146 Royal Society. 
no ordinary share of profound mathematical knowledge, and no 
common degree of industry and sagacity in the application of if.” 
The investigations to which we have just alluded are those upon 
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 
Mécanique Céleste. 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 compete 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 well-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 which 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 formule. 
A fifth subject was treated by Mr. Ivory in elaborate papers in 
