88 
MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
indicated by a telephone, and readings could be repeated within about | 0'01 mm. 
Each cylinder was adjusted in position until the three readings were identical and the 
axes of the cylinders were then approximately parallel to the axis of the shaft. The 
method was sensitive, but irregularities in the thrust-bearing surface of the shaft 
must introduce errors which are difficult to eliminate. 
(2) Settmg of the Coils to be Coaxial with the Shaft. 
(a) Mechanical Method .—A direct-reading spring indicator was used to measure 
the perpendicular distance of the inner surface of each marble cylinder from the 
surface of the shaft, and each cylinder was adjusted in position until the readings at 
all points were practically identical. The indicator was sensitive to a difference of 
about 0'02 mm. and the adjustment of a cylinder occupied only a few minutes. If 
the inner surface of a cylinder is not coaxial with the coil, then of course an error is 
introduced. 
( b) Electrical Method. —The calculations we have made give only the mutual 
inductance of the coils and the brush contact circles, and it is not possible for us to 
give other than general diagrams indicating the manner in which the intensity of the 
magnetic field varies along the radius of a circle and other diagrams indicating the 
difference of potential between the axis and any point on a radius which is produced 
by the rotation of that radius. Such diagrams will, however, serve to explain the 
electrical method of setting the coils. 
In fig. 21 (a), DD' represents the plane of rotation of one of the discs, and BIT the 
position of the brush contacts. The intensity of the magnetic field produced by a current 
in the coils on both sides of the disc is practically zero at BB' and changes in sign as 
we pass radially outwards from the disc. The form of the intensity curve is roughly 
shown by the curve EFGH. When the disc rotates, the difference of potential 
between the centre O and any point A on a radius increases with increase of the 
distance OA to a maximum value at B and B', but afterwards it decreases. The 
potential difference is given by 2 7 m j B?/ dy where OA = y and B is the magnetic flux 
at a distance y from O. The potential difference can be represented as an area if the 
flux he multiplied by y before it is plotted. The area enclosed by the line DD' and 
the curve KCLM shows roughly how the potential difference varies; thus the 
difference of potential between O and A is represented by the area OCA. Areas to 
the left of DD' are counted as positive and those to the right are counted as negative. 
In our apparatus the brush and segment at B are insulated from those at B' and it is 
therefore possible to measure" the difference of potential between the segments and so 
determine whether the field produced by the current in the coil is symmetrical with 
respect to the axis of the shaft. Without the insulation of the segments, i.e., by the 
use of a disc alone as in the old forms of apparatus, eddy currents in the disc produce 
disturbing effects. 
