Photoelectric and Photochemical Action, 



487 



by the following consistent scheme of mutually related 

 functions : — 



<f>(y)=z hv. 0<v<oo,"l 



T„= /<(i/-i/ ), Vo<v<oo-, }> (43) 



7w = w— ^RT, 



$(T)=AT 2 . 



So far as I have been able to discover, this is the only set of 

 functions involving- only a single critical frequency which 

 will satisfy all the relations as laid down (see below) without 

 contradiction. No use whatever has been made of the value 

 of the specific heat of electricity or any other specifically 

 electrical property of the materials, so that the results will be 

 just as valid for photochemical as for photoelectric actions. 



A certain amount of caution is necessary in the applica- 

 tion of these formulae to compare with the results of experi- 

 ments. In carrying out the calculations we have entirely 

 neglected the part played by electron reflexion in the 

 electrical case, and by the corresponding deflexions of the 

 atoms in the types of photochemical action which are more 

 generally regarded as such. From the principle of statis- 

 tical equivalence referred to on p. 479, it follows that this, 

 neglect will not affect the equilibrium values, so that the 

 equations (43) will express the relations which are inherent 

 in the phenomena so far as the action of the radiation on the 

 molecules is concerned. But in photoelectric experiments at 

 any rate we have to deal, not with a state of equilibrium, but 

 with the rate of emission under given illumination. This is 

 less than the ideal emission by an amount which represents 

 the number of electrons deflected back into the interior. An 

 exactly similar difficulty arises in the application of the equi- 

 librium theory of the thermionic emission of electrons to the 

 experimental measurements of the maximum rate of ther- 

 mionic emission at a given temperature *. 



More serious limitations are introduced by the assumption 



that the contribution to the mean internal kinetic energy £ 



arising from the radiation is negligible. It is, in fact, 



possible that the whole of f may arise in this way. To 



* O. W. Richardson, Phil, Mag-, vol. xxiii. p. 604 (1912). 



