J. W. Gihbs — Eqrdlihrium of Heterogeneous Substances. 523 



Page 



Gas-mixtures with convertible components, 234 



Case of peroxide of nitrogen, 237 



Fundamental equations for the phases of equilibrium, 245 



SOLIDS. 



The conditions of internal and external equilibrium for solids in contact with fluids 



with regard to all possible states of strain, -_ 343 



Strains expressed by nine differential coefficients, 344 



Variation of energy in an element of a solid, .- — 344 



Deduction of the conditions of equilibrium, 346 



Discussion of the condition wliich relates to the dissolving of the solid, 352 



Fundamental equations for solids. 361 



Concerning sohds which absorb fluids, 315 



THEORY OP CAPILLARITY. 

 SURFACES OF DISCONTINUITY BETWEEN FLUID MASSES. 



Preliminary notions. — Surfaces of discontinuity. — Dividing surface, 380 



Discussion of the problem. — The particular conditions of equilibrium for contigu- 

 ous masses relating to temperature and the potentials which have already been 

 obtained are not invalidated by the influence of the surface of discontinuity. — 

 Superficial energy and entropy. — Superficial densities of the component sub- 

 stances. — General expression for the variation of the superficial energy. — Con- 

 dition of equilibrium relating to the pressures in the contiguous masses, 380 



Fundamental equations for surfaces of discontinuity between fluid masses, 391 



Experimental determination of the same, 394 



Fundamental equations for plane surfaces, _ 395 



Stability of surfaces of discontinuity — 



( 1 ) with respect to changes in the nature of the surface, 400 



(2) with respect to changes in which the form of the surface is varied, 405 



On the possibility of the formation of a fluid of different phase within any homo- 

 geneous fluid, 416 



On the possible formation at the surface where two different homogeneous fluids 



meet of a fluid of different phase from either, 422 



Substitution of pressures for potentials in fundamental equations for surfaces, 429 



Thermal and mechanical relations pertaining to the extension of surfaces of dis- 

 continuity, 434 



Impermeable films, 440 



The conditions of internal equilibrium for a system of heterogeneous fluid masses 

 without neglect of the influence of the surfaces of discontinuity or of gravity, . 442 



Conditions of stability, 451 



On the possibility of the formation of a new surface of discontinuity where sev- 

 eral surfaces of discontinuity meet, 453 



The conditions of stability for fluids relating to the formation of a new phase at a 



line in which three surfaces of discontinuity meet, 456 



The conditions of stabilit}' for fluids relating to the formation of a new phase at a 



point where the vertices of four different masses meet, 464 



Liquid films, 467 



Definition of an element of the film, 467 



Each element may generally be regarded as in a state of equilibrium. — Prop- 

 erties of an element in such a state and sufficiently thick for its interior to 

 have the properties of matter in mass. — Conditions under which an exten- 

 sion of the film will not cause an increase of tension. — When the film has 

 more than one component which does not belong to the contiguous masses, 

 extension will in general cause an increase of tension. — Value of the elas- 

 ticity of the film deduced from the fundamental equations of the surfaces 



and masses. — Elasticity manifest to observation, 468 



The elasticity of a film does not vanish at the limit at which its interior 

 ceases to have the properties of matter in mass, but a certain kind of 



instability is developed, 472 



Application of the conditions of equilibrimii already deduced for a system 



under the influence of gravity (pages 447, 448) to the case of a liquid film, 473 

 Concerning the formation of liquid films and the processes which lead to 

 their destruction. — Black spots in films of soap-water, 4'75 



