Zeroth Law of Thermodynamics

The following is shown with respect to the zeroth law of thermodynamics. (1) Planck's argument that it follows from a general theorem concerning establishment of thermal equilibrium among numerous bodies does not appear to be conclusive. (2) The zeroth law is a consequence of the first and second laws in classical thermodynamics and need not, therefore, be considered as a separate assumption or law. (3) The zeroth law must be assumed as supplementary to the second axiom in Carathéodory's theory, as Carathéodory did, if one wishes to adhere to that axiom precisely as he gave it. If, however, the axiom be amplified slightly in a natural way, the zeroth law can be derived as a consequence.