﻿On Lorentz's Theory of Long Wave Radiation. 159 



hypotheses regarding the dynamical character of the 

 collisions. The case to be analysed is, therefore, virtually 

 that in which the electrons and molecules are assumed to be 

 perfectly rigid elastic spheres, the molecules being, however, 

 of comparatively large mass so that their energy and motion 

 may be neglected. 



I do not find it necessary to depart very widely from 

 Lorentz's admirable exposition of his theory given in his 

 book ; The Theory of Electrons'*, and I shall take the 

 liberty of quoting verbally in many cases from his work, to 

 which I must here acknowledge my great indebtedness. 



We will, therefore, with Lorentz, consider a thin metallic 

 plate in which a large number of free electrons are moving 

 about in a perfectly irregular manner, consistent with the 

 general laws of the conservation of their total energy and 

 momentum. We know that an electron can be the centre of 

 an emission of energy when its velocity is changing, thus, 

 as a result principally of the numerous collisions of the 

 electrons with the atoms, resulting in alterations of the 

 directions and magnitudes of the velocities of the electrons, 

 a part of the heat energy of the irregular motion of the 

 electrons will be radiated away from the metal. This radiant 

 energy, which is subsequently to be the subject of a detailed 

 examination, is, however, presumed to be so small compared 

 with the energy of motion of the electrons that it can be 

 neglected in any dynamical considerations respecting those 

 motions extended over any finite time. To this extent the 

 analysis offered is only a first order approximation to the 

 actual state of affairs. 



We know also, that as a result of the same collisions 

 between the electrons and atoms, part at least of any regular 

 or organized energy acquired by the electrons during their 

 free motion between the atoms can be dissipated into heat 

 energy of the irregular motion of the same electrons. In 

 this way it is possible for a metal to absorb a portion of the 

 energy from an incident beam of radiation, because the 

 electric force in the electromagnetic field associated with 

 the radiation will pull the electrons about during their other- 

 wise free motion between collisions, imparting kinetic 

 energy to them which will be dissipated by collision at the 

 end of each path into irregular heat-motion. 



Now let tv and w' be two infinitely small parallel surface 



elements, to being on the plate itself and w' at a distance r 



outside it on the normal to the plate through the centre 



of iv. Then of the whole radiation emitted by the metal 



* The Theory of Electrons (Leipzig, 1909), Chapter II. 



