﻿Theory of Dispersion. 47o 



we have 



SW '= *f \ {fB - f+ ■•• )*-f^[^+ +)-8p]<?r, (25) 



since <£ is not to vary. Now integrating by parts into 

 surface {s) integrals and volume integral, we have 



BWs *$VS f + S) s/+ +)dr+ J*^-jW+ 



+)rf*. 



Now from the Lagrangian equation (since f, ff, h may lie 

 taken as generalized coordinates) 



^BT2_BT 2 3W' 

 <** 3/ 3/ + 3/ ' 



or . 47r . ^a 



F+ A,/+ 3 d .f=0, (26) 



where <£> is evidently the potential of distribution p. 



That is (if the medium is at rest) the electrostatic force 

 due to the medium (say Xj 



(the latter of which is due to />) on the understanding that 



22. It will be observed that k of the ordinary electro- 

 magnetic theory becomes Ic . This amounts to the postulate 

 that there is no dielectric other than free aether. 



Remembering that 



4tt3.i" 

 we conclude that 



-,%, 4:77 , 



F =-/, -/<>■ 



23. Returning to the equation (24), we observe that 

 — ^— =the force due to the system of electrons in volume 



\dr + the force brought into play on account of the 

 •displacement of electrons. 



If we take a small sphere of the volume \ dr, the system of 



