720 
PROFESSOR F. G. BAILY ON THE HYSTERESIS OF 
Calculation of Eddy Currents. 
As the armature consists of a row of plates insulated from each other, in which the 
lines of induction lie in the plane of each plate, the problem is reduced to the 
estimation of the eddy currents induced in a thin plate rotating on a central axis 
perpendicular to the plane of the plates in a magnetic field, the direction of which is 
at all points parallel to the plane of the plate. The distribution of the lines of 
induction in the plate is a matter of some uncertainty, and will vary slightly with 
different degrees of magnetisation, owing to the variations in the permeability. Since 
it will be shown, however, that the effect of eddy currents is but small, an approxi¬ 
mately accurate distribution will be assumed that will allow of mathematical 
treatment. 
As it has been shown that even at the ends the lines of force do not pass from 
plate to plate, it will be assumed that their direction is entirely in the plane of the 
plate. 
Fig. 3. 
Since the magnetic reluctance of the air gap is considerably higher than that of the 
armature or pole pieces, the distribution of the lines of force in the air gap will be 
sensibly uniform and radial. It will be assumed that the whole of the lines of force 
pass in this way to the armature, and the fringe from the sides of the poles will be 
neglected. This assumption will somewhat increase the value of the eddy currents, 
as if gives a density in the outer layers slightly in excess of the actual value. 
Inside the plate the paths of the lines will be curved, owing to the curve of the 
circumference and the space occupied by the spindle. Let a distribution be assumed 
such that the rate of cutting lines of force is proportional to the distance from the 
centre (neglecting the hole), and such that the portion of each revolution during 
which any point is cutting lines of force is the same, viz., § of each revolution, and 
