430 Mr. 0. Heaviside on Duplex Telegraphy, 



likewise the batteries, be exactly alike, and the line of uniform 

 insulation. Now let A depress his key. The galvanometer at 

 B will be deflected, but not A's. Let now B depress his key. 

 No change will be produced in the deflection of B's galvano- 

 meter ; but A's will be deflected. But if A and B have both the 

 same pole of their batteries to line, there will be no current in 

 the line, which, by Bosscha's first corollary, may be removed 

 without producing any alteration in the currents in the remain- 

 ing circuits. It is thus evident that A and B are both working 

 their own instruments \ and this supplies us with a very easy way 

 of calculating the strength of the received signals — which would 

 otherwise be very complicated. We have only to consider the 

 current produced in (g + b) by E having resistance/, with an 

 external resistance c, (g-\-b) being shunted by a resistance a t 

 and we find the strength of the signal to be 



{f+c)(a + b+ti+a(b+g) 



I will now describe two original methods of duplex working, 

 which though perhaps not quite so easily put into practice as the 

 foregoing, may be interesting from the theoretical point of view. 



As in the bridge arrangement, the out-going currents do not 

 pass through the receiving instruments at all. In the first of 

 these plans, as shown in fig. 3, the receiving instrument at each 

 station is connected between the middle of two batteries and the 

 earth, r and r ! are rheostats. The condition that the batteries 

 Ej and E 2 at station A cause no current in g is that 



E 1 :E 2 =r + ^i:^ 2 + ^ 

 d being the exterior resistance as before; and similarly for the 



E 



other station. The strength of current sent to line is • -V or 

 ° r + b l 



E 



t — ^. In the second plan, shown in fig. 4, one of the batteries 



at each station (E 2 and E' 2 ) is placed in the same branch as the 



receiving instrument, and both Ej and E 2 tend to send the same 



r-\-b 

 current to the line. When E } :E 2 =H j- 3 [ (d having the 



same meaning as before), the electromotive force E 2 is neutra- 

 ls 

 lized and there is no current in q. The line-current is — =-^ — 7 . 



y r + b x +d 



I have adapted these plans to the direct- writing Morse by using 

 an ordinary reversing key (which is nothing more than two keys 

 insulated from each other and worked by the same lever), in 

 order to put the two batteries Ej and E 2 simultaneously in or 

 out of circuit. I also found it necessary for there to be no in* 



