Phenomena of some Substances and Mixtures. 189 



25. Again, the critical phenomena characteristic of mix- 

 tures were very little marked. As just stated, mixtures con- 

 taining ethane between the limits 0"30 and 0*45 ought theo- 

 retically to show the critical phenomena of the second kind. 

 For mixture 0*43 points P and C were, however, so near 

 together that I could not observe a difference. For mixture 

 0-50 P is between M and C ; for mixture 0*30 M and P 

 coincide, and very nearly also with C ; for mixture 0*15 M 

 seems to lie between P and C. All this agrees with the rules 

 given above. The differences between p b and p e are very 

 small, especially for the maximum mixture. This also is in 

 accordance with theory. The results for this combination 

 are more trustworthy than those for C 2 H 2 -C 2 H 6 , and as good 

 or better than those for N 2 0-C 2 H 6 . 



The v-x diagram (not published) has the same character as 

 for the two other combinations. 



E. Application of Van der Waals's Theory*. 



26. If taken as generally as possible, van der Waals's theory 

 of mixtures depends on the assumption of the existence of a 

 relation between p, v, and t for a mixture of the same cha- 

 racter as for pure substances. The p-v curve must be supposed 

 to have an unstable part below a certain temperature, and in 

 changing the composition of the mixture gradual changes in 

 the relation between p, v, and t should take place. The laws 

 of the condensation, the critical phenomena, in general of the 

 coexistence of phases are then found by an application of 

 thermodynamics in one of its many forms : Van der Waals 

 used the yfr function (-v^ = e — T?;). (T = absolute temperature.) 

 In fact wherever thermodynamics is used for purposes of this 

 kind, the existence of a similar equation of condition must be 

 presupposed, though the actual form of this equation can only 

 be given in the simplest cases, and even then only qualitatively. 

 It is well known that the theoretical equation for single sub- 

 stances given by van der Waals does not agree with the results 

 of experiments, and the same is true for the analogous equation 

 for mixtures of two substances which he uses in his theory. 

 It is well, however, to bear in mind that a number of the 

 results which he arrives at are independent of the form of the 

 equation. Even those results which are not, still may have a 

 resemblance to actual phenomena in the same manner as for 

 single substances. 



* Archives Neerl. xxiv. pp. 1-56 ; Zeitschrift physik. Chemie, v. 

 pp. 133-173; Kon. Akad. van Wet. Amsterdam, Nov. 24, 1894, pp. 133- 

 137; ibid. Mei 25, 1895, pp. 20-30; Juni 29, 1895, pp. 1-12. 



