Page:Scientific Papers of Josiah Willard Gibbs.djvu/439

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VAPOR-DENSITIES.
403

and for perchloride of phosphorus,

(22)

By these equations the values of are easily calculated. The values of may then be obtained by inspection (with interpolation when necessary) of the following table. From the value of may be obtained by multiplying by , viz., by 1.589 for peroxide of nitrogen or formic acid, by 2.073 for acetic acid, and by 3.6 for perchloride of phosphorus.[1]

Table X.
For the solution of the equation:
Diff. Diff. Diff.
.7 1.005 3.0 1.382 5.3 1.932
.8 1.006 1 3.1 1.421 39 5.4 1.939 7
.9 1.008 2 3.2 1.461 40 5.5 1.945 6
1.0 1.010 2 3.3 1.500 31 5.6 1.951 6
1.1 1.012 2 3.4 1.537 37 5.7 1.956 5
1.2 1.015 3 3.5 1.574 37 5.8 1.961 5
1.3 1.019 4 3.6 1.609 35 5.9 1.965 4
1.4 1.024 5 3.7 1.642 33 6.0 1.969 4
1.5 1.030 6 3.8 1.673 31 6.1 1.972 3
1.6 1.037 7 3.9 1.703 30 6.2 1.975 3
1.7 1.046 9 4.0 1.730 27 6.3 1.978 3
1.8 1.056 10 4.1 1.755 25 6.4 1.980 2
1.9 1.069 13 4.2 1.778 23 6.5 1.982 2
2.0 1.084 15 4.3 1.800 22 6.6 1.984 2
2.1 1.102 18 4.4 1.819 19 6.7 1.986 2
2.2 1.122 20 4.5 1.837 18 6.8 1.987 1
2.3 1.146 24 4.6 1.854 17 6.9 1.989 2
2.4 1.172 26 4.7 1.868 14 7.0 1.990 1
2.5 1.202 30 4.8 1.882 14 7.2 1.992
2.6 1.234 32 4.9 1.894 12 7.4 1.994
2.7 1.268 34 5.0 1.905 11 7.6 1.995
2.8 1.305 37 5.1 1.915 10 7.8 1.996
2.9 1.343 38 5.2 1.924 9 8.0 1.997
3.0 1.382 39 5.3 1.932 8 9.0 1.999

The constants of these equations are of course subject to correction by future experiments, which must also decide the more general question in what cases, and within what limits, and with what degree of approximation, the actual relations can be expressed by equations of such form. In the case of perchloride of phosphorus especially, the formula proposed requires confirmation.

  1. The value of diminished by unity expresses the ratio of the number of the molecules of the more complex type to the whole number of molecules. Thus, if , in the case of peroxide of nitrogen there are 20 molecules of the type N2O4 to 80 of the type NO2, or in the case of perchloride of phosphorus there are 20 molecules of the type PCl5 to 40 of the type PCl3 and 40 of the type Cl2. A consideration of the varying values of is therefore more instructive than that of the values of , and it would in some respects be better to make the comparison of theory and experiment with respect to the values of .