328 ANDREWS art. i 



Hi -{• gh = const. 



Mm + 9'A = const. 



[234] 



It is emphasized in the text that we must distinguish the 

 /xi, ... f^m, intr-insic potentials, from the general potentials of the 

 components which include the action of gravity and are anal- 

 ogous to the partial molal free energies. These latter are of 

 course constant throughout the system. 



In the second part of this section (Gibbs, I, 147-150), Method 

 of treating the preceding problem, in which the elements of volume 

 are regarded as fixed, more detailed attention is given to the fac- 

 tors introduced by the discontinuities between phases in a sys- 

 tem under the influence of gravity. The condition of equilib- 

 rium is found to be that "the pressure at any point must be as 

 great as that of any phase of the same components for which 

 the temperature and the potentials have the same values as 

 at the point." 



The deduction which has had the widest application is that 

 summarized in equation [233]. If we apply this to a component 

 which is obeying the laws for an ideal gas we can relate density 

 to pressure as follows 



pv = nRT, *(1) 



nM , ^ 



M being the molecular weight of the component, so that 



1=V^' (3) 



If po be the pressure at some horizontal plane, the reference 

 zero point from which we measure the height h, we can sub- 

 stitute in equation [233], integrate and obtain the famous 



* Since the temperature which appears explicitly in equations (1) to 

 (10) of this article is in all cases the absolute temperature it seems best 

 to conform to current usage by representing it by T . 



