tricle of the heart are examples of a monovariant system. The "pressure phosphenes" of the retina, luminous sensations produced by pressure on the eyeball, and consequently "eye strain," may be due, Zwaardemaker thinks, to displacements of equilibrium through disturbance of the thermodynamic potential. These speculations are, of course, tentative, but there are indications that physiological problems may be attacked in a way that has some show of success in that it is qualitative.
The Law of Critical State.—When we have two contiguous phases of a substance, as a liquefying gas or a vaporizing liquid, there is a point where the two become continuous. This is called the critical state at which the distinction between coexistent phases vanishes. Gibbs's law asserts that a critical phase of independently variable components is capable of n − 1 independent variations. This theorem is the basis of the brilliant work of van der Waals, Duhem, van Laar and Kamerlingh Onnes upon continuous gaseous and liquid states.
Osmosis and the Theory of Solutions.—Gibbs's work is remarkable throughout for his avowed or explicit intention to have "nothing to do with any theory of molecular constitution" as leading to strained and unnatural hypotheses, and the wisdom of his decision is seen in his earlier treatment of the equilibrium of osmotic forces. He bases his theory of osmosis upon the idea of a semi-permeable diaphragm or membrane, which he introduced into physics as a purely theoretical concept, leaving the actual facts about it, he says, "to be determined by experiment." This ideal membrane, which he supposes permeable to one component and impermeable to others, is the key to the theory of solutions, for, to the mathematician, it admits of the condition of reversibility which he finds in algebraic or chemical equations; to the physicist, a solvent in the act of breaking up or wedging its way through a dissolving substance is the dynamic analogue of a liquid forcing its way into a denser liquid through the membrane, while to the chemist, the assumption that the membrane is selective for certain substances only implies some special chemical affinity between these substances and the membrane itself. If two fluids of different composition or concentration, say water and alcohol, are separated by a semi-permeable membrane, the osmotic flow of the water into the alcohol is due to definite forces. These, in Gibbs's argument, are, not a difference in pressure, but a difference in temperature which disturbs thermal equilibrium or a difference in the chemical potentials of components which can pass the diaphragm, the condition for equilibrium being equalized temperature and equality of chemical potentials. "Even when the diaphragm is permeable to all the components without restriction," he says, "equality of pressure in the two fluids is not always necessary for equilibrium." While Gibbs did not attempt a definite theory of solu-
- See his abstract in Am. J. Sc, 1878, 3. a., XVI.