"L 570 ] 



LII. The Theory of Photoelectric Action. By 0. W. 

 Hichakdson, Professor of Physics, Princeton University *. 



IN a recent paper f the writer has developed a theory of 

 photoelectric phenomena which is based on thermo- 

 dynamic and statistical principles. It has been shown that 

 the number N of electrons emitted from unit area of a body 

 in equilibrium with the complete radiation characteristic of 

 its temperature 6 may be expressed in either of the two 

 equivalent forms : 



= ^\?(v,ey-&(v,6)dv. 



T$ = j\ eF{v,8)$i(v,e)dv . . . . (1) 



and f_^ M 



N = «A0"V Be2 , ...... (2) 



where E(v, 0) is the function which expresses the distribution 

 in the spectrum of the steady energy density, eF(V, 6) is the 

 number of electrons emitted in the presence of unit energy 

 whose frequency lies between v and v-\-dv, c is the velocity 

 of light, A is a constant characteristic of the substance and 

 independent of 0, a. is the proportion of the returning elec- 

 trons which are absorbed (i. e. not reflected), w is the internal 

 latent heat of evaporation of one electron, and R is the gas 

 constant for one molecule. 



The right-hand sides of (1) and (2) must be identical 

 functions of since they are true for all values of this 

 variable. If we may assume E(V, 0), a and w to be known 

 functions of v and 6 in so far as they involve these variables, 

 the problem of finding the function eF(v, 0) resolves itself 

 into that of solving an integral equation. There is also 

 a similar equation involving the energy T„ of the emitted 

 particles instead of the number of them. The solutions 

 which make eF(v) and T„ capable of representation by a 

 single analytic function of v throughout the range from zero 

 to infinity have already been considered. It appears that 

 these solutions do not exist when E(v, 6) has the form given 

 to it by Planck or the approximation for Planck's formula 

 which is used below. The object of the present communi- 

 cation is to indicate another type of particular solution. 

 Reasons will be given in a later paper for believing that this 

 second type of solution is the one which actually represents 

 the facts. 

 . Such experiments as have been made on this subject 



* Communicated by the Author. 



t Phvs. Kev. vol. xxxiv. p. 146 (1912) ; Phil. Mag. vol. xxiii. p. 61o 

 (1912)." 



