122 ELECTRICAL MEASUREMENTS 



If the resistance of the apparatus to which the galvanometer 

 is attached is so high that the instrument is underdamped, criti- 

 cal damping may be obtained by shunting the galvanometer. In 

 this case if R is the resistance of the apparatus to which the 

 galvanometer is attached and R that of the galvanometer, 



As no time is lost in bringing the movable system to rest, the 

 critically damped ballistic galvanometer is frequently a most 

 convenient instrument. 



The Use of Shunts with the Ballistic Galvanometer. At first 

 sight it would seem that if a ballistic galvanometer were shunted 

 with a non-inductive resistance, the total quantity of electricity 

 discharged from a condenser would not, on account of the in- 

 ductance of the galvanometer, divide inversely as the resistance 

 of the galvanometer and of the shunt. However, the quantity 

 does so divide as will be seen from the following: 



Let Ro = galvanometer resistance. 

 L = galvanometer inductance. 

 i Q = galvanometer current. 



Qo = quantity discharged through galvanometer. 

 S = shunt resistance. 

 L 8 = shunt inductance. 

 i s = shunt current. 



Qs = quantity discharged through shunt. 

 Then 



p v T dio o T di s 

 K>Q*>Q ~r L/Q JT ' o^ s -h Li a r 



Consequently 



RoQo + L fdio = SQ S + L s fdi a 



Both currents are zero at the beginning and zero at the end 

 of the discharge, so 



G? = A 

 Q 8 Ro 



It is seen that any error caused by the shunt must be due to 

 the variation of the damping when the multiplying power is 

 changed, 



