873 
Now we have to examine whether those changes in volume and 
entropy are positive or negative. When we knew the values of 
w,y,u, Vz..., Hz..., then those changes would be easy to cal- 
culate. When this is not the case, then we have to try to find in 
another way they are positive or not. 
(AV)y and (A Hy; are the increase of volume and entropy at 
the reaction 
Zn eau OH (le) ZZ 
eonsequently at the separation of the hydrate Z, into anhydric salt 
Z and watervapour (7. Consequently we are allowed to assume that 
(AV)y and (AH) are positive. 
(AV)z and (AH)z. We write: 
AVig == y(Vqg —_ Vi) Hul, + 1 =o u) Va —Vr 
As =S y (He — Hi) + wH,, + (1 — w) Bren i ae 
Consequently both are positive for values of y which are not too 
small. For small values of 7 (A//)z becomes negative, for 7 = 0 we 
find viz 
(AAM)z = uA, + (A —u) Hy — Hy 
which is negative, when we assume that heat is wanted for the 
melting of solid substances. 
(AVjz can become negative for very small values of y; for this 
is it necessary that u V,,+(1—w) Va— Vr is negative. 
(AV)g and (4A). It appears from the value of (4 J’)g that this 
may be as well positive as negative. (AH), is the change in entropy 
at reaction 8, in which only solid substances and the liquid / 
participate. When we assume that heat is wanted for the formation 
of liquid, then (AfZ/)g is positive. 
(AV), and (AH), (AV), is always positive on account of the 
large value of Vg. For y =O becomes: 
(AV), =ue Ve+tuad—ez) Vz+a—u) Va — Vr. 
When in fig. 1 the point m is not situated in the immediate vicinity 
of point A, so that w and consequently also ww does not become 
extremely small, then (AJ), is still positive, even for y= 0. 
(AH), is positive; for small values of y it may, however, become 
negative, for this it is necessary that 
we Hg Hul — «) Hz + —u) Ay — Ay 
is negative. 
(AV) and (AH), It is apparent from the value mentioned for 
(AV) that this has the same sign as —(4H)q on account of the 
large value of Vg. Hence it appears that (A V)77< Oand (AH)y > 0. 
56 
Proceedings Royal Acad. Amsterdam. Vol. XIN. 
