to Prof. T. E. Thorpe, from whose memoir in Nature we derive most of the material of this sketch, he extends Kopp's generalizations, and traces the specific volumes of substances through various phases of chemical changes. In a paper on the thermal expansion of liquids above their boiling-points, he showed that the empirical expressions given by Kopp, Pierre, and others are equally applicable to much higher temperatures, and that the expansion-coefficient gradually increases with the diminution in molecular cohesion of the liquid, until, in the case of some liquids, it becomes even greater than that of the gas. In 1883 he contributed to the English Chemical Society a paper giving a simple general expression for the expansion of liquids under constant pressure between zero and their boiling-points—a formula analogous to that which expresses Gay-Lussac's law of the uniformity of expansion of gases; but which, like Gay-Lussac's law, however correct in theory, is subject to deviations in application. These deviations were shown to be related to the molecular weights of the gases.
Researches in thermal chemistry, made in 1882, showed him that the data obtained by Berthelot, Thomson, and others, regarding the "heats of formation" of hydrocarbons, stood in need of correction, because allowance had not been made for the physical changes involving absorption or evolution of heat which accompany the chemical changes considered; and he gave a table giving the heats of formation from marsh-gas, carbon monoxide, and carbon dioxide, of a series of hydrocarbons, for chemical reactions that actually occurred, while the reactions given by Berthelot and others were not realized in practice.
In the investigation of solutions, Mendeleef propounded in 1884 the law that in solutions of salts the densities increase with the molecular weights; but if we take, instead of the molecular weights, the weights of their equivalents or those of the equivalents of metals, the regularity of increase disappears; and, though his research was not yet finished, he submitted an equation as preliminary to ulterior results promising to give a more general formula. The results of the determination of the specific gravity of aqueous solutions of alcohol were applied, according to Prof. Thorpe's memoir, toward the elucidation of a theory of solution in which Dalton's doctrine of the atomic constitution of matter could be reconciled with modern views concerning dissociation and the dynamical equilibrium of molecules. "According to Mendeleef, solutions are to be regarded as strictly definite atomic chemical combinations at temperatures higher than their dissociation temperature; and, just as definite chemical substances may be either formed or decomposed at temperatures which are higher than those at which dissociation commences, so we may have the same phenomenon in solutions; at ordinary temperatures they
