376 VAPOR-DENSITIES. 



where c^ denotes a constant, we have 



Pi 



(5) 



where A' and B' are new constants. Now if we denote by p the total 

 pressure of the gas-mixture (in millimeters of mercury), by D its 

 density (relative to air of the same temperature and pressure), and by 

 D! the theoretical density of the rarer component, we shall have 



p-.p+p^.-.D^D. 



This appears from the consideration that p+p 2 represents what the 

 pressure would become, if without change of temperature or volume 

 all the matter in the gas-mixture could take the form of the rarer 

 component. Hence, 



2D,-D 



Pi=P-P2=P fr--> 

 ^i 



p, D^D-D,) 

 ^"p^-D) 8 ' 



By substitution in (5) we obtain 



(6) 



By this formula, when the values of the constants are determined, we 

 may calculate the density of the gas-mixture from its temperature 

 and pressure. The value of D x may be obtained from the molecular 

 formula of the rarer component. If we compare equations (3), (4) 

 and (5), we see that 



B' = 



Now c 1 c 2 is the difference of the specific heats at constant volume of 

 N0 2 and N 2 O 4 . The general rule that the specific heat of a gas at 

 constant volume and per unit of weight is independent of its conden- 

 sation, would make C^ G^ B = 0, and B' = l. It may easily be shown, 

 with respect to any of the substances considered in this paper,* that 

 unless the numerical value of B' greatly exceeds unity, the term B'logi 

 may be neglected without serious error, if its omission is compensated 

 in the values given to A' and C. We may therefore cancel this term, 

 and then determine the remaining constants by comparison of the 

 formula with the results of experiment. 



* For the case of peroxide of nitrogen, see pp. 180, 181 in the paper cited above. 



