WIRE BRIDGE. 369 



the distance x x' is greater as the auxiliary resistances themselves 

 are greater. 



This observation is utilised in reproducing standards of resist- 

 ance. A series of resistances a and , a-^ and b lt a 2 and b^ are 

 prepared, each pair being equal, so as to keep the readings in 

 the centre of the wire, and the values of which increase in about 

 tenfold order. The resistance b' being the standard, the copy a' 

 is adjusted with the resistances a and b, almost to a single division 

 of the scale, a and b are replaced by a l and b^, and a^ is again 

 adjusted to within a division, and so forth as long as the sen- 

 sitiveness of the galvanometer allows. The error made is given 

 by the preceding formula. If the adjustment has been made to 

 to within a division with coils of the order # n , the error of the 



copy is 



. 



This method of comparison, applied to resistances which are 

 not very small, enables us easily to attain an approximation less 

 than O'OOOOT, which for a copper wire corresponds to a change 



in temperature of about - - of a degree centigrade. 

 400 



971. When the ratio of the resistances to be compared differs 

 too much from unity, a series of intermediate resistances r lt r^...r n 

 is used, such that their successive ratios and those of the extremes 

 with a' and b' are directly measurable. We have, in that case, 



- -.... 

 b' r^' r^"~V 



For very unequal resistances, it would sometimes be advisable 

 to choose the auxiliary resistances so that, when arranged in series, 

 they are almost equal to a', and that, as parallel wires, their con- 

 ductivity is near that of b'. If p and q are ratios thus determined 

 experimentally, the ratio of the resistances a and b' will be deduced 

 from equations 



^fa + 'f+V'+'j/i 



ii ii 



- + - + ... + = . 

 r l r * r n b $ 



If the different resistances r lt r z , . . . r n had the same value r, these 

 equations would reduce to 



a' = nrp , 



nb' q = r , 



VOL. II. B B 



