424 Sir J. J. Thomson on the Origin of 



the frequencies of the vibrations of the electrons are deter- 

 mined by the magnetic and not by the electric forces. An 

 electron, when in a magnetic field, describes a spiral round 

 a line of magnetic force completing a revolution in a time 



/He 



2-7T / — j where H is the magnetic force, e the charge, and m 



the mass of the electron ; it thus gives out radiant energy 



H e 

 whose frequency is ^ , which is independent of the energy 



of the electron. As this energy diminishes, the radius of the 

 spiral described by the electron diminishes, but the frequency 

 ot' the vibration is unchanged. Thus, if the magnetic force 

 were predominant in determining the vibrations of electrons, 

 the frequencies of the vibrations given out by the different 

 kinds of atom would be 



H t e H 2 e H 3 e 



tir m ' 2ir m * 2tt in ' 



where H 1? H 2 , H 3 are tbe values of the magnetic induction 

 at the various places of equilibrium. Suppose, now, that the 

 value of H at a point of equilibrium at a distance r from 

 the centre were equal to /x,(a 2 — r 2 ), a distribution of magnetic 

 force which a priori is not improbable, as it is that inside a 

 sphere uniformly charged with electricity and rotating like 

 a rigid body. 



Since the positions of equilibrium are given by sin c/r = 0, 



i. e, y by - =?i7r or r=c/mr, where n is an integer, the value 



of the magnetic force at the positions of equilibrium, and 

 therefore the frequencies of vibration in these positions, would 

 be proportional to 



c 2 C 2 fa 2 7r 1 \ 



a ~nv to -?{-*- ?)> 



and would thus form a series of the Balmer type. If, in 

 addition, the place r = a, where the magnetic force vanishes, is 



also a place where the electric force vanishes, - = nvn where 



m is an integer, and the expression for the frequency 



becomes Cf — „ 5 ), where C is a constant and m and n 



\m 2 n 2 J 



integers. 



Before proceeding to discuss this expression in detail, we 



