150 



Royal Society :■ 



have avoided being led into error, by repeating the experiment several 

 times with slightly varied connexions ; but I have in consequence 

 sometimes altogether failed to obtain results by either Wheatstone's 

 or any other method hitherto practised, as for instance in attempting 

 to measure the electric resistances of a number of metallic bars each 

 6 millimetres long and 1 millim. square section, which were put into 

 my hands by Mr. Calvert of Manchester, being those of which he 

 and Mr. Johnstone determined the relative thermal conductivities in 

 their investigation published in the Transactions of the Royal Society 

 for March 1858. I have thus been compelled to plan a new method 

 for measuring electric resistances in which no sensible error can 

 be produced by uncertainty of the connexions, even though made 

 with no extraordinary care. 



Let AB and CD be the standard and the tested conductors respect- 

 ively Let the actual standard of resistance be the resistance of the 

 portion of AB between marks * S, S' on it, and let it be required to 

 find a portion TT' of CD which has a resistance either equal, or 

 bearing a stated ratio, to that standard. 



Join BC either by direct metallic contact between them, or by 

 any ordinarily good metallic connexion with binding screws or other- 

 wise ; and join the two electrodes of a galvanic element to their other 

 ends, A, D. Let GPH and KQL be two auxiliary conductors, 

 which, to avoid circumlocutions, I shall call the primary and the 



AS 

 G 





CT 



T 



T'D 



II 



P 



secondary testing-conductors respectively, with their ends applied to 

 the marked points S, T', S', T. Let P and Q be points in these 

 conductors to which the electrodes of the galvanometer are to be 

 applied. 



It is easilv seen, and will be demonstrated below, that if the re- 

 sistances of the testing-conductors be similarly divided in Q and P, 

 and if their ends be in perfect conducting communication with the 

 marked points of the main line to which they are applied, the con- 

 dition that the galvanometer indication may be zero is that the ratio 

 of the resistances of the standard and tested conductors must be the 

 same as that in which the auxiliary conductors are each divided. 



* On the same principle as the "metre a traits" instead of the "metre a 

 bouts" for a standard of length. 



