ON LINES OF INDUCTION IN A MAGNETIC FIELD. 
317 
centric shield. It is interesting to compare this latter stream-line diagram with the 
theoretical diagram of fig. 19 ; the agreement in the shape and general distribution 
of the lines between the two cases is very striking. 
Fig. 21 (Plate 17) is a theoretical diagram for an elliptic cylinder of permeability 
100, and the ratio of whose axes is 2 : 1, placed in a uniform field with the major axis 
of the elliptic section of the cylinder making an angle of 45° with the impressed 
field. Fig. 22 gives a stream-line diagram for a cylinder of the same permeability, 
but the ratio of whose axes is 3:1. Fig. 23 is a similar diagram for a very thin 
elliptic plate, and fig. 24 relates to the hollow cylinder of fig. 16, but here turned 
through an angle of 45°. It will be noticed that fig. 24 confirms the theoretical 
result that the field in the interior of a hollow elliptic cylinder bounded by two 
confocal surfaces is uniform if the impressed field be uniform. 
We have hitherto dealt with cases which may be treated theoretically as well as 
experimentally. But the number of such cases is very limited, and the vast majority 
of two-dimensional magnetic problems are beyond the powers of analysis. It is in 
such cases that the stream-line method employed by us becomes a powerful weapon 
of research. Figs. 25-28 relate to cylinders of rectangular section, figs. 25 and 26 
giving the field distributions for cylinders of square section placed with one of their 
diagonals at 45° to the field and parallel to it respectively. In fig. 25, where the 
width of the cylinder remains constant along the direction of the impressed field, 
we notice that the lines inside the cylinder are concave outwards ; in fig. 26, on 
the other hand, where the cylinder tapers rapidly as we proceed along the field, the 
curvature of the lines presents a convexity outwards. This suggests that an inter¬ 
mediate form between the two might be found for which the lines exhibit neither 
convexity nor concavity, are straight; and, as a matter of fact, we know of one 
such intermediate form—a circular cylinder. Fig. 26 closely corresponds to the 
theoretical case which Dr. C. H. Lees has recently succeeded in working out analyti¬ 
cally in connection with a problem in heat conduction.* Figs. 27 and 28 are intended 
to illustrate the effect of increasing the length of one of the sides of the rectangular 
section while keeping the other constant. We know from theoretical considerations 
that this has the effect of reducing the de-magnetising factor, and thus increasing 
the flux through the cylinder. This point is very clearly brought out by a comparison 
of figs. 25, 27, and 28. 
Figs. 29 and 30 (Plate 19) show the magnetic fields corresponding to a cylinder of 
triangular section in two different positions. 
Figs. 31 and 32—a solid circular cylinder inside a hollow square one, and a solid 
square one inside a hollow circular one—are interesting in connection with the problem 
of magnetic shielding. Both these diagrams are slightly disfigured by air-bubbles. 
These latter are extremely difficult to get rid of, once they are allowed to reach a part 
of the field where the thickness of the liquid film varies. 
* ‘Phil. Mag.,’ February, 1900, p. 225. 
