410 



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 



