Motion of Electrons in Solids. 



785 



body is given by 



A = 



i f<i - 



R 12 ) cos 6i sin #! d0 1 





cos $i sin $i d&i 



) cos 1 sin X d0 1} 



so that the stream of issuing radiation is 

 iAf(T,p)d P . 



Putting A = l we pass to the case of an ideal perfectly 

 black body, and find that the stream of issuing radiation 

 must be J/(T, p)dp. 



Hence, in general the stream issuing from any body is 

 A times the stream issuing from a black body, as required by 

 Kirchhoff's law. 



We have derived KirchhofF's law as a consequence purely 

 of electron theory. It appears that the law is true quite 

 independently of whether the aether is in equilibrium with 

 matter or not: in fact the law is seen to be entirely in- 

 dependent of thermodynamic conditions of all kinds. It is 

 consequently illegitimate to draw any thermodynamical in- 

 ferences from the fact that KirchhofFs law is observed to be 

 true in nature. 



Emission of Radiation. 



17. If charges e, e\ ... move with velocities u, u/ 

 du 



there 



is no radiation if %e , - = 0. If this condition is not satisfied, 

 at 



let EU be the vector which is the resultant of the vectors 



eu, e'u', .... Then 



-r, dJJ , ^ du . 



-*dt +te dt=°> 



so that the radiation from E, 



e,e, 



is nil. Hence the radia- 



tion from e, e,' ... moving with velocities u, u/. . . is equal to and 

 identical with that of a single charge E moving with velocity 

 U. In this result it has to be supposed that the distances 

 apart of the charges e, e,' ... are small compared with the 

 wave-length of the emitted radiation, or at least of that part 

 of it with which we are concerned. 



