﻿Mr. H. Mance on the Measurement of Electrical Resistance. 317 



know the resistance offered to the passage of a current between co 

 and y in fig. 3, I can find it in the following manner. 



Fig. 3. 



£ 



9 



First assume the existence at x of a sixth branch bearing (in resist- 

 ance) the same proportion to R that A does to B ; that is to say, the 

 supposititious branch ^ 



L=R.-. 



Now disconnect r from the point Z, and we have again a diagram 



A L 



similar to that in fig. 1 ; and as we have provided that ^ = ^, 



the connexion or disconnexion of r at the point Z will make no dif- 

 ference whatever in the quantity of current passing from L into the 

 branch G. I may therefore assume that, although the total resist- 

 ance of the circuit between q and y has been decreased, the branch 

 A has at the same time been able to divert a proportionately greater 

 amount of current from the side G, in which the intensity remains 

 unaltered. 

 If, then, 



R x equals the resistance between q and y when the branch r is 

 disconnected, 



S x the shunt-coefficient of AB, which forms a shunt in the absence 

 of r, 



R 2 the resistance between q and y after r is connected at Z, 



S 2 the shunt-coefficient for the part A, ascertained by equation (1), 

 we have 



"^'ra 



and R 2 minus the supposititious branch ( -«- ) will give the required 



combined resistance of the circuit between x and y. 



Let R 3 be the combined resistance. Commencing with the equation 



fRA G.(A + B) \ y A + B + G 



1 B ^G + (A + B) +±t J X a + B _5A 



we obtain 

 R 



G.(B + R + r) + BR B 



A.(B + R+r) + Br 



MA+B+G) , a 



~B "*" RA 



R 3 , 



G.(B + R + r) + BR B 



A-..(B+B+r)+Br ■ 



