Chanye of State : Solid-Liquid. 45 



water-cylinder and form water there. To obtain equilibrium 

 again, the temperature must be lowered to such a point that 

 the pressure makes the two vapour-tensions once more equal, 

 when the ice and water will remain unaltered in amount — that 

 is, the melting-point will be reached. If now the ice alone 

 be subjected to pressure, its vapour-tension will be increased 

 while that of the water remains the same. And now the 

 pressure required to produce equilibrium of vapour-tensions 

 at a given temperature below 0° will only be about 2-23rds 

 of that required when both are subjected to the same pressure. 

 The suppositions which I have made amount to this — that 

 if the space filled with vapour be abolished and the ice and 

 water be brought directly into contact with each other, then the 

 rate of escape of molecules will be the same as before in each 

 case, or bear the same proportion to it. 



Isothermcds of Ice-water : Critical Points. 



If we draw the isothermals for ice and water on a pressure- 

 volume diagram, they are of the general form shown in fig. 2, 

 though the figure is entirely out of proportion. 



If we may assume that the compressibility of water is con- 

 siderably greater than that of ice, the horizontal part of the 

 isothermals representing a mixture of ice and water will in- 

 crease as the temperature falls below 0°, at least just at first. 

 Then, if we call the line passing through the points where the 

 isothermals turn to or from the horizontal part the ice-water 

 line, this line will at first diverge as the temperature falls. 

 Now, while ice contracts on cooling, its coefficient of expan- 

 sion between —19° and 0° being given as '000122 by Brunner, 

 Despretz has shown that water expands on cooling below 0° 

 even more than it expands for an equal rise above 8°. Hence 

 the isothermals for ice and water approach each other at ordi- 

 nary pressures as the temperature falls. 



Using Brunner's coefficient for ice, and for water HalL- 

 trom's formula (Jamin, Cours de Physique, vol. ii.), 



H9 - 1 + -000052939 t - '0000065322 1 2 + -00000001445 1% 

 v t 



and supposing that water could be cooled without freezing, it 

 will be found that between —120° and —130° ice and water 

 would have the same specific volume. This might lead us to 

 suspect that the divergence of the two branches of the water- 

 ice line would not continue if we could examine the isother- 

 mals at very low temperatures and high pressures, and thai. 

 as the temperature fell, the two states would at some point 



