Prof. Thomson on the Measurement of Electric Resistance. 151 



Further, it is clear that by making the testing-conductors of incom- 

 parably greater resistances than any that can exist in the connexions 

 at S, S', T, T', which can easily be done if these connexions are 

 moderately good, the error arising from such imperfections as they 

 must present may be made as small as is required*. To de- 

 monstrate the above and to form an accurate idea of the operation of 

 this method, it is necessary to investigate the difference of potentials 

 (electromotive force) produced between Q and P, when a stated dif- 

 ference of potentials, E, is maintained between S and T'. 



Let SS', TT r denote the resistances between the marks, on the 

 standard and tested conductors respectively. Let GPH, GP, PH, 

 KQL, KQ, QL denote the resistances of the testing- conductors and 

 their parts according to the diagram, implying that 



GPH=GP + PH, and KQL = KQ + QL. 



Let SG, HT', S'K, LT be the resistances in the connexions at the 



SG-f GPH + HT' be denoted by SPT', 

 and 



S'K + KQL-fLT ,-, „ „ S'QT; 



and let S'BCT denote the resistance between S' and T composed of 



* This method may be readily applied to Siemens's mercury standards (see 

 Phil. Mag. Jan. 1861, or Poggendorffs ' Annalen,' 1860, ISTo, 5), by introducing 

 platinum wires through holes in the glass tube near its ends, as electrodes for 

 the testing-conductors, and wires or plates of platinum at the ends, as electrodes 

 for one pole of the battery and for connexion with the conductor to be compared 

 with it, respectively. It will then not be the whole line of mercury from end 

 to end, but the portion of it between the two platinum wires first mentioned, that 

 will be the actual standard. The objection against the use of mercury as a 

 standard of resistance, urged by Matthiessen, that the amalgamated copper 

 electrodes which Siemens found necessary to give very perfect end connexions 

 must render the mercury impure and increase its resistance sensibly after a 

 time, is thus completely removed. It must be shown, however, that different 

 specimens of commercial mercury, dealt with in the manner prescribed by Sie- 

 mens, to remove impurities, shall always be found to have equal specific re- 

 sistances, before his proposal to produce independent standards by filling gauged 

 tubes with mercury can be admitted as valid. But the transportation and 

 comparison of actual standards between different experimenters in different 

 places is, and probably must always be, the only way to obtain the most accu- 

 rate possible common system of measurement : and when a proper mutual un- 

 derstanding between electricians and national scientific academies, in all parts 

 of the world, has been arrived at, as it is to be hoped it may be soon, through 

 the assistance of the British Association and Royal Society if necessary, the 

 use of definite metallic standards, whether the liquid mercury as proposed by 

 Siemens, on the one hand, or the solid wire, alloy of gold and silver, on the 

 other hand, proposed by Matthiessen (Phil. Mag. Feb. 1861), would be essen- 

 tial only in the event of all existing standai'ds being destroyed. 



Weber's absolute system is often referred to as if its object were merely to fix 

 standards of resistance, and the difficulty and expense of applying it indepen- 

 dently have been objected to as fatal to its general adoption. In reality its 

 great -value consists in the dynamic conditions which it fulfils, with relation to 

 electro-magnetic induction, and to the mechanical theories of heat and of electro- 

 chemical action. But it most probably will also be much more accurate 

 than any definite metallic convention, for the re-establislunent of a common 

 metrical system, in case of the destruction of all existing standards. 



