MAGNETISM AND LIGHT 337 



arc was passed through the tube into the spectroscope and the dark 

 D lines appeared. When the current was put on, these too 

 widened. The total widening of each of the lines was about 1/40 

 of the distance between them when the field was about 10,000. 

 As the two lines differ in frequency by about 1 in 1000, the two sides 

 of each broadened band differed in frequency by about 1 in 40,000. 



Lorentz' s theory. Zeeman thought that the electron 

 theory as developed by Lorentz would give the key to his observa- 

 tions, and Lorentz indicated to him a theory of the effect which we 

 may put in the following form. 



The principle is that which was afterwards used by Voigt in the 

 explanation, which we have given already, of the change of velocity 

 of circularly polarised light with change of direction of revolution. 

 The starting-point is the equivalence of a charge e moving with 

 velocity v to a current element ev, so that if there is a magnetic field 

 of which the component perpendicular to the direction of v is H, a 

 force acts on e equal to Ilev and perpendicular to H and v. 



If v be resolved into any components and the force on e due to 

 each component be separately considered, the resultant of all these 

 separate forces will be Hev. It is sufficient to illustrate this by the 

 simple case where the field is perpendicular to the velocity v, and 

 that velocity is resolved into v cos and v sin at right angles 

 and in a plane perpendicular to H. The forces on e moving 

 separately with these velocities will be Hev cos $, H.ev sin 0, and 

 these will have as resultant H.ev. Hence we can resolve v as we like, 

 and the forces acting on e due to the separate components will have 

 a resultant equal to the force due to the actual motion. 



Now take the case of a system in which a single electron revolves 

 round a centre under a force towards the centre proportional to 

 the distance. The orbit will be in general an ellipse, and it may 

 be in any plane. But the motion can always be resolved into 

 three linear simple harmonic motions along three axes O#, O/, 

 and Oz through the centre O, and all three will have the same 

 period, though they will not have the same phase, i.e. will not all 

 pass through O at the same instant, unless the actual motion is 

 linear. Each of the linear motions may now be resolved into two 

 equal and opposite circular motions in any plane through the 

 linear motion, each having the same period but with radius equal 

 to half the linear amplitude. If the period is N and the radius is 

 d the acceleration in each circle is 4?r 2 N 2 d. 



Let a magnetic field H be created in the direction of x. 

 We leave the motion along Qx linear, for it will not be 

 affected by the field, and its frequency will remain N. The 

 motions along Oy, Oz may be resolved into two pairs of cir- 

 cular motions, and it is most convenient to put these in the plane 

 of y, z, each pair consisting of two opposite motions. As we have 

 seen, we may treat each motion separately in considering the effect 

 pf the motion in the magnetic field. Consider a circular motion 



