On the Acceleration of Secondary Waves. 269 



This at once points to an acceleration of phase of £ period at 

 distances remote from the "vibrator." 



The rate at which the magnetic component of the disturbance 

 is propagated can be determined by taking a definite position 

 on the wave and finding how v varies with respect to t on tra- 

 velling out with the wave in this phase. If P = 0, then 



tan (mr—ni) = — 1/mr. 



Here m stands for 2w/\, and n for 2«7t/t. From this we get 

 for the velocity of the wave, 



dr TT m 2 r 2 + 1 

 i?= — = V 



dt m 2 r 2 



where V is the normal velocity, or that at a great distance 

 from the "vibrator." When r = 0, v has an infinite value, 

 but on going outwards rapidly approximates to V. Hertz 

 has pointed out that the true interpretation of this great 

 value for the velocity at points near the origin involves the 

 idea of the energy radiated really coming from points in the 

 surrounding medium, the true seat of the oscillations. 



Thus, from the consideration of velocity an acceleration in 

 phase is observed to occur. To find its amount, the time the 

 disturbance takes to reach a point at distance N\ from the 

 origin can be easily found and compared with the normal 

 time. Thus 



J V = y{ m+ 2^ tan " 1 2^-4J- 



When N is a large number this approximates to the value 



Nt—t/4:, and is an acceleration corresponding to one quarter 



period. 



If the position of maximum or minimum value of P 



dF 

 (i. e. -j- = *) be taken on the wave instead of the zero value, 



we shall have tan (mr—nt) = mr, and the same expression for 

 the velocity is found. The circular electric-line of force in 

 Hertz's diagrams of the disturbance, here reproduced for 

 convenience of reference, also spreads out with this velocity. 



* It is to be particularly observed that in the neighbourhood of the con- 

 ductor, unlike in normal wave motion, the position on the wave where 



dP 



^7 =0 is not the position on the wave of maximum displacement; this 



state of the wave will be found like the electric force to originate at 

 A/4-4, having a very similar expression for the rate of its propagation. 

 On plotting the curve P at a series of stated epochs this is well shown. 



