IN THE FIELD HOUND A THEOBKTICAL HKKT/IAN << n.i.ATOR. 17:* 



)_ 

 We must now differentiate ~ (< r) + /8, = 0, to get the velocity V,, and we 



fad 



X 



Substituting for dfi,/<li; we have, after reductions : 



V, 

 t> ' h ' + 4?e* 4 4-y ( (7- - ) e + 16-y* (4y - 3) 



Nii\v let 



C, = sin 2 X 



(xxjx). 

 = CON- x (3 cos 2 x - sn 2 x) 



Thau 



4 7 3-4r 



- ' fcl " 



V '=l 



Let Co = -.iT'-<A = -Vr./X. Then 



V, 3c08 1 v (r-rj'-f- r] 



7 =1 + (1^ r {(r - r.y - r/JJ ' .' ' ' ' (XXX ^ 



This gives the velocity V, at each distance r from the origin of the transverse 

 electric wave. Its amplitude is given by (xxviii). 

 When r is great, the amplitude approaches the value 



El (2w/\f 



Therefore at such distances 



ty, = 2 (X/2wr), 



or <^ is insensible as compared with <,. Even at distances 5 to 10 times the wave 

 length, <k will be very small as compared with <f> t ; that is to say, the electric vibra- 

 tions at comparatively short distances are to all intents and purposes transverse. 

 Turning now to the velocity V,, wi- will tirst endeavour to trace its changes. Let 



