of Edinburgh, Session 1885-86. 
627 
grammes of water which gives a saturated solution, the contraction 
which takes place amounts to *255 c.c., on adding sufficient water 
to make this 3 grammes the contraction increased to ’256 c.c., and 
on adding another gramme it increased to *278 c.c., and so on 
until 20 grammes of water were added, when the contraction 
amounted to *350 c.c. These results I have represented by 
curves, the ordinates giving the contractions in cubic centims., and 
the abscissas the number of grammes of water added to produce 
those contractions ; the curves start at the point of saturation of the 
solutions, and the height of this point above the line of abscissas 
represents the amount of contraction that takes place when 1 
gramme of the substance is dissolved in as small a quantity of 
water as possible. It will be noticed that there is contraction in 
every case with the exception of ammonium chloride, which gives 
an expansion on dissolving, but as water is added the amount of 
this expansion diminishes — that is, a solution when diluted contracts. 
In order to bring the curves for ammonium chloride into the diagram, 
I have added T c.c. to each of them, which must therefore be sub- 
tracted in order to obtain the true change of volume. 
From the appearance of the curves and by trial, I find that they 
are portions of equilateral hyperbolas having asymptotes parallel to 
x and y , and may be represented by the general equation 
J a + x 9 
where y is the contraction in cubic centims., x the number of 
grammes of water added, a the distance from y of the asymptote 
parallel to y , and b the distance from x of the asymptote parallel 
to x, and C the constant (a + x)(b - y) ; thus, 
for MgS0 4 a = 1 *429 6 = • 374 and C = *500, 
for MgCl 2 a=l-645 6 =-290 and C = -408, 
for CaCl 2 a = 1*857 b= -240 and C = -391, 
for K 2 C0 3 0=1-644 5= -374 and C = *501. 
Although the curves of contractions for all salts appear to be 
portions of equilateral hyperbolas, other substances give very dif- 
ferent curves. Thus alcohol contracts until you have added 3 parts 
of water, and then the amount of contraction begins to diminish; 
