of Duplex Telegraphy. 46 



Rigid fulfilment of the two functions D = and S=0. 

 D can only become zero for finite resistances of the branches 



if 



r. e. if 



A = 0. 



Now, to keep A = 0, we may adopt two essentially different 

 modes of readjustment, namely : — 



Either leave the two coils and their armatures stationary, and 

 adjust balance by altering the resistances of the branches (a + h) 

 and (b + d) separately or simultaneously, or leave the resistances 

 of these branches constant and move the coils or their armatures. 

 These two cases are to be considered separately. 



(a) Readjustment of balance by altering the resistances of the 

 branches. 



As a and b are resistances which in the form of coils have to 

 exert magnetic force, it is impracticable to suppose them vari- 

 able. If they have been once selected, they must necessarily 

 be kept constant, whence it follows that the readjustment of 

 balance is restricted to a variation of one or both of the resistances 

 h and d. 



But as p is a function of h and d, to establish balance by alter- 

 ing one of them only would invariably result in an alteration of 

 p, and consequently immediate balance would become an impos- 

 sibility. 



Thus in order to readjust balance, and at the same time to 

 keep p constant*, we must vary h and d simultaneously. 



Now it can be proved, in exactly the same manner for the dif- 

 ferential method as was done for the bridge, that in order to 

 make the disturbance of balance for any given variation in the 

 system as small as possible we must makep as large as possible, 

 whence it follows from the form of p that 



f=b + d, 



the u regularity -condition " for the differential method. 



* i a . (b + d)f 



keep a, b, and / constant, and vary h and d; whence we should have 



8p={b + d+f)(b+d+f+M)8h+f'8d=0, 



an equation which it is always possible to fulfil for any variations of h and 

 d if taken of opposite signs, although it may be difficult to achieve it prac- 

 tically by a simple motion, such as that of turning a handle. The absolute 

 value of thest; variations depends, of course, on the variation of c which 

 disturbs the balance ; and in order to have accelerated balance we ought to 

 decrease h and increase d when c increases, and vice versa. 



