288 Mr. G. H. Livens : Influence of Density on Position 



If we divide the different electrons present into groups 

 according to their natural free period n = * / — , and if N 



denote the number of electrons in the typical group per unit 

 volume, then the equation is 



k — mn* ' 



where 2 is now taken only over the different groups of 

 electrons present. This can be written in the form 



1=* ap 



n^ — n 2i 

 where 



n J =—, and p= =(Nm) - 1 . 



m ' m ' \mj 



We thus see that the periods of the vibrations of which the 

 system of electrons is capable are modified from the values 

 they would have if each electron were quite free and un- 

 hampered by the presence of the other molecules. 



If there is only one group of electrons present in the 

 substance the period of vibration of the light obtainable from 

 it would be given by 



1= a P 



nJ — n 2 ' 



n= V"n 2 — ap, 



or as the term ap turns out to be small compared with n , we 

 have approximately 



ap 



2n . 



( e \ 2 

 Now p— (Nm) - ) , and therefore depends on the density 



of the electrons present, that is on the density of the gas. 

 Thus the period of a single oscillating electron, or at least 

 the period of the light disturbance obtained from a system 

 of such electrons, increases with an increase in the density 

 of the gas in which the oscillations take place. An increase 

 in the density of the incandescent gas or vapour shifts the 

 lines towards the red end of the spectrum, that is increases 

 the wave-length of the light emitted. The displacement is 

 in all cases proportional to the change in the density, but 

 may be different for different lines, depending on the density 

 of the electrons giving rise to the line. 



