442 J. W. Gibbs— Equilibrium of Heterogeneous Substances. 
If the system is incapable of thermal changes, like the sys- 
tems considered in theoretical mechanics, we may regard the 
entropy as having the constant value zero. Conditions (2) and 
(4) may then be written 
dé=0, dp=0, 
and are obviously identical in signification, since in this case 
namic system. In fact, each of the quantities —e and —¢ 
(relating to a system without sensible motion) may be regarded 
as a kind of force-function for the system,—the former as the 
force-function for constant entropy, (i. e., when only such states 
of the system are considered as have the same entropy,) and 
the latter as the force-function for constant temperature, (i. &, 
when only such states of the system are considered as have the 
same uniform temperature). ue 
In the deduction of the particular conditions of equilibrium 
( 
Notwithstanding these considerations, the author has pre- 
ferred in general to use condition (2) as the criterion of equl- 
portant 
: he slightly different form in 
which the subject would develop itself, if condition (4) had 
been chosen as a point of departure instead of (2), is occasion- 
ally indicated. ' 
