•356 ./ W. Gibhs — Equilibrium of Heterogeneous Substances. 



that the first four terms of this equation represent the work spent 

 upon the solid in bringing it from the state of hydiostatic stress to the 

 other state without change of temperature, and j^' ^ ~ p' [w]/.> evi- 

 dently denotes the work done in displacing a fliiid of pressure p 

 surrounding the solid during the operation. Therefore, the first 

 number of the equation represents the total work done in bringing 

 the solid ichen surrounded by a fluid of pressure p' from the state of 

 hydrostatic stress jk»' to the state of stress jt>',jw",jo"'. This quantity is 

 necessarily positive, except of course in the limiting case when 

 p' =z p" ^p'". If the quantity of matter of the solid body be unity, 

 the increase of the potential in the fluid on the side of the solid on 

 which the pressure remains constant, which will be necessary to 

 maintain equilibrium, is equal to the work done as above described. 

 Hence, //,' is gi'eater than [//,]^, ,and for similar reasons, yu/'is 

 greater than the value of the potential which would be necessary for 

 equilibrium if the solid were subjected to the uniform pressure p", and 

 Ml'" gi'eater than that which would be necessaiy for equilibrium if 

 the solid were subjected to the uniform pressure />"'. That is, (if we 

 adapt our language to what we may regard as the most general case, 

 viz., that in which the fluids contain the substance of the solid but 

 are not wholly composed of that substance,) the fluids in equilibrium 

 with the solid are all supersaturated with respect to the substance 

 of the solid, except when the solid is in a state of hydrostatic stress; so 

 that if there were present in any one of these fluids any small frag- 

 ment of the same kind of solid subject to the hydrostatic pressure of 

 the fluid, such a fragment would tend to increase. Even when no 

 such fragment is present, although there must be perfect equilibrium 

 so far as concerns the tendency of the solid to dissolve or to increase 

 by the accretion of similarly strained matter, yet the presence of the 

 solid which is subject to the distorting stresses, will doubtless 

 facilitate the commencement of the formation of a solid of hydrostatic 

 stress upon its surface, to the same extent, perhaps, in the case of 

 an amorphous body, as if it were itself subject only to hydrostatic 

 stress. This may sometimes, or perhaps generally, make it a necessary 

 condition of equilibrium in cases of contact between a fluid and an 

 amorphous solid which can be formed out of it that the solid at the 

 surface where it meets the flxiid shall be sensibly in a state of hydro- 

 static stress. 



But in the case of a crystalline solid, subjected to distorting stresses 

 and in contact with sohitions satisfying the conditions deduced above, 

 although crystals of hydrostatic stress would doubtless commence to 



