Page:Scientific Papers of Josiah Willard Gibbs.djvu/422

gives a reduction of density from 2.65 to 2.28, which is about one-ninth less. This is, it will be observed, a deviation from the formula in the opposite direction from that which the experiments of Naumann alone, or a comparison of the experiments of Troost with those of Deville and Troost, seemed to indicate. The experiment here compared with Naumann's belongs to the III^d series of Deville and Troost. If instead of this experiment we should take an average of the experiments at lowest temperature in the II^d and III^d series, the agreement with the formula with respect to the effect of change of pressure would be almost perfect.

Formic acid.—In Table III, the determinations of Bineau are compared with the densities calculated by the formula

$\log {\frac {1.589({\text{D}}-1.589)}{(3.178-{\text{D}})^{2}}}={\frac {3800}{t_{\text{C}}+273}}+\log p-12.641.$

(11)

The observed densities are taken from the eighteenth volume of the third series of the Annales de Chimie et de Physique (1846), except in three cases, distinguished by parentheses, which are earlier determinations published in the nineteenth volume of the Comptes Rendus (1844). It may be added that the pressure (687) for the experiment at 108° is taken from Erdmann's Journal für praktische Chemie (vol. xl, p. 44), the impression being imperfect in the Annales, in the copies to which the writer has been able to refer, where the figures look much like 637. (The pressure 637 would make the calculated density 2.28.)

In the column which gives the excess of observed densities, the effect of nearness to the state of saturation is often very marked. Such cases are distinguished by an asterisk. The temperature of 99.5° is below the boiling point of formic acid, and the higher pressures employed at this temperature cannot be far from the pressure of saturated vapor. With respect to lower temperatures, we have the statement of Bineau that the pressure of saturated vapor is about 19^mm at 13°, 20.5^mm at 15°, 33.5^mm at 22°, and 53.5^mm at 32°. By interpolation between the logarithms of these pressures (in a single case, by extrapolation), we obtain the following result:—

Temperature, . . . . . . .	10.5	12.5	16	18.5	22
Pressure of sat. vapor, .	16.6	18.5	22	26.2	33.5
Pressure of experiment,	14.69	15.20	15.97	23.53	25.17