M. Lippmann has in the same way shown that, on the kinetic hypothesis, it is possible to construct such mechanisms that we can so take cognizance of molecular movements that vis viva can be taken from them.  The mechanisms of M. Lippmann are not, like the celebrated apparatus at one time devised by Maxwell, purely hypothetical.  They do not suppose a partition with a hole impossible to be bored through matter where the molecular spaces would be larger than the hole itself.  They have finite dimensions.  Thus M. Lippmann considers a vase full of oxygen at a constant temperature.  In the interior of this vase is placed a small copper ring, and the whole is set in a magnetic field.  The oxygen molecules are, as we know, magnetic, and when passing through the interior of the ring they produce in this ring an induced current.  During this time, it is true, other molecules emerge from the space enclosed by the circuit; but the two effects do not counterbalance each other, and the resulting current is maintained.  There is elevation of temperature in the circuit in accordance with Joule’s law; and this phenomenon, under such conditions, is incompatible with the principle of Carnot.

It is possible—­and that, I think, is M. Lippmann’s idea—­to draw from his very ingenious criticism an objection to the kinetic theory, 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.