26 ELECTRICAL MEASUREMENTS 



The right-hand member of equation (9) may be a function of 

 t, constant, or zero according to the conditions of the problem. 

 In this section i will be taken as constant (circuit closed) or zero 

 (circuit opened). 



The mathematical form of equation (9) and the following dis- 

 cussion should be compared with that for the displacement of 

 electricity in a circuit containing resistance, inductance, and 

 capacity in series. 



The deflection of a galvanometer may be oscillatory or non- 

 oscillatory and its ultimate value will be most quickly attained 

 if the conditions are such that the motion is just becoming non- 



k 2 

 oscillatory. This occurs when the relation = 4P is on the 



point of being fulfilled. The instrument is then said to be 

 critically damped. 



k 2 

 When > 4P the motion of the suspended system will be non- 



k 2 

 oscillatory and when < 4P it will be oscillatory. When the 



instrument is not critically damped the solution of (9) is* 



-f 



(10) 



mi and w 2 are the roots of the equation 



Pm 2 + km + T = 



or 



The constants d and C 2 must be determined to fit the condi- 

 mw of the particular case under consideration. When a current 

 f a definite strength is sent through the galvanometer 



i = I, a constant. 



