ABSTRACT BY THE AUTHOR 365 



analytical processes from the general condition of equilibrium (2). The 

 condition of equilibrium which relates to the dissolving of the solid 

 at a surface where it meets a fluid may be expressed by the equation 



ft -i=*?, (22) 



where e, rj, v, and m x denote respectively the energy, entropy, volume, 

 and mass of the solid, if it is homogeneous in nature and state of 

 strain, otherwise, of any small portion which may be treated as thus 

 homogeneous, fa the potential in the fluid for the substance of which 

 the solid consists, p the pressure in the fluid and therefore one of the 

 principal pressures in the solid, and t the temperature. It will be 

 observed that when the pressure in the solid is isotropic, the second 

 member of this equation will represent the potential in the solid for 

 the substance of which it consists {see (9)}, and the condition reduces 

 to the equality of the potential in the two masses, just as if it were a 

 case of two fluids. But if the stresses in the solid are not isotropic, 

 the value of the second member of the equation is not entirely deter- 

 mined by the nature and state of the solid, but has in general three 

 different values (for the same solid at the same temperature, and in 

 the same state of strain) corresponding to the three principal pressures 

 in the solid. If a solid in the form of a right parallelepiped is subject 

 to different pressures on its three pairs of opposite sides by fluids in 

 which it is soluble, it is in general necessary for equilibrium that the 

 composition of the fluids shall be different. 



The fundamental equations which have been described above are 

 limited, in their application to solids, to the case in which the stresses 

 in the solid are isotropic. An example of a more general form of 

 fundamental equation for a solid, is afforded by an equation between 

 the energy and entropy of a given quantity of the solid, and the 

 quantities which express its state of strain, or by an equation between 

 i/r {see (3)} as determined for a given quantity of the solid, the tem- 

 perature, and the quantities which express the state of strain. 



Capillarity. The solution of the problems which precede may be 

 regarded as a first approximation, in which the peculiar state of 

 thermodynamic equilibrium about the surfaces of discontinuity is 

 neglected. To take account of the condition of things at these 

 surfaces, the following method is used. 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 sensibly coincident with the physical surface 



