﻿of tlie Electron Theory of Matter. 625 



The foregoing discussion has been restricted to the case of 

 a body which is photoelectrically active but devoid of ther- 

 mionic emission. We shall now consider the limitations 

 which have been thus introduced. If we consider the atmo- 

 sphere of electrons close to a flat face of the enclosure and 

 a long way distant from the rest of the boundary, the 

 electrons present will in general have come from a number 

 of different sources. These are : (1) the stream from the 

 interior of the cavity ; (2) those of the incident electrons 

 which are reflected at the interface ; (3) those due to 

 thermionic emission ; and (4) those due to photoelectric 

 action. The distribution of velocity among the totality of 

 these four groups of electrons must be in accordance with 

 MaxwelFs law. The same is true of groups (J) and (3) 

 individually, and must therefore be true of the sum of 

 groups (2) and (4). We have seen in §4 that the reflected 

 group have Maxwell's distribution in the case of matter 

 devoid of photoelectric action, and a similar argument may 

 be used to demonstrate the same property for the photoelectric 

 group when the material does not reflect any of the incident 

 electrons but may emit thermionically. If the acts of re- 

 flexion and photoelectric emission are dynamically inde^ 

 pendent, it follows that (2) and (4) as well as (I) and (3) 

 will each have Maxwell's distribution. It is probable that 

 the two acts are almost independent even if they are not 

 strictly so : in which case each group would have a distri- 

 bution only differing slightly from Maxwell's, Although I 

 have not been able to prove it, I think it probable that 

 Maxwell's law will hold true for each individual group in 

 every case. Thus, to sum up, we conclude that the results of 

 the above theorems which have been deduced for an ideal body 

 devoid of thermionic emission will, in any event, be nearly 

 true and, in all probability, be exactly true for real bodies. 



The foregoing considerations lead to a set of theorems 

 relating to the functions which determine the distribution of 

 velocity among the electrons emitted by the photoelectric 

 effect which are similar to those given in § 4 for the re- 

 flected electrons. They may be expressed in the following 

 fashion : — = 



The oethereal energy of frequency between v and v + dv 

 which is incident on unit area in unit time at an altitude 

 between # and -\-d0 and an azimuth between </> and <£ + </</> is 



^m\ e cos 0dOd(j>E(v)d^ 



when all planes of polarization are included. As the radiation 

 Phil. Mag. 8. 0. Vol. 23. No. 13(5. April 1912. 2 T 



