Contribution to the Theory of Critical Phenomena

If one considers the critical point between the liquid and gaseous phases, it may be shown that the ``principle of superposition'' leads to the result that the critical point is a singularity in the isotherm of fugacity or pressure against density. At this singularity the derivatives of every order of the fugacity or pressure with respect to the density are zero, not only the first two derivatives as in the van der Waals theory. It is postulated that these relations are true despite the uncertain nature of the superposition approximation. If the critical point is such a singular point, it can be shown that Mayer's theory of critical phenomena leads quite reasonably to a single characteristic temperature instead of two separate temperatures for the vanishing of the slope of the isotherm and for the appearance of a surface tension. Experimental observations on the anomalous shape of the isotherms near the critical point are in accord with the theory.