REVIEWS 



MATHEMATICS 



James Stirling : A Sketch of his Life and Works along with his Scientific 

 Correspondence. By Charles Tweedie, M.A., B.Sc, F.R.S.E. 

 [Pp. X + 213.] (Oxford : at the Clarendon Press, 1922. Price i6s. 

 net.) 



The life of James Stirling, of Stirling's Theorem, is full of interest. He was 

 born in 1692, and at Balliol College, Oxford, was involved in the Jacobite 

 disturbances of 1714-16, when " mobbs begun to pull down meeting houses 

 and whiggs houses." In 1716 he was tried at the Assizes for " cursing K. 

 George," but was found not guilty. It is commonly stated that he was 

 expelled from Oxford for his Jacobite leanings, but this is not borne out by 

 the entries in the Diary of Thomas Hearne, the antiquary, which form our 

 chief source of information for this period of Stirling's life. Anyhow, he lost 

 his Snell and Warner Exhibitions " upon account of the Oaths " and went 

 to \ enice with Nicholas Tron, Venetian Ambassador at the English Court, 

 after having published, in 171 7, a commentary on Newton's Lineae Tertii 

 Ordinis. He was offered a chair of Mathematics, in which University is not 

 quite clear, but had to refuse it on account of his religion. To this period 

 belongs a letter of thanks to Newton, which has been printed before by 

 Brewster. From 1719 to 1724 we lose sight of him, but in the latter year he 

 was in London, where he taught Mechanics at Watt's Academy in Little 

 Tower Street, in which he had acquired an interest. He was admitted to the 

 Royal Society in 1726, and became acquainted with most of the mathe- 

 maticians of the day — Maclaurin, Cramer, N. Bernoulli, Euler. In 1735 he 

 was appointed to the managership of the Leadhills Mines in Scotland, and 

 held it till his death in 1770 ; but his removal from London and his business 

 activities, in which he was extremely successful, necessitated his giving up 

 his mathematical work. 



Mr. Tweedie gives a summary of Stirling's works, the commentary on 

 Newton above referred to, the Methodus Differentialis (1730), by which he is 

 best known, which is concerned with the Calculus of Finite Differences, and 

 which contains his series, and his papers in the Philosophical Transactions. 

 But the greater part of the book is occupied with Stirling's scientific corre- 

 spondence, preserved at the family seat of Garden. There are also four letters 

 to Maclaurin in the Maclaurin MSS. at Aberdeen. Most of the letters are to 

 Stirling, from Maclaurin, Cramer, and others, and they throw a good deal of 

 light upon obscure points in the history of mathematics. 



Mr. Tweedie is to be congratulated upon a scholarly piece of work, which 

 it is to be hoped will result in the discovery of further letters of Stirling. 



F. P. W. 



First Course in the Theory of Equations. By Leonard Eugene Dickson, 

 Ph.D. [Pp. vi + 168,] (New York : John Wiley & Sons, 1922. Price 

 8s. dd. net.) 



This book differs essentially from the author's Elementary Theory of Equations, 

 being intended for younger students, the proofs employed being simpler and 



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