Coefficients of Induction. 331 



which reduces to 



L = 2KR(6 + 2G + R), 



since 



, T , / 26R\ 26E-, 



It may not be possible, with given values of b, R, and G, 

 and a given condenser, to make the throws the same. R 

 may, however, be increased or diminished by the introduction 

 of an inductionless resistance in series or in parallel with it, 

 and the same is true for b and G. A slight change in the 

 formula will then be necessary. If, in this way, we find two 

 nearly equal values of K for one of which the throw of the 

 needle is greater and for the other less than that of the 

 former throw, the correct value of K may be found by pro- 

 portional parts. But a much better method is to use a 

 ballistic galvanometer, in which case no adjustment of resist- 

 ances beyond that of getting a perfect balance is required. 

 The two angles of throw a and «' are simply observed, and 

 the coefficient of self-induction is given by the formula 



a . a 



L = 2KR(6 + 2G + K) sin- sin-. 



The following determination of the self-induction of a coil 

 may be given as an example. The coil was a circular coil of 

 mean radius 20*9 centim. wound in a rectangular groove of 

 breadth 1*894 centim. and depth 1*116 centim., and having 

 278 turns. The galvanometer was an ordinary reflecting 

 galvanometer with a resistance of 164'8 ohms, the controlling 

 magnet being placed so as to make the sensibility as great, 

 and the time of swing as long, as possible. An inductionless 

 resistance of 100 ohms was put in series with the coil, and the 

 resistances of the branches AB and AD were each 10 ohms. 

 A balance was roughly obtained by making the branch CD 

 150 ohms, and, in the absence of better means, an almost 

 perfect balance by adding to CD a wire whose resistance 

 was subsequently found to be '51 ohm. The resistance of the 

 branch CD or CB was therefore 150'51 ohms. The following 

 numbers are the means of several readings which agreed 

 very well together : — 



