411 



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 v/hich 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 



