138 J. Trowbridge—The Earth as a Conductor of Electricity. 
Art. XXI.—The Earth as a Conductor of Electricity ; by JOHN 
TROWBRIDGE. 
THE Observatory of Harvard University transmits time sig- 
nals from Cambridge to Boston, a distance of about four miles. 
The regular recurrence of the beats of the clock affords a good 
means of studying the spreading of the electrical current from 
the terminal of the battery, which is grounded at the observa- 
tory; and the establishment of the Telephone Dispatch Com- 
panies in Cambridge, with their various ground connections, 
gave me a means of studying this spreading. In all the tele- 
phone circuits between Boston and Cambridge, in the neighbor- 
hood of the direct line between these places, the ticking of the 
observatory clock could be heard. The ticking heard in the 
telephones at the various 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 evident from a short mathematical consideration : 
expression for the induction produced in one wire by 
making and breaking a current in a parallel wire, is 
R, y,==—M y,,* 
in which y, represents the induced current, R, the resistance of 
the circuit which conveys this induced current, M the coeffi- 
cient of induction between the parallel circuits, and y, the cur- 
rent in the primary circuit; the interruption of which pro- 
U 
duces the induced currents. Now M=/) = in which ds 
and ds’ are elements of the parallel wires, and 7 is the perpen- 
dicular distance between them. The value of M in the case 
we are considering is ere in which R, represents the length 
of the paraliel wires along which the induction takes place and 
r is the distance between the wires. 
2 
We shall therefore have R, yaa Y,, eq. (1). Now the 
electromotive force in the induced current y, is very much 
greater than that of the inducing current y,, and in order that 
the current strength y, should be able to develop even a 
small electro magnetic effect in the receiving telephone, the co- 
efficient of induction must be increased, or the distance along 
employed, no inductive effect will be perceived by the employ- 
* Maxwell’s Electricity and Magnetism, vol. ii, p. 209. 
