382 Mr. Airy on Laplace’s Investigation of the 
dC Cc : 3 : 
Hence 7 =- 3; and putting for C its value V-B, since _ 
is the same with B’, we have 
dV dV 
ane = ay ie or— b= —bB'- 7 B+ 5FV. 
2 
Now B, as we have stated above, is generally — , and therefore 
: Arb? ; : 
oo is — =. ; and making 7 = 6, we have in the present case 
ee Sue pL eee 
B=" 0h, DB =~ P. 
The equation becomes by this substitution, 
dV 20 
eh Se es 
b being the radius of the sphere passing through the given point, 
whose center is the origin of co-ordinates. This is precisely the 
substance of Laplace’s investigation (Liv. III, No. 10,) with a 
slight change of notation, and putting } instead of a, for a reason 
which we shall presently mention. 
It is to this investigation that Mr. Ivory’s objections are 
made. The equation 
dm or dm 
IG Qamsuge 
he allows is quite correct except for the particles very near the 
attracted point, for which f is very small. In that case, taking 
the complete value of f”, orf” ( ree + dr’, it is evident that 
5r> may be comparable with f’; and therefore the value of Pe 
when it is largest, will be erroneous, not only to the greatest 
amount, but also to the greatest proportional amount. And 
