]S75.] Theory of Duplex Telegraphy. 49 



tive and financial point of view. But besides this, without going into de- 

 tails, the differential method has also a very serious objection from a techni- 

 cal point of view. "While in the bridge method the balance is obviously 

 independent of the resistance of the receiving instrument, in the differential 

 method the balance is clearly a function of the resistances of the two coils of 

 which the receiving instrument consists, and as these two coils may alter 

 their resistances independently, and not in proportion as indicated by the 

 balance equation, a new element of disturbance is introduced, which the 

 bridge method does not possess. 



Besides this, differential instruments are necessarily mechanically more 

 complicated than others, and require therefore superior workmanship, en- 

 tailing greater expense to arrive at working efficiency. 



General expressions for the two functions " D" and " S." 



In order to obtain the two functions D and S, we have to develop the 

 general expressions for^, P, and Q; say for Station I. 



p' in our particular case is the force exerted by the two coils a' and h' 

 on one and the same magnetic pole when Station I is sending and Station II 

 is at rest. This force is clearly the difference of the two forces exerted by the 

 coils a' and b'. 



Thus we have 



p' = A' ml — B' n'. 

 where A' and B' are the currents which pass through the two coils a' and V 

 respectively, when Station I is sending and Station II is at rest, while ml 

 and n' are the forces exerted by these coils when the unit current passes 

 through them. At balance in Station I, p' = o 



Further I" = <&' ml + 13' »' 



where %' and 53' are the currents which pass through the coils a' and V re- 

 spectively, when Station II is sending and Station I is at rest (single 

 signals). 



Further Q' = y' m' -f ff' nf 



where y' and g;' are the currents which pass through a' and V respectively 

 when both stations are sending simultaneously (duplex signals). 



To get the most general expressions for these three forces p, P, and Q, 

 we have to fix the signs of the two terms of which they consist. This is 

 best done by considering the forces m and n as absolute numbers, and deter- 

 mining the direction in which they act with respect to one and the same 

 magnetic pole by the direction of the currents passing through the coils 

 a and b. 



To fix the signs of the currents, we shall call, arbitrarily, that current 

 positive which passes through the coil a in the sending station, when the 

 negative pole of the signalling battery is joined to earth. 



