228 



PIERCE. 



By this proposition, refei-ring to Figure 10, we see that 



TT 



IT . 



COS \l/ = COS - COS + sin _~ sin d cos (/> 

 = sin 6 cos 4>. 



(85) 



Figure 10. 



By the same proposition 



or 



TT 



cos - = COS B cos i/' + sin sin yp cos a; 



cos a = — 



cos Q cos i/' 

 sin sin- 1/' 



cos a 



_ cos cos i/ 

 sin i/' sin Q sin^ ^ ' 



and by (85) this becomes 



cos a 

 sin^ 



cos Q cos 

 1 — sin- cos^ <^ 



(86) 



(87) 



(88) 



17. Integration for Mutual Power. — Now substituting the 

 trigonometric relations (83), (84), i^h), (88) into equation (82), we 

 obtain the following integral expression for the time average of the 

 mutual power radiated through the aerial hemisphere'. 



