440 
MR. O. HEAVISIDE ON THE FORCES, STRESSES, AND 
Observe that T 2 and Q a only differ in the exchange of /x to \v ; but U 2 , the potential 
energy, is not the same function of n and D that T 3 is of v and q. But if we take 
k = 0, we produce similarity. An elastic solid having no resistance to compression is 
also one of Sir W. Thomson’s ethers. 
When n = 0, [x — 0, v = 0, we come down to the frictionless fluid, in which 
f-VP = 3,. (78) 
ot 
and 
2PV 2 = -Pdivq,. (79) 
with the equation of activity 
fq = U + T + div (U + T + P) q,.(80) 
the only parts of which are not always easy to interpret are the Pq term, and the 
proper measure of U. By analogy, and conformably with more general cases, we 
should take 
P = — Jc div D, and U — \Jc (div D) 2 , 
reckoning the expansion or compression from some mean condition. 
The Electromagnetic Equations in a Moving Medium. 
§ 14. The study of the forms of the equation of activity in purely mechanical cases, 
and the interpretation of the same is useful, because in the electromagnetic? problem 
of a moving medium we have still greater generality, and difficulty of safe and sure 
interpretation. To bring it as near to abstract dynamics as possible, all we need say 
regarding the two fluxes, electric displacement I) and magnetic induction B, is that 
they are linear functions of the electric force E and magnetic force H, say 
B = /<H, D = cE,.(81) 
where c and /x are linear operators of the symmetrical kind, and that associated with 
them are the stored energies U and T, electric and magnetic respectively (per unit 
volume), given by 
U = l ED, T = \ HB, .(82) 
In isotropic media c is the permittivity, /x the inductivity. It is unnecessary to 
say more regarding the welhknown variability of /x and hysteresis than that a magnet 
is here an ideal magnet of constant inductivity. 
As there may be impressed forces, E is divisible into the force of the field and an 
impressed part; for distinctness, then, the complete E may be called the “ force of 
the flux ” D. Similarly as regards H and B. 
