The idea of corresponding states originated when van der Waals cast his equation in the dimensionless form, p r = p ( v r , T r ) . However, as Boltzmann noted, such a simple representation could not correctly describe all substances. Indeed, the saturation analysis of this form produces p r s = p s ( T r ) , namely all substances have the same dimensionless coexistence curve. In order to avoid this paradox an extended principle of corresponding states has been suggested in which p r = p ( v r , T r , ϕ ϕ ) where ϕ ϕ is a substance dependent dimensionless parameter related to the only physical feature associated with an individual substance, its critical point.