620 Mr. J. Viriamu Jones [May 24, 



the measurements, is, however, some indication of the accuracy with 

 which the individual measurements in the machine can be made, even 

 in the case of a coil of insulated wire. 



My coil, then, is faulty on account of this ellipticity. I have not 

 yet calculated the possible error due to this cause ; it cannot be very 

 great. How much it is only calculation can settle ; and the calcula- 

 tion is not without difficulty. But this, after all, is only a question 

 of my apparatus, and does not affect the general question of the possible 

 accuracy of the method. 



A more solid metal frame might, no doubt, be turned true to the 

 accuracy required, and if so turned might then be measured with the 

 requisite accuracy in the Whit worth machine. 



A still further improvement may be made by making the coil 

 frame of insulating material, say paraffined marble, and winding on 

 it naked wire instead of silk-covered wire. The radius might then 

 be measured with certainty to something much better than 1 part in 

 10,000. The use of a coil with a single layer of wire instead of 

 many layers greatly facilitates the determination of the mean radius. 

 It, of course, necessitated the finding of a new formula for the 

 coefficient of mutual induction. 



This I obtained by direct integration of the general integral for 

 the case in point, viz. a circle and coaxial helix. The coefficient of 

 mutual induction is given us as a sufficiently converging series 

 involving elliptical or quasi-elliptical integrals. 



We may, then, in the result conclude that, though I cannot 

 guarantee my own coefficient of mutual induction as correct to 

 1 part in 10,000 till I have calculated the effect of the coil ellipticity, 

 it lies well within the resources of our mechanical engineers to make 

 a coil and disc free from uncertainty to this degree of accuracy. And 

 if this be so I am warranted in stating that a resistance can be 

 measured in absolute units to 1 part in 10,000. 



Now, in the Order in Council, from which I quoted in the early 

 part of my discourse, it is stated that in the use of the ohm standard 

 the limit of accuracy attainable is one-hundredth part of 1 per cent. — 

 i. e. one part in 10,000. Hence the Government gains nothing in 

 precision to compensate for the risk it has taken in adopting as unit 

 the resistance of a standard coil, which may vary from time to time 

 in consequence of changes in the physical condition of the coil. 



There is no valid ground left for adopting as ultimate unit any 

 other unit than the absolute unit itself. We have not in our electrical 

 standard legislation given full credit to the mechanical engineer for 

 what he can do for us. He can make a machine that will measure 

 resistance in absolute units with a precision as great as — I might even 

 say greater than — that with which the Government is prepared to 

 guarantee its comparisons. Such a machine ought to be at work in 

 the Board of Trade laboratory, in order that there may be opportunity 

 from time to time, at regular intervals, to measure the Government 

 coil or coils in absolute units. It is necessary that this should bo 



