152 



Mr. W. H. Preece. On the 



[Mar. 3> 



III. " On the Limiting Distance of Speech by Telephone." By 

 William Henry Preece, F.R.S. Received February 17 y 

 1887. 



The law that determines the distance to which speaking by tele- 

 phone on land lines is possible, is just the same as that which de- 

 termines the number of currents which can be transmitted through 

 a submarine cable in a second. The experimental evidence upon 

 which this law is based was carried out in 1853 by Mr. Latimer 

 Clark (whose assistant I then was). The experiments were made by 

 me in the presence of Faraday ; many were his own ; he made them 

 the subject of a Friday evening discourse at the Royal Institution, 

 January 20, 1854, and they are published in his ' Researches ' (vol. 3, 

 p. 508). They received full mathematical development by Sir William 

 Thomson in 1855 ('Roy. Soc. Proc.,' May 24), who determined 

 the law, the accuracy of which was proved by Fleeming J enkin and 

 by Cromwell Yarley, and the 110,000 miles of cable that now lie- 

 at the bottom of the ocean afford a constant proof in their daily 

 working. 



Hockin reduced Thomson's law to the following series : — 

 x = C(l-2{(|)^'^-(})^/ a +(i) 9 ^ a -(i) 16 ^ a +&c.}), 

 which allows it to be expressed by the following curve (1) : — 



Now a is a time-constant dependent on the conditions of the circuit,, 

 invariable for the same uniform circuit but differing for different 

 circuits. It represents the time that elapses from the instant contact 

 is made at the sending end to the instant that the current begins to 

 appear at the receiving end. It is given by the following equa- 

 tion : — 



a = BJcrl 2 , 



B being a constant dependent principally on the units used ; k the 



