198 Mr. Gr. A. Schott on the Electron 



By using Poynting's Theorem we find for the radiation 



A P u •=-* Jo 



S— — CO 



+ { ^(m 2 + *W -2mZ/2 2 - 3 -^} ^ [ J 2 ,„(2^)^] 

 -2ABsin«X Z/3r^^- 2 //3J 2 „,(2^) + ^~^i f J 2) „(2M^] 



+ { i^ (m 2 + P,3 2 ) -2m/y3 2 - ^^ j I j* J 2 ,»(2/.f)&] j . 



The expressions for the forces show that at a great distance 

 from the ring the electric and magnetic forces are transverse 

 and at right angles. They consist of an infinite series of 

 harmonic terms, the frequency of the 5th harmonic being 

 <7 + (& + sw)g>. Since negative values of s occur, there are in 

 reality two distinct series, one with positive and the other 

 with negative frequencies. The amplitude of the 5th har- 

 monic is of the order J m (l/3), and the corresponding term in 

 the radiation of order J 2m (-fy3). For small values of Z/3, 

 such as correspond to waves of light, the orders are 

 (i//3>/|/*, and (//3) 2/ 7 |2/x, where yu, = Mod. to. 



The fact that a single vibration of the ring, corresponding 

 to one degree of freedom of the ring, gives rise to an infinite 

 series of harmonics is due to the presence of the aether, which 

 possesses an infinite number of degrees of freedom. 



§ 9. Let \ be the wave-length of the vibration considered; 

 then 



For the extreme ultraviolet, X = 10"~ 5 cm., //3 = *0063; for 

 the extreme red, \ = 8xl0~ 5 cm., l/3 = '0008. In this case 

 we need only retain the lowest power of 1/3, and the 

 harmonic of greatest amplitude, given by s = 0, /* = Mod. k. 



