Photoelectric and Photochemical Action. 479 



We have also from (5) 



^=$fH? + R T ^t^n^% (8) 



since eF(j/) = when v = v . 



Differentiating (4) by T, we have 



= E 1 + N 1 ( WT -|RT), .... (9) 



where Ej = 2N!RT is the kinetic energy returned to the 

 substance by the motion of thermal agitation of the gas. 

 In the steady state E l — E 2 and Ni = N 2 . This is true, so 

 far as the present use of these equations is concerned, even 

 if there is scattering or reflexion of atoms at the surface of 

 the substance. For by a well-known principle in atomic 

 statistics there are as many deflexions of returning atoms 

 outwards, of a given class, as there are deflexions inwards 

 •of escaping atoms of the same class. Substituting for E t 

 and N x in (9) the values given by (7) and (8) we get 



hv 



(10) 



This equation is true for all values of v and T and for all the 

 admissible forms of eF(v) characteristic of different sub- 

 stances. In general it appears from (10) that <fr[v) may be 

 dependent not only on v but may also involve the properties 

 of the substance, through eF(v) and v and the temperature 

 T. The experimental evidence all goes to show that at 

 sufficiently low temperatures photoelectric action is approxi- 

 mately independent of the temperature of the substance for 

 light of a given intensity ; so that at low temperatures (such 

 for example as are employed in ordinary laboratory experi- 

 ments on these effects) equation (10) reduces to 



r 



hv 

 .3 „ 



eF(v)hv*e bt {<j>(v)-hv}dv=Q. . . (]]) 



If photochemical and photoelectric actions are (funda- 

 mentally) independent of temperature at low temperatures 

 then e¥(y) and <j>(v) will be functions of v and v only and 

 will not involve T. In that case either eF(j/) = or 6(v)=hv 



2K2 



