258 Messrs. Porter and Morris on the Measurement 



is the rate of change of the galvanometer current 



where ~ 

 dt 



y=0 



at the instant when it passes through zero, and x is the 

 instantaneous value of the current in the coil at that 



instant. It is therefore necessary to evaluate -~ for each 



Clt y — Q 



value of e. Let g be the resistance from A to C (through the 

 galvanometer) together with that of the lead from B to D, and 

 p the total resistance of the potentiometer circuit, i. e. of the 

 slide wire and the cell (E 2 ) ; let p denote the resistance of 

 the portion CD of the slide wire ; and let the currents be as 

 shown in the figure (fig. 1) . 



The general equations which must be satisfied at every 

 instant are 



and Ag + & + r+»y + /w-r*=O l 



pz+py=T& 2 . 



E F o 



Now the normal current in the slide wire is — and — — =e 



P ... P 

 the difference of potential recorded for a position of the 



slider corresponding to a resistance p. Hence, eliminating 



E 2 and z, the general equation becomes 



A dy 



dt +(d + r + p-f)y = ™-e. ... (2) 



If this equation is differentiated with regard to t and solved 

 for dt > P uttin S 



1 g + r + p-?- 



p 



A 



we obtain 



r dt J dt 



Since when *==0, ■£ =0. This last statement follows from 



the fact that at the initial instant there is no abrupt change in 

 the fall of potential between A and B. 



Now at the instant of balance t for which y=0 ; equation 



