Prof. Thomson on the Measurement of Electric Resistance. 153 



term vanishes, that is to say, if 



/SPT'S'Q x -> 



VS'QT SP ; 

 we have > : ..... (6) 



TT'=-|^.SS' 



and this is the condition aimed at in the arrangement. Now the 

 connexions at S and T' must be made so good that the resistance 

 SG in the first is inappreciable in comparison with GP, and the 

 resistance HT', in the second, inappreciable in comparison with PH ; 

 so that we may have 



PT ; PH 



SP^GP' 



where P' denotes an equality not perfect, but having no appreciable 

 error : and hence 



The condition 



PH 

 TT'agp.SS'. 



/SOT S^_ v 

 VS'QT 'SP / 



is to be secured by one or other of two ways or by both combined ; 

 that is, by making 



RHO (a) 



or 



SPT' S^Q 



S'QT SP^ ' K J 



or each as nearly as possible. If the connexion BC were quite perfect 

 and the marks S' and T were at the very ends of the conductors, 

 the condition (a) would be fulfilled and there would be no necessity 

 for the condition (b). We should then have a perfect Wheatstone 



balance, — the secondary testing-conductor { y [ Q becoming merely 



a part of the galvanometer electrode. Hence whenever the re- 

 sistance S'T can be made absolutely insensible, Wheatstone' s balance 

 leaves nothing to desire, provided the ends of the testing-conductor 

 are applied to marked points on the standard and tested conductors, 

 and the battery electrodes to their outer ends, or to points of them 

 between their outer ends and those marked points. When, how- 

 ever, as very frequently is the case, S'T may be made small but 

 not absolutely insensible in comparison with the resistances of the 

 standard and tested conductors, the addition of the " secondary test- 

 ing-conductor" becomes valuable, even if it be only arranged to give 



a rough approximation to the condition arryr "op = * > smce xt wul 



* This of course is equivalent to SPT' : SP : : S'QT : S'Q, and means that the 

 secondary conductor is to be divided by one galvanometer electrode in the same 

 proportion as the primary is divided by the other. 



Phil. Mag, S. 4. Vol. 24. No. 159. Aug. 1862. M 



