[ 303 J 
IX. Lines of Induction in a Magnetic Field. 
B>j Professor H. S. Hele-Shaw. LL.D., F.R.S., and Alfred Hay, B.Sc. 
Received June 13,—Read June 21, 1900. 
[Plates 14-21.] 
The following paper, which is partly experimental and partly mathematical, has 
arisen from the discovery that two-dimensional cases of magnetic lines of force 
could apparently he represented by the flow of a viscous liquid. # The original 
experiments upon which this assumption was made, showed that the stream lines 
which were obtained by the method in question, gave results very similar to those 
which had been calculated and plotted for the cases of an elliptical and circular 
cylinder. In order to ascertain definitely that the stream lines under these circum¬ 
stances actually gave the exact position and direction of the corresponding magnetic 
lines of force, a result which, if verified, could be used for many practical investi¬ 
gations—it was necessary to undertake a long research dealing with the various 
points involved, a research which has proved extremely laborious, extending without 
intermission over a period of nearly two years. 
In the first place it was necessary to devise some method by which a thin sheet 
of transparent or semi-transparent medium could be obtained of any required 
thickness, and on which, when placed between two sheets of glass, the required 
section of the body to he investigated could he formed. 
Next it was necessary to determine the laws connecting the thickness of the thin 
film of liquid with the quantity flowing through it in a given time, so that the 
relative differences of thickness corresponding to the differences of permeability of 
the substances in a magnetic field could be ascertained. 
Lastly, a mathematical investigation was undertaken of some cases suitably 
selected so as to afford, when plotted out, as severe a test as possible for ascertaining 
if the experimental method really determined for any case, accurately, the position 
and character of the lines of force in a magnetic field. 
It may at once be stated that after overcoming in succession a very large number 
of difficulties, the case selected, viz., that of an ellipse with the major axis parallel 
* “ Streamline Motion of a Viscous Film ” : 1 British Association Report ’ (Section A), Bristol Meeting, 
1898. 
20.12.1900 
