Page:Scientific Papers of Josiah Willard Gibbs.djvu/435

formula. In fact, the densities obtained by Cahours at atmospheric pressure and those obtained by Troost and Hautefeuille at pressures a little less than one-third of an atmosphere seem to form a continuous series, notwithstanding the abrupt change of pressure. Yet it is difficult to admit that the density is independent of the pressure. So radical a difference between the behavior of this substance and that of the others which we have been considering requires unequivocal evidence. Now it is worthy of notice that the experiment at 182°, in which the greatest discrepancy is seen, is not given in the first record of the experiments, which was in the Comptes Rendus in 1845. It is given in the Annales de Chimie et de Physique in 1847, where it is called the first experiment. (The experiment at 336° is also omitted in the Comptes Rendus and that at 208° in the Annales, otherwise the lists are the same.) If it was the first experiment in point of time, which is apparently the meaning, it was made before the publication in the Comptes Rendus, and we can only account for its omission by supposing that it was a preliminary experiment, in which its distinguished author did not feel sufficient confidence to include it at first with his other determinations, although he afterwards concluded to insert it. If we reject this observation as doubtful, the disagreement between the formula and observation appears to be within the limits of possible error, but additional experiments will be necessary to confirm the formula.^[1]

Experiments have also been made by M. Wurtz in which the vapor of the perchloride of phosphorus was diluted with that of the protochloride.^[2] These experiments may be used to test equation (8), which, when the values of its constants are determined by equation (13), reduces to the form

$\log {\frac {p_{5}}{p_{2}p_{3}}}={\frac {5441}{t_{\text{C}}+273}}-13.751$

(14)

where $p_{5},p_{2}$, and $p_{3}$ denote the partial pressures due respectively to the PCl₅, the Cl₂, and the PCl₃, existing as such in the gas-mixture. Since these quantities cannot be the subjects of immediate observation, a farther transformation of the equation will be convenient. Let ${\text{M}}_{3},{\text{M}}_{2}$ denote the quantities of the protochloride and of chlorine of which the mixture may be formed, and ${\text{P}}_{3},{\text{P}}_{2}$ the pressure which

1. Additional experiments on the density of this vapor have been made by M. Cahours, concerning which he says in 1866: "Les déterminations qui je viens d'effectuer à 170 et 172 degrés (ce corps bout vers 160 à 165 degrés) m'ont donné des nombres qui, bien que notablement plus forts que ceux que j'ai obtenus antérieurement à 182 et 185 degrés, sont encore bien éloignés de celui que correspond à volumes," Comptes Rendus, t. 63, p. 16. So far as the present writer has been able to ascertain, these determinations have not been published. The formula gives 6.025 for 170° and 5.973 for 172°, at atmospheric pressure. The number corresponding to four volumes is 7.20.
2. Comptes Rendus, vol. lxxvi (1873), p. 601.