Induction- Coil Potentials. 567 



therefore equal to the "mutual inductance " of the coils as 

 usually defined, i. e. the induction through the secondary 

 due to the primary current divided by the value of the 

 latter. 



For similar reasons the self-inductance L 2 of the secondary 

 coil is less than the value for steady or for uniformly distri- 

 buted currents, while L x has the usual meaning. The 

 coefficient of coupling, k, of the coils is defined by 



VL12 • IWLiL 2 . 



The value of the secondary capacity, C 2 , depends upon the 

 manner in which the charge is distributed in the secondary 

 coil, but it is unnecessary to determine it. For the purpose 

 of calculating the secondary potential V 2 from the expres- 

 sion (1) it is sufficient to know the A^alues of the six 

 quantities I^C], L 2 C 2 , L al , k, Ri/Lj, E 2 /L 2 . H, and R 2 are 

 the effective resistances of the primary and secondary 

 circuits. 



These six quantities were determined as described below 

 for an 18-inch-spark coil *, with three primary condensers of 

 capacities about 3, 2, and 1 microfarad respectively. These 

 condensers had mica insulation, and for the sake of definite- 

 ness were connected directly across the terminals of the 

 primary coil. If the condenser is connected across the 

 interruptor in the usual manner, the primary circuit then 

 includes the battery, amperemeter, and rheostat, and the 

 self-inductance and resistance of the primary circuit will, 

 therefore, be different in different experiments. 



The secondary terminals were connected directly to the 

 oscillograph, in parallel with which was a variable spark- 

 gap consisting of two brass spheres, each 2 cm. in diameter, 

 supported on ebonite pillars. The oscillograph has been 

 described in a former paper f . The instrument has very 

 small electrostatic capacity, and in its present form it can be 

 used directly for potentials sufficient to give a 24-cm. spark 

 between the ball electrodes. 



Determination of L 21 . 



This coefficient, which, as explained above, is equal to the 

 mutual inductance of the primary and secondary coils, was 

 determined by two methods. In the first it was compared 

 with a known mutual inductance by the ballistic galvanometer 



* The primary coil was in four sections. Except where otherwise 

 stated these were all in series. 



t E. T. Jones, Phil. Mag. xiv. p. 238 (1907). Cf. also /. c. (2), p. 708. 



