460 Mr. L. Schwendler on the General Theory 



principle are required, and that, therefore, the introduction of 

 duplex telegraphy based on the differential method would at once 

 involve also a total change of the receiving-instruments hitherto 

 used. This is clearly a serious disadvantage from an adminis- 

 trative and financial point of view. But, besides this, without 

 going into details, the differential method has also a very serious 

 objection from a technical 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 certainly does not possess. 

 Besides this, differential instruments are necessarily mechani- 

 cally more complicated than others, and require therefore supe- 

 rior workmanship, entailing 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. P, and Q, say for station I. 



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

 a' and V on one and the same magnetic pole when station I. is 

 sending and station II. is at rest. This force is clearly the dif- 

 ference of the two forces exerted by the coils d and V . 



Thus we have 



p' = AW-BW, 



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

 coils a! and b' respectively when station I. is sending and station 

 II. is at rest, while m f and n l are the forces exerted by these coils 

 when the unit current passes through them. At balance in 

 station I. 



p f =0. 

 Further, 



f= aw +»'»', 



where &' and W are the currents which pass through the coils 

 a 1 and V respectively when station \i. is sending and station I. 

 is at rest (single signals). 

 Further, 



Q'=yW+gW, 



where ^' and g 7 are tne currents which pass through a' and b' 

 respectively when both stations are sending simultaneously (du- 

 plex signals). 



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



