RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 
105 
sign and must be quite negligible apart frdm a constant error in the clock rate. But 
this latter is clearly impossible in the case of a standard clock the error of which is 
taken daily. The daily rate was small and time comparisons were made with another 
standard clock the daily rate and error of which were also known. At any hour of 
the day the difference between the clocks agreed, within the possible error of the 
observations, with that calculated from the errors and rates of the clocks. This 
agreement is evidence that both clocks were going uniformly or that there was a 
similar want of uniformity in the going of both. Such similarity is very improbable. 
As an additional precaution the resistance observations were made at times ranging 
from 9 a.m. to 6 p.m. but no systematic differences were observed. 
The possibility of error due to our coils being of wire of finite section has not been 
overlooked. The formula developed by J. Viriamu Jones gives the mutual inductance 
when the coils can be treated as infinitely fine helical filaments, and small corrections 
may be necessary. The case of the coils of the Ayrton-Jones current balance was 
examined by Dr. G. F. G. Searle, F.R.S., # who showed the correction to be negligible 
in that instrument. In the present instance, no special treatment is necessary as the 
mutual inductance calculations made during the work are sufficient to show that no 
correction need be made. To illustrate this, consider the mutual inductance M of a 
helical filament coinciding with the axis of the wire and the nearer brush contact 
circle. Next consider two helical filaments of the same diametral dimensions as the 
previous one, but let one helix be nearer to, and the other farther from, the circle by 
0’25 mm. Table X. shows that the mean mutual inductance of these two helical 
filaments and the circle is greater than that of the central helical filament by 2 parts 
in 1,000,000. The wire with which the coils are wound is about 0'557 mm. in diameter, 
so that strictly we ought to consider filaments 0'28 mm. away from the central one, 
but in view of the result obtained we think it unnecessary to calculate the small and 
certainly negligible difference. Next consider two circles coaxial with the disc and at 
equal distances from it, and let the diameter of one circle be greater than that of the 
other by 0'556 mm., the mean diameter being 35’88 cm. At distances of 7'3135 cm. 
and 23'3150 cm. the mean mutual inductance of these two circles and the circumference 
of the disc does not differ by more than 2 parts in 1,000,000 from the mutual inductance 
of the disc and circle of radius equal to the mean of the two previous ones (see 
Table XVI.). The coil of wire may therefore be treated as a helical filament. 
The determination of a resistance in absolute measure is therefore subject to a number 
of small errors, the greatest of which is associated with the determination of the mean 
radius of the coils. This error is probably not greater than 1 part in 100,000, and if 
the remaining errors were all of the same sign it is unlikely that their sum would 
exceed another part in 100,000. 
We believe, therefore, that the absolute measurements of resistance which we have.- 
made are correct within 2 parts in 100,000. 
* ‘ Phil. Trans.,’ A, 207, pp. 541-514. 
VOL. CCXIV.—A. 
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