ON PRACTICAL STANDARDS FOR ELECTRICAL MEASUREMENTS. 107 



and it may not be out of place to give a well-known rule which, if applied 

 to any system of conductors, will quickly give all the desired information. 

 ' In any network of conductors the current in one arm due to an 

 electromotive force in another arm is equal to the current in the latter 

 when an equal e.m.f. is placed in the former.' 



(This rule results from an application of Kirchoff's Laws.)- 



The most complicated system of conductors considered in the present 



paper is that known as the Kelvin double bridge, ^ and this is dealt with 



here by way of example. Let the current through P be i, and through 



R, i', and let P/Q=R/S=a//3. Also let the applied e.m.f. remain 



Fig. 1. 



constant. On completing the galvanometer circuit the distribution of the 

 currents will remain unaltered. Let P be changed to P + SP. The 

 current through it will change to i — ci, and the change in p.d. of P is 

 i^P — 'Phi ; of Q it is QSi. If the galvanometer circuit is now completed 

 the current through it will be equal to that produced by an e.m.f. idV—'Pci 

 in P and an e.m.f. equal to Qci in Q. If an e.m.f. equal to the latter is 

 placed in the galvanometer branch, the current through Q is PQSi/ 

 (P + Q)r, where r is equal to 



a/3 (P + R)(Q + S) ^ 

 a + i3 P + R + Q + S^ ' 



i.e. the resistance of the ' external galvanometer circuit ' plus that of the 

 galvanometer. Similarly the current through P due to an e.m.f. Poi in 

 the galvanometer branch is equal to Q7ci/(P + Q,)r. Hence, by the rule, 

 the current through the galvanometer due to an e.m.f. Qci in Q, is equal 

 to the current through the same due to an e.m.f. Pei in P. As these must 

 be in opposite directions through G, we have only to consider the current 

 due to an e.m.f. iSP in P. The current through G due to this e.m.f. is 

 found in a similar manner and is equal to 



i3P 



C , «/3 (P + RXQ+S) 

 ci+fi'^ P + RfQ + S 



P+R+Q+S 



(A) 



This, therefore, is the current through the galvanometer when the balance 

 of the bridge is disturbed by an alteration in P of ^P. 



' W. Thomson, Phil. Mag., 1862, 24, 149. 



