146 Mr. G. F. 0. Searle on the 



Integrating with respect to Jt, we find 

 „ T uQ 2 iv 2 ,_, .> . « , x* 



§ 32. In the pulse, H^rKVi^E, and thus the momentum 

 per unit volume is (K/47rr)VE Vi^E or rJ&.W/^irv, since E is 

 perpendicular to r. Hence, if P : be the momentum in the 

 pulse in the direction of u, 



P 1= |^-W 2 cos # sin <9 



>Wd6. 



Using the values of \ cos 7^ and \ cos^y d<f> given in § 31 

 and writing (l — h)/)i for cos 6, we find 



P^C-Dsin 2 ^ 

 n MQVf[l 3 3-n 2 l-n 2 i 7/ 



l—n 



l+n 



n /»<y» ,S f/3 + n' !>-» 2 (3-n 2 V .-» s Y3-n») 1 „ 



1 — ?? 



Integrating with respect to h, we find 



-p, LiQhv 1 T, 1 + n 2w(3 — 5n 2 ) 



Pi= 7 loo-:; —: ^r 



1 4av/i 4 L ^1—n 3(1— n 2 ) 2 



. o, f3 + ?r\ l + n n(9 — 12n 2 — h 4 ) 1 1 

 - sm-t | -y- log j— _ - 3(1 _ a3)i ' - } J • 



If 02 (fig. 5) be in the plane of u and w and at right 

 angles to u, the cosine of the angle between r and 02 is 

 sin 6 cos (£. Hence, if Po be the momentum in the direction 

 of 02, 



P 2 = | ( Ml 2ar 2 cos <j> sin 2 6 cW J<f> 



From (53) we find 



n2tr 



\ cos 7 cosc/> d(f} = '277 . \ sin 6 sin-v/r. 



Jo 



cos 2 7 cos <£ dcj) = 27r . sin # cos 6 sin -^ cos -v^. 



* Dr. O. Heaviside Las calculated W for Unite values of ic, when w 

 is in the same direction as u. ' Xature,' Nov. G, 1902. 



