198 ELECTRICAL MEASUREMENTS 



The bridge resistance is 



mn 



_ __ 



lo - [Ro (R s + RB) + RsR B ] (M + N + X + P) 



The resistance which, in any case, it is necessary to add to 

 that of the galvanometer to produce critical damping is R K , 

 that is, 



Re RO -h RK> 

 The value of R K is 



/. 1 Q = 



R S +RB 



I f x XR K 8P 



+ R K )(X+P)R B 

 and 



Compare formula (12) on page 189. 



Precision Measurements with the Thomson Bridge. 7 In 

 the proofs already given M, N, m, n, are the total resistances 

 of the various bridge arms, that is, they are the sums of the 

 resistances of the coils in the arms and of the necessary leads. 

 The lead resistance can never be zero; consequently, though the 



coils themselves are adjusted so that the relation ^- = 



is fulfilled, yet when they are connected into circuit by the 

 necessary leads this relation will be slightly disturbed and the 

 elimination of a from the results will not be complete. In the 

 careful comparison of resistance standards this matter is of im- 

 portance, for of necessity the resistances of the potential terminals 

 are included in the bridge arms. 



If the resistances in the arms are separated into two parts, 

 that in the coils being denoted by the subscript c and that in the 

 leads by the subscript L, equation (15) becomes 



im c + m L _ M c + M L \ 



' * 



x -P __ . c t C L 



~ m c + m L + n c + n L + a 



