﻿316 



Royal Society :- 



zation-current from a leakage of low resistance in a cable would 

 enable us to find the resistance from either side through the fault 

 without the application of a battery. And, lastly, this method may 

 be used to ascertain the internal resistance of a battery. 



The above method occurred to me about two years since, during 

 some experiments made to determine the resistance of the bridge- 

 circuit, and the exact proportion of current traversing each branch 

 of the "Wheatstone balance, when the potentials at W and Z are 

 unequal. 



Fig. 2. 



If I equals the intensity of the current at x or y, and i lS «L i 3 , ?' 4 , i. 



the intensities in the sections G, R, A, r 

 G.(B + R + r) + BR 



B, then 



+!*£ 



+ 1 



A.(B + R+r)+Br 

 A.(B + R+r)+Br 

 G.(B + R + r) + BR 

 B.(A+B + G) + BG . I 



r.(A + B + G) + AB + i 2 ' 



r.(A + B + G) + BA I 



R.(A + B + G) + BG"*" i, 



B.(R-f-r) + (B-;-R + r).(A + G) _ I 



■0) 

 .(2) 



CO 



(4) 



(5) 



Gr-AR i 5 



Or if the current in the branch B passes from "W to Z, 

 AU-Gr 



should be substituted for the denominator of the last equation. 



Equations (1), (2), (3), and (4) give the shunt-coefficient of the 

 respective branches A, G, r, R ; thus, if G were a galvanometer, the 

 strength of the deflection recorded multiplied by equation (1) would 

 give the value of intensity I. 



If, then, we consider G a galvanometer and the resistance r a 

 leakage applied at Z/ we have a similar diagram to that given in 

 fig. 1 ; and the first of the five equations given above will enable us 

 to determine the shunt- coefficient for the part A wbich lies between 

 L and the leakage at Z. 



Now this, together with the plan of testing described in the first 

 paragraph, suggests an easy method for ascertaining by calculation 

 the combined resistance of any system of derived circuits connected 

 in the form of the Wheatstone' s parallelogram j thus, if I wish to 



