112 ELECTRICAL MEASUREMENTS 



nometer is calibrated by methods in which e is applied to the 

 circuit ' 'instantaneously." 



To obtain the necessary data, the logarithmic decrement and 

 the time of vibration must be found and a preliminary test made 

 which will experimentally determine the curve connecting e and 

 t. This curve must be one that fairly represents the conditions 

 which will exist in the subsequent work, and is to be used as 

 described below. If the computations show that the first elonga- 

 tion will be greatly influenced by the manner in which the dis- 

 charge is sent through the galvanometer, it will be necessary to 

 modify the instrument by giving it a longer period of vibration. 



Suppose that the experimentally determined graph connecting 

 e and t shows that e has become sensibly equal to zero before the 

 galvanometer deflection has reached its first elongation. If the 

 time which elapses before e becomes sensibly equal to zero be 

 denoted by t', the values of the integrals in (8) taken for times 

 greater than t' are practically constant. In the case where the 

 galvanometer is over-damped, that is, where m\ and m^ are real, let 

 M and N be two quantities defined as follows : 



t 5 f 



ft 

 Jo 



rt 



Jo 



? > a constant (9) 



edt 



r^- m t 



N = -~ ^ , , a constant (10) 



I edt 



Jo 

 Then 



0i, which is the observed reading of the instrument, occurs at a 

 time h, when ^ = 0. Neglecting the constant coefficient in (11) 



or 



( mi - mz )t = 



Mm i 



