152 Royal Society : — 



the resistance in the connexion and the resistances in the portions of 

 the main conductors from the marks S' and T to their ends. Lastly, 



!S'RPT 1 

 9'OT ( between 



»' and T. By the well-known principles of electric conduction, we 

 have 



R= ? (1) 



1 1 v J 



S'BCT + S'QT 



for the resistance in the double arc between S' and T. Then, by 

 addition, we have 



SS'+R+TT', 



for the resistance from S to T' by the channel SS' { |'q£ T j TT\ 



This whole resistance is divided, by Q and its equipotential point 

 in the direct channel S'BCT, into the parts 



SS' + lg.R.and^.R + TT'. 



Hence if, for simplicity, we suppose the potential at S to be 0, 

 and at T' to be E, and if we denote by q the potential at Q, we 

 have 



ss , _^Q R 



E _ +S'QT 



* SS' + R + TT' K ' 



Again, since P divides the resistance between S and V, along the 

 channel SPT', into the parts SP and PT', we have 



i>= E njr (3) 



if we denote by p the potential at P. Hence 



SS' + |^.R-^ (SS' + R + TT') 



q-p=Ya SS + R+TT' ; 



SP PT' 

 or, since i QP r jv~"""Qp r iv» 



-^ SS'-- ^ TT' + R^-^ 

 SPT' * °° SFF * l L + 1X IS'QT SPT'j 



ff -jp=E SS + R+TT' ' ' W 



Now let us suppose that, by varying one or more of the component 

 arcs in the balance-circuit, we reduce the galvanometer indication 

 to zero, that is to say, make q — p = 0. We shall have by equating the 

 numerator of the preceding expression to zero, and resolving for TT', 



To interpret this expression, it may be remarked that if the second 



