36 
Figure 12. Element on spherical surface. 
Also, the direction cosines expressed in spherical coordi- 
nates are 
cosa = sinycosy 
cos8 = sinysiny 
cos y = cosy 
Where y is the angle measured from the x-axis to projec- 
tion of the unit vector (cosa, cos8, cosy) on the x-y plane. 
Let H(x, y,z) = 1, then substituting the above relationships 
into the expression for #, and simplifying 
sinddga 6 
TT oT 
R =a" \ j Jesse [singsin,{ cos(9-x)teospcos )| 
B30 =O 
Then, integrating with respect to 6, 
TT 
R = 20a” | f{expjkacosycos@} Jo (kasinysing)singdg 
Bao 
