1S75.] Theory of Duplex Telegraphy. 51 



If we now substitute for A', B\ <&', W their values, we get : 



N" * 



and Q= — /* * +]v' 



the sign of p' being contained in A', and 



where 



N' ^=f (V + cl' + a' + ft' + c') + (5' + el') («' + 7*' + c') 

 ]$■"=/' (b" + <T+ a" + ft" + c") + Q>" + O («" + ft" + O 

 , i 



A' = (5' + cl') m' — (a' -f ft' + O w' 

 f 



A' == Wl' 4- - 7/ ; s » 



Thus the general expressions for the two functions D and 8 are : 



TV _ £ — ^ ' ^ — ^ 



1 7V'— li'—" 5 " ^ A " 1 



-^ " P - F- F« V~< I for gtation n 



Rigid fulfilment of the two functions D = o «m(7 $ — o. 



D can only become zero, for finite resistances of the branches, if 

 ^> = $ = o 

 i. e. if A = o 



Now, to keep A = o we may adopt two essentially different modes of 

 re-adjustment, namely : — 



Either leave the coils and their armatures stationary, and adjust ba- 

 lance by altering the resistances of the branches (« + li) and (b + d) sepa- 

 rately or simultaneously, or leave the resistances of these branches constant, 

 and move the coils or their armatures. These two cases are to be consi- 

 dered separately. 



(#.) Re-adjustment of balance hy 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 variable. If they have 

 been once selected, they must necessarily be kept constant, whence it follows 



