IN THE FIELD ROUND A THEORETICAL IIKKT/.IAN ( II.I. \K.|; 171 



with 0, hut that the amplitude of l*th the total transverse and the total electric radial 

 forces does. So far as tin- tl ..... rv -if wave transmission goes, the wave-speed of the 

 total radial force is really discussed under the treatment of <j, '""' axial component, 

 in Art. 7. Similarly, the total transverse electric force has a \vave-sj>eed determined 

 from <, + fa and, therefore, it will !* found fully discussed under our treatment of the 

 function <, + <f>.,, the equatorial wave in Art. 1'J. In addition, our analysis ciiahles 

 us to deal separatelv svitli that portion of the total transverse force <|. or the trans- 

 verse component in our case, which alone is propagated to considerable distances, and 

 which gives at all distances the total force perpendicular to the axis. 



(7.) Let us deal first with the case of the component force parallel to the axis or the 

 <^, factor of the total radial electric force. We may write 



*=P,(r)e-'^-^Bin{2(^-^) + &} . , . . (xxiii). 

 where 



P s (r) cos A = ~ 2EJ y) (tan x - O- 

 Thus, 



f ^ P t (r) = 2E/ (**)> { 1 + (tan X - ^) 2 }', 



and, 



cot /ft. = tan x + f ..... . ..... (xxiv). 



Hence 



1 <>& \ J_ _ -V 

 MII-/S. /! "" -' f* ' X ? ' 



and dift'erentiating 2w (- -- '. - ] -f & = with regard to the time to find V 2 = dr/dt, 



we have 



v = V 2 (l-rHin'&). 

 Thus the wave is 



and its velocity is given hy 



2wr . 



x (\ -- si "- 



We see at once that V., =. V , or the magnetic wave and the wave of component electric 



z 2 



