106 EEPORTS ON THE STATE OF SCIENCE. 



APPENDIX. 



On Methods of High Precision for the Comparison of Eesistances. 



By F. E. Smith. 



( From the National Physical Laboratory.) 



The object of the author is to give a brief account of the high precision 

 methods used at the National Physical Laboratory for measuring standard 

 resistances. Up to and including the year 1 903, the standard unit coils 

 of the British Association were compared by Carey Foster's method, the 

 Fleming circular wire bridge being used. The probable error of such 

 comparisons is of the order 0-00 1 per cent. The build-up of a 10-ohm coil 

 from the unit was very conveniently effected by a process suggested by 

 Lord Kayleigh.' Three 3 -ohm coils are arranged in parallel, and their 

 combination value determined by comparison with a unit resistance. 

 They are then placed in series ; by the addition of a unit coil to the series 

 formation, the ' build-up ' is complete. The probable error of this build- 

 up is also small, but when combined with the error of comparison of 

 nominally equal coils, the observed value of a 1 to 10 ratio may be in 

 error by 0-002 per cent. The use of this ratio for the evaluation of 

 resistances of 10" units results in a possible error of n x 0-002 per cent. 



The resistance standards of the National Physical Laboratory are of 

 three kinds — mercury, platinum-silver, and manganin. When comparing 

 standards of mercury and of platinum-silver, comparatively small currents 

 must be employed, because the temperature-coefficients of these materials 

 are large and the resistances are surrounded by bad thermal conductors. 

 The manganin coils are wound on brass cylinders, have small temperature 

 coefficients, and may be immersed in oil ; the maximum permissible 

 current is therefore much greater. The accuracy of all methods of com- 

 parison is directly proportional to the current employed, from which it 

 follows that for all building-up processes, manganin coils are to be 

 preferred. The question of preference for permanency is not discussed in 

 this paper. 



In order to compare the various methods of measurement it is 

 necessary to give the formula for sensitiveness. In presenting these 

 latter I do not wish to suggest that they are new. The subject has been 

 previously treated by Mr. O. Heaviside,^ Mr. T. Gray,^ Lord Rayleigh,* 

 Professor Schu&ter,^ Professor A. Gray,*' Dr. Ja^ger,^ Dr. St. Lindeck, 

 Diesselhorst, and others, and some of the formulae are given in text-books. 

 In the present paper the considerations of many of these writers have been 

 extended. Professor Schuster first pointed out that it is the heating of 

 the conductors which puts the limit to a measurement of resistance, and the 

 formulae derived by him are in terms of the current conveyed by the resist- 

 ance to be measured. Dr. Jaeger has recently discussed the question of 

 sensitiveness from the same point of view, and in this paper the subject is 

 similarly treated. The formulae may be derived in several ways, as will be 

 seen on reference to the authorities quoted. Many of these ways are long, 



' PMl. Trans., 1883, 174, 310. See also B.A. Report, 1883. 



» Phil. Mag., 1873, xlv., p. 114. » Ibid., 1881, xii., p. 283. 



* Proc. Boy. Soc, 1891, 49, 203. > Phil. Mag., 1894, p. 175. 



* Absolute Measurements, vol. i., p. 331. 



' Zeitschr. Instrumentenlt., March 1906, 26, 69. See also Jaeger, St. Lindeck, 

 and Diesselhorst, Zeitschr. Instrumentenk., 1903, 33. 



