Generalizations of Van der Waals. 185 



and he has pointed out that the critical temperature is pro- 

 bably a little higher than 193'8, and that the critical volume 

 of this substance is certainly lower than 4 cubic centim., and 

 is more probably about 3*5 cubic centim., a value that agrees 

 fairly well with that calculated by the method described. 



In the case of the alcohols the critical volumes given by 

 Ramsay and myself were estimated by inspection of the 

 curves representing the relation of the specific gravities of 

 liquid and saturated vapour to the temperature, and of the 

 specific volumes to the pressures, and they were admittedly 

 only approximate values. 



M. Guye has shown (Comptes Rendus, cxii. p. 1257) that 

 an approximate relation exists between the critical tempera- 

 ture, pressure, and volume of a substance and its theoretical 

 vapour-density compared with air. This is expressed by the 

 equations 



Cl ~ D 7r(1070 + <9) 28-87' 



where S is the specific gravity at the critical point compared 

 with water at 4°, 6 the absolute critical temperature, it the 

 critical pressure, and M the molecular weight. The critical 

 volumes of ether and the alcohols previously given by 

 Ramsay and myself are certainly in better agreement with 

 this relation than those which I now find ; but it may be 

 mentioned that, with the exception of iodobenzene, all the sub- 

 stances referred to in this paper give somewhat higher values 



M 



of d than the quotient 9 o.o 7 if the molecular volumes in 



Table XXII. be taken as correct. 



It may, I think, be safely stated that the true critical 

 volumes are not lower than those directly observed, but it is 

 possible that they may be a little higher. It is therefore 

 perhaps too much to say that the values given in the table 

 are definitely established, but I am inclined to think that they 

 may be accepted as fairly close approximations to the truth. 



If that is so, it would appear from Table XVII. that the 

 ratio of the actual critical density to the theoretical density is for 

 very many substances about 4*4. Ethyl and propyl alcohol 

 give somewhat higher values, while for methyl alcohol and 

 acetic acid, especially the latter, the ratios are extremely 

 high. 



Phil, Mag. S. 5. Vol. 33. No. 201. Feb. 1892. 



