182 M. E. Edlund on the Nature of Electricity . 



be doubted ; but tbe same cannot be said with respect to r. The 

 force of induction at a given moment upon the mass of aether 

 /i'cfe' of the induced circuit is proportional to the difterence be- 

 tween the repulsion exerted upon [jJds' by the element of the 

 inducing current (in which the mass of sether [uds moves with 

 the velocity h) and the repulsion upon the same mass of all the 

 rest of the aether. The first of these repulsions diminishes (as 

 is evident from the preceding reasoning) inversely as the square 

 of the distance between the elements ds and ds^ . ISqw, if this 

 were also the case with the latter^ viz. the repulsion exerted upon 

 y.Uy by all the rest of the mass of aether, F would evidently be 

 independent of r ; for we could express_, for a given instant^ by 



-^ the repulsion proceeding from the element ds of the inducing 

 current^ and that of all the remaining mass of sether by-g, expres- 

 sions in which a and b would be constants. The force of induction 

 for that moment would then become —^(a — h), which may be 



written pKr, p being a constant. As long as the sether molecules 

 are in their normal primitive positions of equilibrium, the repul- 

 sion exerted upon [jJdb! by all the surrounding mass of sether 



klsds^ 



with the exception of fids is = + ~ — ^^^^^-^ , and therefore indeed 



diminishes inversely as the square of the distance. But this can 

 no longer be the case after the molecules are displaced and the 

 mass of sether about ii'ds' has undergone a distribution difi*erent 

 from its normal condition ; for the repulsion exerted upon /^V/i' 

 by the surrounding aether is of course not independent of the 

 distribution of the sether. F must necessarily depend on r ; 

 and hence we shall write F(r) instead of E. 



We have therefore obtained the following formula to, express 

 the magnitude of the induction-current : — 



+ '^^U cos e-\--^kh cos2 d\ cos &dsds\ . (17) 



or; if vre neglect the last term^ 



ai¥ 

 -}- -^ cos 6 co?> 6' dsds' (18) 



We now suppose that the inducing current is closed, and that 

 its form is such that it can be divided by a plane into two sym- 

 metric halves. Then each element a on one side of the plane 

 has a symmetrically corresponding element a' on the other side. 

 We suppose further that the induced circuit is closed and sym- 

 metric about the same plane ; so that to each element b on the 



