M. E. Edluud on the Nature of Electricity. 1 83 



former side corresponds a symmetric element b' on the other. 

 It thence follows that the distance between a and b' must be as 

 great as that between a' and bj that the cosine of the angle be- 

 tween the element a and the line of junction ab' must be equal 

 to the cosine of that between a' and a'b, but that the cosines will 

 have opposite signs, since the directions of the elements on the 

 two sides of the plane are determined by the direction of a cur- 

 rent which traverses the circuit. In the same way, the cosines 

 of the angles formed by the above-mentioned lines of junction 

 and the elements b and b' of the induced circuit will be of equal 

 magnitude but have contrary signs. Thus, in the induction of 

 the element a upon b' and of a' upon b, the two cosines of 6 will 

 be equal to each other in magnitude, but v/ill have contrary 

 signs, which is also the case with the two cosines of 6'. It hence 

 results that the part of the induction which corresponds to the 

 term in formula (17) intow^hich cos^^ enters will be =0 for the 

 two symmetric elements combined. It will be the same w^ith all 

 the other symmetric elements. Consequently, if the two cir- 

 cuits, inducing and induced, be each cut symmetrically by one 

 and the same plane, the integral of the term into which cos^ 9 

 enters will be equal to zero. In this case, then, the integrals of 

 the formulae (17) and (18) will be perfectly equal. 



We will now compare the theoretic result with the results of 

 experiment. 



Yie suppose that the circuits of both the inducing and the 

 induced current are circular, that the radius of the first is R, and 

 that of the second is H^ that the planes of the two circles are 

 parallel, and that the line joining the two centres makes a right 

 angle with those planes. In this case the two circuits are placed 

 symmetrically about the same plane, and the induction-formula 

 (18) is applicable. Imagining then the inducing circle situated 

 in the plane of ocy of a system of rectangular coordinates of which 

 the origin is at the centre of the circle, the induced circle is at a 

 certain distance z from this plane. The distance r from an ele- 

 ment ds, of which the coordinates are ^ = and ?/= — E, an ele- 

 ment situated in the inducing circle, to an element ds' with the 

 coordinates cc^, y^, z^, situated in the induced circle, is then 

 equal to -^^ x^^-{-{y^-{-'KY^z\,0Vj\Nhdi.t como^^io t\iQ 'id.me,io 

 -}- \/E2 4- 1^2 _|_ 2^y^ _|- z\. The tangent of the element ds is 

 parallel to the axis of the x'^ ; and if we assume that the 

 inducing current passes in the positive direction of the axis, 



^cos^ = — and consequently changes sign with Xy If the cle- 

 ment ds^ of the induced current be reckoned in the direction 



