"constant" is remarkably constant. Schiff's work was most carefully done by the same method and hence his results are at once reliable and comparable in an eminent degree; and, as a matter of fact, the extreme values of the constant calculated from his data differ from the average value by hardly three per cent. Such a regularity as the above implies that the liquids at their boiling points are in corresponding states (the term corresponding states " being used in the sense given it by van der Waals (loc. cit.) As far as the pressure is concerned, it may be stated that atmospheric pressure can be reckoned as "corresponding" in questions of this sort. That boiling points for certain properties of liquids are "corresponding temperatures" in a not inconsiderable measure has been shown by C. M. Guldberg who in comparing the quotient of the absolute boiling points by the absolute critical temperature found it to remain close to an average value of about, and concluded that quantities which vary slowly with the temperature (among which latent heats of vaporization are to be counted) may be reckoned as being approximately in corresponding states at their points of ebullition. This conclusion follows directly from equation (4) which indicates that the relation must obtain ( being an unknown function). Guldberg then states that through comparison of various liquids the equation is found by means of graphic interpolation, and accordingly at the boiling points the relation Guldberg thus obtains about the same constant as has been shown in the foregoing to be the average of reliable determinations. As stated above, the values of με given in the table differ * Zeitschr. für phys. Chemie, v, p. 374, 1890. considerably from the normal average value in the case of the acids, nitro-methane and nitro-ethane, the alcohols, acetone and water. For the acids and nitro-compounds they are too small; for the alcohols, water, and acetone, they are too large. The cause of this abnormal behavior is to be found in the "association" of the molecules of these liquids, and in the changes which the molecular aggregations undergo during the process of vaporization. We will consider the case of the alcohols, water, and acetone first. The brilliant experiments of Ramsay and his associates on the surface tensions of liquids, and his theoretical deductions have taught us that the liquids in question are made up of molecules in a state of association. No facts are known, however, which indicate that an appreciable amount of molecular association is persistent in the vaporous state; on the contrary, the normality of the vapor density, and other properties of the vapors, show that they consist exclusively, it may be said, of simple molecules. Accordingly, when the alcohols, etc., are evaporated, there occurs a decomposition of the complex molecules into simple ones. This requires the expenditure of a certain amount of energy, which is manifest as heat energy. The heat necessary to convert a molecularly polymerized liquid into its normal vapor consist then of two terms, the heat expended in actually turning the liquid into a gas, and the heat used up in decomposing the molecular aggregations or "tagmas." The value of p, then, in the expression = const. is ρμ T greater for associated than for normal liquids; hence the value of the "constant" becomes greater, and, indeed, so much the greater, the more complex the liquid molecule. It seems at present impossible to make a reliable correction for the heat employed in decomposing the complex molecules. In the case of the acids, the state of affairs is somewhat different. It has long been known that the organic acids, as formic, and acetic acid, have abnormal vapor densities due to the association of the molecules in the vaporous state; as the temperature rises, the degree of association becomes less and less until the normal molecule is reached. At the boiling points under ordinary atmospheric pressure, the vapor density of formic acid may by extrapolation from the data due to Petersen and Ekstrandt be put at 2-5 at 100°; this multiplied by 28.87 gives a molecular mass of 72; and this value of u με when introduced into the relation = const., gives for the Tabs *See Guye's paper: Sur la polymirisation moléculaire des liquides: Archives des Sciences physiques et naturelles, III, xxxi, 160, 1894. Ber. der deutschen chem. Gesell., xiii, 1194. "constant," 19-89. Likewise from extrapolation of Cahours* determinations of the vapor density of acetic acid, its vapor density at 118° may be set at 3:3, which by multiplication by 28.87 gives as molecular mass 95; and this in turn shows the value of the "constant" to be 20-34. Now we have every reason to believe that the gaseous associated molecule does not dissociate on passing into the liquid state; on the contrary, there can scarcely be any doubt but that it increases more or less in complexity. Accordingly, the molecular masses calculated for the gaseous molecules may be set as very near those of the liquid molecules of the two acids in question, and, indeed, the experiments of Schall+ indicate that for acetic acid, at least, such is the state of affairs. The values of the "constant" found for these corrected molecular masses are seen to be practically identical with that found for normal liquids, and the exception presented by the acids is seen to be but seeming. For butyric and valeric acids, however, the "constants" cannot be corrected as for the two preceding acids, since they are found to be too large even when calculated on the assumption that their molecular masses are normal. If their determinations of latent heat of volatilization are sufficiently accuratewhich is somewhat doubtful-it is probable that the complex liquid molecules in their case undergo decomposition on passing into the vaporous state, similar to the alcohols, etc. the absence of experiments on their vapor densities it is not possible to judge what is the true state of the case. Nitromethane and nitroethane also give values of the constant less than the normal. Ramsay and Shields have measured the superficial tension of nitroethane, finding it such as to legitimatize the assumption that the molecules of this liquid are in a state of association; by analogy it may be admitted that nitromethane is also an associated liquid, although no experimental data are at hand. If what has been said in explanation of the seeming abnormality in the behavior of the acids as regards the "constant" be in accordance with fact, it is necessary to suppose that the two nitro-compounds also pass from the liquid into the gaseous condition without the complex molecule suffering much dissociation. The immediately preceding considerations indicate a method of getting an approximation of the degree of association of a liquid. If any liquid, whose latent heat of volatilization be known, gives a value for the "constant" close to 20-7, it is pretty certain that it is normal. If it gives a less value, it is associated in the liquid as well as in the gaseous state; if it *Comp. Rend., xix, 771. + Ber. der deutschen chem. Gesell., xvii, 2199, 1884. AM. JOUR. SCI.-THIRD SERIES, VOL. XLIX, No 293.-MAY, 1895. gives a greater value, it must be associated in the liquid state alone. The greater the variation from the normal value of the "constant," the greater the amount of the association. Tabs Thus far, we have considered the application of the formula με const. only to determinations made under the pressure of about one atmosphere. But how will it be at other pressures and hence other temperatures? All of the deductions of the formula have been made on the assumption that the pressure was that of one atmosphere, with the exception of the one developed by Le Chatelier, which contains a term referring to pressure (Equation 17). This equation, however, was derived on the supposition that the latent heat of vaporization is independent of temperature and pressure; such an assumption, however, does not accord with the experimental results obtained by Regbault, Ramsay and Young, Jahn, and others. The heat of vaporization of a liquid decreases with rise of temperature and concomitant increase of pressure until at the critical point it becomes equal to zero. Yet for all temperatures and concurrent pressures below the critical, the relation (17) obtains, and the lower the temperature, the larger the "constant." The number of reliable data at hand for the comparison of the theory with experiment at other pressures than the atmospheric is relatively small. Most of them have been. made at the freezing point of water under the pressure of the saturated vapor at that temperature. In Table II are given such data as are reliable, and only for normal liquids. In the first column is given a reference number to the investigator's names and places of publication, directly below the table. Columns a, b, c, and d give the name, formula, molecular mass, and the latent heat of vaporization, respectively of the liquids in question. The sixth (e) column contains the value of the με expression and the seventh (f) the value of twice the " Tabs natural logarithm of the pressure. (The pressure in the case of such liquids as have had their vapor tension determined is generally set as equal to that of the saturated vapor at 0°; for the others, the pressure has been put at 60mm of mercury, as Jahn, in his experiments, reduced the pressure to this point before allowing evaporation to take place, and the others examined by him have not been investigated thoroughly as regards their vapor tensions. The pressure is reduced to absolute measure by multiplication by 13-6.) The last column gives the value of Le Chatelier's relation (17), obtained by adding the values found in columns e and ƒ for each liquid. I, Jahn, Zeitschr. f. phys. Chem., xi, 790, 1893. II, Regnault, Memoires de l'Académie, xxvi, 761, 1862. III, Winkelmann, Wiedemann's Annalen, ix, 208 and 358, 1880. Table II shows that, while it is impossible to speak of a constancy for the values contained in the sixth column, through the introduction of the pressure correction in equation (17) a value is found equal in mean to about 40.5; it is remarkable that such a constancy is to be found in the values, since no great amount of accuracy can be attributed to the determinations of the latent heat or of the pressure. If the pressure correction be applied to the determinations of the latent heats of vaporization carried out under or nearly under atmospheric pressure, the "constant" is found to become equal to 39-18, since 2 log 760 equals 18.48; this value, as is to be expected, is very near to that found for the liquids under the circumstances given in table II; undoubtedly, approximately the same value for the expression would be found under other pressures and concurrent temperatures, although the data at hand are too meager to make it worth while to perform the necessary calculations. As a conclusion to all that precedes and as a prediction of all future experimental work on latent heats of vaporization, it may be stated that the relation deduced by Le Chatelier may be put equal to about 40.00, thus In accurate determinations of temperatures of ebullition, it is often necessary to make a correction for the variation of the pressure from the normal pressure of 760mm of mercury. In |