178 M. E. Edliind on the Nature of Electricity, 



This is the maximum value of the force ; after the first moment, 

 it diminishes continually until, at last, it becomes =0 when the 

 molecules have reached their new positions of equilibrium. 

 Formula (14) can be divided into two parts, viz. 



+ -^ cos 6 ds els', and ^ i/ju'h ( 1 — 9 cos'^ O) ds ds\ 



If in the second part we denote by i' the intensity of current 

 indicated by i^h, that part of the formula becomes 



2rA 2 



1 — :r cos^ 6 ds ds 



«) 



Now this expression indicates half of the electrodynamic repul- 

 sion between two circuit-elements ds and ds' when they are 

 parallel and respectively traversed by the currents i and i'. 



In the theoretic deduction of the electrodynamic formulse, we 

 have assumed that the repulsion between two molecules of sether 

 is communicated without diminution even to the elements of the 

 circuit in which they are moving. Of course this hypothesis 

 applies only to the part of the repulsion-force between the mo- 

 lecules which remains in the electrodynamic formulae, and not 

 to the part which vanishes (of itself) in the formation of those 

 formulae. It consequently applied to the terms in the expres- 

 sion of the repulsion which are m.ultiplied by k, and not to that 

 containing the constant a. But if we maintain this hypothesis 

 for the terms multiplied by k in the expression of the repulsion 

 between two sether molecules, the theoretic deduction gives a 

 result perfectly accordant with Ampere^s empiric formula. 



But the communication of the part in question of the repul- 

 sive force entirely to the circuit-elements in which the molecules 

 move, presupposes necessarily that that part cannot communi- 

 cate any proper motion to the molecules themselves in their re- 

 spective circuits ; for, if it did, a portion of the repulsion would 

 be expended in generating that motion and in producing the 

 heat resulting from the resistance opposed by the circuit. In 

 this case^ then, the whole of the repulsion could not pass to the 

 circuit-elements. Still the molecules of sether may possibly 

 receive some motion from the repulsion mentioned, but too 

 slight to permit a difference between theory and experiment to 

 be observed in electrodynamic phenomena. Be it as it may in 

 this respect, we obtain, as a necessary consequence of the hypo- 

 thesis we have made in the deduction of the electrodynamic phe- 

 nomena, that the terms in formula (14) which are niultiphed by 

 the constant k exert only an insignificant influence on the dis- 

 placement of the sether particles in the induced circuit, and that 

 consequently their importance for the induction is very little. 



