150 Prof. 0. W. Richardson on the 



certain that the values of b for the two effects are not 

 •identical for the same substance. The value of A, on the 

 other hand, is left entirely arbitrary by the thermodynamic 

 considerations, which do not therefore enable us to determine 

 the scale of magnitude of the complete photoelectric emission. 

 Thus the theoretical argument leads us to the conclusion 

 that the complete photoelectric emission varies in the same 

 general manner with temperature as the observed thermionic 

 effects: it is possible, although not certain, that the indices 

 X and b are identical in the two cases contrasted, in which 

 case the two emissions would be in the same relative pro- 

 portion at all temperatures ; on the other hand, the absolute 

 value of the complete photoelectric emission is left entirely 

 undetermined, so that we are unable to determine by such 

 calculations what proportion it bears to the observed therm- 

 ionic emission. 



This information can, however, be obtained from known 

 photoelectric data in the case of the metal platinum. The 

 calculations are not exact, but it is improbable that the 

 sources of uncertainty in the calculations will lead to errors 

 in the final results which are as great as those pertaining to 

 the experimental measurements of the absolute values of 

 photoelectric and thermionic emissions from a given material. 

 Data* now available give the number of electrons emitted 

 from certain metals, including platinum, when unit light 

 energy of the different effective frequencies falls on them at 

 normal incidence (or at some other angle which is definitely 

 specified). The magnitude of the complete photoelectric 

 emission will not, however, be obtained if we simply multiply 

 this number by the corresponding intensity of the light in 

 the black-body spectrum and integrate the product over the 

 whole range of frequency, on account of the different optical 

 conditions in the two cases. In the photoelectric experiments 

 in which a beam of light is incident normally, the intensity 

 of the exciting illumination is greatest at the surface and 

 falls off exponentially as the depth of penetration increases. 

 In the natural emission, on the other hand, the electro- 

 magnetic radiation is isotropic, and its intensity is the same 

 at all depths. This particular difference between the two 

 cases can be allowed for if we have a knowledge of the 

 coefficients of absorption of the electromagnetic radiations of 

 different wave-lengths and of the electrons which they cause 

 to be emitted. 



It is usual to assume that both the light and the electrons 



* Kichardson and Rogers, Phil. Mag. vol. xxix. p. 618 (1915). 



