4 ° 
Mr. Ivory on the Method of computing the 
whole fluent will likewise be equal to nothing, when the eva- 
nescent factor is raised to a higher power in the numerator 
than in the denominator. 
The explication here given is sufficient to clear up the 
paradox of Lagrange; and it certainly proves the inconclu- 
sive nature of Laplace's demonstration. One more remark 
is suggested by what has been said : the theorem of the last 
mentioned geometer is investigated by means of the direct 
method of fluxions alone, whereas the rules of the integral 
calculus are required in order to make the process rigorous 
and exact. 
3. Lagrange having, in No. 7, obviated the difficulty in 
regard to the particular case when the thickness of the mole- 
cules spread over the surface of the sphere is a constant quan- 
tity, proceeds, in No. 8, to consider the general case when the 
thickness of the molecules is any function of the sines and 
cosines of the angles & and that determine the position of 
a molecule with regard to a fixt pole on the surface of the 
sphere. In this case also the equation in the Mecanique Celeste , 
viz. 
27 
T~ 
iV + «[f) = - 
cannot be exact, unless the equation 
is + a = — zna' . v 
be proved to be true instead of the equation f s -f- a J^-j 
which would result from the demonstration of Laplace. 
It must be recollected that 
S — ad . 
V r r — 2 ra . y + a z 
and that v is the same function of the sines and cosines of the 
