474 On the General Theory of Duplex Telegraphy. 



These two equalities certainly do not contradict equation (VIII.) ; 



but they do not necessitate it. 



The additional reason why equation (VIII.) should be chosen 



follows from the balance condition 



ad— bc=0, 



, ad 

 .'. b= — 

 c 



Therefore b becomes largest for any given c and any given 

 (a + d) if we put a=.d. 

 But b largest is required for two separate reasons : — 



1. If the immediate balance is disturbed by an alteration of 

 the resistance of one or more of the four branches, which may 

 happen especially by f (i. e. (3, battery resistance) varying, then 

 p becomes at once a function of b } i. e. an increasing one with b. 

 Thus in order to keep p as large as possible and at the same time 

 as constant as possible, b should be selected largest. 



2. Further, by making b as large as the circumstances will 

 admit, we clearly have the largest sent and largest received cur- 

 rents — which will be clear without calculation. In fact later on 

 (page 23.2*) it has been shown that a = d is the condition for the 

 maximum signalling-current. 



Note. — Since the 3rd of February, 1875, the main line from 

 Bombay to Madras has been successfully worked duplex by means 

 of the " double-balance method." 



This line is worked direct, i. e. without any translating instru- 

 ments, and is 797 miles in length ; it consists almost throughout of 

 No. 5| wire, B. W. Gr. (diameter 5| millims.), and is supported 

 chiefly on the Prussian insulator. 



The section of this line from Bombay to Callian is exposed to the 

 destructive influence of a tropical sea climate. Between Callian 

 and Poona the line passes over the Western Ghauts ; the dense fogs 

 during the cold weather and the heavy rains during the south-west 

 monsoon on these hills seriously affect its insulation. From Poona 

 to Sholapore and Bellary the line runs inland, and experiences a 

 climate on the whole favourable for the maintenance of constant 

 and high insulation. Between Bellary and Madras, however, the 

 line again comes under the influence of a most unfavourable climate, 

 especially just before and during the continuance of the north-east 

 monsoon, when the atmosphere at a high temperature is saturated 

 with moisture and salt, leaving conducting deposits on the surface 

 of the insulators. 



Consequently during the south-west monsoon the resultant fault 

 is near Bombay; during the hot weather it shifts towards the 

 middle of the line ; and in November, when the rains set in at 

 Madras and the weather on the Bombay side is clearing up, the 

 resultant fault is situated close to Madras. 



* Phil. Mag. S. 4. vol. xlix. p. 124. 



