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Sends paper on fluxions written for Edinburgh Encyclopaedia. Uses new formulas, dispensing with binomial theorem. Brings logarithmic and exponential formulae within power of common algebraic processes.
WW's elegant presentation of doctrine of limits is best basis for elementary treatise but not for extensive work, because it involves imaginary functions. Charles Babbage is making progress in theory of functional equations.
Invites WW and [Thomas] Leybourn to join JH for dinner while Charles Babbage is visiting JH at Slough.
Accepts invitation to visit Slough and meet Charles Babbage. [Thomas] Leybourn may accompany WW. Seeking area of conic sections.
Please recommend London instrument makers to supply new Edinburgh observatory. Josef Fraunhofer was asked to make only lens for transit instrument, but wants to make entire instrument. [JH annotation: Recommended Fraunhofer for entire transit instrument and Robert Molyneux for clock.]
Let Josef Fraunhofer make WW's whole transit instrument, and mural circle as well. Attests to Fraunhofer's artistry. Germans will soon leave no stars to discover. Wishes someone would import G. F. Reichenbach's meridian circle and use it on F. W. Bessel's plan. Suggests WW order clocks from [Robert] Molyneux or [William] Hardy.
Introduces Dionysius Lardner, author of system of algebraic geometry, visiting England.
Received volume on double stars by JH and James South. Followed JH's advice, ordered instruments from Germany. Asked Josef Fraunhofer to design transit instrument to fit pillars designed by Edward Troughton. Quotes Fraunhofer's response [in French] that pillars should be moved to accommodate his instrument. David Brewster anxious for JH to answer last letter.
Edinburgh Institution's decision to order instruments from Josef Fraunhofer should send message to 'dilatory and ... abominably expensive' English artists. Axis of Fraunhofer's 8-foot transit instrument is too long. Compares those of Cambridge, Greenwich, Paris, and James South. [Robert] Woodhouse's paper in 1825 R.S.P.T. eliminated JH's hope that Cambridge would devote time to general catalogue.
Thomas Henderson will visit London and inform JH of events at Edinburgh Observatory. Will WW's paper on instrument for multiplication interfere with Charles Babbage's proposed machine?
Notes loss of many old friends. Three years seclusion with bad health produced WW's treatise on conic sections, translated to Russian. Sends book on geometrical theorems and two memoirs. Discovered JH stated in 1813 what WW thought was recent discovery about catenary.
Gratified by WW's volume. Recalls JH's catenary theorems. Writes function to complete theory of exponential transcendents. WW's applications have greater practical bearing than JH's early efforts, which JH now finds difficult to decipher. Sorry that WW declared Mr. Gilbert's tables defective.