2, may be found by adding to the heat required for the change of temperature at constant volume, **sdo**, or at constant pressure, **Sdo**, the heat absorbed in isothermal expansion as given by relations (4).

We thus obtain the expressions dH = **sdo** +0 (dp I dO) dv = Sd0 - o (dv/do) dp..

The change of energy at constant volume is simply **sdo**, the change at constant temperature is (odp/de - p)dv, which may be written dE/de (v const) =s, dE/dv (0 const) =odp/do - p .

The energy E and the total heat F are functions of the temperature only, by equations (9) and (I I), and their variations take the form dE = **sdO**, d F = Sd0.

The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, **Sdo**/dp= (n+I)c - b..