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PROFESSOR HELE-SHAW AND MR. ALFRED HAY 
to the lines of force in the undisturbed magnetic field, showed unmistakably absolute 
agreement between the results obtained by calculation and experiment. 
On account of the great practical importance of magnetic phenomena, various 
methods have from time to time been devised for the study of magnetic fields, and by 
means of such methods the approximate distribution of the lines of magnetic 
induction in various cases may be investigated. One of the earliest of these 
methods was that in which the lines are approximately mapped out by means of 
iron filings. This method, which has been known for a long time (La Hire mentions 
it as far back as 1717), was very largely used by Faraday in his study of magnetic 
fields. It must, however, be regarded as a very rough-and-ready method, and does 
not enable us to trace out the exact shape of the lines with any degree of accuracy. 
Another method, which when carefully applied is capable of giving good results, 
is that in which a magnetic needle is moved from point to point of the field, the 
consecutive positions of the two ends of the needle being marked, and a line drawn 
through the points so determined. This method gives the shape of the lines very 
accurately if the length of the needle is small in comparison with the radius of 
curvature of the lines. But although in a diagram so obtained the relative intensity 
of the field at various points may be roughly estimated by noting the convergence 
or divergence of the lines, yet it is impossible to indicate this variation of intensity 
by the distance apart of consecutive lines, since there is no means of ascertaining 
how far apart the consecutive lines should be drawn. A third method, which we 
owe to the genius of Faraday, and which is one of very great practical importance, 
is that of a search-coil connected to a ballistic galvanometer. In applying this 
method, the search-coil is either jerked out of a given position in the field, or turned 
through a small angle, or else the field is suddenly removed, or reversed, while the 
search-coil remains stationary. This method, however, notwithstanding its great 
importance as a method for ascertaining the magnetic flux through a given area in 
the field, can hardly be regarded as a method for delineating lines of induction. 
The same remark is applicable to two other methods; that in which the field 
intensity is ascertained by measuring the resistance of a bismuth spiral; and that 
in which a conductor conveying a known current is placed in the field, and the pull 
on the conductor is measured. 
The experimental method which the above investigation proves to be accurate, is 
applicable to two-dimensional problems only. In so far as this is the case, its scope 
may appear restricted. But when we consider the fact that in the practical applica¬ 
tions of magnetism, the bulk of the phenomena with which we have to deal are of 
the two-dimensional order, it will be recognised that it offers a solution of problems 
whose interest and importance are by no means inconsiderable. The magnetic field 
in and around the armature of a dynamo or alternator, and that in and around 
a cylindrical case which is used for purposes of magnetic shielding, are examples 
of important practical problems in two dimensions. 
