[ +°I ] 
Therefore the fum of all the fimilar ellipfes which 
X ' • 2 2L 
compofe the terreftrial hemifpheroid, is f • 
ia 
Tu.%x*dr= - — —XTru.xf{aa — rryxdr, 
r ia 
which, as has been feen at the end of Prob. I. when, 
after the integration T has been made = a t will be 
i — 2.a 
— 7r [x x t 8 t ^ 5 , and multiplying by 2, the fum 
2 Cl 
of all the points of the terreftrial fpheroid will be 
( [ — 2a) x 7T x t 8 7 a \ Which was to be found. 
Corollary. 
4. If you would find the fum of the moments of 
all the points of the ring E £>^E' Jig. 1. n° 2 . 
turning about the axe * 
The moment of an element L of the crown placed 
at the diftance X from the axe of rotation is 
a a d u x — 
a 
tity of matter by the motion, and by the arm of the 
a dP 
leaver. But in the circle E $JE' E we have, d u j 
X 
therefore the moment of an element of the crown is 
a a julY. X d P, whofe integral, which is a a ^ x a a tt, 
gives the fum of the moments of all the points of the 
crown. Which was to be found. 
E e e 
Pro- 
