DRS. J. AND E. HOPKINSON ON DYNAMO-ELECTRIC MACHINERY. 
333 
A 3 the area of core of magnet, l 3 the total length of the magnets. All the tubes of 
induction which pass through the armature pass through the space A 3 and the magnet 
cores, and by our assumption there are no others. We now assume further that these 
tubes are uniformly distributed over these areas. The induction per square centi¬ 
metre is then in the armature core, -- in the non-magnetic spaces, ~ in the 
magnet cores; the corresponding magnetic forces per centimetre linear must be 
The line integral of magnetic force round a closed curve must be 
\Ai/ A 2 \Ag/ 
l x /(^) + 24^ + hf ( J*)- I n this approximation we neglect the force required to 
magnetise pole-pieces and other parts not within the magnet coils to avoid complica¬ 
tion. The equation of the characteristic curve is then 47 — ) -}- 2 — f 
\Ai/ "A 2 
This curve is, of course, readily constructed graphically from the magnetic property 
of the material expressed by the curve a==/ (a). In Sheet I. curve A represents 
x = the straight line B x=2l 2 ~, curve C x=l 3 f(^^~j, and curve D the calcu¬ 
lated characteristic. When we compare this with an actual characteristic E, we shall 
see that, broadly speaking, it deviates from truth in two respects : (1) it does not 
rise sufficiently rapidly at first; (2) it attains a higher maximum than is actually 
realised. Let us examine these errors in detail. 
(1) The angle the characteristic makes with the axis ot abscissae near the origin is 
mainly determined by the line B. We have in fact a very considerable extension of 
Fig. 1. 
the area, of the field beyond that which lies under the bored face of the pole-piece. 
The following consideration will show that the extension may be considerable. 
Imagine an infinite plane slab, and parallel with it a second slab cut off by a second 
