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.