558 THE POPULAR SCIENCE MONTHLY 



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 dis- 

 turbance of the thermod}Tiamic 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 w — 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 

 Teversibility 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 con- 

 centration, 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 equi- 

 librium 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. 



