Empirical relationship as a stepping-stone to theory
  We consider parsimonious construction of empirical equations, to promote interest in them as a stepping-stone model to the physical law. To this end, we provide a variety of historical examples and simulate a parsimonious empirical calculation of Planck law, and of van der Waals equation. Thereby we provide a) Empirical forms of Planck law, and b) Collation of verified symmetries and catastrophes-like properties of empirical P-T surface of real gases. An empirical equation of state for a real gas should take account of these properties. 
Marijan Ribaric and Luka Sustersic