h the substance divides itself, we are led to regard the
geometrical surface which for a given temperature represents the free
energy.

I am unable to enter here into the detail of the questions connected
with the theories of Gibbs, which have been the object of numerous
theoretical studies, and also of a series, ever more and more
abundant, of experimental researches. M. Duhem, in particular, has
published, on the subject, memoirs of the highest importance, and a
great number of experimenters, mostly scholars working in the physical
laboratory of Leyden under the guidance of the Director, Mr Kamerlingh
Onnes, have endeavoured to verify the anticipations of the theory.

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, Kuenen, Lehfeld, etc., throw, however, some light on
the question.

The daily more numerous applications of the laws of corresponding
states have rendered highly important the determination of the
critical constants which permit these states to be defined. In the
case of homogeneous bodies the critical elements have a simple, clear,
and precise sense; the critical temperature is that of the single
isothermal line which presents a point of inflexion at a horizontal
tangent; the critical pressure and the critical volume are the two
co-ordinates of this point of inflexion.

The three critical constants may be determined, as Mr S. Young and M.
Amagat have shown, by a direct method based on the consideration of
the saturated states. Results, perhaps more precise, may also be
obtained if one keeps to two constants or even to a single one--
temperature, for example--by employing various special methods. Many
others, MM. Cailletet and Colardeau, M. Young, M.J. Chappuis, etc.,
have proceeded thus.

The case of mixtures is much more complicated. A binary mixture has a
critical space instead of a critical point. This space is comprised
between two extreme temperatures, the lower corresponding to what is
called the folding point, the higher to that which we call the point
of contact of the mixture. Between these two temperatures an
isothermal compression yields a quantity of liquid which increases,
then reaches a maximum, diminishes, and disappears. This is the
phen