Motion of Electrons in Solids. 789 



frequency p. The proper value to use for c when we suppose 

 the motion made up of free-paths of equal duration is that 

 given by Thomson, namely (in our notation) 



_ 9 sin 2 \pr Ne 2 



P 2r ~ 



m 



Using this value of c, and equating the emission (33) to 

 the absorption (34), we obtain 



E 



jrRTK/. ^ 2 RT 



tt 2 C 2 V 



■V*' 



. (35) 



19. We next examine how this must be modified when we 

 do not assume the existence of free-paths. 



If tjj t 2 are any instants within the interval from to t, 

 and if i lf i 2 are the values of i at these instants, we have, by 

 equation (29) 



A p =p l i x sinjiti dti =p I u sin pt 2 dt 2 , 



Jo Jo 



so that, by multiplication, 



A 2 p =p 2 I I %y i 2 sin pt x sin pt 2 dt x dt 2 . 



Jo Jo 



Similarly from equation (30) 



ii i 2 cos pti cos pt 2 dti dt. : , 

 ) 

 and by addition 



Aj + Bp =p 2 \ \ ii i 2 cos p(ti — 1 2 ) dti dt 2 



Jo Jo 

 ti=t t. 2 -t 



=P 2 i \ iii2Cosp(ti — t 2 )d(ti — t 2 )df^-^\{M) 



Let the two instants t { , t 2 be at equal intervals 6 from their 



middle instant t' of which the value is ( — — J. Let i' be 



the current at t ! : The expectation of rate of change of i is 

 (cf. equation (8)) 



di N* 2 . 



dt 



mrc 1 



of which the integre 



•ai is 



i = ine 



-et 



(37) 

 (38) 



Phil. Mag. S. 6. Vol. 17. No. 102. June 1909. 



3H 



