286 Mr. T. Gray on arranging Wheatstone' s Bridge 



and then the subsequent adjustment of c is easy after a first 

 rough test for R. 



The effect of using the resistances given by this rule is very 

 striking, and is illustrated by means of the subjoined curves. 



The first, second, and third sets of curves (Plates IV. & V.) 

 show the effect of using a value of a differing more and more 

 from */fg, the value of c being in each case determined so as to 

 give the best effect for that particular value of a. An examina- 

 tion of the curves will show that, for any particular battery and 

 galvanometer, the resistance which is best measured is that 

 which is equal either to the resistance of the galvanometer or the 

 battery, the arrangement being equally sensitive for both. Care 

 must be taken, however, not to confound this with the best ar- 

 rangement for measuring the resistance here referred to; for it 

 does not follow that no better arrangement can be made for the 

 measurement of a resistance because it is the one which gives 

 the best result in a particular arrangement. For instance, if 

 we have a battery- resistance 100 and galvanometer 10, we find 

 the greatest sensibility will be obtained when R=10 or 100 ; 

 but, as we shall see below, if the battery be rearranged so that 

 / shall also be 10, a still greater degree of sensibility will be 

 obtained for the measurement of the resistance 10. 



The fourth set of curves (PL VI.) illustrates the effect of vary- 

 ing the ratio of a to c from that which gives the best effect. In 

 these curves, then, a is supposed constant, while c varies — the 



abscissae being proportional to c and the ordinates to zL*£S. 



i.e 

 where e denotes the electromotive force per unit of battery- 

 resistance. In the first three sets of curves the abscissae are 



proportional to a and the ordinates to — - — 2. It must be ob- 



i.e 

 served, however, that in the third set the ordinates are ten 

 times greater than they would be if plotted to the same scale 

 as the first and second sets. Curves II. and III. of the third 

 set are shown on the right-hand side, with their abscissae also 

 multiplied by ten. 



Part II. 

 The second case investigated is that in which the galvano- 

 meter-resistance is also supposed to vary, the battery-resistance 

 being supposed constant in this case. This assumption is 

 made with regard to the battery, because for any given value 

 of E the maximum effect is obtained when/=0. It is to be 

 remembered, then, that diminishing / always increases the 

 sensibility of the bridge. 



