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XXIV. On the Resistance of Telegraphic Electromac 

 By Oliver Heaviside*. 



1. r I ^HE RE appears to be some uncertainty regarding the 

 J- proper resistance which electromagnets for signalling- 

 purposes should have — whether a receiving instrument should 

 have a resistance equal to that of the remainder of the circuit, 

 or a half, or a fifth, or some other fixed fraction thereof. Prac- 

 tical experience, especially with high-speed instruments, has 

 shown that the resistances in general use are too high — and 

 that advantage is gained by reducing the resistance of an elec- 

 tromagnetic receiving instrument, employing fewer windings 

 of a thicker wire in place of more windings of a thinner, 

 thereby reducing the self-induction as well. Ohm, as long 

 ago as 1826, showed that the resistance of a galvanometer 

 should equal that of the rest of the circuit in which it is placed, 

 to obtain the maximum magnetic force. When the correction 

 needed on account of the thickness of the insulating covering 

 of the wire is also reckoned, then the thickness of the wire of 

 the galvanometer should be such that the external resistance 

 is to the resistance of the galvanometer-coil as the diameter of 

 the covered wire is to the diameter of the wire itself (Maxwell, 

 vol. ii. p. 321). 



Now if, in telegraphic signalling, sufficient time were 

 allowed during every signal (positive, negative, or no cur- 

 rent) for the full effect to be produced in the circuit by the 

 electromotive force, or for the current to entirely die away, 

 the above result would hold good also. But such is not the 

 case ; for by reason of electrostatic and electromagnetic induc- 

 tion, the current has not time to reach its full strength during 

 every signal. On a land-line, unless it is very long, electro- 

 magnetic induction is the principal retarding cause ; and it is 

 this case which is here considered. 



2. Let there be a simple harmonic variation of electromotive 

 force 



E sin mt, 



where E and m are constants, and t is the time, in a circuit of 

 resistance R and electromagnetic capacity L. The equation 

 of the current is 



Esinm^(R + Lj^V, (1) 



where 7 is the current at time t. The solution of (1) is 



7= 7™ sin (" ,( " fan "'T)' 



* Communicated by the Author, 

 Phil Mag. S. 5. Vol. 6. No. 3G. Sept. 1878. N 



