134 ./ TK fribbs — Equilibrium of Heterogeneous Substances. 



fore, the condition (56) (relating to the various homogeneous parts 

 of the given mass) and (53) (relating to any bodies which can be 

 formed of the given matter) with (43) are always sufficient for equi- 

 librium, and always necessary for an equilibrium which shall be 

 practically stable. And, if we choose, we may get rid of limitation 

 in regard to equations (43). For, if we compare these equations 

 with (38), it is easy to see that it is always immaterial, in applying 

 the tests (56) and (53) to any body, how we consider it to be com- 

 posed. Hence, in applying these tests, we may consider all bodies to 

 be composed of the ultimate components of the given mass. Then 

 the terms in (56) and (53) which relate to other components than 

 these will vanish, and we need not regard the equations (43). Such 

 of the constants M ^, M.^ . . . 3I„ as relate to the ultimate compo 

 ponents, may be regarded, like T and P, as unknown quantities sub- 

 ject only to the conditions (56) and (53). 



These two conditions, which are sufficient for equilibrium and 

 necessary for a practically stable equilibrium, may be united in one, 

 viz., (if we choose the ultimate components of the given mass for 

 the component substances to which Wj, w-g, . . . m^ relate) that it 

 shall be possible to give such values to the constants T, P, J/j, J/2? 

 . . . M^ in the expi'ession (o*?) that the value of the expression for 

 each of the homogeneous parts of the mass in question shall be as 

 small as for any body whatever made of the same components. 



Effect of Solidity of any Part of the given Mass. 



If any of the homogeneous masses of which the equilibrium is in 

 question are solid, it will evidently be proper to treat the proportion 

 of their components as invariable in the application of the criterion 

 of equilibrium, even in the case of compounds of variable proportions., 

 i. e., even when bodies can exist which are compounded in pro- 

 portions infinitesimally varied from those of the solids considered. 

 (Those solids which are capable of absorbing fluids form of course an 

 exception, so far as their fluid components are concerned.) It is true 

 that a solid may be increased by the formation of new solid matter 

 on the surface where it meets a fluid, which is not homogeneous with 

 the previously existing solid, but such a deposit will properly be 

 treated as a distinct part of the system, (viz., as one of the parts 

 which we have called new). Yet it is worthy of notice that if a homo- 

 geneous solid which is a compound of variable proportions is in 

 contact and equilibrium with a fluid, and the actual components of 

 the solid (considered as of variable composition) are also actual com- 



