274 SCIENCE PROGRESS. 



In the table the temperatures are given under /, the 

 observed y (Mvf under the column headed "found," the 

 calculated y (Mz/) ! using the constants given above, 

 under "calculated," and the molecular complexity under x. 

 Methyl alcohol is the only substance at ordinary tempera- 

 ture having a complexity much greater than 2. The 

 molecular complexity of the other substances is usually 

 rather less than 2, and becomes less and less as the critical 

 point is approached. 



Without going to the trouble of finding a formula which 

 represents the variation of molecular surface energy of 

 associating liquids with temperature, it is possible to obtain 

 a fairly good approximation to the degree of molecular com- 

 plexity from the equation — 



7 (M») f = .Jr x 2 * 121 x 0--«0; 



but this involves the assumption that the actually found 

 critical temperature of the liquid is not far removed from 

 the critical temperature of the liquid, supposed to consist of 

 simple molecules. Thus we obtain — 



i 2 ' 121 ( T ~ ^) ) * 



' \ " ~7Tm^ ' } • 



The results obtained in this way differ very little from 

 those calculated by the formula — 



{ 2*121 , ,1! 



x= I -g- (1 + ,«-) j "; 



so that when only a few data are at hand this formula will 

 generally be found to give a very fair idea of the molecular 

 complexity of the liquid. 



The chief result which has been gained by the investiga- 

 tions on the surface tensions of liquids is that liquids have 

 been divided into two groups. One group contains the 

 normal or unassociated liquids, the other those which form 

 complex molecules or are associated. The degree of com- 

 plexity of the associated liquids as given in the previous 

 table is probably correct within certain limits, which are 

 conditioned by the fact that the number chosen for the con- 

 stant 2' i 21, is not absolutely constant but varies with the 

 nature of the compound. 



x = 



