564 Prof. 0. W. Richardson on a Theory of the 



In the calculation which led to equation (8) we assumed 

 that the field was propagated instantaneously, i. e. we assumed 

 that the effect on A of the doublets induced in a molecule B 

 at a distance r from A was determined by the instantaneous 

 state of A. As a matter of fact the induced field at A is 

 determined by the state of B at a time r/c previously, and 

 again that of B is determined by the state of A at a time 

 r/c earlier still. If we allow for this we find that equation (9) 

 up to the accuracy of the first term would have to be replaced 

 by the real part of 



On evaluating the integral it does not appear to differ from 

 the first term of equation (9) by more than one part in ten 

 thousand. 



§ 4. Change in Wave-length of the Emitted Lines. 



We have seen that the doublets induced in neighbouring 

 atoms give rise to an additional force on a vibrating electron 

 of amount 



|^ ^J[8L x +l-26L 2 /« 3 ]. 



In deducing this formula we have left out of account effects 

 due to the motion of the ft atoms and have also assumed that 

 the full field of force of the various doublets is available out- 

 side the atoms. Admitting the validity of these assumptions 

 tentatively, we are in a position to calculate the change of 

 wave-length of the emitted light. Comparison with equation 

 (3) shows that the equation of motion of the emitting electron 

 now becomes 



m w-=- ei \xr^ n ~ -j — )•• (12) 



If T is the periodic time, \ the wave-length in free aether, 

 and c the velocity of light, we have 



If X is the wave-length of the light emitted by A in the 



