Motion of Electrons in Solids. 787 



and now have* 



The total emission of the element do in time £ is accordingly 



3^C (V+B * 2) ^' • • • • ( 2 ») 



and in this expression the coefficient of dp represents the 

 emission of radiation of frequency between p and dp. 

 Instead of (27) we may take 



A»= l — cos pt dt 



I. I 4 f*. . 



= i cos pt\ + p 1 e sin pt dt ; 



I o Jo 



when t is large enough, the first term may be ignored, and 

 we may take 



Ap=p I i sin ptdt, (29) 



Jo 



B*=— pj z cos ptdt (30) 



Jo 



The calculation of the emission requires the evaluation of 

 these integrals. 



18. Let us first perform the calculation on the simplifying 

 assumption that the time t can be divided into n equal free- 

 path periods each of time t, and let us suppose that at the 

 end of each of these periods the velocities of the electrons 

 are replaced by new velocities whioh have no reference to 

 the old. We have, by equation (29), 



s-71-i r*~ 



A ? =JJ S I i sin p(t + st) dt 



s=o Jo 



s=?>— 1 



= 2 2% sin p{ t+(s + i)r\ sin ±pr, 



5 = 



so that, since there is no relation between the values of i on 



* Rayleigh, Phil. Mag. [5] xxvii. p. 466. 



