266 
MR. J. LARMOR ON A DYNAMICAL THEORY OF 
perpetual motion postulate, is the same as the free energy of vox Iielmholtz s 
exposition : he has explained (“ Abhandlungen,” IL, p. 870) how its form can he 
experimentally ascertained lor the different phases of mattei, except as legards 
an undetermined part, as above, of form L + MT, where L and M are constants ; 
that then the equilibrium state of a system of reacting bodies at any assigned 
temperature is the one that makes it minimum for that temperature, thereby formu¬ 
lating the general solution of the i)rohlem of physical and chemical equilibrium ; 
while the other properties of the system, heat-changes and heat-capacities, as well as 
total energy and entropy, are obtained from it directly by processes of diffeientiation. 
The available energy is thus a single cliaracteristic function which includes and 
determines completely the circumstances, mechanical, thermal, and constitutive, 
of the steady states of an inanimate material system. 
Application to Fluids: Laplace’s Intrinsic Pressure: Laiv of Osmotic Pressure : 
Laws of Chemical Equilihrium. 
52. In an incompressible fluid medium in equilibrium, no part of the bodily 
extraneous forcive is compensated by reaction arising from special strains produced 
around the element of volume itself; it is all transmitted by fluid pressure 
independently of the special physical constants of the medium. For equilibrium to 
subsist in a polarized fluid, the applied mechanical forcive must simply be derived 
from a potential, ^^hen the induced polarization follows a hiieai lav, this 
potential must also be equal and opposite to the oi’ganized energy induced per unit 
volume in the medium on which this extraneous foicive opeiates , foi the total 
organized energy that has been spent in the polarization of the element Sr is equal 
to St multiplied by the scalar product of the polarization and the polarizing foice, 
and of this one half is mutual energy of the polarizations of the elements of volume 
and one half is mechanical work done in the process (cf. §71). If therefore the 
organized energy of the internal excitation of the medium is expressible as a volume- 
density of energy represented by a continuous function, the fluid medium will be in 
internal mechanical equilibrium ! but if that function is discontinuous so that in 
crossing some interface the density of induced energy abruptly changes its value (as 
for example may be the case v/hen the interface separates two different substances) 
then in order to maintain equilibrium the applied forcive must include a traction 
applied to this interface along its iiormal, of intensity equal to the difference of the 
densities of energy on its two sides, and acting towards the side of smaller density 
of energy. At an external boundary there must similarly be applied an outward 
traction along the normal, equal in intensity to the density of organised energy 
induced in the })art of the substance that is just inside. 
To illustrate and elucidate this by the electric phenomena, consider the interface 
between two dielectric fluids to be maiutained in position by an applied traction ; 
