1887.] Limiting Distance of Speech by Telephone, 157 

 If we put equation (1) into this form, 



A = kra?, (2) 



and give to A the following values : — 



Copper (overhead) 15,000 



Cables and underground 12,000 



Iron (overhead) 10,000 



we can find the limiting distance we can speak with any wire ; for 



x* = A/kr. 



Take copper, whose constant is 15,000, and a wire whose resistance 

 is l w per mile, and capacity 0'0124 per mile, then — 



2 _ 15000 

 x " ~ 0-0124' 



x = 1100, 



which is the limit of speaking upon such a wire. 



The wire used between Paris and Brussels has a resistance of 

 2*4 ohms and a capacity of about 0'012 microfarad per kilometre, and 

 as that distance is only about 200 miles the speaking must be excellent. 

 Moreover, there is reason to believe, from the difference between 

 observation and calculation, that the static capacity on Continental 

 and American lines is less than that of English lines, owing to the 

 use of earth wires on all poles in England, and therefore the distance 

 would be greater. 



Take an Atlantic cable — 



2 _ 12000 

 x ~3x 0-43' 



x = 96. 



Now I had found in 1878* that it was just possible to speak through 

 100 miles of such a cable — a very close agreement. 



Moreover, by the law of the squares, 100 miles of an 'Atlantic cable 

 ought to transmit 1562 reversals, if 2584 miles transmit 2J, and 

 this is probably the average number of sonorous vibrations imparted 

 by the human voice, when hearing by telephone begins to get difficult 

 by the loss of the higher partials and overtones. 



There is another interesting consequence of Thomson's law which 

 comes out of these experiments, and that is, whether the line be a 

 single wire completed by the earth, or a double wire making a 

 metallic circuit, the rate of speed between the two ends is exactly the 



* £ Phil. Mag.,' April, 1878. 



