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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.
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.
News of several lady friends and JG's progress in law studies.
Asks about nature of Classics examination JG must take to be considered for admission to Cambridge.
Speculates that JH may one day rival Isaac Newton. Awaits JH's visit next Tuesday. JH's parents ordered chairs to be ready [Wednesday], when PW's sister will accompany JH to Slough.
Apologizes for long delay in writing; is coming to Cambridge in October.
Is coming to Cambridge on 10 Oct.