36 Mr. Ivory on the Method of computing the 
the attracted point, will likewise prove that the same equation 
is true, when the solids do not touch, and when 1/ is constant, 
or has any other value whatever. 
At present I shall pass by what is said in Nos. 4 and 5 of 
Lagrange’s memoir, on which I shall offer some remarks 
below. In No. 6 he proceeds to inquire into the reason of the 
difficulty or inconsistency above-mentioned : and as it is im- 
possible to suggest any other cause than an omission in cal- 
culation, he resumes the algebraical operations of No. 2, 
carefully retaining every part of the expression concerned. 
In this manner he finds a term multiplied by the evanescent 
factor r — a ; and having valued this term, in No. 7, he ar- 
rives at the true equation f s - f a (£) = 
From the account of that part of Lagrange’s memoir which 
we have already examined, it is impossible to deny that the 
method of reasoning employed in Laplace’s demonstration 
leads directly to the formula \ s -f- a = 0 ; which never- 
theless, in a particular case, is proved by Lagrange to be a 
false equation, the true one being -§■ s + a (^) == — 2 7m 2 . v. 
Nor can it be controverted that the real reason of this diffi- 
culty, or rather error, is the omission of quantities which are 
indeed multiplied by the evanescent factor r — a, but which 
are not on that account, equal to nothing. In so far therefore 
the investigations of Lagrange coincide entirely with the con- 
clusions obtained in my paper : and in effect the method of 
analysis which he employs does not differ materially from that 
made use of in No. 6 of my paper. 
2. Let us now consider what is said in No. 4 and 5 of 
