﻿of Radiation in any Material System. 



523 



substituted. So regarded the change is beyond the pale of 

 dynamical actions. 0£ course it may be urged that the 

 point of view is not ultimate. What is before us is really 

 a dynamical process. I have argued that this may be doubted. 

 In practice at all events we are forced in the present state 

 of our knowledge or ignorance to deal only with the 

 enumerable infinite. 



§ 4. Expansion in Normal Functions. 



The value of F x satisfying (28) is to be normal at S. 

 Write therefore 



F — V a F 



(42) 



where 



(V 2 + *„;)F w ,:=0 "1 

 DivF,„ = 

 $F*dv = 4tt 



F m normal at S 



(43) 



_ The last of (43) is the normal property holding for any two 

 different values of m, it follows from "the others. Where 

 V is large these normal functions became ordinary trigono- 

 metrical functions and ^tt-j" 1 is the wave-length corre- 

 sponding to F m . 



As in (34) and (35) at 8 



av dv l 



So that 



Also JF 1 F w ^v=:47r^ i 



Multiply (24) throughout by F m dv and integrate 



| F„(V»-**)F,rft,4 *» j'^F. dv= (V.V.(-. -*»)* 



Now 



(44) 

 (45) 



