eory, if we
admit the absolute value of the principle; but we may also suppose
that here again we are in presence of a system where the prescribed
conditions diminish the complexity and render it, consequently, less
probable that the evolution is always effected in the same direction.

In whatever way you look at it, the principle of Carnot furnishes, in
the immense majority of cases, a very sure guide in which physicists
continue to have the most entire confidence.

Sec. 4. THERMODYNAMICS

To apply the two fundamental principles of thermodynamics, various
methods may be employed, equivalent in the main, but presenting as the
cases vary a greater or less convenience.

In recording, with the aid of the two quantities, energy and entropy,
the relations which translate analytically the two principles, we
obtain two relations between the coefficients which occur in a given
phenomenon; but it may be easier and also more suggestive to employ
various functions of these quantities. In a memoir, of which some
extracts appeared as early as 1869, a modest scholar, M. Massieu,
indicated in particular a remarkable function which he termed a
characteristic function, and by the employment of which calculations
are simplified in certain cases.

In the same way J.W. Gibbs, in 1875 and 1878, then Helmholtz in 1882,
and, in France, M. Duhem, from the year 1886 onward, have published
works, at first ill understood, of which the renown was, however,
considerable in the sequel, and in which they made use of analogous
functions under the names of available energy, free energy, or
internal thermodynamic potential. The magnitude thus designated,
attaching, as a consequence of the two principles, to all states of
the system, is perfectly determined when the temperature and other
normal variables are known. It allows us, by calculations often very
easy, to fix the conditions necessary and sufficient for the
maintenance of the system in equilibrium by foreign bodies taken at
the same temperature as itself.

One may hope to constitute in this way, as M. Duhem in a long and
remarkable series of operations has specially endeavoured to do, a
sort of general mechanics which will enable questions of statics to be
treated with accuracy, and all the conditions of equilibrium of the
system, including the calorific properties, to be determined. Thus,
ordinary statics teaches us that a liquid with its vapour on the top
forms a system in equilibrium