604] 
ELLIPSOIDAL SHELL ON AN EXTERIOR POINT. 
311 
and the mass of the shell is fgh. 3m 2 dm, where the first factor is the mass of 
O 
the ellipsoid; whence 
3mfl 2 dm 
+ 0)(g* + d)(b? + 0y 
6 being here a function of m, and m extending from 0 to 1. But taking 6 as the 
variable in place of m, the equation 
u 2 , & 2 , c 2 
f* + O + g* + 0 + h?+0~ m 
gives 
— ^dd — 2mdm; that is, 3mQ?dm = — fd6. 
Moreover m = 0 gives 0 = x>, and m = 1 gives 0 = its value as defined by the equation 
a 2 b 2 c 2 i 
f 2 + ~0 + tfTe + ¥T0~ ’ 
so that, reversing the sign, the limits are oo, 0; or, finally, writing under the integral 
sign (f> in place of 0, the formula is 
,® It 
Resolved Attraction 4- Mass of Ellipsoid = fa I . ■■ ^ — , 
- » (/ s + <*>) '/(P+4>) (f + 4>) № + 4>) 
Resolved Attraction -r Mass of Ellipsoid = 7=4 
which is a known formula.