OX LINES OF INDUCTION IN A MAGNETIC FIELD. 
315 
to the experiment. Instead of this, the slide was taken to a place where it could be 
illuminated by strong daylight, and the exposure given to the sensitive photographic 
plate was of course correspondingly increased. Zinc templates of the shapes required 
were made, and by placing the template on the wax, the outline was cut with a 
sharp knife, and the particular well thus formed. In cases where the flow in the 
well was very slow, air bubbles became imprisoned, and could only be removed after 
great difficulty; in fact, in one or two cases—as will be seen in the photographs, figs. 
31 and 32 (Plate 19)—they could not be removed at all. 
Section II. 
(a) In order to test the applicability of the stream-line method to the solution of 
two-dimensional magnetic problems, it was decided to work out mathematically 
the case of an infinite cylinder of elliptic section placed in an originally uniform 
magnetic field with its major axis along the field, to plot the lines of magnetic 
induction corresponding to a permeability of 100, and to compare the diagram 
so obtained with a stream-line diagram. The theoretical diagram is given in fig;. 9 
(Plate 14) and the corresponding stream-line diagram in fig. 10. In making the com¬ 
parison, a greatly enlarged photograph of fig. 10 was prepared, and fig. 9, # which 
.was actually drawn to a much larger scale, was then superposed on it : the coinci¬ 
dence of the lines in the two diagrams satisfactorily established the soundness of the 
stream-line method. It may be noted, however, that slight local divergences along 
the elliptic boundary are clearly observable. Instead of the sharp refraction of the 
lines as they enter the elliptic cylinder in the theoretical diagram, we have in fig. 10 
a slight curvature at the ends of the otherwise perfectly straight lines crossing the 
ellipse. This feature is noticeable, to a greater or smaller extent, in all the stream¬ 
line diagrams accompanying the present paper. It is more marked in those cases 
where the difference between the thicknesses of the two liquid layers, i.c., the perme¬ 
ability in the corresponding magnetic problem, is greater. It is clear that the 
presence of the highly permeable cylinder disturbs the originally uniform distribution 
of the lines, and in order to effect a satisfactory comparison between the theoretical 
and the experimental diagrams, it became necessary to assign to the liquid layer an 
external boundary whose shape corresponded to that of a particular stream-line in the 
theoretical diagram. The boundary of the liquid in fig. 10 is clearly shown by the 
dark shadows on either side of the diagram, and the shape of their boundaries is the 
same as that of the outer stream-lines in fig. 9. The method by which the solution 
was obtained for the theoretical case will be found fully explained in the mathematical 
appendix to the present paper. 
(b) In most of the succeeding diagrams the boundaries of the liquid layer are 
straight lines. Interpreted magnetically, this means that the diagram gives the 
* For details see Mathematical Section of this paper. 
2 S 2 
