of Duplex Telegraphy. 535 



put 



i + l" + p" _j 



and 



^ 



Now keeping *, J, V, and v> constant, D\ becomes smaller 

 for any given $K' the larger f is selected ; while D' 3 becomes 

 smaller for any given 8V the smaller ^ is selected, and D' s 

 becomes smaller the krger E / is chosen. 



Now TJr' = B' \f^f nas a maximum for a' = V ; for 



and putting r/=W, we have 



which, for a' + Z/ and tf constant, has clearly a maximum for 

 a' = &'. This proceeding is right, because we take & as the 

 original variable, and vary a' and / simultaneously with & in 

 order to keep *' and a! + V constant; while J and s are inde- 

 pendent of a', V, and ttf. , , V TO 



In order to be sure that d = V makes also D' 8 a minimum 

 we must show that T keeps constant, i. e. p f keeps constant 

 when a' varies. But p' = a' +f; thus we have only to consider 

 /' simultaneously variable with a% equal and opposite to the 

 variation of a, whichis allowed. Therefore the condition a =6 

 makes undoubtedly the disturbances T)\ and D, minima; 

 while the disturbance D' a , which contains B' in the denomi- 

 nator only, is not affected by this relation, but depends on the 

 absolute value of V only, which should be chosen as large as 

 possible. 



