differential forms of equations (1) and (2) do not readily permit. of direct comparison with empirical facts; they must first by suitable hypotheses and integrations be thrown into other forms. The comparison of the deductions and discovered relationships with the experimental data generally shows a close correspondence. Sometimes, however, variations and exceptions occur which cannot be referred to experimental errors. The object of this paper is to give an account of the efforts that have been made and the results that have been obtained in regard to the relations between pressure, temperature, and latent heat of vaporization; to subject to a critical revision all experimental data bearing upon the question; to discuss the differences seemingly present between theory and experiment; and to apply the results to certain practical problems. The division of the matter is the following: first, a historical account of such papers as have dealt with the theoretical side of the question; second, a review in tabular form of experimental data together with a discussion of their comparative value; third, a comparison of the results of theory and experi ment; fourth, an application of results to a practical problem. I. The first paper in which an endeavor was made to find out relations between latent heats of vaporization and other energyfactors is due to Ure;* this pioneer in this field of research determined the heats of vaporization of a number of common liquids, and concluded from his results that under the same pressure the latent heat of vaporization is inversely proportional to the vapor density. Desprets, in a paper read before the French Academy towards the end of the year 1818, but of which merely an abstract seems ever to have been published, communicated the results of some determinations of the latent heats of vaporization of water, alcohol, ether, and essence of terebinthine. An inspection of his data led him to state that a liquid at its point of ebullition requires for volatilization so much the less heat, the denser its vapor; latent heats of vaporization are approximately proportional to densities at the boiling points. Persont after determining the latent heats of vaporization of ten additional liquids, notwithstanding that his results were not as accurate as those of Desprets, as he himself admits, and without giving any data, formulated a law, which is "for the heat of vaporization what the law of Dulong and Petit is for the specific heat," and "even more general, since it applies to *Phil. Mag. liii, 191, 1819. Ann. Chim. et Phys., xxiv, 323, 1823. simple and to compound bodies without distinction." This law is: "The heats of vaporization of different substances range themselves exactly in the order of their temperatures of ebullition, when, instead of equal weights, atomic weights are taken. In a "Note" three years later Person* reverts to his law, and drawing up a table of latent heats of vaporization from the data due to Favre and Silbermann shows how well his previous statements are corroborated by these determinations. The exceptions presented by the acids are explained away by making allowance for their abnormal vapor densities. In this paper, he puts his law in a somewhat different form: "The amount of heat needed to vaporize substances under the same pressure is identical, when the volume produced is the same, and it is smaller or greater according as the volume produced is smaller or greater." Trouton "on comparing the quantities of heat necessary to evaporate at constant pressure quantities of different liquids taken in the ratio of the molecular weights,"-found that the amount of heat required by any body is approximately proportional to its absolute temperature at the point of ebullition." He then propounded the following law : The molecules of chemically related bodies, in changing from the gaseous to the liquid state at the same pressure, disengage quantities of heat, which may be called the molecular latent heat, directly proportional to the absolute temperature of the point of ebullition." The above laws are purely empirical; they were found through observation of rows of figures; they have no theoretical grounding; being subject to exceptions and irregularities, they can never as deduced rise to the rank of great generalizations; they have been drawn up by the inspection of experimental data, which is an inversion of the usual order of discovery, experimental data as a rule being a means of corroboration rather than of deduction of laws of nature. We now pass to the consideration of the work that has been done along theoretical lines in the finding out of relations between heat of vaporization, temperature, and pressure. The first effort made in this direction is due to Raoul Pictet, in a paper truly remarkable for its time, although it seems to have attracted but little attention. Pictet considers a cycle in which a liquid is evaporated from one chamber, condensed in another, and finally returned to the first. Admitting the validity for the case in hand of the laws of Boyle and GayLussac, he then finds mathematical expressions for the work done and the heat absorbed. In order to equate these essen*Comptes Rend., xxiii, 524, 1846. Phil. Mag., V., xviii, 54, 1884. tially independent expressions he makes two hypotheses: 1, the cohesion of liquids is the same for all: 2, Carnot's cycle is applicable to volatile liquids, and to their changes of volume: and there exists a relation between heat taken in and work performed. The expressions finally arrived at show a satisfactory correspondence for the most part with the determinations of latent heats of vaporization made by Regnault. The conclusions which have a bearing upon our subject are: I-The product of the latent heats of liquids at the same pressure by their atomic weights, divided by the absolute temperature at which the vaporization takes place, is the same for all: IIThe difference between the internal heats of vaporization at any two temperatures, multiplied by the atomic weights, is a constant number for all liquids. We will not enter into any discussion of these results, contenting ourselves with remarking that the first conclusion is a plain enunciation of "Trouton's law" mentioned above. If priority of publication has any moment in the choice of the name of a discovery, the law in question ought to be called Pictet's law since the date of Pictet's paper is 1876 and that of Trouton's 1884. b P, Equation (1) seems first to have been made use of by van der Waals* for the establishing of relationships between temperature, pressure, and latent heat of evaporation. If for T, and v, ep, m T,, and (m) (p, being the critical pressure, T,, the critical temperature, b, the covolume, and ɛ, m, 4(m), coefficients) be substituted in equation (1), and it be kept in mind that υμ b =f(m), results. Now when m is the same, that is, at the same reduced dε dm temperature, must have the same value, and as a necessary consequence it follows that * Continuität des gasförmigen und flüssigen Zustandes, p. 137. (5) where F is a constant number for all bodies. But equation (5) is nothing else than the mathematical expression for "Trouton's law," and again the rightfulness of this name may be justly questioned, for the German translation of van der Waal's book appeared three years before Trouton's paper. Van der Waals called to mind the similarity of the expression as developed just above to the law proposed by Desprets (loc. cit.), and drew up a little table of data to see if experiment corroborated theory, which in a certain measure he found to be the case. Bouty* sought to transform the fundamental equation (1) so as to get the quotient of the molecular heat of vaporization by the square of the absolute temperature equal to a constant. His course of reasoning is as follows. If, in the formula the specific volume of the liquid be neglected in comparison with that of the vapor, and if the density of the latter be normal, it ensues that where D is the absolute specific gravity of hydrogen at the temperature zero and under the pressure of 760mm of mercury. By the combination of (6) and (7) the equation is obtained; and if T, be the boiling point under the pressure Po If it be admitted with Dalton that all vapors have the same tensions at temperatures equidistant from the boiling points of the liquids which give them off, the expression must be the same for all liquids, and the expression becomes equal to a constant. Although Bouty is inclined to admit that Dalton's "law" is incorrect, and hence (10) cannot be constant, he gives a table of "constants" for a number of liquids, of which, as de Heen *Journ. de Phys., II, iv, 26. remarks "it is needless to say that the variations to be found ρμ in the values of are enormous." If, however, it be assumed με that T be constant, it at once follows that = constant, dT T which is Trouton's or better Pictet's law. Le Chateliert also has transformed equation (1) into another directly comparable with the results of experiment. After putting it in the form (o in Le Chatelier's calculations is always taken to be the molecular heat of vaporization) by multiplying and dividing the second term by p, he obtained this expression If the volume of the liquid be neglected in comparison with that of the vapor, and the gas equation pv=RT be introduced, after division by T, the expression dT dp =0 PTAR dT p P+2 log p=0 (13) (14) is obtained. If this equation be integrated between the limits T and T., it being admitted that the heat of vaporization is constant, the equation results, and, all calculations being made on the assumption that p is independent of T, dp * Bulletin de l'Académie royale de Belgique, III, ix, p. 281, 1885. The results of Ramsay's and Young's experiments show that Tdp for considerable differences of pressure. If it be true that T is constant then must be constant also, for ρ dr dT dp T Ramsay and Young have also experimentally proven the truth of this relation. See Phil. Mag., V, xx, p. 515, 1885; ibid., xxi, pp. 33 and 135; and ibid., xxii, p. 33, 1886. Recherches expérimentales et théoriques sur les equilibres chimiques, Ann. des Mines, Mars-Avril, 1888, p. 337. |