ON LINES OP INDUCTION IN A MAGNETIC FIELD. 
305 
One very important feature which characterises the method, is the fact that it 
enables us to obtain the exact shape of the lines of induction not only in air, hut 
in the pcira-magnetic or dia-magnetic material itself. This cannot be accomplished 
by any of the older methods. The method has therefore been applied to determine 
the exact form of the lines of induction for a number of cases of mathematical 
interest, several of which have been also plotted by calculation. Inasmuch as the 
laws connecting the relative thicknesses of two liquid films with the corresponding 
values of the permeability, have by the above investigation been determined, it is 
possible to investigate any practical case which may be of interest, and some 
examples are given of the application of the method in cases of interest to 
electricians. * 
The mathematical portion of the work which has been necessary, has not—as far as 
the authors are aware—hitherto been available in any published form, and although, 
as will be seen from the historical statement, parts of the problem have been dealt 
with by various writers, it is hoped that the account given will be found of use in 
the further investigation of this subject. 
The scheme of the paper is as follows:—- 
1 . (a) The experimental determination of the relation between the thickness of 
film and the corresponding rate of flow. 
(b) Statement of results and comparison with theory. 
(c) Description of appliances used in obtaining the stream-line diagrams. 
11. (a) Account of the test case worked out mathematically and plotted, and its 
comparison with the actual photograph obtained by experiment. 
(b) Examples of various cases of mathematical interest, and also some of 
practical importance to the electrical engineer. 
111 . (a) Brief history of mathematical investigation of the subject, and 
(b) A general method of dealing with elliptic cylinders and con-focal elliptic 
shells. 
Section 1. 
(a) The liquid is contained in the cylinder A, fig. 1, from which it is forced by 
means of compressed air, the pressure being determined by the pressure gauge B. It 
then passes through the cock C (fine adjustment being secured by the lever D which 
travels over a scale) to the thermometer box, E, where its temperature is recorded 
upon the thermometer F, and from thence to the slide J. 
The slide consists of two sheets of plate-glass fixed within the frame P ; a well is 
cut in the lower sheet into which the liquid is introduced, a channel being formed 
between the plates by using tin-foil as a border. The correct thickness is obtained 
by screwing down the plates upon the thickness gauges N, N, N, N, placed at the 
VOL. CXCV.— A. 2 R 
