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Charles Hutton (14 August 1737 – 27 January 1823) was an English mathematician. He was professor of mathematics at the Royal Military Academy, Woolwich from 1773 to 1807. He is remembered for his calculation of the density of the earth from Nevil Maskelyne's observations on Schiehallion.
Hutton was born at Newcastle-on-Tyne.^{[1]} the son of a superintendent of mines, who died when he was still very young.^{[2]} He was educated at a school at Jesmond, kept by Mr Ivison, a clergyman of the Church of England. There is reason to believe, on the evidence of two pay-bills, that for a short time in 1755 and 1756 Hutton worked in the colliery at Old Long Benton. Following Ivison's promotion to a living, Hutton took over to the Jesmond school, which, in consequence of his increasing number of pupils, he relocated to nearby Stotes Hall. While he taught during the day at Stotes Hall, he studied mathematics in the evening at a school in Newcastle. In 1760 he married, and began teaching on a larger scale in Newcastle, where his pupils included John Scott, later Lord Eldon, who became Lord High Chancellor of England.^{[1]}
In 1764 he published his first work, The Schoolmasters Guide, or a Complete System of Practical Arithmetic, which in 1770 was followed by his Treatise on Mensuration both in Theory and Practice.^{[1]} At around this time he was employed by the mayor and corporation of Newcastle to make a survey of the town and its environs. He drew up a map for the corporation; a smaller one, of the town only, was engraved and published.^{[3]} In 1772 he brought out a tract on The Principles of Bridges, a subject suggested by the destruction of Newcastle bridge by a high flood on 17 November 1771.^{[1]}
He left Newcastle in 1773, following his appointment as professor of mathematics at the Royal Military Academy, Woolwich.^{[1]} He was elected a Fellow of the Royal Society in July, 1774 ^{[4]} He was asked by the society to perform the calculations necessary to work out the mass and density of the earth from the results of the Schiehallion experiment – a set of observations of the gravitational pull of a mountain in Perthshire made by the Astronomer Royal, Nevil Maskelyne,^{[5]} in 1774–76.^{[1]} Hutton's results appeared in the society's Philosophical Transactions for 1778, and were later reprinted in the second volume of Hutton's Tracts on Mathematical and Philosophical Subjects. His work on the question procured for him the degree of LL.D. from the University of Edinburgh. He became the foreign secretary of the Royal Society in 1779. His resignation from the society in 1783 was brought about by tensions between its president Sir Joseph Banks and the mathematicians amongst its members.^{[1]} He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1788.^{[6]}
After his Tables of the Products and Powers of Numbers, 1781, and his Mathematical Tables of 1785 (second edition 1794), he issued, for the use of the Royal Military Academy, in 1787 Elements of Conic Sections, and in 1798 his Course of Mathematics. His Mathematical and Philosophical Dictionary, a valuable contribution to scientific biography, was published in 1795 and the four volumes of Recreations in Mathematics and Natural Philosophy, mostly translated from the French, in 1803. One of his most laborious works was the abridgment, in conjunction with G. Shaw and R. Pearson, of the Philosophical Transactions. This undertaking, the mathematical and scientific parts of which fell to Hutton, was completed in 1809, and filled eighteen quarto volumes.^{[1]} From 1764 he contributed to the The Ladies' Diary (a poetical and mathematical almanac established in 1704), and became its editor in 1773-4, retaining the post until 1817.^{[7]} He had previously begun a small periodical called Miscellane Mathematica, of which only to thirteen numbers appeared; subsequently he published five volumes of The Diarian Miscellany which contained substantial extracts from the Diary.^{[1]}
He resigned his professorship in 1807, due to ill health, although he served as the principal examiner of the Royal Military Academy, and also to the East India College at Addiscombe for some years after his retirement. The Board of Ordance had granted him a pension of £500 a year.^{[2]} During his last years he worked on new editions of his earlier works.^{[8]}
He died on 27 January 1823, and was buried in the family vault at Charlton, in Kent.^{[2]}
During the last year of his life a group of his friends set up a fund to pay to have a marble bust made of him. It was executed by the sculptor Sebastian Gahagan. The subscription exceeded the amount necessary, and a medal was also produced, engraved by Benjamin Wyon, showing Hutton's head on one side and emblems representing his discoveries about the force of gunpowder, and the density of the earth on the other.^{[2]}
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