10 
Davies.—Some Electric and Elastic Analogies . 
the separate equations which give rise to the biquadratic A a must = — B s 
and A 2 = — B 0 then the expression H=H l sin nt + H 2 cos nt will take 
the form H=(AM+BN) sin nt + (AN — BM) cos nt, as given above. 
M—Ni=J 0 (r^/xi) 
M+Ni=J 0 (r -]/— xi) 
J a is the Bessel Function of zero order. 
(-H’)' 2 =,(-A 2 + B' 2 )(M' 2 + N-)={47tN)\ry if F is coil current, and N is turns 
per unit length of core, and parentheses denote average amplitudes of 
current and force.* 
It will be noticed that the magnetic force is a function of r, and that 
on the right side of the equation we have this force multiplied by — x 2 . 
This requires that z in the elastic problem should stand for H in 
the magnetic one, and that the load per unit area, Z , in the elastic prob¬ 
lem should be a multiple of z the displacement. Again, one is positive, 
the other negative. The one would seem to imply a greater effect the 
further we go from the center of the core, the other the nearer we go to 
the center of the plate. 
What may be the physical meaning of this analogy, if any, I do not 
know. The mere fact of the appearance of oscillatory functions to de¬ 
note results of analysis does not by any means imply the necessary ex¬ 
istence of vibrations. The same equation is often satisfied by an 
expression which denotes a variety of things in physics — witness the 
celebrated equation of Laplace in partial differential coefficients V 2 =0 
and others. It may be that the analogy is merely formal or mathemati¬ 
cal and without any physical significance whatever. It is somewhat 
singular, however, that the equation is one closely related to waves, and 
that certainly waves of magnetic force penetrate into the interior of 
iron cores surrounded by currents, very much after the manner which 
Fourier shows to be the manner of diffusion of heat waves into the 
interior of solid bodies. 
It is very likely that it is in this conception of diffusion that the 
whole analogy lies. One cannot help recalling how the equations which 
Fourier has given for the transmission of heat along a wire are made to 
give the necessary formulae for the transmission of signals along a sub¬ 
marine cable, and possibly also there may be some hint of the form of 
potential that the magnetic force in the interior of a core ought to be 
derived from, when one reflects that Lame has shown that while the 
equation V 2 d=0 is satisfied by a potential 
* See Oliver Heaviside Phil. Mag., July, 1886, and elsewhere. 
