ON LINES OF INDUCTION IN A MAGNETIC FIELD. 
327 
x — constant, in the innermost space, 
J> / _ 
K sec 6 — sinli u -P——cosh u, in the substance of the shell, and 
A i 
A/ + H 
K sec 6 = sinli u -- — cosh p, in external space. 
In working out numerical examples with the view of plotting curves, it is con¬ 
venient to use a table of hyperbolic sines and cosines, such as the one compiled by 
T. H. Blakesley and published by the Physical Society of London. Corresponding 
values of u and 6 having been found, it is an easy step to pass to Cartesian rect¬ 
angular co-ordinates, which are more convenient for plotting the curves. 
The method given above may, as already mentioned, be extended to any number 
of confocal elliptic cylindric shells. In general, however, when numerical data are 
available, it is best to substitute these at once in the equations instead of first 
trying to obtain a solution in general terms. 
The case of concentric circular cylindric shells may be regarded as a limiting case 
of elliptic shells, the two axes of the ellipse becoming equal. If in the expressions 
obtained for the constants A, Aj, &c., in the case of a hollow elliptic shell we 
regard a as constant and h as variable, and then proceed to the limit b — a, we find 
that the values so obtained are in agreement with those deduced by Du Bois for a 
circular cylindric shell in his articles on “ Magnetic Shielding.But although an 
interesting verification of the method for a special case is thus obtained, it is much 
simpler, when dealing with circular cylindric shells, to follow the method developed 
by Stefan in the paper already referred to.f 
* ‘ The Electrician,’ vol. 40. 
t ‘ Wien. Akad. Sitz. Ber.,’ vol. 85, Section 2, p. 613. 
