14 L. Schwendler — On the General Theory of Duplex Telegraphy. [No. 1, 



Suppose that at a certain moment 



S = K is rigidly fulfilled, and remembering that 

 R = b + d + a 



K = 2 (a +f) + L (for a perfect line, i. e., i ■= oo ) 

 and further, that 



« = Z> 

 and /= tv + (3 



we have d-Ha = a + 2w + 2/3 + Z. 



Now, in this equation suppose everything constant except a and f3, the 

 internal resistance of the two batteries _E" and e respectively. Hence if 

 we could achieve that 



8 a = 2 S/3 invariably, 

 the variation of the internal resistance of the two batteries would not disturb 

 the equation R = K, and therefore also not affect the balance. With 

 absolute certainty we cannot fulfil this desirable relation between the two 

 variations, but with some probability we may. For it is well known that 

 the internal resistance of a galvanic battery decreases in time by the current 

 passing through the battery. Hence, if we suppose that the two batteries 

 consist of identical cells (equal in nature, size, and internal resistance) we 

 may say that the variation of the internal resistance of a single cell by the 

 unit current in the unit of time is the same for both the batteries. Further, 

 if we make the other not improbable supposition, that the variation at any 

 one time is proportional to the current which passes at that time, we have 



and 28iJ= e «. K + SK ¥'■> = ' J ¥'■> 



where e is the variation of the internal resistance of a single cell in unit of 

 time by unit of current ; </>W a certain unknown function of the time which, 

 as the two batteries are working simultaneously, is not required to be known. 



Hence from 8 a = 2 8 (3 

 and K = B 



E /- 



it follows that A = — = \/2 



e 



and v = — = /\ 



q V 2 



These values of A. and v bring the compensation method, with respect 



to regularity of working, as close to the differential method as is possible for 



us to do. For the disturbance of balance in the sending station by the 



steady decrease of the internal resistance of the two batteries has now been 



probably eliminated, which defect is excluded from the other two methods, 



