RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 
37 
brought about by using a brush consisting of a single wire perforated by a channel 
through which a constant flow of mercury was maintained. With regard to the 
variation of speed, Prof. Jones was of opinion that “ no time or trouble spent in 
securing a constant speed will be lost for the purpose in view.” It was suggested 
that the standard coil should consist of a single layer of wire, as the mutual 
inductance of the coils and disc could then be calculated with great accuracy. 
The apparatus made by Messrs. Nalder Bros.* for Prof. Callendar, who was then 
at the McGill University, Montreal, was, in general arrangement and dimensions, 
similar to Prof. Jones’s Cardiff apparatus. Contact with the edge of the disc was 
made by three small tangential phosphor-bronze tubes lightly pressed on it, at points 
separated by angular distances of 120 degrees, and through these tubes mercury 
flowed on to the edge of the disc. The employment of three brushes was suggested 
by PtOWLAND to eliminate small errors due to imperfect centering of the coil and disc, 
and was a distinct improvement. The possible sources of error were considered, and 
in a paper by Prof. Ayrton and Prof. Jones* an equation is given showing the rates 
of variation of the mutual inductance of the coil and disc with changes (l) in the 
radius A of the coil, (2) in the radius a of the disc, and (3) in the axial length 2x of 
the helix. The equation given is 
^ = 1 '246 ^ +2'346 — -(T0997 —. 
M A a x 
The value of M was 45814'5 cm., of A 267039 cm., and of a 16‘5354 cm., from which 
it is readily calculated that an error of 0'002 cm. in the measurement of the diameter 
of the disc introduced an error of nearly 5 parts in 100,000 in the value of M. An 
error in the measurement of the diameter of the coil of 0'002 cm. introduced an error 
of 14 parts in 100,000 in the value of M. 
It will be seen that the experimental difficulties experienced by observers using the 
Lorenz method were mainly due to thermo-electric troubles at the brush contacts, 
want of uniformity of speed, and the effect of terrestrial magnetism. There are no 
difficulties attendant on the accurate evaluation of the mutual inductance of a coil 
and disc if the dimensions are accurately known. If a single layer coil is used, its 
dimensions may be determined with great accuracy ; if a coil of many layers is 
employed, it appears best to follow Lord Rayleigh’s practice and use two coils at a 
considerable distance apart in order that errors of measurement of the radius of a coil 
may be rendered negligibly small. 
The Lorenz apparatus described in this paper was designed in 1908, our object being 
to determine a resistance in absolute measure with a precision within a few parts in 
a hundred thousand. The apparatus described eliminates the effect of terrestrial 
magnetism and largely reduces thermo-electric troubles at the brush contacts by the 
employment of two discs of equal diameters. The coils are of one layer only and 
* ‘British Association Reports,’ 1897. 
