522 .7. W. Gibhs — JEquilihrium. of Heterogeneous Substances. 



Page 

 In the same homogeneous mass we may distinguish the potentials for an indefinite 

 number of substances, each of which has a perfectly determined value. Between 

 the potentials for different substances in the same homogeneous mass the same 



equations will subsist as between the units of these substances 149 



The values of potentials depend upon the arliitrary constants involved in the defi- 

 nition of the energy and entropy of each elementary substance 151 



COEXISTENT PHASES. 



Definition of phases — of coexistent phases, 152 



Number of the independent variations which are possible in a system of coexistent 



phases, 152 



Case of w + 1 coexistent phases, .. 153 



Cases of a less number of coexistent phases, 155 



INTERNAL STABILITY OP HOMOGENEOUS FLUIDS AS INDICATED BY FUNDAMENTAL 



EQUATIONS. 



General condition of absolute stability, 156 



Other forms of the condition, 160 



Stability in respect to continuous changes of phase, 162 



Conditions which characterize the limits of stability in this respect, 169 



GEOMETRICAL ILLUSTRATIONS. 



Surfaces in which the composition of the body represented is constant, 172 



Surfaces and curves in wliich the composition of the body represented is variable 

 and its temperature and pressure are constant, 176 



CRITICAL PHASES. 



Definition, 1 88 



Number of independent variations which are possible for a critical phase while 

 remaining sucli, 188 



Analytical expression of the conditions which characterize critical phases. — Situ- 

 ation of critical phases with respect to the limits of stability, 189 



Variations which are possible under different circumstances in the condition of a 

 mass initially in a critical phase, 191 



ON THE VALUES OF THE POTENTIALS WHEN THE QUANTITY OF ONE OF THE 



COMPONENTS IS VERT SMALL, 194 



ON CERTAIN POINTS RELATING TO THE MOLECULAR CONSTITUTION OF BODIES. 



Proximate and ultimate components, 197 



Phases of dissipated energy, 200 



Catalysis. — perfect catalytic agent, 201 



A. fundamental equation for phases of dissipated energy may be formed from the 

 more general form of the fundamental equation, 201 



The phases of dissipated energy may sometimes be the only phases the existence 

 of which can be experimentally verified, 201 



THE CONDITIONS OF EQUILIBRIUM FOR HETEROGENEOUS MASSES UNDER THE INFLU- 

 ENCE OF GRAVITY. 



The problem is treated by two different methods : 



The elements of volume are regarded as variable, 203 



The elements of volume are regarded as fixed, 207 



FUNDAMENTAL EQUATIONS OF IDEAL GASES AND GAS-MIXTURES. 



Ideal gas, 210 



Ideal gas-mixture — Dalton's Law, 215 



Inferences in regard to potentials in liquids and solids, ... 225 



Considerations relating to the increase of entropy due to the mixture of gases by 



diffusion, r 227 



The phases of dissipated energy of an ideal gas-mixture with components which 



are chemically related, — 230 



