CONDENSATION AND CRITICAL PHENOMENA. 273 



curve traced out by the points of contact gives the co- 

 existing phases, and thus the volume at which any of the 

 mixtures will be in equilibrium as a vapour with a liquid, 

 or as a liquid with a vapour. In other words it gives the 

 points /? and e on the isothermals for the chosen tempera- 

 ture. By doing the same thing at other temperatures the 

 border curves may be traced out in full. The results 

 obtained may then be compared with the border curves, 

 as found by actually observing the volumes and pressures 

 at d and e. 



A drawback of the xp v x surface is the indirect way in 

 which the pressure manifests itself. The pressure depends 

 on the slope of the tangent plane in the \p x plane. In 

 general this slope changes continually in one direction 

 during the motion of the tangent plane over the plait, and 

 the maximum pressure is obtained at the plait-point P. 

 This is not in contradiction with the distinction made 

 between the points P (plait-point) and M (point of maxi- 

 mum pressure) in figs, i and 4. At M a given mixture 

 has a maximum pressure on the border curve, or above 

 that pressure no condensation is possible for that mix- 

 ture. P on the other hand is a point of maximum 

 pressure on the plait at a given temperature. At that 

 temperature no mixture can exist in two phases at a 

 higher pressure than belongs to P. But at a different 

 temperature higher pressures may occur unless P and M 

 coincide. 



Sometimes the pressure on the plait, instead of rising 

 or falling all the time, passes through a maximum or mini- 

 mum. This occurs where there is a mixture of constant 

 boiling-point. The co-existing phases have the same com- 

 position in that case, though different density, as was first 

 demonstrated by Konowalow. It follows that the straight 

 line connecting the corresponding points on the border- 

 curve (fig. 3) is parallel to the v axis for that mixture. 

 The straiorht lines on the two sides of the maximum or 

 minimum line are spread out like a fan ; the fan opens out 

 in the direction of the positive v axis for a minimum, and 

 in the opposite direction for a maximum. The latter case 



19 



