314 PROCEEDINGS OF THE AMERICAN ACADEMY 



metrics are straight lines.* For liquid thymol this is very nearly 

 true. § 10. 



2. In relation to a, I shall postulate : (1) A liquid or a gas 

 solidifies whenever, in consequence of changes of the physical or 

 chemical environment (temperature, stress external or internal, etc.), 

 the cohesive valency of the constituent atoms is sufficiently increased 

 to admit of the permanent construction of a tridimensional chain, the 

 type structure and the molecular weight of which (solid) are each a 

 multiple of the given structure and molecuhir weight. (2) A gas 

 liquefies whenever in consequence of changes of environment the cohe- 

 sive valency of the constituent atoms is increased, without affording 

 means for the permanent construction of the chain in question. 



Thus, it is supposed that the same molecular nucleus is present in 

 the three states of aggregation, and that the aggregations are produced 

 by relatively weak affinities. Since, therefore, it is my purpose to 

 bring these forces to bear, at constant external pressure, when the mole- 

 cules are at successively different distances apart, it will facilitate 

 reasoning to assume at the outset that the energy necessary to effect 

 the change a, § 1, is constant as to temperature, at least within the 

 interval 0° to 50°, under experiment. §§ 8, 9, 12. 



3. In relation to b and c, § 1, conjointly, I will proceed as fol- 

 lows. Anywhere within the given body let a small sphere be described ; 

 and conceive the expansion work between solid and liquid done 

 within this sphere by the applied heat to be represented by the iso- 

 thermal expansion against a pressure, p, acting on the surface of the 

 sphere. Then p may be called the molecular pressure and the expan- 

 sion work will be, 



w 



^Jpdv (1) 



4. Now, if a substance can be found which under the same pres- 

 sure may be kept either in the solid or in the liquid state through a 

 considerable range of temperature, then if the latent heats within this 

 range regarded as functions of temperature, be co-ordinated with the 

 corresponding volume changes solid-liquid, relations for the energies 

 b and c, § 1 , are deducible. 



Again, if with the knowledge of b and c in hand, specific heat 

 regarded as functions of temperature, be co-ordinated with the corre- 

 sponding thermal expansions, the characters of the energies e and f, 



* Fitzgerald, Proc. Roy. Soc, Vol. XLII. p. 50, 1887. 



