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be regarded as the constrained one, since the response is to be diminished by a constraint.
The justification of this view does not seern difficult. The gas may be supposed to be confined in a cylinder under a piston, and the walls of the cylinder may be taken to be so massive as to control the temperature of the gas when undergoing slow alterations of volume. The necessary interchanges of heat take place of themselves, and the condition is one of freedom from constraint. We pass to the adiabatic condition by preventing this accommodation. The How of heat may be stopped by the introduction of a nonconducting layer or in any other way, and the operation has the character of a constraint. Since the motion of heat in a conductor is due to differences of temperature, the former is assimilated to the displacement and the latter to the force of the purely mechanical problem. The same conclusion follows from a consideration of the thermodynamic potential.
Instead of a gas we may take a vapour in contact with liquid, say steam in contact with water. The pressure is now a function of temperature only, so that if the pressure is increased while the temperature remains unchanged, the whole of the steam is condensed, and the volume is greatly reduced. If by a constraint the outward passage of heat is prevented, the temperature rises and the reduction of volume soon ceases, in accordance with the principle.
Or again, we may suppose that the temperature is raised by a given amount, in the first case under constant pressure (no constraint), or, secondly, under constant volume, namely, with constraint. The passage of heat is less in the secorid case.
Electrostatic problems, governed by a potential energy function, are seen to be included under those of ordinary mechanics. Imagine two conductors, near enough to influence one another, of which the first can be connected with a battery (the other pole of which is earthed), whilst the second can be connected directly to earth. In the first case (of no constraint), the second conductor is earthed, and a certain charge enters the first conductor as the result of the battery contact. In the second case, the earth connexion of the second conductor is broken before battery contact is made. The breaking of this contact introduces a constraint, and the charge on the first conductor is reduced. In all such problems potential corresponds with force and charge corresponds with displacement.
In problems relating to steady electric currents maintained against resistance, the dissipation function takes the place of the energy function. If an electromotive force act on any branch of a network of conductors, it gt-nerates less current, and accordingly does less work, when an interruption occurs, as by breaking a contact in any part of the system.f gelatine, scarcely thicker than thick paper, should be able to tear out fragments of-solid glass, but there is no doubt of the fact.