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Salford, Manchester - EH hopes WW will accept his enclosed essays, and hopes it supplies some of the deficiencies adverted by WW in his preface to his Treatise on Mechanics. As Vice President of the BAAS, would WW allow him to give an abstract of his paper at the next meeting in Cambridge. He hopes WW excuses his boldness in sending him his work, but he was encouraged to do so by the positive reactions he had already received from Dr Gregory [Olinthus Gregory] and Mr Barlow [Peter Barlow].

EH gives the mathematical results which arise out of his paper on impact which he is to read at the BAAS meeting at Cambridge [see EH to WW, 2 June 1832]: 'These deductions, with a formula comparing the deflections with the velocities of impact, and an experimental comparison of impact with pressure in this case, form the basis of the paper'.

Pendleton, Manchester - Thanks WW for the present of his work and on looking over his paper on impact, EH offers a further explanation concerning his method used 'in seeking by an approximate mode for the inertia of the bar'. He is trying to find a near value of the inertia of a beam on impact: 'The inertia, I presume depends on the form of the curve, and its strict determination is above my feeble powers. The curve from impact is obviously in some degree serpentine, particularly where the beam is struck toward the ends. This was mentioned to me by Sir John Herschel at Cambridge. I had not however been able to discover any undulations in the form of the curve, under the small impacts in my experiments. The subject of impact I hope to inquire further into, but I feel I must skim upon the surface for want of more mathematical knowledge. Poisson I have heard has something fresh in the 2nd edition of his mechanics - I must get it'. WW expressed a wish to use some of EH's work on Beams and Chain Bridges in the new edition of his Treatise on Mechanics and he is welcome to do so. The paper on the performance of steam engines was a private communication to one of the secretaries to the Philosophical Society [Manchester], and is by an engineer called Edward Dixon, who is in the office with his brother the engineer of the Manchester end of the railway. They are willing to give as much information as they can: 'The short paper alluded to commences with a definition of 'Horse Power' as applied to Engines - shews the superiority of Engines over horses on Railways gives the amount of friction on them - and some calculations and facts as to the power of Engines to take loads up the small inclinations. The paper when modified and improved by the author, and some additional facts are added to it, will be sent to you to use what you please of it'.

Salford Street, Manchester - Since WW has expressed a desire to publish his paper on impact [see EH to WW, 7 Sept. 1833] in the next volume of the BAAS, EH would like to render it as worthy of the honour as he can: 'Before I sent the paper to Edinburgh, I saw what must be the law that governs the elasticities in collisions between bodies of different natures - but as I had not then sufficient evidence to prove it wholly; I thought it best to restrict myself to what I could prove; I trust however that it is now brought forward with sufficient evidence. Indeed its agreement being greatest where the modulus of elasticity was most in doubt'. This law has an 'interesting application in theoretical inquiries at the end of your mechanics and where the striking body and the body struck are different in nature and introduces modifications which in your hands would be very interesting'.

Salford, Manchester - Could WW give his opinion concerning the mathematical solution to a problem he is to present at Dublin. The problem concerns a perforated ball suspended from a wire, with another ball slipping unresisted down the wire causing it to extend a certain length.

Salford, Manchester - Encloses his paper for a final reading before it is printed. The paper is a combination of the one he read at the BAAS meeting at Cambridge [see EH to WW, 28 Feb. 1835] and later at Dublin on the subject of vertical impacts. If Whewell has no comments to make he would be grateful if he sent the proof sheet to Mr Taylor at Red Lion Court off Fleet Street. Hodgkinson meets 'with great opposition from Dr Dalton [John Dalton] in these matters because I do not use Bernoulli's definition of force (considered as the square of the velocity) and reject the Newtonian as erroneous'. For Dalton to consider force as simply the velocity has introduced numerous errors. What does Whewell think?

Salford, Manchester - Although EH cannot attend the BAAS meeting at Liverpool due to illness, he would like to introduce WW to William Fairbairn - 'the engineer to whose liberal views I am so much indebted - and whose manufactory, while it is supplying models to the scientific man, and machines to all parts of Europe, is - to say nothing of his place in London - one of the lions of this neighbourhood'. EH was sorry not to see the subject of impact in WW's History of the Inductive Sciences.