## James Stirling: |

The life of Stirling has already formed the subject of a very readable article by Dr J C Mitchell, published in his work, *Old Glasgow Essays* (MacLehose, 1905). An interesting account of his life as manager of the Leadhills Mines is also given by Ramsay in his *Scotland and Scotsmen in the Eighteenth Century.*

The sketch I here present to readers furnishes further details regarding Stirling's student days at Balliol College, Oxford, as culled from contemporary records, along with more accurate information regarding the part he played in the Tory interests, and the reason for his departure for Italy. Undoubtedly, when at Oxford, he shared the strong Jacobite leanings of the rest of his family. Readers familiar with Graham's delightful Social Life in Scotland in the Eighteenth Century, and the scarcity of money among the Scottish landed gentry, will appreciate the tone of the letter to his father of June 1715, quoted in full in my sketch.

Whether he ever attended the University of Glasgow is a moot point. Personally, I am inclined to think that he did, for it was then the fashion to enter the University at a much earlier age than now, and he was already about eighteen years of age when he proceeded to Oxford.

Very little is known regarding his stay in Venice and the date of his return to Britain; but his private letters show that when he took up residence in London he was on intimate terms of friendship with Sir Isaac Newton and other distinguished scholars in the capital.

I have taken the opportunity here to add - what has hitherto not been attempted - a short account of Stirling's published works, and of their relation to current mathematical thought. In drawing up this account, I had the valuable assistance of Professor E T Whittaker's notes on Part I of Stirling's *Methodus Differentialis,* which he kindly put at my disposal.

Stirling's influence as a mathematician of profound analytical skill has been a notable feature within the inner circle of mathematicians. Witness, for example, the tribute of praise rendered by Laplace in his papers on Probability and on the Laws of Functions of very large numbers. Binet, in a celebrated memoir on Definite Integrals, has shown Stirling's place as a pioneer of Gauss. Gauss himself had most unwillingly to make use of Stirling's Series, though its lack of convergence was anathema to him. More recently, Stirling has found disciples among Scandinavian mathematicians, and Stirling's theorems and investigations have been chosen by Professor Nielsen to lay the foundation of his Monograph on Gamma Functions.

The Letters, forming the scientific correspondence of Stirling herewith published, make an interesting contribution to the history of mathematical science in the first half of the eighteenth century. I have little doubt that suitable research would add to their number. I have endeavoured to reproduce these as exactly as possible, and readers will please observe that errors which may be noted are not necessarily to be ascribed to negligence, either on my part or on that of the printer. For example, on page 47, the value of /2 given by De Moivre's copy of Stirling's letter (taken from the *Miscellanea Analytica)* is not correct, being 1.57079632679, and not 1.5707963279 as there stated.

A few notes on the letters have been added, but, in the main, the letters have been left to speak for themselves.

I am deeply grateful for the readiness with which the Garden letters were placed at my disposal by Mrs Stirling, Gogar House, Stirling. I am also indebted to the University of Aberdeen for permission to obtain copies of Stirling's letters to Maclaurin.

In the troublesome process of preparing suitable manuscript for the press, I had much valuable clerical assistance from my sister, Miss Jessie Tweedie.

Of the many friends who have helped to lighten my task I am particularly indebted to Dr C G Knott, F.R.S., and to Professor E T Whittaker, F.R.S., of Edinburgh University; also to Professor George A Gibson, of Glasgow University, who gave me every encouragement to persevere in my research, and most willingly put at my disposal his mature criticism of the mathematicians contemporary with Stirling.

Facsimile reproductions of letters by James Stirling and Colin Maclaurin have been inserted. These have never before appeared in published form, and will, it is hoped, be of interest to students of English or Scottish history, and to mathematical scholars generally.

The heavy cost of printing during the past year would have made publication impossible but for the generous donations from the contributors mentioned in the subjoined list of subscribers, to whom I have to express my grateful thanks.

CHARLES TWEEDIE.

JOC/EFR August 2007

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