604 JOHN JOHNSTON AND PAUL NIGGLI 
its melting-point. Into the steps in the derivation of this formula 
it is unnecessary to enter here;* the final differential equation is: 
Om TE 
dP AH 
(V) 
which expresses the lowering of melting-point by unequal pressure 
in terms of the absolute melting-point (7) and the molecular 
volume (V,) of the solid at the temperature and pressure in question 
and AH, the molar heat of fusion under those conditions. The 
quantities V, and JT are always positive, but AH (as here used) is 
always negative; hence application of excess pressure on the solid 
phase always lowers the melting-point. 
If we compare the melting-point depressions (d7, and dT, 
respectively) produced by the same excess pressure (dP) acting 
on (1) the solid phase alone, (2) both phases; that is, if we combine 
equations V and I, we obtain the result 
in Vier ave 
HEE OVE VeVi 
or, expressed in words, the ratio of the lowering of melting-point 
of the solid phase, when this alone is subject to a given pressure, 
to the alteration (raising or lowering) observed with the same 
(given) pressure acting uniformly on both phases is equal to the 
ratio of the (specific) volume of the solid phase to the change of 
(specific) volume on freezing. 
This equation shows how many times greater the melting-point 
lowering is when the pressure acts only on the solid phase. For 
example, the melting-point of ice is lowered by unequal pressure 12 
times as much (or 0°09 per atm.) as by uniform pressure (0°0075 
per atm.); in general AT,/AT, is much greater than 12, because 
the fractional change of volume accompanying melting is usually 
much smaller than it is in the exceptional case of ice. 
The (unequal) pressure (¢, expressed in atmospheres) required 
to cause a substance to melt at the temperature T, can be computed 
if we can integrate equation V. We cannot perform this integra- 
tion rigidly for lack of the necessary data on the variation of 
(VI) 
‘Tt is discussed in another paper: see Jour. Am. Chem. Soc., XXXIV (1912), 
788-802; Z. anorg. Chem., LX XVI (1912), 361-79. 
