In a paper with the above title, Ehrenfest (Zeitsch. physikal. Chem. 1911, 77, 2) has shown that, as usually formulated, the principle is entirely ambiguous, and that nothing definite can be stated without a discrimination among the parameters by which the condition of a system may be defined. The typical example is that of a gas, the expansions and contractions of which may be either (α) isothermal or (β) adiabatic, and the question is a comparison of the contractions in the two cases due to an increment of pressure δp. It is known, of course, that if δp be given, the contraction |δv| is less in case (β) than in case (α). The response of the system is said to be less in case (β), where the temperature changes spontaneously. But we need not go far to encounter an ambiguity. For if we regard δv as given instead of δp, the effect δp is now greater in (β) than in (α). Why are we to choose the one rather than the other as the independent variable?

When we attempt to answer this question, we are led to recognise that the treatment should commence, with purely mechanical systems. The equilibrium of such a system depends on the potential energy function, and the investigation of its character presents no difficulty. Afterwards we may endeavour to extend our results to systems dependent on other, for example, thermodynamic, potentials.