144 Dr. 0. J. Lodge on Intermittent Currents 



The Connexion between Induction-balance Effect and 

 Conductivity. 



20. The way in which the telephone-current depends on 

 the conductivity - of the coin is apparent in equation (40) : 



r 



it is evidently not simply proportional to it in general. But 

 the self-induction \ of a circuit like that in a solid disk of 

 metal must always be a very small quantity; and, except 

 perhaps for highly conducting metals, it must probably be 

 almost negligible compared with p. Assuming, then, that 

 X is infinitesimal, the expression simplifies, and p becomes a 

 factor of one part of it. We get, in fact, 



s t r -Zt ") 



^(B-BH B^-, 



pR(Lr- IS) \L 



, m/tE(S-R) -e« .... 



+ B(L-0 eK • • • • < 45 ) 



The term written by itself does not contain p except as an 

 exponential ; but it has a very great rate of variation depend- 

 ing directly on p, and it soon ceases to exist. The rest of the 

 expression for the current is simply proportional to the con- 

 ductivity, both as regards its own value and its rate of varia- 

 tion. What the precise meaning of all this is depends on 

 what the loudness of the telephone-indication definitely depends 

 on (§ 1); so for the present we will leave it in this state. 



On Measuring with the Induction-balance* 



21. Two methods have been employed both by Professor 

 Hughes and by Mr Roberts, with the view of obtaining 

 quantitative readings from the balance. The first consisted 

 in estimating the loudness of the sound produced by the in- 

 sertion of a coin, and then imitating it by an arrangement of 

 primary and secondary coils called the "sonometer" — a key 

 being used to transfer the connexions of the telephone quickly 

 from one instrument to the other. Mr. Poynting has adapted 

 a formula from Maxwell which suffices to graduate the sono- 

 meter when the secondary coil is some distance from either 

 primary (Phil. Mag. January), though it is rather an unwieldy 

 one. 



But there must always be some objection to readings 

 taken in this way, because of the difficulty of estimating 

 precisely when two sounds have the same strength — especi- 

 ally if, as appears probable from § 18, they differ at all in 

 quality, the sound produced by the coin in the balance having 



