CONDENSATION AND CRITICAL PHENOMENA. 209 



of an experimenter like Amagat the method no doubt 

 yielded a very accurate value. The direct method described 

 above gave the writer of this article 3 1 '2° C. for CO2 con- 

 taining about "0007, a very small difference to be sure. 



The critical volume is now generally obtained by a 

 oraphical method depending on a law discovered by 

 Cailletet and Matthias, that "the mean of the vapour and 

 liquid densities is a linear function of the temperature ". 

 Where this line cuts the border-line of densities the critical 

 density is found. The law holds very well where it has 

 been tested (for instance, for CO2, Amagat ; , isopentane, 

 Young and Thomas, etc.). [Certain exceptions will be 

 referred to in the sequel.] From a minute study of the best 

 results obtained, one would conclude that the line is not per- 

 fectly straight, and therefore the law only approximate after 

 all. This is of importance because it suggests the question 

 in how far one is entitled to use it for determining the critical 

 density. There are other cases in which empirical laws which 

 hold perfectly at some distance from the critical point begin 

 to fail near the critical point. The height of a liquid in a 

 capillary tube is a linear function of the temperature, until 

 ■close by the critical temperature, when a marked curvature 

 in the line appears. It is, however, questionable if the 

 determination of the critical density (even if made according 

 to the principles laid down above) will ever be accurate 

 ■enouQ'h to discover a small deviation in the "diameter" 

 near the critical point, if there is any. But it will have to 

 be tried. There are certain groups of bodies which do not 

 ■obey the law of the diameter, but yield a line with very 

 marked curvature. These bodies, such as the fatty acids, 

 the normal alcohols, water, curiously enough are the same 

 as disobey most of the other laws that hold for other 

 substances. This exceptional behaviour is ascribed to a 

 conglomeration of molecules to groups chiefly at the higher 

 densities ; a similar association of molecules would not take 

 place for the majority of substances which follow the general 

 laws.^ A very satisfactory justification of this explanation 



^ Compare an article by Dr. J. Shields in "Science Progress," pp. 265- 

 278, December, 1894. 



