166 PROFESSOR K. PEARSON AND MISS A. LEE ON THE VIBRATIONS 



2irr/X cos* 



R = ^ ^ sin 0cos 0- . . (xv). 



2irr/X cos* x 



The values in our notation obtained by HERTZ are : 



\ 



sin 0cos 0sin 27r ~ - -- 



27T7-/X 



Now it must be remembered that Q and R and Z are all zero until t is > ar or 



- > - . Hence HERTZ'S formulae imply that at a considerable distance from the 

 JT X 



origin the intensity of the field increases gradually from zero, The formulae (xv) 

 appear, however, to show that the intensity at a distant point of the field rises 

 abruptly from zero to the definite value : 



sn 



2,rr/X * cos'* ' 2w/X 



as the wave reaches it. 



The explanation of this is, however, that, while we make the oscillator start from 

 zero charge, yet the initiation is sudden in so far as it requires definite initial values 

 of the electric and magnetic forces. There is an impulsive action at the wave front 

 due to the sudden starting of the oscillator, and the above expression only represents 

 the* electric force at a considerable distance from the oscillator, when the impulsive 

 action of the wave front has just passed the point under consideration. 



Turning now to the magnetic force P perpendicular to the meridian plane, we 

 have by (vi) : 



l ~p ~dt' 

 or, 



sin* 





cos* x (2?rr/X) 



= <^ 3 sin Q 



