Page:Scientific Papers of Josiah Willard Gibbs.djvu/216

180 reciprocal of the latter quantity is given for each experiment of this series. It seemed best, however, to make a trifling sacrifice of accuracy for the sake of simplicity.

It might be thought that the experiments under discussion would be better represented by a formula in which the term containing $$\log t$$ (see equation (333)) was retained. But an examination of the figures in the table will show that nothing important can be gained in this respect, and there is hardly sufficient motive for adding another term to the formula of calculation. Any attempt to determine the real values of $$A, B'$$ and $$C$$ in equation (333) (assuming the absolute validity of such an equation for peroxide of nitrogen), from the experiments under discussion would be entirely misleading, as the reader may easily convince himself.

From equation (336), however, the following conclusions may be deduced. By comparison with (334) we obtain which must hold true approximately between the temperatures 11C and 90C. (At higher temperatures the relative densities vary too slowly with the temperatures to afford a critical test of the accuracy of this relation.) By differentiation we obtain where $$M$$ denotes the modulus of the common system of logarithms. Now by comparing equations (333) and (334) we see that  which may be regarded as a close approximation at 40C or 50C, and a tolerable approximation between the limits of temperature above mentioned. Now $$B't + C$$represents the heat evolved by the conversion of a unit of NO2 into N2O4 under constant pressure. Such conversion cannot take place at constant pressure without change of temperature, which renders the experimental verification of the last equation less simple. But since by equations (322) we shall have for the temperature of 40C  Now $$Bt + C$$ represents the decrease of energy when a unit of NO2 is transformed into N2O4 without change of temperature. It therefore