Page:Scientific Papers of Josiah Willard Gibbs.djvu/212

 2pressure may by (263) be expressed by the formula $$\frac{P}{a_{s}t}$$, the relative density of a binary gas-mixture may be expressed by  By giving to $$m_{2}$$ and $$m_{1}$$ successively the value zero in these equations, we obtain  where $$D_{1}$$ and $$D_{2}$$ denote the values of $$D$$ when the gas consists wholly of one or of the other component. If we assume that  From (326) we have$$m_{1} + m_{2} = D \frac{pv}{a_{s}t},$$ and from (327), by (328) and (330),    By (327), (331), and (332) we obtain from (320)  This formula will be more convenient for purposes of calculation if we introduce common logarithms (denoted by $$\log_{10}$$) instead of hyperbolic, the temperature of the ordinary centigrade scale $$t_{c}$$ instead of the absolute temperature $$t$$, and the pressure in atmospheres $$p_{at}$$ instead of $$p$$ the pressure in a rational system of units. If we also add the logarithm of $$a_{s}$$ to both sides of the equation, we obtain where $$\mathsf{A}$$ and $$\mathsf{C}$$ denote constants, the values of which are closely connected with those of $$A$$ and $$C$$.

From the molecular formulæ of peroxide of nitrogen NO2 and N2O4, we may calculate the relative densities