74 Intelligence and Miscellaneous Articles. 



during one minute, 1 — a that of the breaks. Calculating I' 2 and I' x *, 

 we find them to be equal, and that they satisfy the relation 



,,_ Ma 



""N+/3 + 6* 



Now, if the wire of the induced coil j3 and that of the resistance 



were extended in a straight line so as 10 avoid induction, and if the 



curreut of a battery were passed the electromotive force and resistance 



of which were M and N, we should have a current of the real inten- 



M 



s ^y xt 5 — a » an( * *f ^ were opened at regular intervals in such a 



N -{-(3-hu 



manner that the duration of the passage were reduced from 1 to a, 

 we should have a mean intensity 



T— Mo c 



~N+^ + 0' 

 Further, the amounts of heat developed in the resistance 6 and in 

 the coil /3 would be, according to Joule's law, 



a a 



The same would be the case if the currents were alternately in op- 

 posite directions. Inverting this reasoning, we are led to identify 

 this hypothetical case with that of induction, and to formulate the 

 law of the induced current as follows. 



1. The successive induced currents, although alternately in oppo- 

 site directions and of varying intensity, have the same mean intensity 

 I' as if they proceeded from a battery with constant current ; I' is 

 expressed by Ohm's law, 



Ma 



I' = 



N+/3 + 0' 



2. The quantities of heat C and C which these currents develope 

 either in an external circuit or in the coil /3, are the same as those 

 which would be created in these resistances by this hypothetical bat- 

 tery. C and C are expressed by Joule's law, 



a a 



3. The electromotive force M of these currents is far greater than 

 that of the inducing battery which sets the whole in action ; and the 

 resistance N is itself far more considerable than the resistance /3 of 

 the coil. 



4. M and N being both very great, the mean intensity I' is very 

 small ; whence it is that the inducing current produces but small 

 chemical actions, although traversing great resistances and giving 

 shocks. If 6 is infinite, the current is zero, there is no heat in the 

 wires ; but their extremities assume alternately contrary tensions, 

 which are very great, since the electromotive force M is considerable. 

 It is the case of Ruhmkorff's inductorium. 



