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Thanks WW for a copy of his ''Mathematical Exposition' ['Mathematical Exposition of Some Doctrines of Political Economy', 1829]; which I feel persuaded will have great effect in placing the doctrines of Political Economy generally, on the footing of mathematical demonstration. I should be much gratified if at any future period you should find time to apply the same processes to other portions of the science. We are at the point now, where seamen were, when they began to suspect that mathematical inductions might be usefully applied to conveying a vessel from one harbour to another'.

Thanks WW for a copy of his Mechanical Euclid ['The Mechanical Euclid', 1837]: 'If I were allowed to criticise, I should feel disposed to submit, that geometry can stir more than 'four steps' without resting her foot upon an axiom. Up to the 28th Prop. of the first book of Euclid...I should be disposed to say there was nothing which it was not mere 'idleness and avoiding of labour' to refer to an axiom. Whether the great sticking-point about Parallels will ever be really got over, time must show; but if anybody should ever be fortunate enough to light on such a discovery, I apprehend there would be an end of Axioms in Euclid'. It is because we are unable to get over this point we retain the axioms. TPT believes 'that the mystery of parallels is lodged, or to be sought for, in what for shortness I will call the Platonic property of the sphere, namely that by which any sphere or spheres can be turned about the centre without change of place' [see his 'Geometry without Axioms. Or the First Books of Euclid's Elements', 1830, in which he tries to establish the theory of parallel lines without recourse to any principle not founded on previous demonstration].

TPT sends WW another attempt at solving the difficulty about the Theory of Parallels [see TPT to WW, 26 June 1837]: 'What I seem to have arrived at, after more than forty years chase, to that the solution of the difficulty, though not in what is called (properly or improperly) the lower Geometry, is in the higher. And not in so very high either' [see his 'Geometry without Axioms. Or the First Books of Euclid's Elements', 1830]..

WW does TPT's 'little books (as the French say) too much honour, in expecting from it any novel presentations of the fundamental relations of space [see his 'Geometry without Axioms. Or the First Books of Euclid's Elements', 1830]...It professes only to stand upon the fact, that the intercepted portion of the radius vector in the Equiangular Spiral is finite (or as has been preferred to call it, limited), for any limited number of revolutions; and this in defiance of the truth or untruth of Euclid's axiom on Parallels'. However the method has 'no more claim to be a novel presentation of the fundamental relations of space, than if the fact had been that, through some oversight of everybody else, it had turned out to be as easy to prove that the three angles of a triangle cannot be less than two right angles, as it is to prove they cannot be greater' [see his 'Theory of Parallels: the Proof that the Three Angles of a Triangle are Equal to Two Right Angles', 1853]. TPT made the distinction between higher and lower geometry 'merely as what exists in language. But I suppose the distinction intended is, that the higher geometry involves the method of infinitesimals or infinitely small parts, which Euclid has ably and successfully evaded by his introduction of a sum to be approached to within less than any magnitude assigned. At the same time I cannot conceal my wish, that the demonstration (supposing it always to be one) had been brought within the narrower pale'.

Gives WW a copy of a second edition of his book on Parallels ['Geometry without Axioms. Or the First Books of Euclid's Elements', 1830, in which he tries to establish the theory of parallel lines without recourse to any principle not founded on previous demonstration]: 'It contains some corrections, and alterations meant for improvements; of which the only one worth specifying, is the alteration in the lemma in the notes, in which perhaps after all, the stress of the argument resides'.

Trinity College - WW has just returned from Cornwall after making a series of pendulum experiments down a tin mine with George Airy in an attempt to measure the density of the earth ['Account of Experiments Made at Dalcoath Mine in Cornwall', 1828]: 'To tell the truth I consider that we have failed in our object nearly or altogether. Mainly in consequence of a rascally piece of steel deviating 1/10,000th of an inch from a straight line, by the fault of Thomas Jones of Charing Cross who is as great and reputable as his illustrious namesake was'. However, 'Airy who opposes a face of adamant to a fist of iron thinks he can still make something of their vagaries'. WW has been reading a pamphlet on rent by a Mr Thompson [Thomas Perronet Thompson] of Queens' College ['The True Theory of Rent, in Opposition to Mr. Ricardo and Others', 1826]: 'One inference to be made from this same pamphlet is how ripe the world is for your speculations...Here you have the fallacy of rent being the excess of richer soils, the case (no doubt most imperfectly) indicated of rent in countries where this does not apply...[in which] the influence of moral causes and national habits' are taken into consideration. If political economists 'will not understand common sense because their heads are full of extravagant theory they will be trampled down and passed over; and it will be the height of indolence and bad management if you allow other heads to take the feet of yours'. WW thinks that he recognizes 'several views which I learnt from you' in the above work of Thompson's.

Trinity College - WW has heard that RJ will be coming into this neighbourhood, and therefore wants to make sure he is around when RJ visits Cambridge. WW hopes RJ is getting his manuscript ready to show the University press syndicate ['An Essay on the Distribution of Wealth, and on the Sources of Taxation: Part 1. - Rent', 1831]. Can RJ give WW the reference to the book in which he saw 'a short list of the alteration in prices of corn pushed by the increase or diminution of the supply in certain propositions. It was in some book of the age of Petty's [William Petty] Political arithmetic'. WW is 'thinking of putting some propositions of Political Economy for instance those in Thompson's [Thomas Perronet Thompson, 'The True Theory of Rent, in Opposition to Mr. Ricardo and Others', 1826] works in a mathematical form. The more I think of it the more likely this appears to be convenient to mathematicians. I expect nothing new from this but some avoidance of confusion. As to Thompson's book you are no doubt right that it takes the case of money rents only, but it pretends not to take more; and it appears to me that with regard to them he has demonstratively shewn the Ricardists to be wrong so clearly that I am persuaded they will soon be compelled, (that is as soon as they have any writers who are not muddleheaded,) to abandon this part of their theory'.

London - WW gives his positive opinion of John Herschel's recent bride [Margaret Herschel]. WW was safely elected to the University Club [see WW to RJ, 19 Feb. 1829]. He has 'been putting on paper and reading at the Philosophical Society my mathematico-politico-economics, and I am really rather pleased with the look of my lucubrations. I shall privately have it finished (as one of our papers) and send it to the Economists whom I know by way of challenge. It does not much interfere with your speculations but I know very much that it will bear traces of what I have learnt from you, especially in the boldness with which I doubt the accuracy of the orthodox economists. It is in fact for the most part Thompson's [Thomas Perronet Thompson] book on Rent translated into formula' ['The True Theory of Rent, in Opposition to Mr. Ricardo and Others', 1826]. WW's 'object is to shew the mode of applying mathematics so as to separate difficulties of calculation from difficulties of moral reasoning - to keep apart the business of reasoning up to principles and down from them'. He wants some statements concerned with land, produce and rent: 'I have told you I do not want accuracy but definiteness'.