of a homogeneous fluid, mass that revolves upon an axis. 95 
respect to nr', from u' = o to nr' = 2 tt, or the whole circum- 
ference. 
The preceding formula is true, whether the attracted point 
be without or within the body. There is however a distinc- 
dr 
and 
tion between the two cases. If we multiply by 
then integrate, we shall get 
V(r) r d_r r r R ' 3 dp dzs 
r 1 j r 3 JJs/r'—2rR y + R ' 3 ’ 
no constant quantity being necessary when the attracted 
point is without the body, because both the quantities vanish 
when r is infinitely great. But when the attracted point is 
within the body, it is necessary to add a constant quantity, 
because d ~^~, is not evanescent when r— 0 : in this case, 
therefore, we have 
v (D__r dr rr . v 
r* —J r'JJ Vr* — zr R'V"+ R'* + 5 
and 
V(r)=r-/J + K 
K being a quantity independent of r. 
It is necessary to find an expression of the value of K. For 
this purpose we have, 
\T ( r \ — f‘— f/ T R' z dR' dp'dzy' 
' r ) *y / ~)JJ V r x - 2 "r R' y + R 7 * ’ 
Expand the denominator in a series of the ascending powers 
of r ; then, 
V(r) =J ffkd'SVdyldv' 
+ rJfJdK. C (,) 
+ rf[fiX-.c (1) d^dv,' 
+ r3 Jff^r-d- }) d v .'dw' 
+ &c. 
