of Emission and Absorption Lines in a Gas-Spectrum. 279 



depend on the time by the imaginary exponential factor 

 e mi we have 



(—mn 2 + Um + k)x=e(Ex + aPx) y, 



c 



teHn 

 ( — mn 2 + ihn + k)y = e(Ey + a? y ) -\ — a?, 



o 



( — mn 2 + ihn + k)z = e(J& z + a? z ). 



By solving these equations for (#, ?/, z) we get the position 

 of the typical electron corresponding to the values E of the 

 electric force and P of the polarization. By forming the 

 sums (2e#, Sey, ^ez) per unit volume we obtain, since they 

 are respectively equal to (P#, By, P^), three linear relations 

 between the components of the electric force and of the 

 intensity of polarization, the coefficients being in general 

 complex functions of the frequency of the periodic light 

 disturbance considered. From these equations we can 

 determine a relation between the electric force intensity and 

 the polarization intensity. It comes out of the form 



P = 4tto-E, 



where cr is in general complex, depending on the constitution 

 of the substance and the frequency of the light used. 



This is the third relation required, connecting the quan- 

 tities involved in the fundamental equations. The relation 

 does not, however, connect quantities which explicitly occur 

 in the fundamental differential equations of the theory in 

 the form in which we have taken. In fact it involves a new 

 vector, the polarization which does not appear in the funda- 

 mental equations at all. We can, however, easily connect 

 the polarization P with the true electric current. 



The true flow of electricity is easily expressed. It can 

 be seen to be a vector equivalent to the vector whose com- 

 ponents are 



2 ex, 2 ey, 2 ez, 



2 being taken per unit volume over the negative electrons, 

 due regard being paid to the meaning of (#, y, z). But this 

 is the vector 



P, 



which is, therefore, the true current. The total current U 

 consists of this true flow of electricity, together with a 

 fictitious current due to a supposed change of the elastic 



