﻿622 Prof. 0. W. Richardson : Some Applications 



to the radiation formulae of Planck and Wien, they contain 



a parameter ^-, where h is Planck's constant. By changing 



7 

 the variable to z = -^ # 3 one finds 



where a> is the part of co which is independent of 6. 



The integrals are now pure numbers, x(z) being a function 

 of z only. For example, if Planck's formula is used, 

 x(z) = (e z — l)" 1 . This solution shows that, provided the 

 series exists and is convergent, and provided the results 

 are not seriously affected by the somewhat arbitrary physical 

 assumptions made, as to the independence of eF(v) and 0, 



and so on, then t— ^ is the same function of ~ for 



aA vh 



all substances. Thus, if we knew the variation of the photo- 

 electric emission from any one substance, with the frequency 

 of the light in the complete radiation, we should be able 

 to construct the emission from any other substance from 

 a knowledge of their respective values of w . Since w 

 is smaller the more electropositive the metal, we should 

 expect the emission to be excited by longer waves as the 

 metals become more electropositive. This is, of course, in 

 agreement with known experimental evidence. Somewhat 

 similar properties hold for the mean kinetic energy of the 

 electrons emitted by light of given frequency. I hope to 

 be able to discuss these ^questions later, in connexion with 

 new experimental results. 



We have as the result of experiment some information 

 about the form of eF(f). We know that it is zero for small 

 values of v, and it may for most substances in all probability 

 be put equal to zero over the part of the spectrum for which 

 the formula 



^v=~h^ e - h ^ e (59) 



is not a sufficiently accurate representation of the facts. 

 This amounts to ignoring the part of integrals like that on 

 the left-hand side of (55) contributed by the long wave- 

 lengths. A theory of photoelectric emission, based on the 

 discrete theory of light, has been proposed by Einstein *. 



* Ann. der Phys. xvii. p. 146 (1905). 



