172 



I'KOFESSOR K. PKAKSOX AND Miss A. I,KK ON THK VII'.UATIONs 



force parallel to the axis are propagated everywhere \vitli tin- saint- velocity at the same 

 distance t'l-Min tin- axis. At the same time the amplitude of this electric wave varies 

 inverselv as the .i'/nitrc of the distance from the centre of the oscillator for considerable 

 distances, while the amplitude of the magnetic wave varies under the same conditinns 

 inversely as the distance. Thus the effect of the former is rapidly insensible as 

 compared with the latter. Meanwhile it is important to observe how this wave keeps 

 pace with the magnetic wave. 



(8.) We may now consider <,, which gives the transverse electric component ^>, sin 9 

 and the total electric force perpendicular to the axis, i.e., <, sin 6 cos 6* 



sin B = P, (r) e-'*- r *> sin 6 X sin {W^ - ^ ) + , i . (xxvii), 



where 



0_\ 3 



- 



A. 



P, (r) sin ft, = El ( 2 f V f (2 tan x - 3f ). 



Hence 

 P 



and 



,-=fflw 



sin 2^ 



: cos 2 x ( 1 + 4 cos 2 



3f 3 sin 2 cos 2 



, a . JJ 



' 1 - tan* x 



cos 



From the last equation we deduce, if 1/f =s - - , 



A, 



- 3(1 + tairy)(- sin 2 



tan (ft,- 2x) = ^ rj - 

 where 



Hence 



e = (1 4. tan 2 x) (C - sin 2 X ), y = ^ tan x . 



cos' (ft - 



r= 3 (l 



3 + -4y- 



^* f / i \ g O / 1 " \ ) * 



^ 3(1 +4y)(3 + e 8 - 4V) 

 X (e 2 + 2 7 e + 47 s - 3) 8 + 9e* 



h This again is an important physical significance for <fa, and enables it to be readily differentiated 

 physically from 0... and 0i 



