PRACTICAL STANDARDS FOR ELECTRICAL MEASUREMENTS. 215 



and so the value of M for the particular values of 2 A and 2 a given 

 above, viz. 21-02772 and 13-01451 can be calculated. When this is done 

 we find 



M= 18037-51 inches. 

 =45814-45 centimetres. 



and this was the value of M which we employed in our final determina- 

 tion, after allowance had been made for the effect of the central brush, as 

 will be described further on. 



The accuracy of the preceding calculations was tested in the fol- 

 lowing way. Values of 2 A and 2a, differing slightly from those em- 

 ployed by Mr. Rhodes, were selected, and by means of the formula for 



-— the proportional change in M was determined by Mr. Twyman. Then 



M 



the value of M for these changed values of 2 A and 2 a, was calculated by 



the authors from a new formula involving an elliptic integral of the third 



kind.i 



The centre brush consists of a tube, 0-135 inch outside diameter, 

 which projects into an axial hole in the disc of 0-144 inch diameter. 

 Oontact with the edge of the disc is made by three small tangential 

 phosphor bronze tubes lightly pressed on it, at points separated by 

 angular distances of 120\ Through all four tubes a small stream of 

 mercury is kept flowing, as this is found to greatly diminish the disturbances 

 caused by variations in the thermo-electric effects ; and the employment 

 of three brushes at the circumference, as suggested by Rowland, eliminates 

 small errors due to imperfect centering of the coil and disc. 



To prevent the mercury which drops out of the central tube-brush 

 touching the disc at a larger radius than that of the hole in its centre an 

 ebonite boss is cemented to the disc, and this causes the mercury to drop 

 away quite clear of the metal of the disc. 



If we take as the effective outside diameter of the central tube 0-139 

 inch, that is the mean of 0-135 and 0-144 inch, calculation shows that tho 

 coefficient of mutual induction is reduced by 4-50 centimetres, so that 

 finally we have 



M= 45809 -95 centimetres.. 



As the allowance for the central brush only diminishes M by one part 

 in ten thousand it is clear that, for that degree of accuracy, an error of a 

 few per cent, in estimating the diameter of the central brush is of no 

 consequence. 



The method of making the observations was the same as that described 

 in the papers on the Cardiff apparatus read before Section A of the British 

 Association at Nottingham and Oxford (vide Report of the Committee 

 on Electrical Standards, Appendices 1893 and 1894). The use of an 

 extremely sensitive Ayrton-Mather galvanometer of the d'Arsonval type 

 materially facilitated the readings being taken. Two such narrow coil 

 galvanometers were specially constructed by Mr. Mather himself for use 



• An account of this new formula as well as of that for -- will shortly be pub- 



M. 



lished by Professor Viriamu Jones. 



