INDUCTANCE AND CAPACITY 379 



6, as the sheath is necessarily grounded. Because of the small 

 effect of battery leakage, this method is very commonly employed 

 in submarine cable work. 



If the rates of absorption of the two condensers are not the same, 

 the results obtained will be dependent on the time of charging. 

 For condensers, and for cables up to a length of about 1,000 

 knots, a correction devised by Muirhead and intended to correct 

 for both absorption and leakage is applicable; it fails, however, 

 in the case of cables of greater length, supposedly on account 

 of the retardation due to the resistance of the cable itself. 12 



The methods of Thomson and of Gott are of importance in sub- 

 marine cable testing. In this work, exceedingly large capacities 

 must be measured, frequently several hundred microfarads. It 

 is in connection with these measurements that the complications 

 due to leakage and absorption become most troublesome. 



Elementary Methods of Determining Inductance and Capacity 

 by Alternating Currents. 13 If a sinusoidal current of known 

 frequency be used, the most obvious method of measuring an 

 inductance is to determine the current and the P.D. between the 

 terminals of the coil. Then if co is 2ir times the frequency, R 

 the resistance, V the applied voltage and / the current, the in- 

 ductance is given by 



- PR 2 



or if the resistance is negligible, by 



When the current wave is non-sinusoidal it is possible to allow 

 for the effect of the harmonics. Suppose that the maximum 

 values of the various components are /i, /a, /5, etc. Then 



i = /i sin ut + 7 3 sin (3o> 3 ) + h sin (5orf 5 ) + . 

 The effective value of the current will be 



" VT + T + T' 



The fundamental equation for the flow of current through an 

 inductive resistance is 



