Phenomena of some Substances and Mixtures. 191 



curve (plaitpoint curve), cannot be found by a simple geo- 

 metrical construction in the p-v diagrams. The connexion 

 between the latter diagrams for different mixtures is not so 

 simple as the connexion between the loops (border-curves) in 

 the p-t diagram. A point of intersection of two loops gives 

 the pressure and temperature at which the two mixtures to 

 which the loops belong will coexist as vapour and liquid*. 

 The enveloping-curve contains the points of intersection of 

 loops infinitely near each other ; in other words, it gives the 

 conditions of pressure and temperature of the coexistence of 

 identical phases : at those points the mixtures are therefore in 

 the critical condition, and will display the critical phenomenon. 

 Evidently these points P do not in general coincide with 

 either M or 0. At the critical point the mixtures do not 

 show the critical phenomenon, the latter belonging to P, 

 where the temperature is lower. This was fully explained 

 on former occasions. 



29. The properties of the v-x diagram were sufficiently 

 discussed in my previous paper. Also its meaning as pro- 

 jection on the v-x plane of curves on the ^ surface studied by 

 van der Waals. It was found in the first place that the 

 maximum mixture in its critical point behaves entirely as a 

 single substance ; this fact would appear in the p-v diagram 

 by the critical isothermal touching the border- curve at the 

 top, and by points M, P, and C coinciding. If the maximum 

 mixture is the same at all temperatures (as is approxi- 

 mately realized b} r N 2 0-C 2 H 6 within the limits of tempera- 

 tures used), the real border-curve coincides entirely with the 

 hypothetical border-curve examined above. If the maximum 

 mixture changes with temperature the two curves coincide at 

 the top only. 



30. The consequence of this coincidence is that the critical 

 point of the maximum mixture may be determined in exactly 

 the same way as for a single substance : the conditions being 



d JP _a ^_o 

 dv ' dv 2 ~ ' 



The direction of the vapour-pressure curve of the maximum 

 mixture at B (i. e. the direction of the maximum-curve at 

 that point) is also the same as for a single substance. This 

 direction may be easily proved to satisfy the equation 



( d A=0 

 \dt) \\ 



* This is not so when a mixture of maximum or minimum pressure is 

 between the two mixtures, 

 t This equation is true for single substances at the critical point, and 



