2G 
'iMESSRS. C. T. HEYCOCK AND F. H. NEVILLE ON 
from them ; it may also in certain cases be a solid solution, or it may be an 
isomorphous mixture of the two bodies, or of a compound with one of them. 
To take the simplest case first. Let us suppose that the pure substance A 
separates in the solid form when we cool the homogeneous liquid AB.* If 6 is the 
equilibrium temperature (the freezing point) reckoned from the thermo-dynamic 
zero, X the molecular concentration of A in the liquid AB, that is, the fraction of a 
molecular weight of A contained in every molecular weight in AB, X the latent heat 
of solution of a molecular weight of A in AB at the equilibrium temperature, then it 
is known that these quantities are connected by the equation 
2 
dx 
X 
( 1 ) 
When X is near unity, that is, when but little of B is present, we may fairly take X 
to be the latent heat of fusion of A, and 6 and dd being known by experiment, we 
may use equation (l) either to deduce x and therefore the molecular condition of B 
from the known value of X, or following the reverse order we may obtain X on some 
assumption as to the molecular state of B. This course has been largely followed in 
the study of solutions in water and in organic solvents, but the method has not, so 
far as w^e know, been applied to the study of metals of high melting point except hv 
ourselves. 
A great and valuable extension of equation (l) is due, we believe, to Le Chateliee. 
He assumes, as a first approximation, that X is independent of x and of 6, and he is 
thus able to integrate the equation, obtaining 
2log.*=x(-I - . (2), 
where 9q is the freezing point of pure A, corresponding to the concentration x = 1. 
If now^ we plot as abscissae the values of x from i to 0, and as ordinates the 
corresponding values of 6 calculated from equation (2), we get the ideal freezing- 
point curve of A. The corresponding curve for B can be plotted in the same wav, 
but from right to left. 
The highest point of each curve gives the melting point of the pure substance ; 
and the intersection of the two curves (see fig. 1) gives, as Ostwwld has pointed out, 
an approximation to the melting point and composition of the eutectic alloy. The 
freezing-point curves found by experiment will resemble fig. 1, but on account of many 
causes, which may be summed up as changes in the value of X, cannot be expected 
to be identical wuth it. In fig. 4, we give ideal curves for silver and copper, 
using in equation (2) the values of X found by us. If wm use Beeson’s value of the 
* By the symbol AB we mean, not a compound of A and B, but any mixtuve ol the two bodies. 
