152 Prof. 0. W. Richardson on the 



except for the fact that the intensity of the radiation is now 

 constant at different depths, shows that this radiation delivers 

 at each unit area of the surface in unit time the number N 2 rfv 

 of electrons, where 



^ 2 dv = 4,7T^^idv = 4cir^°^^i v dv, . . . (4) 

 a v la 



from (2). This method of calculating assumes that the 

 liberation of electrons from the atom by light is a consequence 

 solely of the absorption of the light and is not a result, for 

 example, of ihe process of emission of light. The total 

 number of electrons which escape is obtained by multiplying 

 this by the factor <y and integrating throughout the spectrum. 

 The complete photoelectric emission current J is therefore 

 equal to 



i 



', 87T6f'V+/3 Y N 1 2 hv* , ... 



•&&=-?-) ~ -T* -^m=\ dv - ■ ( 5 > 



«/o 



For any particular temperature T, the integral on the right- 

 hand side of (5) can be evaluated graphically if we know 

 /3/a, r, and 7N 2 /I for all frequencies. 



In the case of platinum, values of (l—p)^~ for all 



frequencies for which the factor hv*/(e hv!kT — 1) is appreciable 

 have been given by Richardson and Rogers*. In this 

 expression p is the reflexion coefficient from platinum at 

 normal incidence for light of frequency v. This quantity 

 has only been measured over part of the effective spectrum, 

 but the data given by W. Meier f, which extend as far as 

 \ = 2'57 x 10" 5 cm., show that we shall not go far wrong if we 

 take p as having an average value 1/3 over the region under 

 consideration. This region extends from \= 1*9 x 10~ 5 cm. 

 to \ = 2*75 x 10~ 5 cm. approximately, the effective average 

 value of \ being in the neighbourhood of 2*46 x 10~ 5 cm. 

 Data also given by Meierf show that the effective average 

 value of r 2 can be taken to be not far from 1*3 over the same 

 region. The only datum bearing on the relative values of 

 a and /3 is an observation by Rubens and Lad en burg $, who 

 found that when ultra-violet light passed through a thin gold 

 leaf the emission of electrons from the front side was 100 times 

 as great as from the side of emergence, whereas the intensity 

 of the incident light was 1000 times that of the emergent 



* Loc. cit. 



f Ann. der Physik, vol. xxxi. p. 1027 (1910). 



% Ver. der deutsch. PJmjs. Ges. ix. p. 749 (1907). 



