Page:Scientific Papers of Josiah Willard Gibbs.djvu/314

278 by the fundamental equation of the mass or surface concerned, or may be immediately derived from it. (See pp. 85–89 and 229–231.)

The variations in (600) are subject to the conditions which arise from the nature of the system and from the supposition that the changes in the system are not such as to affect external bodies. This supposition is necessary, unless we are to consider the variations in the state of the external bodies, and is evidently allowable in seeking the conditions of equilibrium which relate to the interior of the system. But before we consider the equations of condition in detail, we may divide the condition of equilibrium (600) into the three conditions   For the variations which occur in any one of the three are evidently independent of those which occur in the other two, and the equations of condition will relate to one or another of these conditions separately.

The variations in condition (601) are subject to the condition that the entropy of the whole system shall remain constant. This may be expressed by the equation To satisfy the condition thus limited it is necessary and sufficient that  throughout the whole system, which is the condition of thermal equilibrium.

The conditions of mechanical equilibrium, or those that relate to the possible deformation of the system, are contained in (602), which may also be written