406 J. W. Glbbs — Equilibrium of Heterogeneous Substances. 



the conditions of equilibrium relating to tempei'ature and the poten- 

 tials remain satisfied. (The differential coefficients in the equations 

 which follow are to be determined on this supposition.) Moreover, if 



i. e., if the pressure of the interior mass increases less rapidly (or 

 decreases more rapidly) with increasing radius than is necessary to 

 preserve neutral equilibrium, the equilibrium is stable. But if 



the equilibrium is unstable. In the remaining ease, when 



farther conditions are of course necessary to determine absolutely 

 whether the equilibrium is stable or unstable, but in general the 

 equilibrium will be stable in respect to change in one direction and 

 unstable in respect to change in the opposite direction, and is there- 

 fore to be considered unstable. In general, therefore, we may call 

 (523) the condition of stability. 



When the interior mass and the surface of discontinuity are formed 

 entirely of substances which are components of the external mass, p' 

 and (3 cainiot vary and condition (524) being satisfied the equili- 

 biium is unstable. 



But if either the intei'ior homogeneous mass or the surface of dis- 

 continuity contains substances which are not components of the 

 enveloping mass, the equilibrium may be stable. If there is but one 

 such siibstance, and we denote its densities and potential by y\, 1\, 

 and /<!, the condition of stability (523) will reduce to the form 



\ dj-i, chtj dr ^^ ^ ' 

 or, by (98) and (508), 



(rr/+2r,)'^J</'-y. (526) 



In these equations and in all which follow in the discussion of this 

 case, the temperature and the potentials yWg? l-^zi ^tc. are to be 

 regarded as constant. But 



