Page:Scientific Papers of Josiah Willard Gibbs.djvu/433

pressure as determined by Regnault's experiments, have been calculated by the present writer by multiplying the numbers of the third column by ${\frac {p_{{\text{L}}({\text{P}}-p_{\text{E}})}}{p_{\text{R}}({\text{P}})-p_{\text{L}}}}$.

As the height of the barometer in Horstmann's experimente is not given, it has been necessary to assume ${\text{P}}=760$. The inaccuracy due to this circumstance is evidently trifling. The last two columns of the table, which relate to different series of experiments by Horstmann (a distinction not observed in other parts of the table), give the excess of the densities thus obtained from Horstmann's and Regnault's experiments above the values calculated from equation (12) with the use of Regnault's determinations of pressure.

The densities obtained by experiment are without exception less than those obtained from equation (12). At the highest temperatures, where the liability to error is the least, both in respect to the measurement of the pressure of saturated vapor and in respect to the analysis of the product of distillation, the results of experiment are most uniform, and most nearly approach the numbers required by the formula. At the lowest temperatures, the greatest observed density is about one-eleventh less than that required by the formula, the difference being about the same as between the highest and lowest observed values for the same temperature.

Since each successive purification of the substance employed by Regnault diminished the pressure of its vapor, it is not improbable that the pressures might have been still farther diminished by farther purification of the substance. The pressures which we have used are therefore liable to the suspicion of being too high, and it is quite possible that more accurate values of the pressure would still farther reduce the deficiency of observed density.

Perchloride of phosphorus.—For this substance, we have at atmospheric pressure a single determination of vapor-density by Mitscherlich,^[1] and a series of determinations by Cahours;^[2] at lower pressures we have determinations by Wurtz^[3] and by Troost and Hautefeuille.^[4] In the experiments of Wurtz the pressure was reduced by mixing the vapor with air. In Table VIII all these determinations are compared with the formula

$\log {\frac {3.6({\text{D}}-3.6)}{(7.2-{\text{D}})^{2}}}={\frac {5441}{t_{\text{C}}+273}}+\log p-14.353.$

(13)

The differences between the calculated and observed values are often large, in six cases exceeding .30; but they exhibit in general that

1. Pogg. Ann., vol. xxix (1833), p. 221.
2. Comptes Rendus, vol. xxi (1845), p. 625; and Annales de Chimie et de Physique, ser. 3, vol. xx (1847), p. 369.
3. Comptes Rendus, vol. lxxvi (1873), p. 601.
4. Ibid., vol. lxxxiii (1876), p. 977.