James Stirling (11 May O.S. 1692, Garden,

Stirlingshire Stirlingshire or the County of Stirling ( ) is a Shires of Scotland, historic county and registration county of Scotland. Its county town is Stirling.Registers of Scotland. Publications, leaflets, Land Register Counties. It borders Perthshir ...

– 5 December 1770,

Edinburgh Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh ...

) was a

Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-European language family native to Scotland *Scottish English *Scottish national identity, the Scottish ide ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was nicknamed "The Venetian". The

Stirling number In mathematics, Stirling numbers arise in a variety of Analysis (mathematics), analytic and combinatorics, combinatorial problems. They are named after James Stirling (mathematician), James Stirling, who introduced them in a purely algebraic setti ...

Stirling permutation In combinatorics, combinatorial mathematics, a Stirling permutation of order ''k'' is a permutation of the multiset 1, 1, 2, 2, ..., ''k'', ''k'' (with two copies of each value from 1 to ''k'') with the additional property that, for each value ''i' ...

s, and

Stirling's approximation In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of n. It is named after James Stirling, though a related ...

are named after him. He also proved the correctness of

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

's classification of

cubic plane curve In mathematics, a cubic plane curve is a plane algebraic curve defined by a cubic equation : applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an ...

Biography

Stirling was born on 11 May 1692 O.S. at Garden House near Stirling, the third son of Archibald Stirling (1651-1715) and Anna Hamilton, and grandson of Archibald Stirling, Lord Garden, (1617-1668). At 18 years of age he went to

Balliol College, Oxford Balliol College () is a constituent college of the University of Oxford. Founded in 1263 by nobleman John I de Balliol, it has a claim to be the oldest college in Oxford and the English-speaking world. With a governing body of a master and aro ...

, where, chiefly through the influence of the

Earl of Mar There are currently two earldoms of Mar in the Peerage of Scotland, and the title has been created seven times. The first creation of the earldom is currently held by Margaret of Mar, 31st Countess of Mar, who is also clan chief of Clan Mar. Th ...

, he was nominated in 1711 to be one of Bishop Warner's exhibitioners (or Snell exhibitioner) at Balliol. In 1715 he was expelled on account of his correspondence with his cousins, who were members of the Keir and Garden families, who were noted Jacobites, and had been accessory to the " Gathering of the Brig o' Turk" in 1708. From Oxford he made his way to Venice, where he occupied himself as a professor of mathematics. In 1717 appeared his ''Lineae tertii ordinis Newtonianae, sive . . .'' (8vo, Oxford). While in Venice, also, he communicated, through

, to the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

a paper entitled "Methodus differentialis Newtoniana illustrata" (''Phil. Trans.'', 1718). Fearing assassination on account of having discovered a trade secret of the

glassmaker Glass production involves two main methods – the float glass process that produces sheet glass, and glassblowing that produces bottles and other containers. It has been done in a variety of ways during the history of glass. Glass container pro ...

s of Venice, he returned with Newton's help to London about the year 1725. In London he remained for ten years, being most part of the time connected with an academy in Tower Street, and devoting his leisure to mathematics and correspondence with eminent mathematicians. In 1730 his most important work was published, the ''Methodus differentialis, sive tractatus de summatione et interpolatione serierum infinitarum'' (4to, London), which is something more than an expansion of the paper of 1718. In 1735, he communicated to the Royal Society a paper "On the Figure of the Earth, and on the Variation of the Force of Gravity at its Surface." In the same year he was appointed manager for the

Scots Mining Company The Scots Mining Company, or Scotch Mines Company,Peter L. Payne (Ed.) (2013) ''Studies in Scottish Business History'page 119-134Routledge. Retrieved February 2015 was formed shortly after the Jacobite rising of 1715 by Sir John Erskine with the i ...

Leadhills Leadhills, originally settled for the accommodation of miners, is a village in South Lanarkshire, Scotland, WSW of Elvanfoot. The population in 1901 was 835. It was originally known as Waterhead. It is the second highest village in Scotland, ...

, where the

Scots Mining Company House The Scots Mining Company House, also known as Woodlands Hall, is an early-18th-century mansion house in Leadhills, South Lanarkshire, Scotland. The house was built around 1736 for the manager of the Leadhills mines, which were owned by the Earl ...

was built for him in 1736. His next paper to the Royal Society was concerned, not with pure but with applied sciences; specifically, a

trompe A trompe is a water-powered air compressor, commonly used before the advent of the electric-powered compressor. A trompe is somewhat like an airlift pump working in reverse. Trompes were used to provide compressed air for bloomery furnaces ...

, i.e., a water-powered air compressor that was used by a Scottish lead mine. His name is also connected with another practical undertaking, since grown to vast dimensions. The accounts of the city of

Glasgow Glasgow is the Cities of Scotland, most populous city in Scotland, located on the banks of the River Clyde in Strathclyde, west central Scotland. It is the List of cities in the United Kingdom, third-most-populous city in the United Kingdom ...

for 1752 show that the very first instalment of ten million sterling spent in making Glasgow a seaport (a sum of £28, 4s. 4d.), was for a silver tea-kettle to be presented to "James Stirling, mathematician, for his service, pains, and trouble in surveying the river towards deepening it by locks." Another edition of the ''Lineae tertii ordinis'' was published in Paris in 1797; another edition of the ''Methodus differentialis'' in London in 1764; and a translation of the latter into English by Halliday in London in 1749. A considerable collection of literary remains, consisting of papers, letters and two manuscript volumes of a treatise on weights and measures, are still preserved at Garden.

Notes

References

* This work in turn cites: ** WP. Fraser, ''The Stirlings of Keir, and their Family Papers'', (Edinburgh, 1858) ** "Modern History of Leadhills", in ''

Gentleman's Magazine ''The Gentleman's Magazine'' was a monthly magazine founded in London, England, by Edward Cave in January 1731. It ran uninterrupted for almost 200 years, until 1907, ceasing publication altogether in 1922. It was the first to use the term '' ...

'' (June 1853) ** Brewster, ''Memoirs of Sir Isaac Newton'', ii. 300, 307, 411, 516 ** J. Nicol, ''Vital Statistics of Glasgow (1881–1885)'', p. 70 ** ''Glasgow Herald'', 5 August 1886

External links

* {{DEFAULTSORT:Stirling, James 1692 births 1770 deaths 18th-century Scottish mathematicians People from Stirling (council area) James Combinatorialists Alumni of the University of Glasgow Alumni of Balliol College, Oxford Fellows of the Royal Society Scottish expatriates in Italy Scottish Jacobites Scottish surveyors British technology writers

Biography

Notes

See also

References

External links