of Emission and Absorption Lines in a Gas-Spectrum. 277 



fluid media, possibly not so approximately for solids. [P is 

 the vector defining the intensity of polarization in the 

 medium at the point.] The argument was that owing to 

 the translatory mobility of the surrounding molecules their 

 action on the one under consideration averages into that of 

 the uncompensated distribution of poles which would exist 

 on the surface of a small spherical cavity in a continuous 

 uniformly polarized medium"*. By a more general dis- 

 cussion Lorentz has arrived at the conclusion that the force 

 may generally be taken as 



aP, 



in the direction of P, where a is some constant which depends 

 on the local distribution of atoms or molecules at the point, 

 and which would consequently vary with the temperature 

 and pressure, but which in most cases is very nearly equal 

 to J. I shall retain the constant a throughout the algebraical 

 work, and use the value a~^ in the numerical calculations. 

 In any case the way in which the constant a enters into the 

 calculations will always be quite clear. The value a = 

 brings us back to the older theory. 



(d) The magnetic force. — The last of the forces to be here 

 considered only occurs in discussions of the effect of an 

 <; external " magnetic field, denoted by H, and always con- 

 sidered as directed along the s-axis. Its action on the 

 vibrating electron is represented by force components 



eH. . ^ eR . A 



A note should here be added in connexion with the forces 

 discussed in paragraphs (b) and (d). Both of these forces 

 are proportional to the velocity of the electron. 



Now the velocity of the typical electron is not (#, y, z) 

 but (x + u, y + v, z + iv), where (m, v, to) is the velocity of 

 the molecule or atom in which the electron is to be found. 

 This, of course, is a direct consequence of our previous 

 interpretation of (#, ?/, z). We have, therefore, neglected 

 two forces whose components may be written in the form 



— (7m, hv, liw), 



and eH , AN 



-— (v, -u, 0). 



Both of these forces would act on the electron independently 

 * Larmor, Phil. Trans. 1897. 



