191 
As an example, consider a sphere, the diameter of which 
is 2P, and let the direction angles of the primitive diameter 
foe a, p>, y, and let the sphere be divided into sections per- 
pendicular to this diameter. Consider one of these sections 
whose radius is r, let l foe the length of the diameter inter- 
cepted between this section and the lower part of the sphere, 
then we shall have 
The circular section projected on the plane xy will foe an 
ellipse whose semi-axes are r and rcosy, the area of this 
ellipse will be 7rr 2 cosy ; hence we have 
2 is the projection of the line l on the axis of 0 . Therefore 
iz = Aosy 
Substituting this value of l in (16) we obtain 
r 2 = 2Tll-P 
(16) 
r z 
Vs = 7rCOSy / r\lz 
(17) 
o 
r 2 =2R-^-- — 2- 
COSy COS y 
and substituting this value of r 2 in (17) we obtain 
P 9,’Rn.nsiv 
O 
In a similar manner we may obtain 
r>r\c 
o 
o 
Performing the integrations we obtain 
Y z — f 7rR 3 COS 2 y 
Y y = |ttR 8 cos 2 /3 
Y* = |7rR 3 COS 2 a 
