104 ELECTRICAL MEASUREMENTS 



6 = steady deflection caused by a steady current of strength 



I* 



Oi = first elongation, or throw. 



X = logarithmic decrement, or natural logarithm of the 

 ratio of two successive elongations. 



In the following discussion, if the displacement of electricity is 

 "instantaneous," the corresponding value of 0i will be primed; if 

 the displacement is not instantaneous the prime will be omitted. 



With any definite arrangement of the apparatus 



Q = K f e, r . 



A determination of the time of vibration and current sensitivity, 

 together with X, enables the constant of the instrument to be 

 calculated. For most purposes, however, it is preferable to 

 calibrate by discharging a known quantity of electricity through 

 the galvanometer and reading the corresponding deflection 0/. 

 If X at calibration differs from its value during the subsequent 

 work, it must be determined and allowed for. 



To obtain a definite quantity of electricity an earth inductor, 

 a mutual inductance, or a standard condenser charged to a known 

 voltage may be employed. 



The earth inductor is a large coil of many turns mounted on a 

 vertical or horizontal axis so that it can be quickly turned through 

 90 or 180. The total area of the turns is known. The coil is 

 included in the galvanometer circuit. If the plane of the coil is 

 originally in the magnetic meridian and the rotation is through 

 90 about a vertical axis, the quantity of electricity displaced in 



the circuit is Q = - : A is the total area of the turns, H the hori- 

 zontal intensity of the local field and r the resistance of the galva- 

 nometer circuit. Owing to erratic variations of the local field, this 

 method of calibration has ceased to be of importance. 



Duddell has developed the idea embodied in the earth inductor 

 so that an instrument of practical value has resulted. In his 

 magnetic standard two movable coils arranged astatically are 

 used in series with the galvanometer and the local field is replaced 

 by the fields due to two oppositely wound fixed coils, one acting 

 on each movable coil. On releasing a catch the movable system 



