Page:Scientific Papers of Josiah Willard Gibbs.djvu/432

396 The uniformity of the numbers in the last column shows the remarkable precision of the determinations. At the same time it is evident that the differences in these numbers are due principally to the errors of observation, so that numbers obtained by interpolation between the logarithms of the observed pressures will be somewhat better (on account of averaging of the errors) than the original determinations.

The values obtained by such an interpolation have been used for the comparison of Horstmann's experiments with the formula (12) which is given in Table VII. Unfortunately this comparison cannot be extended above 25°, which is the limit of Regnault's experiments. The first three columns of the table give the temperatures of Horstmann's experiments, the pressures corresponding to these temperatures according to the determinations of Landolt, and the density deduced from Horstmann's experiments by the use of these pressures. To

these columns, which are taken from Horstmann's paper, are added the pressure derived from Regnault's observations by the logarithmic interpolation described above, the density calculated by equation (12) from these pressures and the temperatures of the first column, and the densities obtained by combining Horstmann's experiments with Regnault's pressures. This column is derived from the second, third and fourth, as follows. If $$w$$ and $$\text{W}$$ denote respectively the weights of vapor and of air which pass through the apparatus in the same time, $$\text{P}$$ the height of the barometer, and $$p_{\text{L}}$$ the pressure of saturated vapor as determined by Landolt, the densities obtained on the basis of Landolt's pressures, and given in the third column, are evidently represented by $$\frac{w(\text{P} - p_{\text{L}})}{\text{W}p_{\text{L}}}$$. The numbers of the fifth column, which are represented in the same way by $$\frac{w(\text{P} - p_{\text{R}})}{\text{W}p_{\text{R}}}$$, where $$p_{\text{R}}$$ denotes the