1871.] 



of Electrical Resistance. 



251 



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

 graph, suggests an easy method for ascertaining by calculation the com- 

 bined resistance of any system of derived circuits connected in the form of 

 the Wheatstone's parallelogram ; thus if I wish to know the resistance 

 offered to the passage of a current between cc and y in fig. 3, I can find it 



Fig. 3. 



nnn 



in the following manner. 



First assume the existence at x of a sixth branch bearing (in resistance) 

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

 branch 



L-B.f. 



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



A L 



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



or disconnexion of r at the point Z will make no difference whatever in the 

 quantity of current passing from L into the branch G. I may therefore 

 assume that, although the total resistance 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, 



Rj equals the resistance between q and y when the branch r is dis- 

 connected, 



5 1 the shunt-coefficient of A B which forms a shunt in the absence of r, 

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



5 2 the shunt-coefficient for the part A ascertained by equation (1), 

 we have 



-n R X S 



and R 2 minus the supposititious branch will give the required com- 



bined resistance of the circuit between x and y. 



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



RA G . (A + B) , -p 1 % A + B + G 



,_G.(A + B) , .,1 



