and the Theory of the Induction-balance. 139 



other — this being done practically by splitting each into two 

 equal parts, and arranging the two parts so as to oppose each 

 other ; and the third circuit is represented by the piece of 

 metal put near or inside the primary and secondary coils. 

 The primary circuit contains as part of itself a battery and an 

 intermitter ; the secondary contains a telephone. 



Neglecting electrostatic capacity and leakage (which latter, 

 by the way, must be carefully avoided in a good balance), the 

 current in either primary is the same, and the current in each 

 secondary is the same, not only on the whole, but at every 

 instant of time. In fact, the separation of the two halves of 

 the primary and secondary is immaterial to the theory. The 

 current which is induced in the secondary circuit, and which 

 is heard in the telephone, is a tertiary current produced by 

 induction from the third coil or piece of conducting matter. 



The currents in the battery-circuit at any instant being 

 called i } that induced in the metal being k, and that induced 

 by this in the secondary circuit being called j, and being the 

 value appreciated by the telephone, the equations for determi- 

 ning these three quantities are given in § 5, on the supposir 

 tion that the coefficients of mutual induction between the 

 metal and the two coils respectively (m and ft) are small num- 

 bers, which is always true in practice. 



The battery-circuit is then practically undisturbed by the 

 presence of the other parts of the instrument, and may be re- 

 garded as in space by itself (see end of §§ 12 and 13); so that 

 all we have said about the intermittence of currents in such a 

 circuit in sects. 6-11 applies to the primary of an induction- 

 balance : we will, however, only take the case when the re- 

 sistance jumps suddenly from any finite value E to another 

 finite value S. The value of i is then given by equation (4) ; 

 and its rate of variation is 



di_ E(S-B) -••( 



dt EL e L ; 

 but as (equation 2) 



dh 7 di n > 



x dt +pk+/l ir ' 



it is easy to determine k ; viz. 



, /*E(S-E) ■ s _ f 



. This value agrees exactly with that obtained in the general 

 case (§12) when the condition that M 2 might be neglected 

 was put in (see eq. 28), and therefore confirms the correctness 

 of our working. All that was said about the special eases of /- in 



