James Stirling
James Stirling


When James Stirling was about 17, his father was arrested, imprisoned and accused of high treason because of his Jacobite sympathies. However he was acquitted of the charges. Little is known of Stirling's childhood or indeed about his undergraduate years in Scotland. The first definite information that we know is that he travelled to Oxford in 1710 in order to matriculate there. Political events conspired to keep him from graduating from Oxford, but he remained there for some time.

In 1717, Stirling published his first work which extends Newton's theory of plane curves of degree 3, adding four new types of curves to the 72 given by Newton. The work was published in Oxford and Newton himself received a copy of the work. This work also contains other results that Stirling had obtained. There are results on the curve of quickest descent, the catenary, and orthogonal trajectories.

In 1717, Stirling went to Venice. What Stirling did in Venice is not known, but he certainly continued his mathematical research. In 1722, Stirling returned to Glasgow, perhaps around the time that his friend Nicolaus Bernoulli left Padua. In 1724, Stirling travelled to London where he was to remain for 10 years. These are years in which Stirling was very active mathematically, corresponding with many mathematicians and enjoying his friendship with Newton. Newton proposed Stirling for a fellowship of the Royal Society of London, and in 1726 Stirling was elected.

Stirling became a teacher in London when he was appointed to William Watt's Academy. The school's prospectus lists a course on mechanical and experimental philosophy whose syllabus included mechanics, hydrostatics, optics, and astronomy. While in London, Stirling published his most important work Methodus Differentialis in 1730. This book is a treatise on infinite series, summation, interpolation and quadrature. The asymptotic formula for n! for which Stirling is best known appears as Example 2 to Proposition 28.

One of the main aims of the book was to consider methods of speeding up the convergence of series. He also gives a theorem to treat convergence of an infinite product. Included in this work on accelerating convergence is a discussion of De Moivre's methods. The book also contains results on the Gamma function and the Hypergeometric function. These results allowed De Moivre to extend his results.

Stirling also studied gravitation and the shape of the Earth. In 1733 Stirling read a paper to the Royal Society of London entitled Twelve propositions concerning the figure of the of the Earth. In it he stated, without proof, that the Earth is an oblate spheroid, supporting Newton against the rival Cassinian view. Certainly Stirling was considered that leading British expert on the subject for the next few years by all including Maclaurin and Simpson who went on to make major contributions themselves. As Stirling's unpublished manuscripts show, he did go much further than this paper. But in 1735, Stirling returned to Scotland where he was appointed manager of a Scotch mining company. This was a job that Stirling did very well. However the work was very demanding. Probably the pressure of work at the mining company gave him too little time to polish the work.

In 1745, Stirling published a paper on the ventilation of mine shafts. Another non-mathematical contribution by Stirling is he surveyed the Clyde with a view to rendering it navigable by a series of locks, thus taking the first step towards making Glasgow the commercial capital of Scotland. Stirling was elected to membership of the Royal Academy of Berlin in 1746. In 1753 he resigned from the Royal Society of London as he was in debt to the Society and could no longer afford the annual subscriptions.