572 Prof. 0. W. Richardson on tlie 



It shows very clearly that there is a limiting value 



v-o 



helow which there is no photoelectric emission at all. This 

 is in accordance with the results of experiments. 



The index 2 of on the right of (3) and (5) depends on 

 the various approximations which have been made. In 

 general it will depend on the specific heat of electricity a 

 and the way in which a and a depend upon the temperature. 

 Now it may be show n that unless the index of 6 is an integer 

 there is no solution of the type 



cF(v) = when 0<hv<w 

 and 



eFii') — -~ (/> ( p ) when w < liv < co . 



It follows that if this type of solution is upheld by experi- 

 ment, there must he some undiscovered relation between the 

 temperature variation of photoelectric effects, the specific 

 heat of electricity, and the reflexion of electrons as a function 

 of the temperature, which makes the index an exact integer. 

 We have not enough information, particularly in regard to 

 the photoelectric effect, to make it profitable to speculate 

 further about this relation at present. The point, however, 

 is important since it shows that the solutions have a generality 

 which is not limited by the somewhat peculiar physical 

 approximations which have been made. 



It is possible that the index of 6 on the right of equation (5) 

 might be some positive integer X other than 2. The solu- 

 tions may be readily obtained by substituting a series of 



powers of v for eF(V), integrating from ~ to go , and com- 

 paring coefficients of 0. As the general case does not appear 

 to possess special features, it is simpler, and otherwise as 

 satisfactory, to keep to the particular case X= 2, which is 

 much the most likely value of the index. 



We shall now consider the average kinetic energy T v of the 

 electrons which are emitted by light of frequency v. The 

 total energy E emitted under the influence of the complete 

 radiation at 6 is clearly 



E = | f\eFM.E(v,0)«^. ... (6) 



An elementary calculation shows that the energy streaming 

 towards the metal in unit time by virtue of the thermal 

 motion of the external electrons is 2RR0. Of this energy 

 let the proportion 1— ft be reflected, then (3 is the proportion 



