Page:Proceedings of the Royal Society of London Vol 4.djvu/437

Rh been treated by mathematicians is defective, one additional equation being, in Mr. Ivory's views, logicall}" necessary, although he allows that its introduction produces no change of results in the case which he has investigated at great length, namely, that of a homogeneous fluid. The Royal Society have conceived that the acknowledged uncommon abilities of Mr. Ivory, and the great attention which he had given to this particular subject, made it almost imperative on them to afford every facility which their Transactions could give to the elucidation of his views, more especially as the logical foundation of the theory had scarcely been canvassed to the same extent as that of many other physico-mathematical theories. At the same time they think it necessary, in adverting to this j)articular theory, to re- mark, that no other mathematician has agreed v/ith Mr. Ivory in the necessity of his nev/ equation.

While Mr. Ivory still had the subject of the equilibrium of fluids in his consideration, the very remarkable discovery v/as announced, by iM?vI. Jacobi and Liousviile, that it is theoretically possible that a homogeneous ellipsoid with three unequal axes, revolving about one of these axes, may be in equilibrium. In a paper in the Trans- actions for 1838, Mr. Ivory has with great elegance demonstrated this theorem., and has given, with greater det-ail than its authors had entered on, several statements regarding the limitations of the pro- portions of the axes. This may be regarded as the sixth subject.

A seventh subject, the Theory of Perturbations, was treated in papers in the Transactions for 1832 and 1833. The first of these is a treatment of the theory of the variation of the elements, giving no new result, but simplified, in the author's opinion, by the intro- duction of the area described upon the planet's moving orbit. The second relates merely to the expansion of the perturbing function, in which, by departing in some degree from the usual process, Mr. Ivory conceived that he had given greater facilities for the develop- ments to the higher order of excentricities and inclinations.

An eighth subject, which we have reserved for the last, as con- taining nothing of a physical character, is the Theory of Elliptic Transcendents, treated in the Transactions for 1831. Vve are not aware that anything important is added to the theory in this paper, although a new form is given to some of the demonstrations.

The great scientific reputation which Mr. Ivory had established by these and other memoirs not communicated to the Royal Society ensured his election into this Society in 1815, and into many of the other Scientific Societies of this country and of the Continent. He was an Honorary Fellow of the Royal Society of Edinburgh, an Honorary Member of the Royal Irish Academy, and of the Cam- bridge Philosophical Society; Corresponding Member of the Royal Academy of Sciences of the Institute of France, of the Royal Aca- demy of Sciences of Berlin, and of the Royal Society of Gottingen.

In 1831, the Hanoverian Guelphic Order of Knighthood was con- ferred on him by King William IV., and it was intimated that he might also receive the British Knighthood, but this he declined, as the title would have been inconsistent with his circumstances. He