J. TPT Glhhs — Eqailihrimn of Heterogeneous Substances. 499 



It will be observed that for the same solid surface and for the same 

 temperature but for different fluids the values of 6 (in all cases to 

 which the definition of this quantity is applicable) will ditier from 

 those of ? by a constant, viz., the value of a for the solid surface in 

 a vacuum. 



For the condition of equilibrium of two difierent fluids at a line on 

 the surface of the solid, we may easily obtain 



o-AB COS a — ?Bs - ?As, (6V9) 



the suffixes, etc., being used as in (672), and the condition being 

 subject to the same modification when the fluids meet at an edge of 

 the solid. 



It must also be regarded as a condition of theoretical equilibrium 

 at the line considered, [subject, like (679), to limitation on account 

 of passive resistances to motion,] that if there are any foreign sub- 

 stances in the surfaces A-S and B-S, the potentials for these sub- 

 stances shall have the same value on both sides of the line ; or, if 

 any such substance is found only on one side of the line, that the 

 potential for that substance must not have a less value on the other 

 side; and that the potentials for the components of the mass A, for 

 example, must have the same values in the surface B-C as in the 

 mass A, or, if they are not actual components of the surface B-C, a 

 value not less than in A. Hence, we cannot determine the difference 

 of the surface-tensions of two fluids in contact with the same solid, l)y 

 bringing them together upon the surface of the solid, unless these 

 conditions are satisfied, as well as those which are necessary to pre- 

 vent the mixing of the fluid masses. 



The investigation on pages 442-448 of the conditions of equilibrium 

 for a fluid system under the influence of gravity may easily be 

 extended to the case in which the system is bounded by or includes 

 solid masses, when these can be treated as rigid and incapable of 

 dissolution. The general condition of mechanical equilibrium would 

 be of the form 



—fp 6Dv -f fg y6zBv+f0 SDs +fg F 6z Bs 



+ /gdz'Dm + fi6I>s + /g{r) dzl)s=0, (680) 



where the first four integrals relate to the fluid masses and the sur- 

 faces which divide them, and have the same signification as in 

 equation (606), the fifth integral relates to the movable solid masses, 

 and the sixth and seventh to the surfaces between the solids and 

 fluids, (F) denoting the sum of the quantities (/^g), (^3), etc. It 

 should be observed that at the surface where a fluid meets a solid 



