92 
MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
is nearly the mean of the separate potential differences and the error of setting is 
about the same as when the brushes are placed in series. With the brushes in parallel 
it is better, however, to include a resistance in series with each brush before connecting 
the brushes together, for then any difference of resistance between the brush contacts 
is rendered negligibly small. The observed differences of potential due to displacements 
when the brushes were placed in parallel are plotted in fig. 22, and the equation of the 
resulting curve is y = O' 132a; 2 where y is the change in voltage in parts in 100,000 
produced by a displacement of x mm. from the coaxial position. An identical curve 
results when the brushes are placed in series. It is clear that the observations enable 
the coil and shaft to be set coaxial within less than 0'1 mm. and an error of this 
amount introduces an error in the resistance measurements of about I part in 
100,000,000. 
Similar observations were made when one of the cylinders was rotated about a 
vertical axis P. The results are plotted in fig. 23. The equation when the brushes 
are placed in series or in parallel is y = 3'5a; 2 where y is the change in voltage in parts 
in 100,000 produced by a rotation of x°. Thus, if x = 0'1° (a large amount) the error 
introduced is 4 parts in 10,000,000. 
(3) Setting of the Coils on opposite Sides of a Disc to he at the same Mean 
Distance from the Contact Circle of Segments and Brushes. 
The current through the coils on cylinder No. 1 was caused to circulate in the 
same direction as the current through the coils on cylinder No. 4, and the resulting 
flux through disc No. 1 was therefore in the same direction as that through disc No. 2. 
The galvanometer circuit was completed without the inclusion of the standard 
resistance It, and reversals of the current through the coils were made in the usual 
manner to eliminate all effects but that due to a difference of flux through the discs, 
caused by the current. In general there was a want of balance and in such case the 
distance of one of the coils was changed until balance was secured or very nearly 
so. With care equality could be obtained within about 2 parts in 100,000, but in 
general we were content to ensure equality within about 25 parts in 100,000. This 
is equivalent to equality, within about 0'07 mm. of the mean distance of the No. 1 
coils from No. 1 disc, and that of the No. 4 coils from the No. 2 disc. A similar 
setting of the No. 2 and No. 3 coils was next made, and afterwards the current 
through coils Nos. 1 and 3 was made to circulate in the opposite direction to that in 
coils Nos. 2 and 4. If all the coils are at equal distances from the discs, there is 
now no deflection of the galvanometer and the positions of coils Nos. 1 and 4 or of 
Nos. 2 and 3 are changed by equal amounts until a balance is secured. The coils on 
all of the cylinders are thus placed at the same mean distance, within about O'l nun., 
from the brush contact circles and such equality is sufficient. 
