540 



Prof. H. L. Callendar on Electrical 



Let the annexed diagram, fig. 1, represent the arrangement 

 of resistances in a Wheatstone bridge, in which C is the 



Diagram of Wheatstone Bridge. 



current through the resistance to be measured R, and c is 

 the current through the galvanometer of resistance Gr, when 

 the bridge is not balanced. The resistance in series with R 

 is nR' traversed by a current C 4- c ; the resistance in parallel 

 with R on the same side of the galvanometer circuit is mR/ 

 traversed by a current C + c. The resistance in the opposite 

 arm of the bridge to R is nmR', traversed by a current C 

 The currents are assumed to flow in the directions indicated 

 by the arrows, and it is evident that they satisfy the condition 

 of continuity. The numbers n and m, representing the ratios 

 of the arms of the bridge, may have any positive values. The 

 bridge is balanced when R = R', in which case c=0, and 



C'=C/m. 



Since the difference of potential between the ends of the 

 galvanometer circuit is Gc, we have by Ohm's law, 



RC-mR'(C' + c) = Gc = nmR / C'-nR / (G + c). 



Eliminating C, we obtain for the ratio c/G, 



c /C=(R-R / )/(a(l + n)/n + (l + m)R / ). . . (1) 



It is obvious that this ratio, which may be regarded as a 

 measure of the sensitiveness of the arrangement, is quite 

 independent of the resistance or E.M.F.in the battery circuit. 

 It is also at once evident that, for a given defect of balance 

 as measured by R — R', the value of the ratio c/G will be a 

 maximum when n is as large as possible, and m as small as 

 possible, the limiting value of the ratio c/G in this case being, 

 when 



n=oo, and m=0, c/C=(R-R')/(Gr + R'). 



