278 Mr. Gr. H. Livens : Influence of Density on Position 



of the forces due to the electrodynamic field considered in 

 the optical case ; the latter, of course, depends on the con- 

 stant external magnetic field, which is present when we are 

 dealing with the Zeeman effect. 



These forces would account for a slight displacement of the 

 electron from what we have described as its absolute and 

 neutral position of equilibrium in the atom or molecule, the 

 displacement in the latter case probably being a vector one 

 related to the direction of the magnetic field. The displace- 

 ments would depend on the motion of the molecule, being 

 therefore different for different molecules, but would be 

 independent of any of the optical effects to be discussed. 

 If we transfer the origin of (#, y, z) from the absolute to 

 this displaced position of equilibrium we obtain exactly the 

 same equations of motion as before, provided that the acce- 

 leration of the molecule is small compared with that of the 

 electron contained within it. This is a legitimate hypothesis 

 to make for the case of a gaseous substance where the greater 

 part of the motion of a molecule is linear and undisturbed 

 by any action. 



In any case we can, however, neglect the effects of these 

 forces in adopting a statistical theory of the subject. The 

 velocity of the molecule is just as likely to be — (u, v, w) as 

 + (w, v, w) , and on the average will be zero. In any case a 

 retention of these terms could merely account for a broadening 

 of the line about the absolute position, if we consider that a 

 slight displacement of the electron in the molecule alters its 

 free period of vibration. 



We shall neglect the effects of these forces so that we can 

 still confine our discussion to the consideration of the nega- 

 tive electrons alone. The above four kinds of force cover all 

 those we can imagine to act on the electron in any ordinary 

 case, and with them the equations of motion of the electron 

 are of the form 



eR . 



mx = e(E x -\ aPj) y — lilc — kx, 



c 



eR 



my=^e{E y + aFy) + — x — hy — ky, 



G 



mz = e (E g + aF z ) — h'z — kz. 



If now the light incident on the body is a simple harmonic 

 wave-train of frequency n, the electrons are compelled, with 

 more or less success, by the electric force in the incident 



wave to vibrate with a period - — . Thus if the functions 



