James junior, the subject of this biography, was educated at Dundee Academy, then at the University of St Andrews, completing his studies at Edinburgh University. He entered the University of St Andrews at the age of fourteen but at this time the Scottish Universities competed with the schools for the most able pupils, so it is not surprising that he entered university at such a young age. He spent six years in study at St Andrews taking courses so that he might become a Church of Scotland minister. It appears that his step-mother was keen for him to enter the Church since his health was poor and she felt that he would thrive in a profession requiring no physical abilities but one in which he could use of his mental abilities. He excelled in mathematics at St Andrews where he and his fellow student and friend John Leslie were taught by John West. His time at Edinburgh University was supposed to end in him completing his theological studies leading to his ordination, but he changed his plans after enjoying mathematics, physics and philosophy courses in Edinburgh taught by John Playfair, Dugald Stewart and others.
After his university education Ivory taught mathematics in Dundee Academy. However he did not stay long in the teaching profession and, after studying flax spinning in Darlington, he started up his own flax spinning company at Douglastown near Forfar (north of Dundee) in 1789. He never made much money from his business, but he struggled on for 14 years until the mill went into receivership. During these years he had spent much of his spare time in studying the works of Lagrange and Laplace on his own. In 1804, strongly supported by Playfair, he was appointed professor of mathematics at the Royal Military College, Great Marlow (which became Sandhurst in 1812), where he joined William Wallace who had been appointed in the previous year. It would appear that from the time of this appointment he suffered from depression. He wrote in a letter (see for example ):-
... on my coming here I was long subject to low spirits, and I put off from day to day what I would do any day, till at last the putting off became habitual and I could not prevail on myself to sit down and write.By 1815 Ivory's mental state seems to have worsened and he tried to resign his post but was persuaded to withdraw his resignation. In 1817 he suffered a serious breakdown and, for the rest of his life, he lived reclusively in London.
Ivory was elected a Fellow of the Royal Society in 1815. His difficult personality led him to quarrel with many of the British scientific establishment. Nevertheless, the Royal Society of London awarded him the Copley Medal in 1814 for his work on the orbits of comets, and the Royal Medal twice in 1826 and 1839. Between these dates, in 1838, Ivory gave the Bakerian lecture to the Royal Society, entitled On the theory of astronomical refractions. He was also honoured by many foreign scientific societies such as the Göttingen Academy in 1814, the Prussian Academy in 1826, the Academy of Sciences in Paris in 1828, the Academy of Modena in 1829, the Royal Society of Edinburgh in 1935, and the Irish Academy in 1839. He received a knighthood in 1831 which gave him a Civil List pension, and an honorary degree from the University of St Andrews in 1839.
Ivory and Wallace were early supporters of the work of the French analysts, especially Lagrange and Laplace. Ivory's critical commentary of Laplace's Mécanique céleste was praised by Laplace. Ivory wrote several articles for encyclopaedias, including the influential Equations in Encyclopaedia Britannica. His articles on Attraction and Capillary action were also major contributions to Encyclopaedia Britannica. These latter two articles concerned his main research area which involved the applications of mathematics. Most notably he made major contributions to the gravitational attraction of ellipsoids, the shape of self-gravitating rotating fluid bodies, the orbits of comets, and atmospheric refraction. His work on the ellipsoidal equilibrium configuration of self-gravitating fluids was an extension of that of Laplace, and it influenced the achievements of Jacobi and Liouville which followed.
We mentioned above that Ivory, because of his mental problems, tended to quarrel with his fellow mathematicians. His relations with Wallace deteriorated with arguments over Ivory's Attraction article to Encyclopaedia Britannica. Ivory's article on Capillary action for the same publication led to an argument with Thomas Young. Many other cases were simply caused by Ivory suffering from a quite incorrect belief that he was being persecuted by others. In fact he never joined the Royal Astronomical Society, despite his interests in astronomy, since he believed that members of that Society were systematically working against him. As De Morgan wrote that Ivory was of (see ):-
... thoroughly sound judgement in every other respect seemed to be under a complete chain of delusions about the conduct of others to himself. But the paradox is this: - I never could learn that Ivory, passing his life under the impression that secret and unprovoked enemies were at work upon his character, ever originated a charge, imputed a bad motive, or allowed himself an uncourteous expression.
Article by: J J O'Connor and E F Robertson