Displacement of Spectral Lines produced by Pressure. 573 



in which this point of view affects the ordinary electron 

 theory of dispersion, as given for instance by Drude*. 

 The equation of motion o£ the sfch electron is 



.«&***-*'W-& <*> 



where the term ?V? 2 ^r- nas been retained for completeness to 



include cases of absorption. The notation is that previously 

 employed, and is equivalent to that in general usage except 

 that Xx is usually put equal to the electric force X outside 

 the atom (see Drude, loc. cit.). Now X x is obviously the 

 electric force at the electron, and in accordance with what 

 has been said will in general be less than X. We may write 

 it X 1 = yi s X. Proceeding to evaluate the refractive index in 

 the usual way it is found that a factor of type 7! multiplies 

 all the terms in the polarization current,, and we obtain the 

 refractive index /ul and the absorption coefficient x from the 

 equations 



and \ * ■ / 



2^=4^2- x ^f ~ -• • • (20) 



(l-^V) +VrV 



Here v is the number of atoms per c.c, the summation 

 extends over each atom, and p is the frequency of the trans- 

 mitted vibrations. If there is no absorption r 1 = r 2 = r s = 0, 

 and 



^=l + 4w S , 7l '*! , (27) 



Inspection of this result shows that —. measures the 



•±7TJ/ 



sum of the moments of the doublets induced in the atom B 

 by a unit force outside. Since the potential at A is deter- 

 mined by the algebraic sum of the moments of the doublets 

 induced in B, no error has been introduced by omission of 

 the 7i factors as far as the atom B is concerned. 



The procedure outlined would enable us to calculate the 



* Lehrbuch der Optik, p. 353. 

 Phil. Mag. S. 6. Vol. 14. No. 83. Nov. 1907. 2 Q 



