Page:Scientific Papers of Josiah Willard Gibbs.djvu/438

greater. The deviation from the calculated values is therefore in the same direction and about such in quantity as we should expect.^[1]

M. Wurtz has remarked that the average value of $\delta$ (the density of the possible perchloride) is nearly identical with the theoretical density of the perchloride, and appears inclined to attribute the variations from this value to the errors of experiment. Yet it appears very distinctly in Table IX, in which the experiments are arranged according to the value of $\pi$ (the pressure due to the possible perchloride), that $\delta$ increases as $\pi$ diminishes. The experiments of MM. Troost and Hautefeuille show that the coincidence remarked by M. Wurtz is due to the fact that on the average in these experiments the deficiency of the density of the possible perchloride (compared with the theoretical value) is counterbalanced by the excess of density of the protochloride. When $\pi >400$, the effect of the deficiency in the density of the possible perchloride distinctly preponderates; when $\pi <250$, the effect of the excess of density in the protochloride distinctly preponderates. But the magnitude of the differences concerned is not such as to invalidate the general conclusion established by the experiments of M. Wurtz, that the dissociation of the perchloride may be prevented (at least approximately) by mixing it with a large quantity of the protochloride.

Table for facilitating calculation.—The numerical solution of equations (10), (11), (12) and (13) for given values of $t$ and $p$ may be facilitated by the use of a table. If we set

$\Delta ={\frac {\text{D}}{{\text{D}}_{1}}},$

(17)

${\text{L}}=\log {\frac {1000{\text{D}}_{1}({\text{D}}-{\text{D}}_{1})}{(2{\text{D}}_{1}-{\text{D}})^{2}}}=\log {\frac {1000(\Delta -1)}{(2-\Delta )^{2}}}\cdot$

(18)

we have for peroxide of nitrogen,

${\text{L}}={\frac {3118.6}{t_{\text{C}}+273}}+\log p-9.541;$

(19)

for formic acid,

${\text{L}}={\frac {3800}{t_{\text{C}}+273}}+\log p-9.641;$

(20)

for acetic acid,

${\text{L}}={\frac {3520}{t_{\text{C}}+273}}+\log p-8.349;$

(21)

1. The deviation of the protochloride of phosphorus from the laws of ideal gases shows the impossibility of any very close agreement between such equations as have been deduced in this paper and the results of experiment in the case of gas-mixtures in which this substance is one of the components. With respect to the question whether future experiments on the vapor of the perchloride (alone, or with an excess of chlorine or of the protochloride) will reduce the disagreement between the calculated and observed values to such magnitudes as occur in the case of the protochloride alone, it would be rash to attempt to anticipate the result of experiment.