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XXXY. On the best Arrangement of the Wheatstone* s Bridge 

 for the Measurement of a particular Resistance. By Thomas 

 Gray, B.Sc, F.R.S.E* 



[Plates IV., V., & VI.] 



nVfO experimental method is in more general use than is 

 -L ^ that of Wheatstone's bridge for the comparison of elec- 

 trical resistances. It appears, however, that erroneous ideas 

 are prevalent among practical electricians, and have found 

 their way into works on electrical testing, as to the proper 

 resistances to be used in the different branches of the Bridge 

 in order that the most sensitive arrangement may be obtained 

 in any particular case. The following investigation, together 

 with some graphical illustrations of the effect of using different 

 resistances, was originally prepared for the use of my students; 

 but the fact just referred to has led me to believe that it may 

 be found generally useful by those engaged in electrical work. 



The most general case (that in which, for the measurement 

 of a particular resistance, all the other resistances, including 

 those of the galvanometer and battery, may be varied) has been 

 excellently treated by Prof. Clerk Maxwell, and more recently 

 by Prof. Chrystal in his article " Electricity " in the Encyclo- 

 pedia Britannica ; but, so far as I am aware, no one has con- 

 sidered in detail all the different casesf . 



The subject is divided into three parts, each of which may 

 be found useful in particular cases. The first part, however, is 

 that which will be of the greatest service as a guide for practical 

 purposes. In this part the galvanometer and battery are sup- 

 posed to be constants, while the bridge-resistances are changed 

 to suit particular cases. It is seldom convenient to change 

 either the battery or the galvanometer much during a series 

 of tests; and I therefore think this part the most interesting 

 and useful. 



Part I. 



The problem is this : — With a given battery and a given 

 galvanometer, and a certain resistance to be measured, what 

 must the other three resistances be in order to give the best 

 effect? 



Let a, b, P, c (PI. IV. fig. 1) be the resistances in the 

 bridge, g and / the galvanometer- and battery-resistances, and 

 G the current passing through the galvanometer when balance 



* Communicated hy the Author. 



t This paper was prepared for press before the author knew of the ex- 

 istence of Mr. Oliver Heaviside's paper in the Philosophical Magazine, 

 vol. xlv. (1873) p. 114, in which the case treated in Part I. below is con- 

 sidered, and concordant results arrived at, 



Y2 



