IVORY, JAMES, a distinguished British mathematician, was born at Dundee, in 1765, and received the rudintenta of education in the public schools of that town. At fourteen years of Age ha was nut to the University of St.. Andrews; his father, who was a watchmaker, intending that hs should become a clergyman of the church of Scotland. In that university the youug man remained six years, during four of which he was occupied with the study of 'mathematics, languages, and philosophy; but the first of these subjects, from a natural inclination to that branch of science, particularly eugaged his attention : he was encouraged and ably assisted in his favourite pursuit by the Rev. John West, one of the instructor at the university ; and his great progress, which is said to have excited considerable notice, gave already indications of the eminence which, as a mathematician, be was after wards to attain. The two following years were passed in the study of theology; and Mr. Ivory then removed, in company with Mr. (after ward, Sir John) Leslie, who had been his fellow•etudent at St. Andrews, to the University of Edinburgh, where be spent one y ear in completing the course of study required as his qualification for admission to the office of minister in the Scottish Church.
It is not stated what circumstances prevented Mr. Ivory from carrying out the intentions of his father in this respect; but, on quitting the university, in 1780, he accepted an appointment as an assistant teacher in an academy then recently established iu Dundee, and he continued to fulfil the duties of that post during three years. At the end of that time he engaged with some other persona in the establishment, at Douglastown in Forlarshire, of a factory for spiuning flax ; and of this association lie appears to have been the principal person. During fifteen years (from 1769 to 180t) Mr. Ivory wee employed daily in operations apparently very uncongenial with the taste of a Imam of science; but it may be presumed that all his leisure hours were devoted to the prosecution of scientific researches. The under taking proved unsuccessful, and in 1804 the company ceased to exist. Mr. Ivory then obtained the appointment to a professorship of mathe matics in the Royal Military College, and went to reside at Marlow, iu Buckinghamshire, where that institution bad, a few years previously, been farmed. On the removal of the college to Sandhurst, in Berk. shire, Mr. Ivory accompanied it to the latter place, where he remained till his retirement from public service. He fulfilled the duties of his professorship to the great satisfaction of the governor and benefit of the students, his attention to whom was unremitting. An edition of Euclid's ' Elements,' which is known to have been cis work, though his name does not appear on the title-page, was prepared by him fur the use of the students in the college.
In the beginning of 1819 Mr. Ivory, feeling his health decline under tbo great exertions which he made in carrying on his ecieutifio researches and performing his duties as a professor, those duties leaving him but abort intervals of leisure, was induced to resigu his professorship and retire into private life. In consequence of his great
merit there was granted to him the pension due to the full period which, by the regulations, the civil officers of the institution are required to serve previously to obtaining such pension ; and which period he had not completed. After his retirement from Sandhurst, Mr. Ivory devoted himself wholly to scientific researches, and the results of his labours have been printed chiefly in the volumes of tho Philosophieal Transactions.' In 1831, in consideration of the great talent displayed in his investigations, he was by Lord Brougham, to whom he had been know(' in early life, recommended to the king (William IV.), who, with the Hanoverian Guelphic Order of Knight hood, gave him an annual pension of 3001., which he enjoyed during the rest of his life; and, in 1839, the University of St. Andrews conferred on him the degree of Doctor in Laws. Ile lived In great privacy in or near London till his death, September 21st, 1842.
Mr. Ivory's earliest writings were three Memoirs which he commu nicated in the years 1796, 1799, and 1802 to the Royal Society of Edinburgh : the first of these was entitled ' A New Series for the Rectification of the Ellipse ; the second, ' A new Method of resolving Cubic Equations; and the third, ' A New and Universal Solution of Kepler's Problem; all of them evincing great analytical skill, as well as originality of thought. He contributed fifteen papers to the ' Transactions of the Royal Society of London,' nearly all of them relating to physical astronomy, sad every one containing mathematical investigations of the most refilled nature. The first, which is entitled 'On the Attractions of Ifonaugeueous Ellipsoids,' is in the volume for 1809, and contains investigations of the attractions of such ellipsoids on points situated within them and on their exterior : the former case presents few difficulties ; but the process used by Laplace for the eolutien of the other was very complex, and Mr. Ivory bad the merit of discovering one which is remarkable for its simplicity. A. direct investigation of this case has since been given by M. Poisson.
In the volumes for 1812 and 1822 there are three papers on the 'Attractions of Spheroids,' in which Mr. ivory substituted a refined analytical process for the indirect method of Laplace ; the papers contain also some observations on the method employed by that great geometer in computing the attractions of spheroids of any form differ ing but little from spheres. Tho analytical skill shown by Mr. Ivory in these papers was frankly acknowledged by Laplace himself in a conversation which. iu 1826. he had with Sir Hnmnhry Davy.