( 627 ) 



and the couple to be a(UU'j\ to (24) will be given by 



1 dN 



271C ' (It ' 

 'Yiik'nv^ into uccoiml (23), we find for ihc loial coiiijle 



2jrcV ri^y 2:tc dt 



Since this is thf; lale of change of a periocHc qiianlily, liie mean 

 value will be 0, as above asserted. 



Tlie above somewbal eouipjieated reasonijig has been nse<l in 



order to avoid the dirficnilies arising in a closer examinalion of 



the phenomena going on in the ponderable dielectrics. The if-snlt 



may however be vei-ifie<l by making suitable assumptions concei-ning 



these phenomena. It will surtice foi- (;iir j)urpose to replace one of 



the dieleetiic bodies by a single pair of electrons A and B, the 



first of which is immovable, whereas the second may be displaced 



over an infinitely small distance, in a radial direction, by the electric 



forces of the field P\. We shall denote by — e and -f- '^ the charges 



of A and B, by /■ the distance of A to the axis, by .v the infinitely 



small distance A B, and we shall write 5: f'"" ^'i<^ vertical (•om|)onent 



of the magnetic foi-ce in the field J'\ and D for the value of the 



delectric displacement in this field at a distance r from the axis. 



We shall take the positive directions as follows: for .v outwai'ds, for 



f). npwai'ds, and foi- 1) alojig the circular line of electric force in 



a direction coiresponding to the positive direction of ^~^ i. e. in the 



direction of a positive I'OtatioJi about the axis. 



d. 

 Now, owing to the velocity of the electron B, thei-e will be, 



dt 



according to the foj-mula CVII), a force 



e ds 



~~>Tt 



acting on this electj-on along a circle about the axis, and producing 



a moment 



H , ds 

 — -rf),— (24') 



c at 



This is the couple of which Whitkhkao has sought to j»i-ove the 

 existence. It is howevei- ann idled by the moment aiising from the 

 action of the field /'\ in virtue of its electric force D. For the 

 particle A this moment is 



— e rl) 

 and fo)- the [)article /i it is oi>tained if we i'e[)lace — e by -{- '^» 



