James Stirling (mathematician)
Encyclopedia
James Stirling was a Scottish
mathematician
. The Stirling number
s and Stirling's approximation
are named after him.
, where, chiefly through the influence of the earl of Mar, he was nominated (1711) one of Bishop Warner's exhibitioners (or Snell exhibitioner
) at Balliol. In 1715 he was expelled on account of his correspondence with 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 Isaac Newton
, to the Royal Society
a paper entitled “Methodus differentials Newtoniana illustrata” (Phil. Trans., 1718). Fearing assassination on account of having discovered a trade secret of the glassmakers 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, it must be noted, 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 at Leadhills
. We are thus prepared to find that his next paper to the Royal Society was concerned, not with pure, but with applied science — “Description of a Machine to blow Fire by the Fall of Water” (Phil. Trans. 1745). His name is also connected with another practical undertaking, since grown to vast dimensions. The accounts of the city of Glasgow
for 1752 show that the very first instalment of ten millions sterling spent in making Glasgow a seaport, viz. 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.
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. The Stirling number
Stirling number
In mathematics, Stirling numbers arise in a variety of combinatorics problems. They are named after James Stirling, who introduced them in the 18th century. Two different sets of numbers bear this name: the Stirling numbers of the first kind and the Stirling numbers of the second...
s and Stirling's approximation
Stirling's approximation
In mathematics, Stirling's approximation is an approximation for large factorials. It is named after James Stirling.The formula as typically used in applications is\ln n! = n\ln n - n +O\...
are named after him.
Biography
Stirling was the third son of Archibald Stirling of Garden, and grandson of Sir Archibald Stirling of Keir (Lord Garden, a lord of session). At 18 years of age he went to Balliol College, OxfordBalliol College, Oxford
Balliol College , founded in 1263, is one of the constituent colleges of the University of Oxford in England but founded by a family with strong Scottish connections....
, where, chiefly through the influence of the earl of Mar, he was nominated (1711) one of Bishop Warner's exhibitioners (or Snell exhibitioner
Snell exhibitioner
The Snell Exhibition is an annual scholarship awarded to a student of the University of Glasgow to allow him or her to undertake postgraduate study at Balliol College, Oxford. The award was founded by the bequest of Sir John Snell in a will made in 1677, although the original stipulation referred...
) at Balliol. In 1715 he was expelled on account of his correspondence with members of the Keir and Garden families, who were noted Jacobites
Jacobitism
Jacobitism was the political movement in Britain dedicated to the restoration of the Stuart kings to the thrones of England, Scotland, later the Kingdom of Great Britain, and the Kingdom of Ireland...
, 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 Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
, to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
a paper entitled “Methodus differentials Newtoniana illustrata” (Phil. Trans., 1718). Fearing assassination on account of having discovered a trade secret of the glassmakers 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, it must be noted, 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 at Leadhills
Leadhills
Leadhills is a village in South Lanarkshire, Scotland, 5¾ miles WSW of Elvanfoot. Population 835. Originally known as Waterhead, It is the second highest village in Scotland after Wanlockhead, lying 395m above sea-level, near the source of Glengonnar Water, an affluent of the River Clyde...
. We are thus prepared to find that his next paper to the Royal Society was concerned, not with pure, but with applied science — “Description of a Machine to blow Fire by the Fall of Water” (Phil. Trans. 1745). His name is also connected with another practical undertaking, since grown to vast dimensions. The accounts of the city of Glasgow
Glasgow
Glasgow is the largest city in Scotland and third most populous in the United Kingdom. The city is situated on the River Clyde in the country's west central lowlands...
for 1752 show that the very first instalment of ten millions sterling spent in making Glasgow a seaport, viz. 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.