842 JProf . H. A. Wilson on the Electron Theory 



only necessary to indicate where it differs from his and to 

 give the final result. 



Lorentz shows that the amplitude in the radiation of a 

 given frequency from a thin plate of the metal can be repre- 

 sented in the form of a sum of terms ; one term for each free 

 path described by the electrons. Each term contains the 

 factor 



Y x cos-g- 1 t + -)dt, 

 where t is the time of describing a free path. Lorentz 



SIT 



assumes that the frequency is so small that cos-^-t can be 



regarded as constant during a free path, and so (page 87) 

 puts this factor equal to 



r 



z(t+i) 



To make the calculation apply to greater frequencies it is 

 only necessary to put the factor equal to 



6 TT f . S7T ( r\ . stt / , r\~] 



-V I (s n , T ( t+ T + -)- S m T ( 4+ -)) ( 



and carry out the calculation in the same way as H. A. 

 Lorentz gives it. 

 In this way I get 



a ' ~~20W I sV 2 Sm 20 T J ' 

 instead of Lorentz's (page 88) 

 s 2 e 2 



a « = 9/1 /M^Q ^ v )• 



240 4 cV 



If the angle -^- is taken to be very small and t 2 W put 



I 2 

 equal to ^ , the two expressions become identical as they 



should. 



The evaluation of S is similar to that given above in 

 getting the heat produced in the metal. 



The final result for the perpendicular emissivity of the 

 x>late of small thickness A is 



12cV W J 1+i^fJV 2 ' 

 which if p is taken to be very small reduces to Lorentz's 

 expression. 



