IVORY, JAMES (1765-1842), a Scottish mathematician, was born in Dundee in 1765. In 1779 he entered the university of St Andrews, where after four years study he graduated M.A., distinguishing himself especially as an ardent and successful student of mathematics. He then entered on a regular course of theological training ; but, after two sessions at St Andrews and one at Edinburgh, he abandoned all idea of the church, and in 1786 settled in his native town as assistant-teacher of mathematics and natural philosophy in a newly established academy. Three years later he became partner in and manager of a flax-spinning company at Douglastown in Forfarshire, still, however, prosecuting in moments of leisure his favourite studies. He was essentially a self-trained mathematician, and was not only deeply versed in the ancient and modern geometry, but had also, what was extremely rare in his country in those days, a full knowledge of the analytical methods and discoveries of the Continental mathematicians. His earliest memoir, dealing with an analytical expression for the rectification of the ellipse, is published in the Transactions of the Royal Society of Edinburgh, for the year 1796 ; and this and his later papers on " Cubic Equations " (1799) and " Kepler's Problem" (1802) evince great facility in the handling of algebraic formula;. In 1804 after the dissolution of the flax-spinning company of which he was manager, he obtained one of the mathematical chairs in the Royal Military College at Marlow (afterwards removed to Sandhurst); and till the year 1816, when failing health obliged him to resign, he discharged his professional duties with remarkable success, During this period he published in the Philosophical Transactions several important memoirs, which earned for him the Copley medal in 1814, and ensured his election as a Fellow of the Royal Society in 1815. Of special importance in the history. of attractions is the first of these earlier memoirs (Phil. Trans., 1809), in which the problem of the attraction of a homogeneous ellipsoid upon an external point is reduced to the simpler case of the attraction of another but related ellipsoid upon a corresponding point interior to it. This beautiful theorem is known as Ivory's theorem. His later papers in the Philosophical Transactions treat of astronomical refractions, of planetary perturbations, of equilibrium of fluid masses, &c. For his investigations in the first named of these be received a royal medal in 1826 and again in 1839. In 1831, on the recommendation of Lord Brongham, King William IV. granted him a pension of £300 per annum, and conferred on him the Hanoverian Guelphic order of knighthood. His more purely scientific honours sufficiently prove the high position he held among his contemporaries. Thus, besides being directly connected with the chief scientific societies of his own country, the Royal Society of Edinburgh, the Royal Irish Academy, &c., he was corresponding member of the Royal Academy of Sciences both of Paris and Berlin, and of the Royal Society of Gottingen. He died September 21, 1842.