444 Sir J. J. Thomson on the Origin of 



the equation of motion is 



( ^f on (d^W 



m df°=- 2Ce {drf f ' 

 where -< -^ > is the value o£ -/- at the equilibrium position. 



The frequency of the oscillation represented by this 

 equation is equal to 



\ m i dr ' 



so that the case resembles that where the oscillations are 

 determined by the magnetic force, inasmuch as the first 

 power of the frequency is given by a simple expression 

 without square roots in the variable part. By taking 

 appropriate values of <£ we can get series for the frequencies 

 of the Rydberg type. 



When an electron in a magnetic field is acted upon by an 

 electric force, the magnetic forces will deflect it as soon as 

 it gets set in motion, and it will not move along the direction 

 of the electric force. Thus if a plane polarized beam of 

 light in which the electric force is parallel to the axis of x 

 falls upon the electron, it w T ill originate accelerations parallel 

 to y and z as well as to x. The accelerations parallel to 

 y and z will give rise to scattered waves which will not 

 vanish along the axis of x ; now we know that with either 

 visible light or Rontgen rays the light scattered in this 

 direction is in normal cases exceedingly small, so that it is 

 necessary to see if this result is consistent with the existence 

 of strong magnetic forces inside the atom. 



Let the electric force in the wave be parallel to x and 

 equal to E cos pt. Let f, ??, ? be the displacements of an 

 electron parallel to oc, y, z and a, b, c the components of the 

 magnetic induction inside the atom ; then the equations of 

 motion, if we include an electric restoring force proportional 

 to the displacement, are 



md 2 P -j.. s. celn hedt 



md 2 7j _ aed% ced% 



1^-~ m ^^t dT' 



md 2 % _ y bed% acdrj 



