36 
MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
the dimensions of the coil and disc. The results are given of some calculations of the 
mutual inductance M of a coil of radius A and circle of radius a. The rates of 
variation of M with change in the diameter of the coil are calculated for various 
values of ci/ A, and it is shown that when a/A increases in value the rate of variation 
of M with change in a and also of A increases. Further, it is shown that, by using 
two coils separated to a considerable distance, it is possible so to proportion the radii 
and the distance apart of the coils that the error of mean radius of the coil does not 
affect the result; the diameter of the disc and the distance apart of the two coils are 
then the important quantities. Lord Rayleigh remarks: “ It is clear that M 
vanishes both when A is very small and when it is very large ; from which it follows 
that there must be some value of A for which the effect is a maximum and therefore 
independent of small variations of A.” The same is, of course, true for the disc; by 
suitably proportioning the dimensions, the error of mean radius of the disc may be 
rendered negligibly small. This fact led Mr. A. Campbell* to design a standard of 
mutual inductance in which the radius of the secondary is not required to be known 
with great precision ; it also guided us in fixing the dimensions of our coils and discs 
so that the diameters of the latter need not be accurately known. 
In the first and second series of experiments carried out by Lord Rayleigh the 
inductance coils were situated nearly in the plane of the revolving disc as in Lorenz’s 
original use of the method. In the third series the coils were separated from the 
disc to such a distance as to render the accuracy of the results practically independent 
of the mean radius of the coils. It is right to say here that in the design of the 
apparatus described in this paper we were largely influenced by Lord Rayleigh’s 
investigations and by Mr. Campbell’s work. 
Of the experimental difficulties noted by Lord Rayleigh the more important are : 
(l) troublesome thermo-electric effects at the sliding contacts notwithstanding that 
the edge of the disc was amalgamated with mercury, and (2) effects due to terrestrial 
magnetism. As before stated, both of these effects are eliminated by taking a 
sufficient number of readings with reversals of the current, but it is evident that good 
readings cannot be taken if the magnitude of the effects is subject to sudden 
fluctuation. 
In 1890 Prof. J. V. Jones! made a number of suggestions towards a determination 
of the ohm. He had made a number of experiments in his laboratory at the 
University College, Cardiff, and stated that he was of opinion that, if apparatus were 
constructed on a large scale and with a certain perfecting of detail, a single set of 
observations would give a result accurate within 1 part in 10,000. In the electrical 
observations the principal difficulties which he had contended with were: (l) varia¬ 
tions in the thermo-electric effects at the brush contacts, and (2) variations in the 
rate of rotation of the disc. A considerable reduction of the first difficulty was 
* Campbell, ‘ Roy. Soc. Proc.,’ A, vol. 79, p. 428. 
f Paper read before the British Association, 1890. 
