6 
Davies.—Some Electric and Elastic Analogies. 
This is the equivalent of A\J' 2 \/' 2 z^=Z; or in other words the Laplacian 
operator doubly applied, because 
where z is a function of r alone (where as usual V' 2 denotes Laplace’s 
operator), and because the quantity 
d _E 
dx dy 
becomes, in the case of concentric load, a simple function of the radius- 
ratio of k to n is constant and equal to f. The whole question of the 
values of these constants and whether there are ultimately one or more 
in isotropic bodies seems to rest upon whether elastic isotropic bodies 
can be considered as made up of molecules mutually acting on each 
other in the line of their centers and according to a law of variation 
with distance merely, or whether the action of one molecule upon another 
is likewise a function of the action of other molecules upon each of the 
two considered — a function of aspect in other words as well as distance. 
It would seem that this must be true for magnetized bodies where 
polarity must be considered. 
To see that this is so we have only to consider the different expres¬ 
sions for the law of force between two magnets, according as they are 
end-on or broadside-on to each other. The expression in either case 
is a series, involving increasing negative powers of the distance. But 
this series is in the case of end-on, double its value for the other 
case, regarding one of the magnets as movable and the other as fixed. It 
would be an interesting problem to form for a magnetic medium the 
equations of equilibrium and motion on the hypothesis that we have in 
such a medium an infinite assemblage of molecules having polarity; in 
other words an infinite assemblage of molecular magnets whose result¬ 
ant attractions for each other would be represented by a function of 
distance and aspect (orientation) and not of distance alone. Green in 
his remarkable essay on the “ Equilibrium of Fluids analogous to the 
Electrical Fluid,” has treated the case of equilibrium of a medium 
somewhat analogous to such a medium, inasmuch as he applies the 
method of potentials to the case of a medium where the law of force is 
inversly as any power n of the distance, where n may represent any 
number whatever, fractional or irrational. On supposing that n is, as in 
the case of finite magnets sufficiently close to each other to involve a 
consideration of their lengths and orientation as well as their distances, 
a complex function of the molecular magnetic moments and distances, 
all of Green’s results would be immediately available to the considera¬ 
tion of any equilibrium problems of the medium which Ewing regards 
as making up a magnetic one. No doubt the problem of motion would 
be a complicated one, but it is easy to see without any mathematics that 
such a medium would possess most of the properties which Ewing has 
assigned to it in his theory of magnetism.* Green, it is true, conceives 
* An interesting illustration by experiment of such a medium is given by Mr. Crew in the 
New York Electrical World for 1891. It was also given by Prof. Ewing before the British 
Association. 
