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Hopes that JH's mother has had a pleasurable time in London; JH's class went to see Mrs. Mason's (?) baby.
A thank you note for clothes, written at school [Mr. Bull's], and requesting that JH's cyphering and music books be sent.
Writes to parents to say that JH is well, his head has healed, and he is looking forward to his holidays.
Has arrived in Scotland. Recently witnessed a large comet. Thanks JH and family for hospitality at Slough.
Thanks JH for information concerning the comet. Planned to build telescope with object glasses separated from each other. Optician said this would not correct spherical and chromatic aberrations. Wants advice.
Wishes to teach privately. Asks William Herschel to write a recommendation certificate. Weather has been problematic. Sends greeting to the elder Herschels.
Concerned over illness of William Herschel. Discusses 'Evolution of Curve Lines.' Describes [Christiaan] Huygens's terms for evolution of curves. Offers advice to avoid problems with them.
Recalls JH's visit to Hammersmith. Asks TB to permit JH's cousin Mary Baldwin to visit Slough at time of Ascot races. Received letter from [TB's daughter] Sophia.
Grateful for letter from Brighton. Agrees with JH concerning comet. Is suspicious of those who claim it is the same comet that was seen one year previously.
Describes the difficulty of [P. Laplace's] Mécanique céleste. Has a new pupil. Discusses proper boundary of a front view mirror.
Discusses problem of the ellipse and offers a method of solving it. States the proper boundary of a front mirror is too difficult to ascertain. Still having problems with teaching.
Describes lunar rainbow seen on 22 August. Congratulates JH on his mathematical attainments. Describes his enjoyment of mathematics. Hopes JH will continue to correspond.
Identifies a number of the various orders of ape and comments on them.
Found JH's resolution of a biquadratic ingenious. AR used René Descartes's method of resolution, but found it less elegant. Discusses resolution of higher order quadratics.
Informing him of his position in the examinations, and offering congratulations.
Recalls time spent together; asks JH for information about Cambridge colleges, especially St. John's.
Is attending John Playfair's lectures in mathematics; talks of plans to come to Cambridge.