Tables E.2 and E.3 present a compact summary of thermodynamic derivatives in a form convenient for geophysical applications. Individual entries have no meaning; they must be taken in pairs so that, for example, to find (∂T/∂P)S look down the constant S column and take the ratio of entries for ∂T and ∂P, that is γT/KS. An arbitrary mass m of material is assumed, so that m appears in many of the entries. Table E.2 is complete for the eight primary parameters. Any one of them may be differentiated with respect to any other one with any third one held constant. The results are represented in terms of the same parameters plus a set of first derivative properties, α, KT, KS, CV, CP and γ. Table E.3 extends the constant T, P, V and S columns to derivatives of these first derivative properties, using a set of second derivative parameters, K′T, K′S, δT, δS, C′T, C′S and q, defined in Table E.1. There are numerous alternative forms for many of the Table E.3 entries, the usefulness of which depends on particular applications. Substitutions may be made using relationships in Table E.4. A few derivatives of products and third derivatives have been found useful and are also listed.

The compact collection of thermodynamic derivatives in Tables E.2 and E.3 follows an idea, started by Bridgman (1914), that is much more useful than generally realized.