66 
Mr. Ivory on the Attractions of an 
As to the value of V for the whole sphere, it is composed 
of two parts : one relative to the matter within the attracted 
point, which is a sphere whose radius is the distance of that 
point from the centre ; and the other, relative to the remain- 
ing matter of the sphere : the value of the first part is = 
Y . r 2 ; th# value of the second part is == \ff ( p 2 — r 2 ) x dy' . 
d^'\ therefore the w r hole value of V is = y . r 4 - f- \ff ( p 2 — r 4 ) 
. dy' . dur’ . 
By taking the difference of these two values, we get 
this is the value of V when the attracted point is within the 
spheroid ; and the terms in it that are unknown depend only 
on the radius of the surface, as in the case when the attracted 
point is without the surface. 
g. We now proceed to the application of the formulas that 
have been investigated. And in the first place we shall con- 
sider a spheroid differing little from a sphere : in W'hich case 
R = a . (l •+■ a . y'), a denoting a coefficient so small that its 
square and other higher powers may be neglected; andy a 
rational and integral function of y', s/ 1 — y 12 . cos. ■sr' and 
V= — J . r J + i .ffR'.dfi'.dvr’.Q^ 
+ r .Jf R . 4*' . dw‘ . Q 1 ' 1 
+ r ‘ R • ‘V ■ dv ' ■ Q ,2i 
&C. 
