ON STANDARDS FOR USE IN ELECTRICAL MEASUREMENTS. 



127 



It remains to consider the accuracy with which the coefficient of 

 mutual induction of tlie coil and disc is known. 



To calculate this coefficient we must know the radius of the disc and 

 the mean radius of the coil. The circumference of the disc is a suf- 

 ficiently true circle, the disc having been ground true in place. The 

 measurement of its diameter presented no difficulty. It was determined 

 on my Whitworth measui'ing machine to the ten-thousandth of an inch. 



The mean radius of the coil cannot be determined with the same 

 accuracy ; but I believe that it is known to the thousandth of an inch. 

 The coil consists of a single layer of silk -covered wire wound in a screw 

 thread cut on a brass frame. It was measured along eighteen diameters 

 in the Whitworth machine with the following results : — 



•0158 



These measures clearly show that the coil is elliptical in section, the 

 difference between the major and minor axes being about -008 inch, or 

 about one part in 1,300. 



In considering the possible effijct of this ellipticity on the result, it 

 must be borne in mind that the formula Il=M?i implies that the coil is 

 circular. The true formula is 





aUda 



-where a,, and a, are the distances from the centre of the disc at which 

 the internal and external brushes are applied, and H is the magnetic force 

 at a distance a from the centre when unit current is passing through the 

 coil. 



This is an unpleasant integral for an elliptical coil, and it has not yet 

 yielded to persuasion. It is, however, satisfactory to note that as in my 

 iippai-atus the brush radius makes but a small angle with the minor axis 

 (about 15°), I am, in so far as the ellipticity of the coil affects matters at 

 all, underestimating the integral, and heiice undei-estimating the inter- 

 national ohm. Any correction for ellipticity hereafter calculated will 

 make the value of the international ohm deduced from my observations 

 nearer to and not further from the true ohm. 



It is further to be noticed that the formula R = M}i applies only if 

 there is exact coincidence of the axes of the disc and coil. It has been 

 customary to consider the adjustment for centre as of secondary import- 

 ance in Lorenz's method. It would be so if the formula R=M7i were 

 applicable when the centres of coil and disc do not coincide, for a slight 

 displacement only affects the coefficient of mutual induction to a secondary 



