**IVORY, SIR JAMES** (1765–1842), Scottish mathematician,
was born in Dundee in 1765. In 1779 he entered the university
of St Andrews, distinguishing himself especially in mathematics.
He then studied theology; but, after two sessions at St Andrews
and one at Edinburgh, he abandoned all idea of the church, and
in 1786 he became an assistant-teacher of mathematics and
natural philosophy in a newly established academy at Dundee.
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 ancient and modern geometry, but also had 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*
(1796); and this and his later papers on “Cubic Equations”
(1799) and “Kepler’s Problem” (1802) evince great facility
in the handling of algebraic formulae. 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 falling 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 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
he received a royal medal in 1826 and again in 1839. In 1831,
on the recommendation of Lord Brougham, King William IV.
granted him a pension of £300 per annum, and conferred on him
the Hanoverian Guelphic order of knighthood. 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
Göttingen. He died at London on the 21st of September 1842.

A list of his works is given in the *Catalogue of Scientific Papers of the Royal Society of London*.