[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 tangent and cotangent.
Describes JH's public Latin examination in algebra yesterday. James Grahame and sister were dangerously ill, but Grahame returned to Cambridge. [Addendum:] Newspaper clipping naming students (including JH) who received B.A. degrees at Cambridge on 16 Jan. 1813.
[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.
Answer to CB's equation. Bring something to discuss at the forthcoming meeting of the Analytical Society.
About the mathematical formulation for the summation of any series.
Giving equations.
Angry at self and whole world except JW. Has been drunk and travelling. Met brilliant but 'not beautiful' woman. Wonders why he left Cambridge; requests news and offers advice.
Further comment on the calculus equation sent by CB.
Two weeks of examinations begin tomorrow. Experiments writing with glass pen. Describes glassmaker's methods. Suggests application to micrometers.
Regarding the equations in his memoir on the series of tangents. Queries about the Analytical Society.
Philosophizes about society, college, time passing, and the 'fog' of present life. Wants to know all that is going on at Cambridge. Sends fond greetings to friends. [Letter completed 2-22].
Further equations discussed. Has purchased more books. Regarding the printing of the memoir. [Letter continued on 1813-3-2.]
Regarding his memoir: would like to see part of CB's notes.
Warmed by drink and society of 'charming' girls, JH is thinking of Whittaker, and advises him to study less. JH is enjoying reading more than did in school. Sends other news.
Further regarding theorems recently discussed. Regarding the preface for JH's and CB's Memoirs of the Analytical Society.
Comments on decaying British domestic affairs. Deplores religion 'as established by law' in contrast with religion 'established by nature.' Has felt sombre lately. Comments on music as relief from mathematics.
Comments on unfortunately aristocratic world, JW's description of Hamlet, current investigations and perhaps too deep involvement in scientific pursuits. Is correcting friend's novel (The Victim of Villainy or Travelling Tetrahedrons). Asks JW to find mineralogical specimen.
Regarding his new researches into the theory of determining functions from given conditions. The printing of his memoir is proceeding slowly.
Urges to send copies of [S. F.] Lacroix's work and École polytechnique journal. James Grahame is successfully studying law. Grahame's father is staying with JH and his presence makes JH 'better and wiser.' Has been thinking much. Hopes JW will check on printing of Memoirs of the Analytical Society. [Letter completed 1813-8-3.]
Gives further instructions on sending books [see JH's 1813-8-2]. Comments on 'refractory' nature of religious thought. Is not in love, but teases JW about frequent visits to Thackerays. Recounts current heavy involvement in music, asking [Thomas?] Greenwood for help with harmonies.