40 Mr. 0. Heaviside on Duplex Telegraphy. 



or 



x=\{l+>/{l + *g){l + 2g + tf\ 



In single working with the same instruments and batteries 

 the strength of the signals is 



2E? » (12) 



f+fy + V ' ' ' 



when the current passes through both coils in succession. 

 When/, the battery resistance, is very small, we see from (10) 

 and (12) that the strength of the signals in duplex working is 

 nearly one half their strength in single working with the same 

 instruments, since x is a little greater than l+g. 



Since there is only one balancing resistance at each station 

 in this system, there is only one arrangement possible with a 

 given receiving instrument and battery, leaving out minor de- 

 tails. We may, however, inquire what the resistance of the 

 instrument should be to obtain the strongest signals on the 

 supposition that the space to be filled with wire is fixed. In 

 such case m will vary as the square root of g } and 



Sx E ^ . 

 /+£ + * 



Therefore for S to be a maximum, we must have 



/+ , + ,= 2,(l+g; 

 and we find from (11) 



ThprpforA 



?=*{-(*+/)+ «/(/+ **y+*M • ( 13 ) 



is the best resistance for each coil of the receiving instrument. 

 When/=0, g — &. Now (13) is identical with Weber's for- 

 mula for the resistance of each coil of a differential galvano- 

 meter to obtain the maximum sensitiveness at a balance ; thus 

 again we see, just as in the bridge system, the arrangement in 

 which both stations get the strongest signals is also the most 

 sensitive balance, and most liable to disturbance from varia- 

 tions in the external resistance. 



Weber's formula (13) admits of considerable simplification 

 if we arrange the battery so as to obtain the maximum current, 



