42 ELECTRICAL MEASUREMENTS 



increased in the same proportion but the instrument will no 

 longer be dead beat; it will become sluggish in its action so that 

 the time which must elapse before the reading can be taken is un- 

 duly increased. If r is decreased the same is true, so two changes 

 are necessary if the critical damping is to be preserved. 



Suppose the restoring moment of the spring is reduced to 

 one-sixteenth of its original value. Then by (32) and (33) both 

 Si and S v will be increased eightfold, for TV is increased to 64 

 times its former value and both S t and Sv are proportional to 

 \/To 3 . In detail, by (30) if r is reduced to one-sixteenth of its 

 former value, in order to maintain critical damping C must be 

 halved. As the coil is not to be altered, the quantity C = Hbl 

 must be halved by halving the strength of field H. If the field is 

 halved and the restoring moment reduced to one-sixteenth of its 

 first value, the sensitivity will become eight times its initial 

 value. 



The modification will render the instrument less prompt in its 

 action, for the time of an undamped vibration T will be increased 

 to four times its original value. 



Expression for the Field Required to Produce Critical Damp- 

 ing. 7 



C^ TR T 

 ~ Z 2 6 2 



Expressing R in ohms 



TRor 17,800 - 

 = 



This relation can be transformed so that H is made to depend on 

 the resistance of the galvanometer coil and on the lengths of the 

 active and inactive wire. 



The total moment of inertia of the moving parts is (referring to 

 the table of symbols) 



p = mn 



.: 



a m 



p ~ p ' P 



mn 



(" + 3) n " s (" + v ( v 



