318 
PROFESSOR HELE-SHAW AND MR. ALFRED HAY 
Fig. 33 (Plate 20) is a field diagram for a hollow square cylinder ; the shielding 
effect is seen to be very powerful. 
Fig. 35 gives approximately the field distribution between the tapered pole-pieces 
of an electro-magnet ; and fig. 36 is intended to illustrate the pull of an electro-magnet 
on an armature. 
The next few diagrams relate to cases of practical interest and importance, and 
serve to show how the stream-line method may be made to yield results of great 
interest to the electrical engineer. Figs. 37 and 38 (Plate 21) show an ordinary 
Siemens shuttle-wound armature—such as is used in connection with telephone call 
apparatus—in two positions. The direction of the torque acting on the armature in 
its second position may he at once inferred from an inspection of the diagram. It 
is also interesting to note the leakage lines outside the armature. 
Figs. 31 and 39 relate to a toothed-core armature. Fig. 34 shows the symmetrical 
field distribution obtained when the teeth are well under cover of the pole-pieces. 
The induction in the air-gap consists of alternate maxima and minima, and the lines 
are only slightly curved at the level of the teeth. Below this level, they curve 
round sharply to enter the flanks of the teeth. The permeability of the core is 
assumed to be 100. 
It- is evident that a diagram of this description furnishes a means or calculating 
the line-integral of magnetic intensity along a line drawn from the polar surface to 
the base of a tooth, provided the total flux per tooth and the permeability are 
known. 
In fig. 39 we have the same armature, but now shown emerging from under the 
polar surface. The fringe of the magnetic field is clearly exhibited. The distribu¬ 
tion of the lines in the core below the level of the bases of the teeth is not correct. 
In an actual armature, the lines in this region, after passing into the core, would turn 
sharply to the left, proceeding towards the neighbouring pole-piece. In the stream¬ 
line diagram, on account of the straight-line boundary on the left, the lines are forced 
to go on in a downward direction. Yet it is curious to note the strong twist towards 
the left which the lines exhibit immediately after leaving the teeth, and which 
indicates the direction in which the flow would naturally continue if not subject to 
the artificial constraint just mentioned. 
An objection which might be raised in connection with some of the diagrams is the 
fact that in those cases where the induction varies from point to point, the permea¬ 
bility in any actual magnetic substance is also variable. In so far as this is the case, 
of course the stream-line diagrams do not afford a rigid solution of the problem. But 
it must be remembered that there are many cases in which the magnetic intensity 
is either so weak or so strong that the permeability does not vary greatly within 
certain limits of the induction. For all such cases, the solution obtained by the 
stream-line method is a very close approximation. And even in cases where 
considerable variations of permeability occur, the stream-line method affords, at any 
rate, the first rough approximation to the solution of the problem. 
