429 
The variations here spoken of must not involve the trans- 
portation of any matter through any finite distance. 
It follows from this that the quantities 0, p, u,..-@, must 
have the same values in all parts of the mass. For if not, heat 
will flow from places of higher to places of lower temperature, 
the mass as a whole will move from places of higher to places 
of lower pressure, and each of the several component substances 
will pass from places where its potential is higher to ples 
where it is lower, if it can do so continuously. 
Hence Prof. Gibbs shows that if @, P, M,...M, are the 
values of 0, p; #,---44, for a given phase of the compound, and if 
the quantity 
K=e~@n + Po— Mm, — — &. — Mm,, 
is zero for the given fluid, and is positive for every other hase 
of the same components, the condition of the given fluid will be 
stable. 
If this condition holds for all variations of the variables the 
fluid will be absolutely stable, but if it holds only for small 
variations but not for certain finite variations, then the fluid 
will be stable when not in contact with matter in any of those 
phases for which K is positive, but if matter in any one of these 
phases is in contact with it, its equilibrium will be destroyed, 
and a portion will pass into the phase of the substance with 
which it is in contact. . 
Thus in Professor F. Guthrie’s experiments, a solution of 
chloride of calcium of 37 per cent. was cooled to a temperature 
somewhat below — 37° C. without solidification. 
‘In this state, however, the contact of three different solids 
determines three different kinds of solidification. A piece of 
ice causes ice to separate from the fluid. A piece of the cryo- 
hydrate of chloride of calcium determines the formation of 
cryohydrate from the fluid, and the anhydrous salt causes a 
precipitation of anhydrous salt. 
