Inductance by the Aid of a Vibration Galvanometer. 497 



of K or r and S ; (b) that the adjustments are independent 

 of the frequency. Accordingly a balance can always be 

 obtained with great facility *, 



3. Vibration Galvanometers. 



Since Vibration Galvanometer methods are familiar to 

 very few experimenters in this country, I think the following 

 general description will be of interest. 



By a Vibration Galvanometer is meant one in which the 

 natural vibration frequency of the moving part can be ad- 

 justed to be the same as the frequency of the source of 

 alternating or pulsating current used. The two main ad- 

 vantages in using a tuned galvanometer or other instrument 

 are as follows : — (a) when the instrument is in tune with the 

 source of current the vibratory motion of the moving part is 

 enormously increased, due to resonance ; thus a high 

 sensitivity is obtained, usually about 100 times greater than 

 that without tuning, (o) Since the sensitivity is so very 

 much greater for the proper frequency than for others, when 

 the wave form is other than a sine curve the instrument, .if 

 tuned to the fundamental frequency, responds to this, and is 

 practically unaffected by the harmonics ; if the instrument 

 is tuned to one of the harmonics instead, all but this com- 

 ponent is practically ignored by it. For this reason the 

 theory of each method in which a tuned instrument is used 

 can be worked out on the assumption that the wave forms of 

 voltage and current are all pure sine curves. 



The deflexion is usually proportional to the amplitude. 



This use of a tuned instrument in null methods is, I believe, 



* The above investigation can be carried out more readily by the use 

 of the operators ~Lp\f — 1 and 1/Kj?*/ — 1, but to some readers the 

 method given will be clearer. 



Equation (1) becomes 



(H-LpV^T-Mp J.~~l)i i =Mp*/ ~l.i 2 ; 



and the next equations give 



Hence 



Separating the real and imaginary parts we have 



M=KRr 



and L=M — ry- as beiore* "■ 



