IN THE FIELD ROUND A THEORETICAL HERTZIAN OSCILLATOR. 1G7 



where fa is a function of r and t only, and is constant at any time for a spherical 

 surface round the centre of the oscillator. 



Clearly P does not, as in HERTZ'S formula, appear to gradually rise from a zero 

 value, but suddenly springs to the value 



E/( 

 or, 



at a considerable distance from the oscillator.* This must again be interpreted as 

 representing the value of the magnetic force immediately after the impulsive action 

 at the wave front has passed by. 



(5.) We shall now consider what modifications are made in the velocity of trans- 

 mission owing to the damping of the wave train. HERTZ, GRAY, and others have 

 considered this problem, but have confined their attention to the equatorial plane or 

 the axis, and to a simple harmonic train. There appears to be no real simplicity 

 gained by these limitations. Dealing first with magnetic force in (xvi), we may 

 write the value of P above 



k . . . (xvii) 

 i \~ - / / 



where we have 



Hence 



tan & = 



sinycoav >.... (xviii). 



-* : A 4- cos 2y 

 2*r/X 



sin 2y 



2TTT/X 





* The apparent equality of the initial electric and magnetic forces arises from the unite selected by 

 HKKTZ, which have Ixsen here adopted for purposes of comparison Itetwocn the two theories. See ' Electric 

 Waves,' pp. 138-9. 



