﻿314 Dr. S. R. Milncr on the Use of the Secohmmeter 



With F = '5X2, single adjustments of R and P practically 

 gave the complete balance, for two figures of the resistances 

 were as much as the galvanometer would indicate with the 

 arrangement so unsensitive. With *1 12 two sets of adjust- 

 ments were required, and with still smaller resistances F the 

 approximation became laborious. But it is very simple to 

 proceed as in the first experiment, and adjust to the first two 

 figures of R and P with a high resistance in circuit, when 

 the balance may be completed to the fourth figure by a single 

 further set of adjustments with the resistance shortcircuited 

 and the arrangement thoroughly sensitive. 



General Conditions for Balance at S=|. — This commutator 

 position is unique in the ease with which it may be adjusted 

 to in practice, and the fact that the incomplete balance here 

 may be obtained independent of the speed. It thus forms 

 much the most convenient position in practice for an incom- 

 plete balance. The relation corresponding to the balance is 

 moreover easy to investigate in the general case. Zero 

 galvanometer deflexion at 8 = i independent of the speed 

 must imply that the curve for the unreversed current through 

 the galvanometer branch is an undistorted copy of that for 

 the E.M.F. The relation is consequently simply the condition 

 that the differential coefficient D shall vanish by cancelling 

 from the general relation (2) in which the operators R'and S' 

 of (3) have been substituted. This may be determined by 

 simple algebra. The condition is twofold : (#) F must be 

 large compared with the rest of the bridge variables, and \b) 

 the relation 



must be satisfied. This result shows the necessity for the 

 restriction in the methods above on the magnitude of F, and 

 also the relation which results when / is not negligible. 

 When either / or P and Q are negligible (14) degenerates 

 into R/kS = K/H, hence the condition that / should be small 

 in the methods may be replaced by this alternative. 



Parallel Combinations : — An investigation exactly similar 

 to the above reveals the fact that similar methods of balancing 

 are equally applicable when R & H, and S & K, are m 

 parallel instead of in series with each other. The operators 

 R / and S' to be introduced into (2) are now such that 



& = * + **>' B' = S +KD - • • (15 > 

 The conditions that D shall vanish from equation (2) 



