﻿534 Mr. S. B. McLaren on Emission and Absorption 



k' 1 is the molecular radius. For waves of ordinary light the 

 terms containing k 2 are very great compared with the others. 

 (79) becomes 



(£-?*)* +te ? =°- • • • w 



Or substituting (77) and multiplying by g-*>*+«*^ 



(£+V-tf + 2ink\F l e-*+4w^e-*+ i "=*0 . (81) 



/|! +#J_„2 + 2m#) ^-^ + 47T^^-^+^ = . (82) 



Now integrate each of these equations over any finite 

 area of the wave-front and from z = z 1 to z = z 2 . Then (81) 

 becomes 



(K+&-n 2 + 2ink\FS 2 e~ kz dv + 4tt C* 2 ^A™~pt)dv=0 



*x . . . (83) 



and a similar result from (82). It is not the whole irregular 

 motion of the material system with which we are concerned 

 but only that part of it which is caused by the passage of 

 the wave-train. Thus (83) may be rewritten 



fe +k*-?i 2 + 2ink\F 1 f%-* 2 dv + ±7r8C 2p —e^-P0dv=0 



... (84) 



As in our previous notation 8 denotes the deviation due 

 to the force F^ In order to calculate the last term in (84) 

 we may therefore put in (59) 



and 



H 



P ~(*{nz-Pt)dv, (85) 



c 



®= (If, ~+£i^) &*—*)-*&>. . . (86) 



Now it is evident that the average value contributed to 

 the last term in (84) by a group of molecules in the volume 

 element dV will be proportional to dY provided that instead 

 of an infinitesimal element of volume we take one large 

 enough to contain a very large number of atoms. Also 

 owing to the presence of the factor e~ kz in <£ this 

 amount will decrease with e~ kz where z is the distance of 



