Mr. 0. Heaviside on Duplex Telegraphy. 33 



ient currents due to that cause are inappreciable. When the 

 capacity of the line cannot be neglected, it may be perfectly 

 balanced by distributing artificial capacity along the resistance 

 c with the same uniformity it has along the line ; and this may 

 be approximated to by subdividing the resistance and required 

 capacity as much as possible. If I is the resistance and Z x tiie 

 capacity of the line, and c x the required capacity, then the con- 

 dition of balance as regards capacity is cci = lli. 



Since each station has three adjustable resistances, «, b, and 

 c, and they are connected by the single relation ax=bc, it fol- 

 lows that any two of them may be taken arbitrarily and balance 

 made with the third. Thus we may take b and c as indepen- 

 dent variables, and eliminate a. The question then arises, in 

 what respects an arrangement in which the resistances b and c 

 have particular values differs from another in which b and e 

 have other values. There are three principal differences : first, 

 the received currents will be in general different ; next, the 

 balances will be of different degrees of sensitiveness, so as to 

 be more or less affected by changes in the resistance of the line ; 

 and, lastly, different amounts of artificial capacity will be re- 

 quired to produce a balance with respect to the capacity of the 

 line. Since a duplex apparatus is generally set up for perma- 

 nent use, it is clearly of the first importance to obtain the 

 maximum current with a given receiving instrument and bat- 

 tery. On cables this is quite a minor consideration, on account 

 of the great delicacy of the instruments employed. But du- 

 plex telegraphy has not hitherto been very successful on cables ; 

 whereas on land lines, where such delicate instruments would 

 be quite out of place, and much larger batteries are employed, 

 the cost of the current is considerable, and it is desirable to get 

 as much out of it as possible. I shall therefore in the first 

 place endeavour to discover what the actual magnitudes of the 

 resistances a, b, and c should be to render the received current 

 a maximum, — and when that is done, consider the sensitiveness 

 of the resulting arrangement, or its liability to disturbance. 



In order to avoid useless complication, I shall suppose that 

 the line is perfectly insulated, and that the receiving instru- 

 ment at each station has the same resistance, and likewise the 

 battery at each station ; i, &•/=/ and g—g'* This is very 

 nearly fulfilled in practice ; for the same description of instru- 

 ment and battery is generally used at each end of a line. Then 

 symmetry tells us that the resistances a, b, c should be the 

 same at each station ; or rather there is no reason why they 

 should be different ; and besides, if we do not make use of this 

 simplification, the problem will become almost intractable. 



Let E be the electromotive force of each battery, and Gr the 

 Phil Mag. S. 5. Vol. 1. No. 1. Jan. 1876. D 



