THE CONDITIONS OF EQUILIBRIUM FOR HET- 

 EROGENEOUS MASSES UNDER THE INFLU- 

 ENCE OF GRAVITY AND OF CENTRIFUGAL 

 FORCE 



[Gibbs, I, pp. lU-150] 



DONALD H. ANDREWS 



The effect of gravity on the equilibrium of fluids has interested 

 physicists and chemists for many hundreds of years. A Hst of 

 those who have contributed observation and theory to this field 

 includes many famous names such as Galileo, Laplace and 

 Boltzmann. It is Gibbs' characteristic role to have shown how 

 these special relations of gravity and fluid equilibrium fit into 

 the general scheme of thermodynamics in a way that permits 

 of the widest sort of application. 



Little comment is needed on the actual derivation of the 

 equations.* The usual thermodynamic system is postulated, 

 including in this case the force of gravity. The laws of thermo- 

 dynamics and the various equations of condition then lead to 

 the equations which define the state of the system. 



Temperature must be constant throughout, i.e., 



t = const.; [228] 



and the pressure must vary with the height,i.e., 



dp = -gydh. [233] 



The chemical potentials (mi, . . . m^) of the individual com- 

 ponents (essentially the partial pressures if the system is not 

 far from ideal) must satisfy the equations 



* Compare Section XIII of Article L of this volume. 



327 



