Lot 66
Machin, John (1680-1751)
Two autograph letters signed to James Stirling
The Library of James Stirling, Mathematician
Auction: 23 October 2025 from 13:00 GMT
Description
First letter, ‘Thursday morning’, otherwise undated, possibly c.1733, on a dispute with Bernoulli, noting that ‘I shall be able to give him entire satisfaction as to every objection that he makes' on ‘whether there be a point in his locus from whence the planet will appear to move equally swiftly in the apsides and one of the middle distances', and requesting to raise the matter at the Royal Society, addressed ‘To Mr Stirling at the Academy in little Tower Street’ on integral address leaf, faint pencilled annotation ‘Mr Gregory, Mr Klingensterna, Mr Campbell, Mr [?], 2 for myself’ at end of letter, possibly by Stirling, 2 pages, 20 x 16cm;
Second letter dated 22nd June 1738, containing a detailed discussion of Maupertuis's La figure de la terre, encouraging Stirling to publish his own proposition on the subject and noting the positions of Maclaurin and Newton, together with references to ‘the scheme of a grand project of the Czarina [Catherine the Great] for making a compleat mapp of her whole empire’, Euler's work on series, and the publication of De Moivre's new book (very likely the second edition of The Doctrine of Chances): ‘Monsr Maupertuis has sent you a present of his book, which I have deliverd to Mr Watts for you. It contains a complete account of the measurement in the North. Mr Celsius likewise published two or 3 sheets on the same subject, chiefly to shew that Cassini’s measurement was far inferior … There have been great wrangles and disputes in France about this measurement … You will see that this measurement in the North … will serve to prove that the figure is much more oblate … But perhaps it will be safer to wait for the account from Peru before any conclusion be drawn … Your proposition concerning the figure … could never find a time to appear in the world with a better grace … Mr Macklaurin … taking occasion to speak of the figure of the Earth, and that Sir Is. has supposed but not demonstrated it to be a spheroid, proceeds on in the following words: “Mr Sterling if I remember right told me in April that none of those who have considered this subject have shewed that it is accurately of that figure”…', 4 pages, 23 x 18cm, splits to folds (2)
Footnote
John Machin was appointed fellow of the Royal Society in 1710, acting as secretary from 1718 and 1747. In 1712 he sat on the committee appointed to adjudicate the Newton-Leibniz priority dispute, and became professor of astronomy at Gresham College the following year. His essay ‘The Laws of the Moon’s Motion, according to Gravity' was printed in the first edition in English of Newton's Principia (1729).
His first letter, containing a riposte to Bernoulli, is probably connected to Bernoulli's lengthy letter to Stirling of 1st April 1733, for which see lot 29 (and Tweedie, pp. 141-150). The second letter contains a lucid summary of Maupertuis's newly published La figure de la terre: the presentation copy from Maupertuis to Stirling, which Machin mentions as having deposited at Watts's Academy, can be found at lot 58. Stirling had recently written his own paper on the subject, 'Of the Figure of the Earth, and the Variation of Gravity on the Surface', published in 1735, and considered it 'an important contribution to the theoretical study of the earth's shape and its gravitational forces' (ODNB). He was overtaken in his work on the subject by Colin Maclaurin and others, though it is clear from his surviving correspondence he would have made a more substantial contribution but for his commitments as manager of the mines at Leadhills.
Published:
Charles Tweedie, James Stirling: a Sketch of his Life and Works along with his Scientific Correspondence, Oxford, 1922, pp. 172-5.