294 PROCEEDINGS OF THE AMERICAN ACADEMY. 



esting results, as will be shown. In the case of a perfect gas Wi = Wi', 

 hence the above equation reduces to the form U :^ W, the fact pointed 

 out by Mayer. W, and Wi' are of course fuuctions of the respective heat 

 capacities. 



The analogy which has been shown to exist between the work of 

 chemical compression and the work of gaseous compression * seems to 

 afford a means of extending this logic to tlie liquid and the solid condition, 

 and thus to afford a clue to the vexed question as to the relationship of 

 free energy and total energy. 



It is well known that the heat capacity of a solid or liquid system 

 usually changes slightly during the course of a reaction, and it has been 

 shown in numerous isolated instances that compression usually tends to 

 diminish the heat capacity of solids and liquids, f The diminishing 

 specific heat with increasing specific gravity of the allotropic forms of 

 sulphur, phosphorus, silicon, and carbon may be mentioned as other 

 examples of the same general principle. 



We should expect, then, if no other complications are involved, to 

 find an excess of heat evolved, over and above the chemical work 

 concerned in the reaction, in all those eases where the heat capacity 

 diminishes during the reaction, and vice versa. But what measures 

 have we of the chemical work involved ? 



By many the " free energy," or the energy available for outside work, 

 is taken to represent the chemical energy. | For the sake of argument, 

 let us assume temporarily that this is the case, always bearing in mind 



* After tlie preceding paper was printed, my attention was kindly called to the 

 fact that in 1881 Miiller-Erzbacli pointed out the parallelism of contraction and 

 heat of reaction in some cases (Ber. d. d. cli. Ges., 14, 217, 2043; Wied. Ann., 

 13, 522.) More recently, Hagemann has called attention to the same relation (a 

 brief paper published privately by Friedlander of Berlin in 1900). These facts were 

 wliolly unknown to me at the time of writing. Tlie reason why the discovery has 

 not liad more effect upon cliemistry is undoubtedly because these investigators did 

 not call attention to the effect of the different compressibility of different sub- 

 stances, and drew no corresponding conclusions from the observations. Unless 

 compressibility is considered, the exceptions to the rule are too frequent to permit 

 satisfactory generalization. For examples of the express or implied denial of the 

 significance of this relation, see Ostwald, Grundriss der allgem. Chem., 187 (1899), 

 also Beketoff, Chem. Centralblatt 1894, II. 229. In neither case was compressibil- 

 ity considered. 



t Richards, These Proceedings, 37, 399 (1902) ; Regnault, Ann. Chim., 73, 15 

 (1840); Thomsen, Thcrmo-chem. Untersuch., 1, 52 (1882); Kahlbaum, Zeitschr. 

 anorg. Chem., 29, 177 (1902). 



t Ostwald, The Chemometer, Zeitschr. phys. Chem., 15, 399 (1894). 



