502 Mr. W. C. M. Lewis : Experimental Examination 
first takes up the consideration of the mass or bulk equi- 
librium of a heterogeneous system, i. e. equilibrium in which 
any surface phenomenon is of insensible magnitude, and then 
proceeds to examine the case in which the surface area is 
relatively large and the influence of surfaces of discontinuity 
upon the equilibrium of heterogeneous masses becomes of 
importance. To use his own words : — 
* " The solution of the problems which precede may be 
regarded as a first approximation in which the peculiar state 
of thermodynamic equilibrium about surfaces of discontinuity 
is neglected. To take account of the condition of things at 
these surfaces, the following method is employed : — 
" Let us suppose that two homogeneous fluid masses are 
separated by a surface of discontinuity, i. e. by a very thin 
non-homogeneous film.- Now we may imagine a state of 
things in which each of the homogeneous masses extends 
without variation of the densities of its several components, 
or of the densities of energy and entropy, quite up to a 
geometrical surface (to be called the dividing surface) at 
which the masses meet. We may suppose this surface to be 
sensibhy coincident with the physical surface of discon- 
tinuity. 
" Now if we compare the actual state of things with the 
supposed state, there will be in the former in the vicinity o£ 
the surface a certain (positive or negative) excess of energy, 
of entropy, and of each of the component substances. These 
quantities are denoted by e s , if, m s v m* 2 , etc., and are treated 
as belonging to the surface. The * is simply used as a 
distinguishing mark, and must not be taken for an algebraic 
exponent. 
"It is shown that the conditions of equilibrium already 
obtained relating to the temperature and the potentials of the 
homogeneous masses are not affected by the surfaces of dis- 
continuity, and that the complete value of oV is given by the 
equation 
Be s = thrf + ads + fi^m J + fi 2 ^ s 2 + e f c « 
in which 5 denotes the area of the surface considered, t the 
temperature, jx x /x 2 etc. the potentials for the various com- 
ponents in the adjacent masses " - 
" The quantity a we may regard as defined by the [above] 
equation itself or by the following : 
e' = tT) 8 + (rs + fi 1 ml + fi.2m' 3 + etc. 
* Gibbs, ' Scientific Papers/ vol. i. p. 3Co. 
