ON PRACTICAL STANDARDS FOR ELECTRICAL MEASUREMENTS. 109 



The best conditions for sensitiveness are here clearly indicated. The re- 

 sistance R should be small compared with S and with P, i.e. P should be 

 connected to a comparatively large resistance Q and a small resistance R. 

 If i is the maximum permissible current through P, Q must be a resistance 

 of large cooling surface and small temperature coefficient ; if it is of the 

 same type and dimensions as P, then it should be of the same nominal 

 value. In the latter case, which is the general one for precision measure- 

 ments, P=Q=R=S, and the sensitiveness is proportional to iA^.P/4 

 It is generally recognised that for coils of the same type and dimensions 

 i\/P is constant. 



3). — Let the resistances of the two circuits be 

 is the current through P, the current through 



The Poteyitiometer (fig. 

 P + Ri and Q + Ro. If i 

 the galvanometer is 



iAP 



G+PR,/(P+R,)+QR2/(Q+R2) 



and the best resistance for the galvanometer is PR|/(P-|-R,)-1-QR2/ 

 (Q + Ro). The sensitiveness is therefore proportional to 



iA^/P~ 



2VR,/(P + R,) + QR2/P(Q+R2)' 



In the case of precision measurements, Ri and Rg may be made very 

 great compared with P and Q respectively. If this is so, the sensitiveness 

 is proportional to iAn/P/ 2 n/I+Q/ P. If Q is small compared with P, 

 this becomes iA^/P/S, and the best resistance for the galvanometer is P. 



Fig. 3 



Unless P and R are nominally equal the galvanometer resistance cannot 

 be the most suitable for both observations, and the sensitiveness of one 

 of the measurements must be less than that stated. If P=R and Q=S, 

 the latter being comparatively small, the sensitiveness is twice that of 

 the Wheatstone bridge with equal arms. It has to be remembered, 



the battery arm and the e.m.f. of the battery. If for the latter i (P + Q) i 

 substituted, the resistance of the battery may be taken as zero, and on substituting, 

 the value given in this paper is obtained. 



