Intelligence and Miscellaneous Articles. 299 



coefficient of self-induction, the work of the extra current during 

 the time dt has the value UI — dt. We have, then, the equation 



-ELdt=I 2 dt + UI^dt, 

 dt 



or, dividing by I and by dt, 



E = IR+ < « 



This equation is no other than that given by Helmholtz, from which 

 he deduced the laws of the induced currents which are produced at 

 the moment of the closing and of the opening of the circuit of the 

 pile — with this difference, however, that in M. Helmholtz's formula 

 the quantity E is a constant, while here it is a function of the 

 time. 



To determine this function I operated as follows : — I put the 

 induced system into communication with a Thomson galvanometer 

 with the oscillations not deadened ; and, the arc corresponding to 

 the half-period of the machine having been divided into ten equal 

 parts, by means of a very simple arrangement I caused the induced 

 system to run over abruptly in succession the ten consecutive 

 intervals. The arc of impulsion of the galvanometer measures each 

 time the total quantity of electricity set in motion, and consequently 

 the electromotive force corresponding to the successive displace- 

 ments. The electromotive force thus measured is certainly that 

 resulting from the primitive field, since in each displacement the 

 quantities of electricity due to the reactions have a sum identically 

 nil. The curve thus obtained does not sensibly differ from a 

 sinusoid ; we can therefore assume that E is of the form E sin mt, 

 the time being counted from the moment when the axis of the 

 induced coincides with that of the inducing coil. Under these 

 conditions, and putting 



tan2^+^, (2) 



the integral of equation (1 ) can be written 



E„ 



(B*+^7 



sin 2tt f i - <p j = A sin 2n (L - J, 



the constant being determined by the condition that t = <j>T when 

 the intensity is nil. The intensity of the current at each instant 

 is therefore represented by a sinusoid, of which A is the amplitude 

 and the phase. 



The total quantity of electricity which passes in the circuit 

 during half a period has for its value 



2 idt = A I 2 sin (mt - 2^)dt — ; . . (3) 



f=T<p J< = <PT *" 



