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.

Corresponding states are those for which the numerical values of the pressure, volume, and temperature, expressed by taking as units the values corresponding to the critical point, are equal; and, in corresponding states any two fluids have exactly the same properties.
M.Natanson, and subsequently P.Curie and M.Meslin, have shown by various considerations that the same result may be arrived at by choosing units which correspond to any corresponding states; it has also been shown that the theorem of corresponding states in no way implies the exactitude of Van der Waals' formula.

In reality, this is simply due to the fact that the characteristic equation only contains three constants.
The philosophical importance and the practical interest of the discovery nevertheless remain considerable.

As was to be expected, numbers of experimenters have sought whether these consequences are duly verified in reality.

M.Amagat, particularly, has made use for this purpose of a most original and simple method.