320 
PROFESSOR HELE-SHAW AND MR. ALFRED HAY 
variable 2 = x + iy. The real factor of the imaginary part of this function is U = 
A y — B y/r~, and this gives the system of lines of induction. 
Stefan further deals with the case of a hollow cylinder along whose axis are 
placed two wires (infinitely close together), conveying currents in opposite directions. 
In 1894, ItucKERV considered in detail the question of magnetic shielding by 
spherical shells, with special reference to the problem of maximum shielding effect 
for a given total weight of material. In the same year Perry f contributed a brief 
paper to the Physical Society on the magnetic shielding of external space by a 
hollow iron cylinder enclosing two parallel conductors conveying equal currents in 
opposite directions in a diametrical plane of the cylinder, each conductor being at the 
same distance from the axis. 
In 1897, fresh interest was given to the problem of magnetic shielding by the 
discussion which followed the reading of Mr. Mordey’s paper on “ Dynamos,” 
before the Institution of Electrical Engineers.| Towards the close of that year, 
Du Bois§ commenced the publication of an elaborate series of articles on magnetic 
shielding, in which he briefly reviewed the history of the subject, and gave diagrams 
of magnetic fields for the case of hollow circular cylinders of varying thickness 
placed in a uniform field. || 
Almost simultaneously with Du Bois, Searle* ** ! published, in January 1898, a 
mathematical paper on the magnetic field due to a current in a wire placed parallel 
to the axis of a cylinder of iron. This paper is accompanied by some extremely 
interesting diagrams of magnet ic fields. 
The latest contribution to this subject is a paper by A. P. Wills, ## “ On the 
Magnetic Shielding Effect of Trilamellar Spherical and Cylindrical Shells,” which 
may be considered as an extension of Du Bois’ investigations to triple shields. 
(b) The problem of the induced magnetisation due to a uniform impressed field in 
infinite cylinders of elliptic section or infinite cylindrical shells bounded by confocal 
elliptic surfaces, may be dealt with by the following method. 
The general problem of magnetic induction in space of two dimensions may be 
regarded as consisting in the determination of a continuous potential function Y, i.e., 
goy 02\ T 
a function satisfying Laplace’s equation for two-dimensional space, g-y + g-y — 0, 
which fulfils the condition of continuity of normal induction across any surface of 
separation between two media, viz., 
0v, sv _ 
s, ^ ^ s„, - 0> 
* 1 Phil. Mag.’ [5], vol. 37, p. 95. f ‘ Proc. Phys. Soc.,’ vol. 13, p. 227. 
I ‘ Journal,’ vol. 26, p. 564. § ‘ The Electrician,’ vol. 40. 
|| Ibid., vol. 40, p. 513. H Ibid., vol. 40, p. 453. 
** ‘ Physical Review’ [9], pp. 193-213, October, 1899 
