IRON AND STEEL IN A ROTATING MAGNETIC FIELD. 
721 
that the rate of cutting lines of force during that time is uniform. For the remaining 
3 - revolution, the point is travelling along the lines of force. A reference to the hg. 3, 
illustrating this distribution, will show that such a distribution is very approximately 
the actual condition. 
Fig. 4. 
Let QP Q'P' be a plate in the armature, fig. 4, and let ABCD be a section of this 
plate at some point QQ’ between G and P, this part being covered by the pole piece 
and PK being between the pole pieces. 
Let the thickness of the plate AB = 2 cl, and let the diameter GH = 2 rad, and let 
the angle subtended by the pole piece = 120 °. In the samples used, m has a value 
of 150 to 200. 
In any section QQ' the path of the current induced in the plate by its revolution 
in a magnetic field parallel to the plane of the plate, will be approximately rectangular 
and similar to ABGD. 
Let ON = x, and let abed be the path of the current through a point in OF at a 
distance 2 from O. 
Then the length of the path 
= 4 2 + 4 mz 
QN 
QO 
42 1-f m 
v /(mW - * 8 ) 
mcl 
Let the thickness of the element be dx, and the breadth along be — dz. Then 
breadth along ab — mdz. Let p = specific resistance of the metal in ohms. 
Then the resistance of element 
p ( 1 , y/(vi~d : - \ 4.p / 7 i / o 7.) o\ 
= r 7 - Y m - --- = - r j — 7 - {d + m v wrd 1 — x~). 
dz . dx ' m mcl j rn . d. dz . dx v 7 
Let the induction across diameter of plate = B. Then the induction in the air 
gap = B assuming a distribution of magnetisation as above. 
And according to the previous assumption the induction at right angles to tire 
g j) 
tangent at any point in the path as far as the line OP will be also = 
7r 
4 z 
MDCCCXCVI.—A. 
