Page:Scientific Papers of Josiah Willard Gibbs.djvu/424

between the observed and calculated densities is .05, and the average difference .016; nine experiments at pressures ranging from 29^mm to 7^mm, in which the maximum difference is .07 and the average .035; and three experiments at pressures of about 3^mm, in which the average difference is .17. The extraordinary precision of the determinations at low pressures is doubtless due to the large scale on which the experiments were conducted. All the experiments at temperatures below 99° were made with a globe of the capacity of 5${\tfrac {1}{2}}$ liters with a stem of suitable length to hold the barometric column.

The agreement is certainly as good as could be desired, and shows the accuracy of which the method of observation is capable. But in no part of the thermometric scale do we find so great a range of pressures as might be desired, without using pressures too low for accurate results, or observations which are to be rejected for other reasons.

Acetic acid.—For this substance the densities have been calculated by the formula

$\log {\frac {2.073({\text{D}}-2.073)}{(4.146-{\text{D}})^{2}}}={\frac {3520}{t_{\text{C}}+273}}+\log p-11.349,$

(12)

the constants 3520 and 11.349 being derived from the determinations of Cahours and Bineau, which with those of Horstmann and Troost are given in Table IV. The experiments of Cahours and Horstmann were made under atmospheric pressure, those of Horstmann^[1] by the method of Bunsen, those of Cahours presumably by the method of Dumas. The numbers in the first column of the densities observed by Cahours are taken from the twentieth volume (1845) of the Comptes Rendus, except a few cases, distinguished by parentheses, which are taken from the preceding volume (1844).

The numbers in the second column are taken from his Leçons de chimie générale élémentaire, 1856. These numbers seem to be based in part upon new experiments and in part upon a revision of the observations recorded in the Comptes Rendus, the calculations being carried out to another figure of decimals. They are therefore entitled to a greater weight than the numbers of the preceding column.

The agreement of the formula with the numbers given in the Leçons de chimie is very good, the greatest divergences being .080 at 190° and .062 at 180°. But at 190° the table in the Comptes Rendus agrees precisely with the formula, and at 171 (the next experiment) it shows a divergence in the opposite direction. The next divergences in the order of magnitude are -.033, -.036, -.032

1. Lieb. Ann., suppl. vi, p. 65.