528 WEBER ON THE MEASUREMENT 



consequently the electromotive force is 



= + I — i sin 6 cos^ Q .av. 



This value is always joosi/ive, because we must consider e< 180° ; 



and this positive value here denotes an induced current of the 



same direction as the inducing current, in conformity with that 



which has been found by experiment for this case. 



Under the same conditions, with the difference merely that the 



element a' by its motion becomes approximated to the element oc, 



we have 



= e', cos »! = — sin e, cos s = ; 



consequently the electromotive force becomes 



- «a' . . „ 2 „ 

 = — # — ^ sm COS'' . av. 



The negative value of this force denotes an induced current, in 

 the opposite direction to that of the inducing current, also in 

 conformity with that found by experiment for this case. 



As is well known, voltaic induction may be produced in two 

 essentially different ways; for currents may be induced by 

 constant and by variable currents. It is produced by constant 

 currents either when the conductor through which the current 

 passes is moved towards that conductor in which a current is 

 about to be induced, or vice versa. It may be induced by 

 variable currents even when the conductor through which the 

 variable cun-ent passes remains undisturbed as regards that 

 conductor in which a current is about to be induced. 



Just as the particular law of the first kind of voltaic induction 

 was at once found from the general laws of voltaic induction de- 

 duced above by the conditional equation 

 di 



^^ 

 so we also find the peculiar law of the latter kind of voltaic in- 

 duction by the conditional equation 



v = 0. 

 Thus if we take, secondly, the case in which no motion of the 

 conductors as regards each other takes place, or where v = 0, the 

 law of the induction of a variable current upon that element of a 

 current which is not moved as regards it, or the value of the 

 electromotive force becomes 



T ««' ^ ^1 d i 



= ^ 5 — a cos cos 6' . — - . 



r dt 



