[ 397 ] 
V ad — XA7,or the fum of the moments of all the points 
which compofe the elliptic zone E P' E' P E F E 1 F E 
. 6 a S V u 7r a+ 
is X . 
J 3 * 4 
If the terreftrial fpheroid be cut by any plane pa- 
rallel to the plane P E P' E' P of the circle of de- 
clination, fig. l. n 2. the fedion will be an ellipfe 
fimilar to the ellipfe E F 1 E F E j and if the greater 
femiaxe c' L of this ellipfe be called X , it will be 
found, as has been already in the ellipfe E F' F F E y 
that the fum of the moments of all the points of this 
... r , r • 6a S UttX * 
elnpie to turn about its centre L, is — x . 
f o 3 4 
It has not been taken into confideration, that here 
the centre S of the fun is a little below the plane of 
the fedion, the line c S making an infenlible angle 
with the line C S. 
Calling C c ; , the moment of all the fedions pa- 
rallel to E F' E' F E to turn about the axe C c will 
be the integral of ^—7- x 
3 a S V UttX* 
x d T] or the inte- 
1 f ^ U 7T , y~>y~\x l U 7T 
s;ral of - — - x x (aa Lx ) x d 7 — - — x x 
(<2 + d T — 2a z 2 2 dT - f- T* d 2"), and this integral is 
3-^ x X (<2+ T — 1 a " 1 2~ 3 -f- } T 5 )- } and when 
V— a , the integral is 
3 a S Vu 
. x ~ 
0 1 
x IT s . 
This is 
the fum of the moments of all the points of the 
hemifpheroid of the earth formed by the fed ion 
E P' E' P E of the circle of declination, and the fum 
of the moments of all the points of the whole fphe- 
