102 
2. The heat of mixing (generation of heat when 1 gr. of dry 
substance absorbs 7 gr. of water) is strongly positive, and is very 
well rendered by a hyperbola: 
Ai 
Bs 
3. The volume contraction c by the mixing (in cm’. when 1 gr. 
of dry substance absorbs 7 gr. of water) is strongly positive, and fol- 
lows a line which closely resembles a hyperbola. 
fa 
C ‘5 IL . - ° : 
4. If we compute 5 for small #s (lim. == 0), we find that this 
quotient is of the same order of magnitude for the most different 
swelling substances viz. between 10 and 25> 10-*, and that this 
quotient is of the same order of magnitude as for mixtures of sul- 
phurie acid, phosphorie acid, and glycerin with water. 
The analogy of the latter substances with the swelling substances 
is the more striking, because they present all the properties described 
under 1 (a, 6, and c), under 2 and under 3 exactly as for the swelling 
substances. There is only one difference: they are miscible in all 
proportions, whereas some swelling bodies exhibit the characteristically 
excentric region of unmixing described under 1d. Other swelling 
substances have an unlimited power of imbibition, but behave for 
the rest as described above. So this difference will not be essential. 
Limited or unlimited miscibility, it seems, may depend on small _ 
factors, as closely allied substances may belong to different types. Further 
quantitatively there exists this difference that for the swelling sub- 
stances the vapour pressure line begins to ascend much less steeply, 
the lines for the volume contraction and for the heat of mixing on 
the other hand much more steeply than in the usual case. We may 
express the latter also in this way that for swelling substances the 
quantity b in the equation of the hyperbola for the volume contrac- 
at 
_is remarkably small, just as the quantity 4 in the for- 
+4 
mula of the heat of mixing. 
tion c= 
§ 3. The integral equation of the vapour pressure line, Let us 
begin our investigation with the vapour pressure lines. To investigate 
whether they agree with the experimentally determined ones also 
with respect to the peculiarities not yet treated in $ 1, it is easier 
to use the integral relation between p and z instead of the differential 
