EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 79 



are familiar examples. Such an equilibrium will, however, be practi- 

 cally unstable. By this is meant that, although, strictly speaking, 

 an infinitely small disturbance or change may not be sufficient to 

 destroy the equilibrium, yet a very small change in the initial state, 

 perhaps a circumstance which entirely escapes our powers of percep- 

 tion, will be sufficient to do so. The presence of a small portion of 

 the substance for which the condition (53) does not hold true, is 

 sufficient to produce this result, when this substance forms a variable 

 component of the original homogeneous masses. In other cases, 

 when, if the new substances are formed at all, different kinds must 

 be formed simultaneously, the initial presence of the different kinds, 

 and that in immediate proximity, may be necessary. 



It will be observed, that from (56) and (53) we can at once obtain 

 (50) and (51), viz., by applying (53) to bodies differing infinitely 

 little from the various homogeneous parts of the given mass. There- 

 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 v M 2 , . . . M n as relate to the ultimate components, 

 may be regarded, like T and P, as unknown quantities subject 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 m v m 2 , . . . m n relate), that it shall be 

 possible to give such values to the constants T, P, M v M 2 , . . . M n in 

 the expression (57) 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 



