which Mr. Ivory's European reputation as a consummate mathema- tician was principally founded ; and deservedly so. It is no small praise, even at the present time, to assert of any mathematician, that he thoroughly understands the remarkable investigations of Laplace applying to the attractions of spheroids ; and it would be still greater to assert that he is able to substitute a new, clear, and elegant pro- cess, in place of one portion which seems doubtful and indirect. But at the time when these papers were written (1808 and 1811) the merit was vastly greater than it would be now. Very few English mathematicians could then read with ease an investigation written in the notation of the differential calculus ; scarcely any could un- derstand a process of partial differentials ; and probably not another person in the kingdom besides Mr. Ivory had read that part of the Mecanique Celeste. In acknowledging that Mr. Ivory most justly earned the reputation which he acquired (and our remarks above, detracting from the necessity of his criticism, do not in the least detract from its singular skill and command of mathematics), we must not omit also to acknowledge, that to his example we owe, in no inconsiderable degree, that direction of mathematical study which has enabled England, at last, to comjDcte in the field of mathematical science with the other nations of Europe, to which she was during a long interval inferior.
The third subject is the investigation of the orbits of comets, Mr. Ivory's method, printed in the Transactions for 1814, is founded on the supposition that the orbit is a parabola, and it tests the trial- assumption of the distance of the comet by the v/ell-known expres- sion for the time depending on two radii vectores and the chord joining them. Although the analysis is elegant, there is not much of originality in this process.
The fourth subject is the investigation of atmospheric refraction. The papers relating to this are contained in the volumes for 1823 and 1838. The former of these proceeds solely on the supposition that the temperature of the air (as entering into the factor which connects the density with the elasticity) decreases uniformly for uniform increase of elevation. The investigation is not remarkably different from those of other writers on the theory of astronomical refractions. The latter contains the effects of adding to the ex- pression for the density of the air resulting from the first supposition, a series of terms following a peculiar law which make the expression perfectly general for all laws of temperature, and Vvhich at the same time offer great facilities for mathematical treatment. The whole investigation deserves particular notice as a beautiful instance of mathematical skill. Considerable labour was also bestowed by Mr. Ivory, in these papers, on the ascertaining, from the best accredited experiments, of the values of the constants which enter into different parts of the formulse.
A fifth subject was treated by Mr, Ivory in elaborate papers in 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
