Page:Scientific Papers of Josiah Willard Gibbs.djvu/39

Rh On the other hand $$W$$ and $$H$$ are not functions of the state of the body (or functions of any of the quantities $$v$$, $$p$$, $$t$$, $$\epsilon$$ and $$\eta$$), but are determined by the whole series of states through which the body is supposed to pass.

Now if we associate a particular point in a plane with every separate state, of which the body is capable, in any continuous matter, so that states differing infinitely little are associated with points which are infinitely near to each other, the points associated with states of equal volume will form lines, which may be called lines of equal volume, the different lines being distinguished by the numerical value of the volume (as lines of volume 10, 20, 30, etc.). In the same way we may conceive of lines of equal pressure, of equal temperature, of equal energy, and of equal entropy. These lines we may also call isometric, isopiestic, isothermal, isodynamic, isentropic, and if necessary use these words as substantives.

Suppose the body to change its state, the points associated with the states through which the body passes will form a line, which we may call the path of the body. The conception of a path must include the idea of direction, to express the order in which the body passes through the series of states. With every such change of state there is connected in general a certain amount of work done, $$W$$, and of heat received, $$H$$, which we may call the work and the heat of the path. The value of these quantities may be calculated from equations (2) and (3),