1887.] 



Limiting Distance of Speech by Telephone. 



153 



inductive capacity per unit length (mile or knot) ; r the resistance 

 per unit length, and I the length in miles or knots. 



therefore, limits the number of vibrations per second that can be 

 sent through any circuit. If a be 0'196 second, as it was in the 

 French Atlantic cable of 1869,* 2584 knots long, then it is impos- 

 sible to send 5'1 currents per second through that cable; but it would 

 be possible to send 5 or 2J complete reversals per second. Moreover, 

 as the number of reversals varies inversely with the square of the 

 length, it shows that such a cable if of 100 miles length would 

 allow 1562 reversals to pass through it. It is necessary to remark 

 that these expressions involve no mention of E.M.F., or of current, 

 and therefore the number of reversals which can be produced at the 

 end of a wire is quite independent of the impressed E.M.F., and 

 therefore of the strength of the current. But the number of reversals 

 is dependent upon the sensitiveness of the apparatus used to receive 

 the currents, for if we use an instrument which will respond to a cur- 

 rent indicated by the full line, we get two currents per second ; and if 

 we use an instrument which will respond only to the dotted line, we 

 get oniy one current in two seconds, which is about the current used, 

 with delicate relays in this country. This is why such discordant 

 results are obtained by different observers who attempt to measure the 

 velocity of currents of electricity. It is also why the telephone is 

 such an admirable instrument for research — for it is sensitive to the 

 least increment or decrement of current. 



Before proceeding with this inquiry it was necessary to determine 

 very accurately the inductive capacity of overhead and underground 

 wires. This was done with great care on very dry days in different 

 parts of the country by means of a Thomson mirror galvanometer 

 and a standard condenser. 



The results come out as follows : — 





Capacity 

 per mile 

 microfarads. 



[Resistance 

 per mile 

 B. A. ohms. 





0-0168 

 0-0124 

 -2500 

 0-2900 



12-0 

 5-7 

 23 -0 

 10-25 





The capacity can be calculated from the following formula (also due 

 to Sir William Thomson) : — 



2 log (u/dy 



* Fleeming Jenkin, 'Electricity and Magnetism,' p. 331. 



