140 Dr. 0. J. Lodge on Intermittent Currents 



§ 13 is therefore now true of k. What we want to find, how- 

 ever, is not k hutj, the current induced in the telephonic cir- 

 cuit ; hence, differentiating the above expression for k and sub- 

 stituting it in 



we get, remembering the initial condition that ^'=0 when t = 0, 



.__ m^E(S-R) / r -U 



J ~ R \(Lr-m)(lp-\r) e 



1 (lp--\r)(\S-L P y ' (\S-L/>)(Lr-/S) 



And this is the current heard in the telephone. 



The expression I jdt identically vanishes; hence this current 



cannot affect a galvanometer (see § 1). 



At " make " R=co , and the three terms in the brackets are 

 all present, the factor outside reducing to +m//,E. But at 

 " break " S = oo , and the third term disappears, leaving 



>=if^{K f '-F*'}< • ■ <«) 



which is the tertiary current at break, and has some of the 

 characteristics of the secondary current at make, see equa- 

 tion (28). 



17. If the battery and telephone circuits are similar, so that 



S r 



j- = -j , the value of j at the make simplifies considerably, be- 

 coming 



which in this case therefore bears a constant ratio to the se- 

 condary current at make under the same circumstances (see 

 equation 31). 



Theory of the Induction-balance continued, 



18. Having now integrated equations (2) and obtained an 

 expression (40) for the current passing through the telephone 

 at any instant, several things may be noticed about it. First, 

 the current produced by the piece of metal is in general dif- 

 ferent in character to that produced by a slight shift of the 

 secondary coil (that is, by M being made not quite zero) ; and 

 consequently it is impossible in general to balance the effect 



