of Varying Currents in Inductive Circuits. 259 



= rx T — e; or by 



(2) reduces to equation (1) which is A-,- 



substitution 



e C r * dx _ 



r J ' dt 



This has to hold for each successive value given to e, and the 

 corresponding value of t; it is therefore a running equation 

 between e and r, and we may differentiate it with regard to t. 

 Strictly speaking, a is now a variable, since to different 

 balancing instants there correspond different values of p ; but 



2 



the quantity p — — which occurs in a cannot exceed the value 



j , so that the extreme variations of a can always be kept small 



by using a galvanometer whose resistance is high compared 

 with that of the slide-wire employed (in our experiments it 

 did not vary more than 1 part in 700). We shall therefore 

 treat it as a constant ; we then obtain by differentiation 



d 



(9 



dr 

 or 



e dx T dx T 



+ a r = d\+ ax ?-~aV 



1 d (-) 

 x -*. + l}lL, (3) 



r a ar 



d-i 



which gives the actually occurring coil current in terms of e, 

 the experimentally obtained function of t. 



It should be observed that at the instant of balance, the coil 

 circuit and potentiometer constitute electrically unconnected 

 circuits, hence at that instant the coil current is unmodified 

 by any contribution from the potentiometer ; previous to the 

 balancing instant, however, the galvanometer which forms 

 the connecting link between the two conveys a gradually 

 diminishing current, and effects thereby a corresponding 

 though very small change in the value of the current in 

 the coil. 



Now we saw that a might be regarded as a constant, and in 



that case its value is simply — ~- : hence, when the quantities - 



have been plotted against their time intervals r, all that is 

 necessary is to multiply the slope of the curve thus obtained 



\ 



