SPECTRAL LINES 449 



completely isolated : there is an additional term arising from 

 the polarisation of the surrounding matter, and since only the 

 matter in the immediate neighbourhood of the electron produces 

 any appreciable effect on it, this polarisation (which is, of 

 course, a vector quantity) may be assumed constant and equal 

 to its value at O ; and just as, in the theory of magnetism, any 

 distribution of magnetism may be averaged out into a volume 

 and surface distribution of "imaginary magnetic matter" so, in 

 the present case, the effect of the polarisation of the medium is 

 equivalent to that of a surface distribution of electricity on 

 the wall of the spherical cavity, of density Pcos# at any 

 point, where P denotes the magnitude of the polarisation and 

 is the angle between its direction and the line from the point to 

 the centre of the sphere, and so the force on the electron is at 

 once obtained as -f 7reP in the direction of P. If now the matter 

 which was removed from the sphere be replaced there will, due 

 to it, be an additional force, esP, which, as Lorentz 1 has shown, 

 vanishes if the molecules have a regular cubic arrangement. 

 In general for a gas, S will be small, and the complete expression 

 for the force of the typical electron due to the electric intensity 

 may be written in the form e (E + 47raP), where a is approxi- 

 mately equal to one-third in the case under discussion, but for 

 solids and liquids it may depart widely from its value. The 

 polarisation is analogous to the magnetic vector called the 

 " intensity of magnetisation " and defined as the magnetic moment 

 per unit volume. It is equal to 2er, where r denotes the dis- 

 placement of any electron from its position of equilibrium and 

 the summation is with regard to all the electrons per unit 

 of volume. 



The equation of motion of the typical electron when vibrating 

 under the action of an external periodic electric intensity E may 

 accordingly be writen in the form 



m'r + hf + mn-r = e(E + 47raP) 



The term hf represents a frictional or resistance term. Its 

 presence is found to be necessary to account for the phenomena 

 of absorption and of selective dispersion, although its exact 

 physical significance is obscure. Lorentz sought to explain it as 

 arising from the disturbance of the motions of the electrons 

 consequent upon molecular collisions, but although his hypo- 



Theory of Electrons (B. G. Teubner, Leipzig), p. 306, 



1 7- 



