OF ELECTRO-DYNAMIC FORCES. 527 



= i (sin © sin >) cos y — ^ cos cos »)) . ae' v cos ©' 



— 1 — c e . cos (y cos fe)' . -t-. 

 r a^ 



This expression, divided by e', gives the electromotor force 

 exerted by the inducing element « upon the induced element «', 

 in the ordinary direction, 



= i (sin sin >j cos 7 — i cos cos >j) . a v cos 0' 



, « «' „ ^, di 



— i — a cos cos 0' . TT. 



^ r at 



This is therefore the general law of voltaic induction, as found 

 by deduction from the newly laid down fundamental principle of 

 the theory of electricity. 



If we now, frst, take the case in which no alteration occurs in 

 the intensity of the current, thus 

 di 



Tt = ''' 



we have the law of the induction exerted by a constant element of 

 a current upon the element of a conductor moved against it, i, e. 

 the electromotive force becomes 



= ^ i (sin sin >) cos y — ^ cos cos r)) . av cos 0', 



or, when e denotes the angle which the direction of the inducing 

 element of the current forms with the direction in which the in- 

 duced element itself is moved, by a transformation which is 

 readily made it becomes 



= ; — i (cos e — I cos cos ri) . av cos 0'. 



The induced current is positive or negative according as this 

 expression has a positive or negative value ; by a positive current 

 being understood one, the positive electricity of which moves in 

 that dii-ection of the element «', which with the produced right 

 line r forms the angle 0'. 



Now if e. g. the elements a and a' are parallel to each other, 

 and if the direction in which the latter is moved with the velo- 

 city V is contained within the plane of these two parallels, and 

 at right angles to their direction, we have, when a! by its motion 

 recedes from a, 



= 0', cos ») = sin 0, cos s = ; 



