﻿audible in the Telephone. 289 



where C 2 = A 2 + B 2 ; and if m be the magnetic moment of the 

 magnet, and cf> the angle of rotation, the mutual potential M 

 may be represented by * 



M=G-7nsin$ (2) 



If the frequency of revolution be /?/2tt, <j>=pt ; and then 



dM/dt = G mp cos pt (3) 



The expression (3) represents the electromotive force oper- 

 ative in the circuit. If the inductance can be neglected, the 

 corresponding current is obtained on division of (3) by K, the 

 total resistance of the circuit. 



The moment m is deduced by observation of the deflexion 

 of a magnetometer-needle from the position which it assumes 

 under the operation of the earth's horizontal force H. If the 

 magnet be situated to the east at distance r, and be itself 

 directed east and west, the angular deflexion 6 from equili- 

 brium is given by 



tan 9 = *£.. 

 xl 



The relation between the angle 6 and the double deflexion 

 d in scale-divisions, obtained on reversal of m, is approximately 

 = <//4D, where D is the distance between mirror and scale ; 



so that we may take 



,n= w (*) 



The amplitude of the oscillatory current, generated under these 

 conditions, is accordingly 



4C 3 KD ( °) 



If c.G.s. units are employed, H = \18. A must of course 

 be measured in centimetres; but any units that are convenient 

 may be used for r and C, and for d and D. The current will 

 then be given in terms of the C.G.S. unit, which is equal to 

 10 amperes. 



The inductor-coil used in most of the experiments is wound 

 upon an ebonite ring, and is the one that was employed as the 

 " suspended coil " in the determination of the electro-chemical 

 equivalent of silver f. The number of convolutions (n) is 242. 



* Maxwell, ' Electricity and Magnetism,' vol. ii. § 700, 

 t Phil. Trans, part ii. 1884 .p. 421. 



