50 Louis Sehwendler — On the General [No. 2, 



Further, if we suppose at the outset, that the movement of the key k 

 does not alter the complex resistance p of its own station, i. e. } the fulfil- 

 ment of the key equation 



a condition which is essential, it is clear that the currents y' and g"' are the 

 algebraical sums of the cm-rents A!, %' and B', 53' respectively, whence it 

 follows that 



q = (A' -f %') m' + (B' + W) n' 

 where the currents contain the signs. 



Now, with respect to the manner of connecting up the two signalling 

 batteries E' and JE'', we have the following two different cases : 



1st. The same pole of the signalling battery is connected to earth in 

 each station, thus : 



p' = + A' on' + B' n' 

 P = -f &' on' + B' »' 

 Q' = (+ A' + a') m' + CF -B' + B') »' 

 where the upper signs are to be used when the negative poles of the signal- 

 ling batteries are connected to earth in both stations, and the lower signs 

 when the positive poles of the signalling batteries are connected to earth in 

 both stations. 



2nd. Opposite poles of the signalling batteries are connected to earth 

 in the two stations, thus : 



p' = + A' m' + B' n' 

 !*—+&' m ' ± B' n 

 Q' = (+ A' ± <&') on' + (+ B' ± W) n' 

 where the upper signs are to be used when the negative pole in Station I 

 and the positive pole in Station II are connected to earth, and the lower 

 signs when the reverse is the case. 



Subtracting in either of these two eases P' from Q', it will be seen that 

 invariably 



#' = q — P' = p' 

 or that, on account of having fulfilled the key equation w -f (3 = f, the 

 difference of force by which single and duplex signals are produced is equal 

 in magnitude and sign to the force by which balance is disturbed. Further, 

 that it is perfectly immaterial whether the same or opposite poles of the 

 signalling batteries are put to earth. For reasons already explained I pre- 

 fer to use the negative poles of the signalling batteries to earth in both 

 stations, and this alternative we will suppose is adopted. 

 Thus we have : 



p' = A' on' — B' oi' 



P'= — {% m' + W O 



q = (A! — a') on' — (P/ + W) n' 



