1221 
Hence, if we compare two systems |S and S’ which are converted 
into each other, at: a constant temperature, by a small alteration in 
pressure, it follows from the foregoing that : 
If S exists at a higher pressure than S’, the volume of Sis smaller, 
if S exists at a lower pressure than S’, the volume of S is greater 
than that of S’. And reversally : 
if S has a smaller volume than S’ it exists at a higher, if it has 
a greater volume than JS’ it exists at a lower pressure than S’, 
We may express this also a follows : 
a system S is corverted by increase in pressure into a system 
with a smaller and on reduction in pressure into a system with a 
greater volume. And reversally : 
if a system S is converted into another with a smaller volume, 
the pressure must increase, and if converted into one with a greater 
volume the pressure must decrease. We may then compare the volu- 
mina of the two systems either both under their own pressure or 
both under the pressure of the system S, or both under the pressure 
of tbe system S’. 
It is evident that a similar consideration applies to two systems 
S and S’ which, at a constant pressure, are converted into each 
other by a small change in temperature. For the case in question, 
the equilibrium : solid + liquid + gas we may also deduce the above 
rules in a different manner. For this, we take at the temperature 7’ 
and the pressure P a complex consisting of » quantities / + i 
quantities L,-+ q quantities G. We now allow a reaction to take 
place between these phases at a constant 7’ and P wherein: 
(n + dn) quantity + (m+ din) quantity L' + (¢-+ dq) quantity G’ 
is formed and in which Z’ and G’ differ but infinitesimally from Z and G. 
The increase in volume A in this reaction is then determined by: 
: OV an OV, Ov, 
vdn + Vdm + V‚dg + m — de + m— dy + q de, + 94 du. 
Ow Oy Òw, Oy, 
As the total quantity of each of the three components remains 
unchanged in this reaction we have: 
adn + edm + a,dq + mde + gdz, = 0 
Bdn + ydm + y,dq + mdy + qdy, = 0 
dn + dm+dq=—0. 
After elimination of dn, dm, and dq we find: | 
my, B) A + (By) (A+ OC) dx —m ed) A + (aw ) (A + ©} dy 
—a(y—B8) A, aa (3 ae) (A, 3e Cs da, + qi(x —a) A + (aa) (A, + C4); dy, 
(ee) (y —B) — (e—a) YI A 
which for the sake of brevity we write: 
mAyde — mA,dy — qA,,dz, + qAxndy, = E.A 
