﻿of the Electron Theory of Matter. 621 



comprised between those wave-lengths is 



ce 



N 



-jEOOrfv, ...... (52) 



where c is the velocity of light. Let us suppose that the 

 emission or absorption of unit quantity of radiant energy of 

 frequency v at the temperature causes the liberation of 

 F(V#) electrons. Then the total number of electrons emitted 

 in unit time by the complete radiation is 



= |[*eF(,0)E w ^ (53) 



But this number must be equal to the number of electrons 

 returned to the body per unit time from the external atmo- 

 sphere. Now the electrons behave like the molecules of a 

 gas (since they satisfy equations (49) and (49 a)), so that the 

 number which reach the emitting surface in unit time is 

 ftnO*, where /3 is a constant which may be calculated from 

 the kinetic theory of gases. In general some of these will 

 be reflected. Let the proportion absorbed be a. Then 



N= a /3n0z = *0iAl3e^ .... (54) 



Thus for all values of 



|f eF(v6)V(v)dv = oL0lM e +im . . . (55) 



According to Wien's law (p. 47) 



B(v)dv=v*f(!£\dv (56) 



If experiments at low temperatures may be taken as a guide* 

 eF(j/#) is independent of 0, so that we may expand this 

 function as a series of powers of v±*. By comparing the 

 coefficients of the powers of with those of the expansion of 

 the exponential on the right-hand side, the undetermined 

 coefficients may be evaluated. In this way I find, putting 



-r^ = ^R in accordance with § 3, 



Jo 

 The integrals in (57) are not mere numbers, since, according 



