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



tradicting, experiment much rather confirms the result arrived at 



theoretically — namely^ that the terms in formula (14) multiplied 



kh 

 by — may be neglected in comparison with the first. Experi- 



ment alone can decide if this is permitted in reality. 



The action upon the aether of the circuit-element cls\ ex- 

 pressed by formula (14), is exerted along the line of junction 

 between ds and ds\ But as the aether of ds^ can only move along 

 this element^ we must, in order to have the measure of the mo- 

 tion produced in the aether of ds, multiply that expression by 

 the cosine of the angle formed by the acting force with the cir- 

 cuit-element. CalUng this angle 6\ we must multiply by cos ^'. 

 By electromotive force of induction is meant the accelerative 

 force exerted by the inducing wire upon the aether contained in 

 unit of length of the induced wire. The value of this we obtain 

 by dividing the expression (14) by [jJ ; and thus w^e get as ex- 

 pression of the induction of a current-element upon an element 

 of the induced circuit during the first instant : — 



-fj^r^eos6'-^(^l-|cos^^)]cos^'^5^5'. . (15) 



The induced circuit must always be closed that an induction- 

 current may be possible. In the integration of the formula (15) 



khi 

 with respect to f/s'; the term independentof cos(9 (viz. ^c^cos6'dsds') 



vanishes, whatever be the form of the induced circuit, provided 

 it is closed. This is easily proved by the following reasoning. 

 Imagine two spherical surfaces with the element ds for centre, 

 the one having the radius r, and the other the radius r + dr. 

 Now, if a part of the induced circuit be upon either of these 

 concentric surfaces, evidently the above-mentioned term must 

 vanish for that part of the circuit. Everywhere, in this case, 

 cos ^ is =0, since the radius of a sphere always makes a right 

 angle w^ith the lines drawn from the terminal point of the radius 

 upon the surface of the sphere. The elements of the induced 

 circuit w^hich fall between the two concentric surfaces must be 

 in pairs, since the circuit is closed. A current, then, in the in- 

 duced circuit will pass as often from the outer to the inner sur- 

 face as from this to the former. The cosine of the angle 6', 

 which any one of the elements included between the surfaces 



dr 

 forms with the corresponding radius, is equal to — ; and the 



number of these cosines bearing a positive sign is equal to that 

 of the cosines with a negative sign. It hence follows that, for 

 all the elements which fall between the two surfaces^ the product 



