates.

Recently "whip grafted" 'Ilex' on common oak, having been unsuccessful in the common way, and has one 14 feet high plant cleft-grafted on common oak in uncommon health. They were taken from 100 year old wild trees which are much more hardy than his native trees of beech, lime, sycamore, and horse chestnut, which have graudually died since an unmerciful thinning in 1785, though the 'Ilex' seems uninjured.

Smith's 'Glaucium' was in flower last November, and some raised from seed had yellow flowers. Packed 'Nuphar' seeds received from [James] Brodie in earth, paper, and matting, and sunk with stone in a hard water stewpond secreted by planatation.

Illustrates "lamentable colouring" of 'Ulva plumosa' in "English Botany", which should have been "sap green", as in small coloured sketch [extant]; forgot to send one of the late flowering Gordon Castle, [Scotland], specimens. The late "tormenting" wife of [Alexander Gordon, 4th] Duke of Gordon [(1743-1827)] is now on road to be buried in Scotland and he has never been so happy.

Grafting: in [Thomas] Martyn's edition of [Philip] Miller's "The gardener's and botanist's dictionary" root grafting described as "a newer invention" but has succeeded in whip grafting 'Ilex' onto common oak, and surprised to find root grafting accurately described and extolled in Lowthorp's "Abridgement" vol 2 p.654. Delayed in coming to London by son's illness.

'Salix caprea' "Flora Britannica" is abundant in his woods but called 'sauve', reference to Marshall's "Yorkshire Glossary" "Saus - 'Salix caprea'". Found "host of holly natural layers, & shall layer some hundreds".

Discussion of apple trees: received "Downton pippin, Golden Harvey, Grange apple, & Foxley" from Hereford. Canker developed on his south wall Newton pippin which had fine crops for two years, observed with a lens the destruction of the eggs and insects under the diseased bark with turpentine. Forsyth says train oil is used in Kent, Forsyth himself prefers Torp seeds with terrie, thinks turpentine is as efficacious, plus more fluid and searching and its evaporation does not clog pores. Recommends Indian ink for nurserymens labels as it does not wash out.

Sketch of 'Ulex plumosa'.

Concerned by Smith's illness and abscence from London. [Lewis Weston] Dillwyn [(1778-1855)] apologised for detaining his 'Conferva' drawings. Sir Joseph Banks well and last October increased dose of his gout medicine from 12 to 15 drops daily; it is not proven if it has undermined his constitution. Banks has entire management of the Royal Mint and "pays great attention to it"; Marchant has executed dies for a new 3s & 1/6 pieces; has recommended a coinage of good sixpences to Banks. Drury Lane Theatre proceeding "magically, & will certainly be open early in Oct[obe]r next"; only regret is that the avenues around it "will remain blocked up precisely as they are now".

Previously sceptical of the fiorin grass called 'Agrostis stolonifera', or couch, but now convinced on its excellent qualities and on encouragement of Dr Richardson and Mr Miller set to convert his "dreary moors" to "the finest hay grounds". He is also improving a new farm which was only £20 rent, expecting in a few years for it to be worth hundreds, independent of the trees; he shall be "a better compatriot than either Pall Mall or Manchester Square [both in London] can boast of". Comments on an event that was a "total dereliction of principle & of all honourable feeling" and is very sorry for his country.

Has known [Thomas William] Coke since childhood at Eton [College, Berkshire], but ashamed to have never taken up any of his many invitations to Holkham, [Norfolk]. Struggling to catalogue his books. The weather is "miserably wet". Does not think his wife will ever regain her spirits to enjoy company.