232 Dr. P. Zeeman on the Influence of Magnetism 



explain the variation of the period. Prof. Lorentz, to whom 

 I communicated these considerations, at once kindly informed 

 me of the manner in which, according to his theory, the motion 

 of an ion in a magnetic field is to be calculated, and pointed 

 out to me that, if the explanation following from his theory 

 be true, the edges of the lines of the spectrum ought to be 

 circularly polarized. The amount of widening might then be 

 used to determine the ratio between charge and mass, to be 

 attributed in this theory to a particle giving out the vibrations 

 of light. 



The above-mentioned extremely remarkable conclusion of 

 Prof. Lorentz relating to the state of polarization in the 

 magnetically widened lines I have found to be fully confirmed 

 by experiment (§ 20). 



18. We shall now proceed to establish the equations of 

 motion of a vibrating ion, when it is moving in the plane of 

 (^, y) in a uniform magnetic field in which the magnetic force 

 is everywhere parallel to the axis of z and equal to H. The 

 axes are chosen so that if x is drawn to the east, y to the 

 north, z is upwards. Let e be the charge (in electromagnetic 

 measure) of the positively charged ion, m its mass. The 

 equations of relative motion then are : — 



The first term of the second member expresses the elastic 

 force drawing back the ion to its position of equilibrium ; the 

 second term gives the mechanical force due to the magnetic 

 field. They are satisfied by 



,— ~rtf 



provided that 



x=zae l (2) 



ms z a=—k 2 cic + eHs/3 

 ms 2 j3= -Pj3-eB.su 



} (3) 



where m, Jc, e are to be regarded as known quantities. 



For us the period T is particularly interesting. If H = 0, 



it follows from (3) that 



V ; _._k_ _.2tt 



* These equations are like those of the Foucault pendulum, and of 

 course lead to similar results. 



