Displacement of Spectral Lines produced by Pressure. 571 



the other. With these limitations, then, -\jr will be expressed 

 with close approximation by 



V mrrv p — 7 K u 



If we replace /3 by p/v, 7 by e/v^/\m=p f /v, and (r Q — r{) by 

 vt, this becomes 



2e 2 % cos pt 



mt'i p 2 —p' 2 



This is identical with the solution for the case where the 

 atom B remains fixed at a distance r\ from A so that the 

 calculated displacement will only be slightly in error on 

 account of our having neglected to take into account the 

 motion of the atoms. It is therefore necessary to seek some 

 other explanation for the discrepancy between the calculated 

 and observed effects. 



§ 6. Causes tending to diminish the effect. 



In view of the disagreement between theory and experience, 

 the suspicion naturally arises that the view of the structure 

 of the atom which we have used as a working hypothesis is at 

 fault somewhere. We have taken as a fundamental assump- 

 tion that the emitting system can be represented by the linear 

 vibration of an electron. There appear to be at least two 

 reasons why this assumption leads to too big a calculated 

 effect, both of which depend on the probability of an atom 

 having a more complex structure than that we have assumed. 

 In the first place it is possible that the emission of spectral 

 lines is due to perturbations in the motion of electrons rotating 

 in closed orbits within or about the atom. If spectral 

 lines do originate in this way, it is clear that the effect here 

 investigated will be diminished by the variation of phase intro- 

 duced by the rotation. But since this explanation of the 

 origin of spectral lines is a very special and uncertain hypo- 

 thesis which has not hitherto met with much success in 

 explaining the f acts, it scarcely seems necessary to pay much 

 attention to it. This position is strengthened by the fact that 

 the hypothesis of linear oscillators gives a satisfactory account 

 of dispersion phenomena on lines similar to those which have 

 been followed in this paper. It is, however, worthy of 

 remark that when this type of dispersion theory is used to 

 calculate the number of electrons present in different sub- 

 stances, the values obtained are lower than we should have 

 expected on other grounds, a discrepancy which is in the 



