526 WEBER ON THE MEASUREMENT 



in p. 511, i and i' be substituted for aeu and a' e'u', the above 

 sum, with slight transposition, becomes 



= (cos s — I cos cos &), 



the same expression at which Ampere arrived where the elements 

 of the current are invariable and undisturbed, i. e. the electro- 

 dynamic force acting upon the entire element «' is determined in 

 the same manner when the conductors are in motion and the 

 intensities of the current variable, as when the intensities of the 

 current remain invariable and the conductors undisturbed. Hence 

 Ampere's law is of general application in the determination of 

 the forces, which act upon the entire element of the current vihen 

 the position of the elements of the current and the intensities of 

 the current are given. The application of this law merely re- 

 quires that the intensities of the current when variable, as also 

 the position when variable, be given for each individual moment, 

 and further, the intensities of the currents, including that part 

 added at each moment in consequence of induction. 



But as regards the difference of the forces which act upon the 

 positive and negative electricity in the element «', by which these 

 two electricities are separated from each other, and move in the 

 conductor in opposite directions, this now becomes 



= . aeu . ae' V (sin sin >j cos y — ^ cos © cos »)) 



du 



aaee cos 



dt' 



or, because aeu ■= i and ae .du := di. 



i (sin © sin rj cos y — \ cos @ cos tj) 



r r 



— i — a e . cos .- 



di 



~di' 



The force thus determined then tends to separate the 2^ositive 

 and negative electricity in the induced element a' in the dii'ection 

 of the right line r. When the conductor is linear, however, 

 separation cannot occur in this direction, but only in the direc- 

 tion of the induced linear element «' itself, which forms the 

 angle ©' with the produced right line r. By thus decomposing 

 the whole of the above separating force in this direction, i. e. by 

 multiplying the above value by cos 0', we find the force, which 

 effects the true separation. 



