320 PROCEEDINGS OF THE AMERICAN ACADEMY 



liquid and for the solid, kept at the same volume and temperature. 

 Suppose also that the solid and the liquid isopiestics for a given 

 pressure do actually intersect at the transitional temperature, § 5. 

 If, therefore, the latter be taken as a point of departure, the total 

 energy communicated to the liquid up to the temperature t and 

 volume V, when a is the transitional volume, will be 



q + J PdV+F(£), 



where the three terms represent dissociation, expansion, and purely 

 thermal energy, respectively. The corresponding total energy im- 

 parted to the solid up to the temperature t will be 



0+ r pdv+f(t). 



a being the common volume at the transitional temperature. The 

 difference between these quantities is the latent heat, X, at t. Hence 

 the increase of latent heat from t^ to t will be, (since X is constant, and 

 F (t) — f (t) is assumed to be constant,) 



f Pdv + f pdv = (3') 



an equation which differs from equation (3) in so far as P and p de- 

 note the internal pressures for the liquid and the solid states respect- 

 ively, under conditions in which external pressure is pronouncedly 

 variable. The equation (3') would still apply if the specific heats 

 at constant volume differ only by a constant appreciably within the 

 limits of observation (0°-50°), but it is not available for practical 

 comparisons. 



10. 27ie Isometrics. — Some time ago I showed* that within a range 

 of 1,000 atmospheres of external pressure, at least, and within rea- 

 sonable limits for the thermal stability of organic bodies, the iso- 

 metrics of liquids, and particularly of thymol, f are very nearly 

 straight. Thus the extension of equation (4) would be 



ip+p') (V->i)=cT, 



* Phil. Mag., (5,) Vol. XXX. p. 348, 1890. 

 t Ibid., p. 358, and Plate XI. 



