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

and for perchloride of phosphorus,

${\text{L}}={\frac {5441}{t_{\text{C}}+273}}+\log p-11.353.$

(22)

By these equations the values of ${\text{L}}$ are easily calculated. The values of ${\text{A}}$ may then be obtained by inspection (with interpolation when necessary) of the following table. From $\Delta$ the value of ${\text{D}}$ may be obtained by multiplying by ${\text{D}}_{1}$, 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: $\log {\frac {1000(\Delta -1)}{(2-\Delta )^{2}}}={\text{L}}.$

${\text{L}}$		$\Delta$		Diff.		${\text{L}}$			$\Delta$		Diff.		${\text{L}}$			$\Delta$		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 $\Delta$ 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 $\Delta =1.20$, 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 PC_l3 and 40 of the type Cl₂. A consideration of the varying values of $\Delta$ is therefore more instructive than that of the values of ${\text{D}}$, and it would in some respects be better to make the comparison of theory and experiment with respect to the values of $\Delta$.