Page:Scientific Papers of Josiah Willard Gibbs.djvu/52

16 distinctly visible. The line of liquidity is a curve $$AB$$ (fig. 5) determined by the relation between $$t$$ and $$\eta$$. This curve is also an isometric. Every point of it has a definite volume, temperature, entropy and energy. The latter is indicated by the isodynamics $$E_{1}E_{1}$$, $$E_{2}E_{2}$$, etc., which cross the region of partial vaporization and terminate in the line of liquidity. (They do not in this diagram turn and follow the line.) If the body pass from one state to another, remaining liquid, as from $$M$$ to $$N$$ in the figure, the heat received is represented as usual by the area $$MNnm$$. That the work done is nothing, is indicated by the fact that the line $$AB$$ is an isometric. Only the isopiestics in this diagram are superposed in the line of fluidity, turnin downward where they meet this line and following its course, so that for any point in this line the pressure is undetermined. This is, however, no inconvenience in the diagram, as it simply expresses the fact of the case, that when all the quantities $$v$$, $$t$$, $$\epsilon$$ and $$\eta$$ are fixed, the pressure is still undetermined.

There are many cases in which it is of more importance that it should be easy to draw the lines of equal volume, pressure, temperature, energy and entropy, than that work and heat should be represented in the simplest manner. In such cases it may be expedient to give up the condition that the scale ($$\lambda$$) of work and heat shall be constant, when by that means it is possible to gain greater simplicity in the form of the lines just mentioned.

In the case of a perfect gas, the three relations between the quantities $$v$$, $$t$$, $$\epsilon$$ and $$\eta$$ are given on pages 12, 13, equations, and. These equations may be easily transformed into the three   so that the three relations between the quantities $$\log v, \log p, \log t, \log \epsilon$$ and $$\log \eta$$ are expressed by linear equations, and it will be possible to make the five systems of lines all rectilinear in the same diagram,