1S76.] L. Schwendler — On the General Theory of Duplex Telegraphy. 11 



clearly a maximum for a = b' . This proceeding is right, because we take 

 b' as the original variable, and vary a' and y simultaneously with b', in or- 

 der to keep f and a' + b' constant ; while J" and s are independent of a', V , 

 and y'. 



In order to be sure that a' = V makes also Z> 3 ' a minimum, we must 

 shew that T keeps constant, i e,p' keeps constant when as' varies. But p' 

 = a' +y, thus we have only to consider f simultaneously variable with a' 

 ecpial and opposite to the variation of a, which is allowed. Therefore 

 the condition a' = b' makes undoubtedly the disturbances D x ' and D 3 ' 

 minima. While the disturbance -D 2 ', which contains R' in the denominator 

 only, is not affected by this relation, but depends on the absolute value of b' 

 only, which should be chosen as large as possible. 



a = b is therefore the second regularity condition, the fulfilment of 

 which makes the relative disturbance of balance by a variation of K and X 

 as small as possible. 



Substituting now a' = b' in the expression of the D disturbances and 

 remembering that 

 R' = E7 

 we get 



DJ = s v' — 8 X' 



3 J£ 



Thus D x \ and D s ', for constant s, A.', and v', become smallest the 



J T 



smaller — is, while _D ' becomes smallest the smaller — , is. 



Now remembering that 



and 



J = 



i 



K' - 



(I" + P ") (i + I' + p') +i {V + p) 





i + l" + P " 



T = 



r , , . . , V + P) C + P") 

 = -L> + P + P + 



J 



(i + i" + p"f 



E! 



* {( l " + p") (» + v + p) + » Q' + p)} 



T 

 K' 



i + I" + P " 



i [a 



