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69 Gower Street - Has sketched out a proof 'of the composition of forces which seems to separate the mathematical from the mechanical part better than Poisson's, and to shew the mathematical bearing of one or two steps much better'. If [D. F.] Gregory approves of it, ADM would like WW to communicate it to the Cambridge Philosophical Society Journal. Has been looking at [Jacob] Hermann's Phoronomia and would like to learn more about Hermann.

St James's Place - Thanks WW for the Calendar 'which exactly suits the purpose'. Not much is going on in Paris in the way of science. JWL gives the references to Cauchy's [Augustin Louis Cauchy] investigations connected to the theory of light. JWL is anxious to know what WW thinks of them and of Poisson's [Simeon D. Poisson] work on Capillary Attraction. Poisson told JWL that he thought it desirable that the moon should be treated like the planets. He also promised to examine Laplace's theory of the tides when he got JWL's tables: 'He seemed not to have thought much on the subject'.

Edinburgh - JDF would like WW to be at the next meeting of the Council of the Royal Society, where they are going to discuss JDF's paper - 'On the Hot Springs of the Pyrenees and the Verification of Thermometers'. The Society referees suggested the results should begin in a tabular form, which would have meant JDF restructuring more than two thirds of the paper. He complained to the Secretary of the Society and convinced the referees that they were wrong in their suggestion: 'excellent as is the system of Reference employed by the council, it has a dangerous tendency to degenerate into a system of minute interference to which few authors will submit, when papers of acknowledged merit stand a chance of rejection because their form or construction may not coincide with that which the individual to whom they may be referred, may think the best possible'. The paper is soon to be brought before the Council and JDF is keen for it to appear in the next issue of the Transactions of the Royal Society. JDF understands that 'a very engaging young man' (Robert Leslie Ellis) - who JDF met two years ago in Bath - is to be WW's student. JDF has 'set about getting Thermometers constructed up to 25 ft long for sinking in the ground. I mean to have one set in solid Trap Rock and another in sand or clay' [The purpose of these experiments was to ascertain the progress of solar heat in the crust of the globe]. What JDF has seen of Poisson's book on heat [S.D. Poisson, Theorie Mathematique de la Chaleur, 1835] 'does not at all raise my opinion of him as a Physician'.

The Athenaeum Club - JDF did not suppose that WW's Report [Report on the Recent Progress and Present Condition of the Mathematical Theories of Electricity, Magnetism and Heat, Report of the BAAS, 5th meeting, 1835] would cover his subject [heat], neither was his last letter meant to influence WW's conclusions [see JDF to WW, 2 Oct. 1836]: 'but knowing that your attention had been generally turned to the subject and to Mr Murphy's [Robert Murphy] views I thought it probable that you might have heard the objection which having a certain mathematical plausibility might have struck you'. If WW can he should read JDF's short article on the subject drawn up for the Philosophical Magazine - if WW is at Taylor's ask him for a copy. What does WW think of Poisson's views? [S.D. Poisson, Theorie Mathematique de la Chaleur, 1835]: JDF has 'bought the book but only read the statement of them inserted by himself in the Annales de Chimie. I confess it is very provoking to see him knocking down Fourier's [Joseph Fourier] results right and left (they were on bad terms when he was alive) and above all giving space a temp. of - 13 cent. seems too absurd. Whatever his transcendent merit as a mathematician may be I have lost a good deal of my respect for him as a physician lately'.

Clermont-Ferrand - JDF has 'an inborn love of mountains and detestation of plains' and consequently 'lingered in the Pyrenees' and explored them all summer: 'On the hot springs and their connexion with geology I have collected a quantity of good facts, while I must try to methodize a little sooner those I have been able to do with the results of my last tour'. He has also been pursuing magnetic researches on the Spanish border. However, the Pyrenees 'are not to be named beside the Alps'. The people of Gavarnie have peculiar manners and dress, while their 'language is singularly corrupt, generally approaching the Catalan, and totally distinct from the Basque which is only spoken at that extremity of the Pyrenees which I did not visit'. Thanks WW for the news he sent concerning the BAAS meeting in Dublin. Does WW like Poisson's book ? [S.D. Poisson, Theorie Mathematique de la Chaleur, 1835]. JDF has not seen it: Poisson 'refuses still assent to the undulatory theory (an old grudge) says he thinks we shall return to the true theory by the way of Heat; of course I thought exactly the reverse'.

Boroughmuirhead, nr. Edinburgh - JDF thanks WW for his letter and is very satisfied with his recommendations to his queries [see JDF to WW, 29 May 1831]. He has subsequently purchased a copy of Poisson [S. D. Poisson's Traite de Mechanique, 1811?]. JDF has been studying some of the more difficult parts of the Integral Calculus: completing a paper on the barometer, and conducting an 'experimental examination of a curious question on heat which appears to me to be yet quite unexplained'. JDF read WW's paper on David Ricardo 'with a great deal of pleasure', and gives some minor corrections [Mathematical Exposition of some of the Leading Doctrines in Mr Ricardo's Principles of Political Economy and Taxation, 1831]. The Edinburgh University library has an incomplete collection of the Transactions of the Cambridge Philosophical Society and would like WW to forward the missing volumes. He hopes WW will make the first BAAS meeting at York. 'Is Herschel's [John Herschel] Treatise on finite differences only to be found in his translation of Lacroix, which is now very scarce?'.

S. A. Street - WW should have little difficulty in gaining the Professorship in Mineralogy at Cambridge: 'Were there any chance that this would confine you exclusively to minerals, I should be sorry for its having come into your head: though no doubt you will be able to find excellent 'sermons in stones'. But as of course nothing will induce you to shut yourself up even in a diamond cage, I rejoice heartily in the prospect of having their German science so well got up for our market, in a more practical and substantial form, and of having much to send them back in return'. The Johnians will be very proud of their [academic prize] medals. Taylor asked JCH whether an English translation of Simeon D. Poisson would be a saleable work in Cambridge: 'A certain Thomas Atkinson had proposed it to him. I answered, I believed not, but knew nothing about the matter. If you think it would be a desirable work, send me word, and I will desire him to undertake it'.

7 Camden Street, N.W. - ADM has found 'a mechanical mistake which I find in all writers - Poisson states it broadly in his last edition. I take the case of it which belongs to a point vdv = Xdx + Ydy + Zdz throwing out reactions, which produce no effect', which he then works out. In a postscript he shows a simple construction to find the centre of gravity of a four sided figure.