Ivory, Sir James

(1765-1842), mathematician and mill manager

by R. E. Anderson, rev. I. Grattan-Guinness

© Oxford University Press 2004 All rights reserved

Ivory, Sir James (1765-1842), mathematician and mill manager, born in Dundee, on 17 February 1765, was the eldest son of James Ivory, watchmaker. At the age of fourteen he matriculated at St Andrews University, and after six years' study with a view to becoming a minister of the Scottish church, he went to Edinburgh to complete his theological course. He was accompanied by John Leslie (1766-1832), a fellow student at Aberdeen, who like himself had already evinced a strong mathematical bias.

Ivory returned to Dundee in 1786, and for three years taught in the principal school, introducing the study of algebra and raising the standard of general instruction. He was afterwards one of the founders of a flax-spinning mill at Douglastown, on the Carbet, near Forfar, and acted as managing partner. Henry Peter Brougham (1778-1868), later first Baron Brougham, lord chancellor, but at the time a young advocate, cultivated his acquaintance and visited him at Brigton, near the factory.

Ivory devoted all his leisure to mathematical work, especially to mathematical analysis as it was then practised on the continent. His first papers, read to the Royal Society of Edinburgh in the mid-1790s, included rectifying the ellipse, approximating to the root of an equation, and Kepler's problem.

The flax-spinning partnership was dissolved in 1804 and soon afterwards Ivory was appointed professor of mathematics in the Royal Military College, then at Marlow, Buckinghamshire, and from 1812 at Sandhurst. His work at the college was thorough and successful, though the advanced parts of the science absorbed much of his attention; he also prepared an edition of Euclid's Elements for military students. In 1809 he published the paper for which he is best remembered: it contained a theorem relating in effect the components of the attractions at any surface point to those at a particular point in its interior (or alternatively to surface attractions on two confocal ellipsoids). Although it only unified two results due to the French mathematician P. S. Laplace, it was valuable (in generality, for example), and was praised even in Paris. In 1814 he produced a study of the orbits of comets which won the Copley medal of the Royal Society; the next year he was elected fellow.

On resigning his professorship in 1819 Ivory was allowed the full retiring pension, although his period of office was shorter than the rule required. He was then in his mid-fifties and retirement allowed him time for remarkable productivity; he published nearly eighty papers between 1821 and 1842, mostly in the Philosophical Magazine, but a dozen with the Royal Society. Several concerned attractions, including the properties of equipotential surfaces (where he was the loser in a dispute of 1827 with Laplace's disciple S. D. Poisson) and the conditions for the equilibrium of bodies (including the surprising cases of rotating fluid ellipsoids with three unequal axes, which had been discovered by C. Jacobi and J. Liouville). In celestial mechanics he examined the effects of perturbation upon the orbits of planets. For planetary mechanics he focused on the shape of the earth and its determination by use of pendula, and on methods of surveying. In planetary physics he examined capillarity and the use of hygrometers, and the 'graduation of heat' and especially the refraction of light in the atmosphere. For the latter two papers he was awarded royal medals of the Royal Society in 1826 and 1839 respectively.

In 1831, on the recommendation of Lord Brougham, then lord chancellor, Ivory received a knighthood, in company with Herschel and Brewster. While not in their rank as a researcher, his work was well acknowledged, not only at the Royal Society but also abroad, where he was elected a member of the Royal Academy of Sciences of France, the Royal Academy of Berlin, and the Royal Society of Göttingen.

Ivory seems to have suffered from mental illness, maybe paranoia, in later life, thereby spoiling some of his personal relationships. He died, unmarried, at Hampstead, Middlesex, on 21 September 1842. In 1829 he had made an offer of his scientific library to the corporation of Dundee, his native town, and as there was then no public building suitable for the purpose, James Ivory (Lord Ivory), his nephew and heir, kept the books in his own collection until his death in 1866, when they became part of the Dundee Public Library in the Albert Institute.


Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London, 4 (1837-43), 406-13
N. Guicciardini, The development of Newtonian calculus in Britain, 1700-1800 (1989)
I. Grattan-Guinness, Convolutions in French mathematics, 2 (1990)
I. Todhunter, A history of the mathematical theories of attraction and the figure of the earth, 2 vols. (1873), vol. 2
A. D. D. Craik, 'James Ivory, FRS, mathematician', Notes and Records of the Royal Society, 54 (2000), 223-47

NA Scot., papers |  BL, letters to C. Babbage, Add. MSS 37182, 37185-37186, 37188, 37200
BL, letters to Macvey Napier, Add. MSS 34611-34612
RS, letters to J. W. Lubbock

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