OF ARTS AND SCIENCES. 59 



in Cambridge alone, in the neighborhood of the direct line between 

 Boston and Cambridge, the ticking of .the Observatory clock can be 

 heard. This transmission of the time signals to the various telephone 

 stations has been attributed to the proximity of the telephone circuit 

 wires to the time wires from the Observatory. This is evidently an 

 erroneous conclusion, as will be seen from a short mathematical con- 

 sideration. 



The expression for the induction produced in one wire by making 

 and breaking a current in a parallel wire* is R.^ y.^ = ± ^^^v i» 

 which 3^2 represents the induced current, E^ the resistance of the circuit 

 which conveys this induced current, M the coefficient of induction 

 between the parallel circuits, and y^ the current in the primary circuit, 

 the interruption of which produces the induced currents. 



Now M= j j , in which ds and ds' are elements of the par- 

 allel wires, and r is the perpendicular distance between them. The 

 value of 31 m the case we are considering is 31= — , in which A rep- 

 resents the length of the parallel wires, along which the induction 

 takes place, and r is the distance between the wires. We shall there- 

 fore have ^ A- „ 



^2^2= ± 7 ^'i- Eq. (1) 



Now the electromotive force of the induced current i/.^ is very much 

 greater than that of the inducing current y^ and in order that the cur- 

 rent strength y^ should be able to develop even a small electro-mag- 



A'^ 

 netic effect in the receiving telephone, the coefficient of induction — 



must be large, or in other words the distance along which the lines run 

 parallel must be great, and the distance r between these lines must be 

 small. An arithmetical consideration of Eq. (1) will convince one 

 that, with telephones of the resistance usually employed (50 units) no 

 inductive effect will be perceived, by the employment of even ten 

 quart Bunsen cells, between wires which run parallel to each other a 

 foot apart for the distance of thirty or forty feet. In order to detect 

 an inductive effect under these conditions, a telephone of three or four 

 units of resistance and a large battery must be employed. With a 

 telephone of 30 or 40 units of resistance similar to those employed on 

 district circuits, no induction can be perceived under the conditions we 

 have prescribed. 



For still stronger reasons it is impossible to hear telephonic messages 



♦ Maxwell's Electricity and Magnetism, ii. 209. 



