of Duplex Telegraphy. 467 



makes P either as large as possible or, which would be still 

 better, a maximum. 



Now P' = A/A', 



where A" is the current which enters the line at point 2 (fig. 2) 

 when station II. is sending alone, while p! is the factor wh ch 

 determines the loss through leakage of the line, and X 1 is the 

 factor to which the magnetic force exerted by the current A"/jJ 

 in station I. is proportional. 



fj and A/ are functions of the resistances in station I. 

 only*, but not of those in station II. 



Now, for constant values of p 1 and V (i. e. leaving every thing 

 in station I. constant), P' becomes larger the larger A" is. 



b" + a" 



A" = E"- 



N" 



Substituting its value for N", and dividing numerator and de- 

 nominator bv b" + d", we get 



E" 



fll J ifl +h) „ ?,, ,, /, J 



J + b n + d ii + a + /l + c (/+ b n + d , 

 Supposing balance in station II. rigidly fulfilled, we have 

 (W + d") m" - {a" + h" + c")n" = ; 



... c "=(^+^)^-K + ^')- 



Substituting this value of c" in the expression for A" and re- 

 ducing, we get 



A ' = /WP + q"(b" + d" +/") \/W ' 



r n 

 Dividing by q" and putting -^ = v", we have 



A"=E". 



vWb" 



/V v / i"+(i"+^"+/V«"' 



This expression has a maximum f for 



bP=nf" + d", 



t In order to keep the balance in station II. rigid when b" varies, we 

 must suppose v" simultaneously variable with b". This is perfectly jus- 

 tified ; for v" can be altered by an appropriate movement of the coils to 

 keen up the balance in station II. without altering the outgoing current A". 

 1 2H 2 



