Royal Society. 147 
our Transactions for 1824, 1831, 1834, and in a portion of a paper 
in the Transactions for 1839. The object, in these papers, was to 
show that the method in which the equilibrium of fluid bodies has 
been treated by mathematicians is defective, one additional equation 
being, in Mr. Ivory’s views, logically 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 particular theory, to re- 
mark, that no other mathematician has agreed with Mr. Ivory in the 
necessity of his new equation. 
While Mr. Ivory still had the subject of the equilibrium, of fluids 
in his consideration, the very remarkable discovery was announced, 
by MM. Jacobi and Liousville, 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 detail 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. We 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 Guelphie Order of Knighthood was con- 
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