160 



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



a good deal of HERTZ'S original theory of interference requires modification, if we are 

 to obtain quantitative accordance between theory and experiment. The object of 

 the present paper is to give a fuller theory of the nature of the vibrations in the field 

 round a typical Hertzian oscillator. 



(2.) Assuming that BJERKNES' experiments have shown that the Hertzian oscillator 

 vibrates very nearly according to the type : 



C-*' ( sin (p4 + a), 



we have to find a solution for the equations for the disturbance in the surrounding 

 field on this basis. 



Using HERTZ'S notation* for the case of symmetry about the axis of z, then if Z and 

 R be the components of electric force parallel and perpendicular to this axis at a 

 point whose coordinates are z and p = \/x* -j- y 2 , and P the component of magnetic 

 force perpendicular to the meridian plane through the same point, we have to find 

 a solution of 



dC- 



suitable to the initial and boundary conditions. If this be done, 



d 



a d I d-Jr 



V = ~TAPi 



p dt. \ r dp 



(iii). 



The component of magnetic force parallel to 2 is zero. 



Now if we suppose that at some distance from its centre the oscillator may be looked 

 upon as a " double point " or as producing an oscillation, which has a very small range 

 /, and with poles having E electricity at the maximum, then we may write for V 2 , 



1 d / ., d\ 

 -- I r 1 

 r 2 dr \ drj 



Assume / = /, (r) e rt , and we find 



dr 



Writing r' = apr, and/ 2 = r'fi, we have 



See ' Electric Waves,' English edition, p. 140, 



