INDUCTANCE AND CAPACITY 437 



An idea of the magnitudes of the constants in (54) will be given 

 by data applying to an instrument investigated by Wenner. 



C = 1.4 X 10 5 c.g.s. 

 r = 5,700 

 k = 0.018 

 P = 0.015 



Resistance = 30 ohms 

 Resonating frequency = 100 cycles per second. 



The vector solution of (54) is 



CI " (55) 



If co is 2w times the- frequency of the vibrating coil of the 

 galvanometer, 



The maximum sensitivity will be obtained when the instrument 

 is exactly tuned to the frequency of the circuit by changing T or 

 when coo = to, N = 1. When tuned, the galvanometer is but 

 little affected by the harmonics in the current wave. For ex- 

 ample, the deflection due to the fundamental will be 



and that due to a current of N times the fundamental frequency 

 will be, as kNu is then negligibly small, 



~ Pco 2 [l - A^ 2 ]' 

 That is, for the same value of the current, 



0i = Pco[l - ( . 



e N k 



Using the data given above for a particular instrument, 



a 



-^ = 4,200 approximately; 



#3 



or the sensitivity to the third harmonic is less than J^.ooo that 

 for the fundamental. 



The resonance range of a vibration galvanometer is an arbi- 

 trary measure of the exactness of tuning required if a high sensi- 



