J. TTT a ihhs— Equilibrium of Heterogeneous Substances. 239 

 and from (327), by (828) unci (;i80), 



2 m, -{-»i.,z= I>J~-=i2J)- , 



whence 



m, = (D,~lJ)i^-^, (331) 



m, = 2(7>-y>,)f3- (•'^^2) 



By (327), (331), and (332) we obtain from (320) 



los^~ r.\ = log^ . (333) 



^2 (Z> - i>i) a, a^ a„ ° « ^ ' 



This formula will be more convenient for purposes of calculation if 

 we introduce common logarithms (denoted by log,g) instead of 

 hyperbolic, the temperature of the ordinary centigrade scale t, instead 

 of the absolute temperature t, and the pressure in atmospheres p„t 

 instead of p the pressure in a rational system of units. If we also 

 add the logarithm of a, to both sides of the equation, we obtain 



•°g.» -^(i-S-x = ^ + 1 '"=■» <' +^"^" - ^3- (^•^*) 



where A and C denote constants, the values of which are closely con- 

 nected with those of A and 0. 



From the molecular formula? of peroxide of nitrogen NO^ and 

 NgO^, we may calculate the relative densities 



14 + 32 ^^^^^ _ ^ .^ ^^^^^ j^ — !^jhlf ,0691 r= 3.178. (335) 

 1 2 ' - 2 ^ ' 



The determinations of MM. Deville and Troost are satisfactorily 

 represented by the equation 



iogio 2 (i> - 1.589) ^,+ 273' ^ ^ 



which o'ives 



i)= 3.178+ (y - VW(3.178H-0) 



3118.6 , 

 where log ^o^J= 9.47056 - f_^^ - logi oP<u- 



In the first part of the following table are given in successive col- 

 umns the temperature and pressure of the gas in the several experi- 

 ments of MM. Deville and Troost, the relative densities calculated 

 from these numbers by equation (336), the relative densities as 

 observed and the difference of the observed and calculated relative 



