of Emission and Absorption Lines in a Gas- Spectrum. 287 



consideration, and will therefore exist in our case, even 

 though the gas is not polarized as a whole. This is the local 

 effect, and depends solely on the local conditions, and from 

 this point of view the body is polarized. It is, of course, a 

 statistical measurement of the effect. We do not, and cannot, 

 take any account of the very possibly large variation in the 

 local forces. We average them up and express the result 

 statistically. 



The equations of motion of the typical electron in the 

 element are thus all like 



m'x + lix + kx = eaP x . 



The forces governing the motion being exactly the same as 

 in the previous case, with the single exception that there is 

 no electric force E acting. 



But according to experiment, light coming from a flame 

 may maintain its capability of interfering after a distance of 

 paths of a million wave-lengths, and so we may assume that 

 the single emitting electron maintains its motion through a 

 very large number of periods. We can thus neglect the 

 resistance terms in these equations, and they then become 

 like 



mx-\-Jcx = eaPx. 



To obtain the possible periods of the light disturbance which 

 can proceed from the volume element dr we proceed in the 

 manner usual in such problems. Assume the quantities 

 depend on the time by the factor e int , and then 



( - mn 2 + k)x = eaVx. 



Thus summing up per unit volume over all the electrons in 

 the volume element dr we get 



F x =tex=Y x t T ^ e ~ Y 

 k — mn 1 



We thus deduce 



and thereby eliminate all ideas of any vector effect in the 

 volume element dr. This result is true for any intensity 

 and direction of polarization in the element. 



This is the period equation for the oscillations in the light 

 disturbances obtainable from the element or, since the element 

 is merely a typical one, it is the period equation of the light 

 emitted from the substance. 



