74 
THE ENERGY OF THE ELECTROMAGNETIC FIELD. 
By Proressor W. H. Brace, M.A. 
[Read May 3, 1892.] 
In an address given to Section A of the Australasian Associa- 
tion for the Advancement of Science, at the Hobart meeting, in 
January of this year, I showed that an exact analogue of the 
electromagnetic field due to currents and magnets existed in the 
case of membranes displaced by uniform pressures or to fixed 
amounts in an infinite elastic medium ; a medium in which, if any 
element be displaced, there is a force of restitution proportional 
to the volume of the element and the amount of its displacement. 
It is interesting to start with the supposition of the existence 
of such a medium, and hence develop the theorems which we 
know to be true of the energy of the field. They follow very 
simply from this hypothesis. 
Suppose a thin membrane in such a medium as I have described 
above. A uniform pressure per unit area will cause displacement, 
supposed small. Let the uniform pressure be 47C, and the total 
displacement of the membrane, 7.e., the volume it moves through, 
b LC 
€ Ase 
circuit represented by the edge of the membrane, and causing a 
total induction through its contour equal to LC. The energy so 
stored up in the elastic medium is 4 x force x displacement, 
10.5 4 LG? 
Now, in the medium so disturbed, let a second membrane be 
placed, and acted on by a uniform pressure, gradually increasing 
to 47 C’. The medium, although already strained, will make 
exactly the same opposition to the new straining force as if it 
were unstrained, because from the nature of the medium the 
force resulting from a new displacement of any small volume 
already displaced is independent of the previous displacement. 
So the second membrane will be displaced just the same as if it 
were the only one, and the work done in displacing it will be 
a li C2 Asay): 
But—and this is the point-—whilst this second membrane has 
been undergoing displacement, so has the frst; and the amount 
of displacement of the first is of course proportional to C’, say 
MC’ 9 . 
dr” °° 16r? 
Then C corresponds to the current running round a 
is the amount of displacement through the first 
