﻿618 Prof. 0. W. Richardson : Some Applications 



The true answer will be given if the radiation is entirely 

 ignored. For, if we compare the two states when the radia- 

 tion is present and when it is not, in the former case every 

 particle which has lost energy by radiation will be compen- 

 sated for by another which has just gained an identical 

 amount from the radiation. Thus the two cases are statis- 

 tically identical except for the energy of the sethereal radia- 

 tion, and the problem becomes the well-known problem of 

 statistical mechanics. The solution is 



4 = Ar (w+L) / Re dx l dxc L dx z dp Y dp 2 d'p z , . (49 a) 



where dn is the number of particles whose coordinates lie 

 between x\ and x 1 + dx 1 &c, and whose momenta lie between 

 p 1 and Pi + dp x &c* A is constant throughout the system, 

 and may be determined in terms of the total number of 

 particles (electrons) by integrating throughout the system. 

 The potential energy w is a function of x Y x 2 x s and the 

 kinetic energy L is a quadratic function of the momenta 

 Pip 2 pz' It follows that the average kinetic energy of the 

 electrons is independent of their potential energy and is 

 equal to f R#, and also that the average number n per unit 

 volume at a point where the potential energy of an electron 

 is co is given by 



m\ogn + co = C. 



Thus equation (49) still holds good when photoelectric 

 actions are considered to be operative in liberating the 

 electrons, as well as thermionic emission. 



The sethereal radiation may be shown to obey Stefan's law 

 and Wien*s law by the usual methods of proof if the ap- 

 pliances are slightly modified. We may separate the sethereal 

 radiation from the electronic atmospheres by means of an 

 ideal transparent solid devoid of thermionic and photoelectric 

 emission. The radiations may subsequently be allowed to 

 intermingle in a reversible manner through a similar filter. 

 The dynamical operations are carried out in perfectly re- 

 flecting enclosures lined with the same transparent non- 

 emissive material. In this way the complications arising 

 from the presence of an electronic atmosphere mixed with 

 the sethereal radiations are avoided, and one arrives at the 

 usual results that the total radiation density 



=§E x d\=A l 6* and E A =A 2 5 </>(\<9), 



where A 1 and A 2 are universal constants. 



The relation between the concentration (number per unit 

 * Jeans, he. cit. p. 70. 



