382 ELECTRICAL MEASUREMENTS 



quantity of electricity displaced through the instrument during 

 the establishment of the permanent state of the circuit is zero, 

 or when 



r, 

 iadt 



If i = continuously, then necessarily Q = 0. The converse 

 is not true, for the net quantity may be made zero by a current 

 which flows through the detector first in one direction and then 

 in the reverse direction. When deducing the conditions which 

 must be fulfilled in order that the galvanometer may remain 

 undeflected, it is best to impose the condition that no current 

 shall flow through the galvanometer at any time, for in some 

 cases the galvanometer needle will be disturbed even though the 

 integral current is zero. 27 The disturbance depends on the 

 alteration of the strength of the galvanometer needle by the 

 transient current. In a general way, the reason for the deflec- 

 tion may be seen by supposing the instrument to be traversed 

 by an alternating current. If the magnetism of the needle is 

 affected by the current, the galvanometer becomes in effect a 

 soft-iron instrument with a magnetic control and there will be 

 a deflecting moment proportional to the square of the current. 

 In the case of the steadily applied alternating current the needle 

 will come to rest in a deflected position depending upon the 

 strength of the current. 



Some moving-coil instruments are subject to this same error, 

 when used as detectors for integral currents. 



As an example of a method where the phenomenon is of im- 

 portance, take the comparison of two mutual inductances by the 

 method given on page 416. The integral flow of current through 

 the galvanometer will be zero if 



m x = r x 

 m P r P 



That the current through the galvanometer may be zero con- 

 tinuously it is necessary that 



m* = rx 

 m P r P 

 and 



ni P 



