Self-induction of Wires. 441 



the long than to the short distances than the above asserts. 

 For no one, when multiplying the distance and size of circuits, 

 say ten times, would think of putting ten telephones in circuit 

 to keep rigidly to the rule. Thus it may be that only a slight 

 increase of e x is required, on account of M being multiplied in 

 a far greater ratio than the resistances, or the self-inductances. 

 Thus, it is not uncommon for the R and L of a telephone to 

 be 100 ohms and 12 million centim. These form the prin- 

 cipal parts of the R and L of a circuit of moderate size, and 

 of course do not increase when we enlarge the circuit. It is 

 therefore certain that we can signal long distances on the 

 above basis, with a margin in favour of the long distances, 

 which will be large or small according as the circuits are 

 small or large. 



Again, if e l in the primary be periodic, of frequency nj27r y 

 the ratio of the amplitude of the current in the secondary to 

 that in the primary will be 



Now, without any statement of the magnitude of the cur- 

 rent in the primary, if it be largely in excess of requirements 

 for signalling in the primary, so that t Jq part, say, would be 

 sufficient for the purpose, then we shall have enough current 

 in the secondary if the above ratio is only T J- -. But, without 

 going to precise formulae, it may be easily seen that the above 

 ratio may be made quite a considerable fraction, in comparison 

 with T J q, with closed metallic circuits whose linear dimensions 

 and distance are increased in the same ratio. But we should 

 expect a rapid decrease of effect when the mean distance 

 between the circuits exceeds their diameter, keeping the cir- 

 cuits unchanged. (It should be understood that squares, 

 circles, &c. are referred to.) 



The theory seems so very clear (though it is only the first 

 approximation to the theory), that it would be matter for 

 wonder and special inquiry if we found that we could not 

 signal long distances by induction between closed metallic 

 circuits, starting on the basis of a short-distance experiment, 

 and following up the theory. 



[As a matter of fact, it was found possible to speak by 

 telephone between two circuits of J mile square, J mile between 

 centres, using two bichros with the microphone.] 



Now coming to metallic lines whose circuits are closed 

 through the earth, the theory is rendered far more difficult on 

 account of there being a conduction-current from the primary 

 to the secondary due to the earth's imperfect conductivity. 

 We therefore have, to say nothing of electrostatic induction, 



