I\ THE FIF.1,1) R0r\l A THEORETICAL HERTZIAN (MMU.ATf >|; 



,,,-t/titii><: This hr.lils until = cosec 2\, and then V become indefinitely great 

 positively. Thus, from the surface of tin- sphere r = (lie waves move 



L'TT 



inwards and outwards with indefinitely great velocities. When ^ = 0. this sphere 

 closes in on the oscillator. ;m<l it will generally he well within the sphere round the 

 oscillator within which it is not legitimate to :ipply the theory. But for a verv 

 rapidly damped wave train and n very considerable wave length, it is ]*o8sible that its 

 existence could l>e physically detected. 

 We may write (xxi) 



v 



= 1 + . 





1-irr l-l-nr , \ 



x (x -""-'*/ 



(xxii). 



Hence V /r is symmetrical ahout 27r? 1 /X = ^ sin 2x, and we have the following curve 

 for Vo/v plotted to '2irr/\ : 



Ob-ba-AinXCosX 



be -i-casic* x. 



rl 



N.B. This figure is purely ilingiiinmiatic. Ori is not really comparable with Ol, and be is 



20,000 uniu of the vertical scale. 



The diagram illustrates the rapidity with \\lm-h the velocity of the magnetic dis- 

 turbance approximates to ,-. and shows the minimum negative velocity vcosec*^ 

 occurring at a distance r = sin -.'^ from the centre of the oscillator. 



(6.) Turning now to the \\a\e-speed for the electric force, we see from the remarks 

 on (xiv) that we can treat the wave as made up of two components corresjMinding to 



r\rill. A. / 



