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It was not until M. Van der Waals exhumed the memoir of Gibbs, when numerous physicists or chemists, most of them Dutch Professor Van t'Hoff, Bakhius Roozeboom, and others utilized the rules set forth in this memoir for the discussion of the most complicated chemical reactions, that the extent of the new laws was fully understood.
We are a little less advanced as regards abnormal substances; that is to say, those composed of molecules, partly simple and partly complex, and either dissociated or associated. These cases must naturally be governed by very complex laws. Recent researches by MM. Van der Waals, Alexeif, Rothmund, Künen, Lehfeld, etc., throw, however, some light on the question.
M. Van der Waals has sought out the modifications which must be introduced into the simple characteristic equation to bring it nearer to reality. He extends to the case of gases the considerations by which Laplace, in his famous theory of capillarity, reduced the effect of the molecular attraction to a perpendicular pressure exercised on the surface of a liquid.
No general rule was found until M. Van der Waals first enunciated a primary law, viz., that if the pressure, the volume, and the temperature are estimated by taking as units the critical quantities, the constants special to each body disappear in the characteristic equation, which thus becomes the same for all fluids. The words corresponding states thus take a perfectly precise signification.
Rankin and, subsequently, Recknagel, and then Hirn, formerly proposed formulas of that kind; but the most famous, the one which first appeared to contain in a satisfactory manner all the facts which experiments brought to light and led to the production of many others, was the celebrated equation of Van der Waals.
It results also from this that the characteristic equation of a fluid cannot yet be considered perfectly known. Neither the equation of Van der Waals nor the more complicated formulas which have been proposed by various authors are in perfect conformity with reality.
Professor Van der Waals arrived at this relation by relying upon considerations derived from the kinetic theory of gases.
Calculation has enabled M. Van der Waals, by the application of his kinetic theories, and M. Duhem, by means of thermodynamics, to foresee most of the results which have since been verified by experiment.
But the most remarkable result of M. Van der Waals' calculations is the discovery of corresponding states. For a long time physicists spoke of bodies taken in a comparable state.
In this particularly simple case M. Van der Waals has established a characteristic equation of the mixtures which is founded on mechanical considerations. Various verifications of this formula have been effected, and it has, in particular, been the object of very important remarks by M. Daniel Berthelot.
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