18i.)4."j Dissociation of the Molecules of Liquids. 175 



fact indeed is pointed out in the first part of the series of papers 

 (ibid., 291). Again the ratios of total to external work produced on 

 evaporation (ibid., 293) show that the total work is a higher multiple 

 of the external work or work employed in expansion against pressure, 

 in the case of the alcohols, acetic acid, and water, than in the case of 

 other compounds. 



Enough has been said to show that a great mass of evidence exists 

 in favour of molecular complexes in certain liquids. It remains now 

 to consider the methods by which the degree of complexity can be 

 ascertained. 



II. Methods of. Deducing the Molecular Complexity of Liquids from 

 Measurements of their Molecular Surface-energy. 



It was shown by Ramsay and Shields (' Phil. Trans.,' 1893, A, 662) 

 that the relation of molecular surface-energy of many liquids to 

 temperature may be expressed by the equation 



(1) 7 (Mi;)* = &(T-cZ), 



where 7 is surface-tension, measured in dynes, (Mv) ! the molecular 

 surface measured in square centimetres, Jc is an approximate constant 

 for most liquids varying little from 2*12, and T is the temperature 

 numbered downwards from the critical point ; d is a nearly constant 

 number of degrees, usually 5, which must be subtracted from T. 



For liquids which associate, such as the alcohols and fatty acids,. 

 the value of Jc is not constant, but increases with rise of temperature. 



The projblem is, knowing the average value of Jc for non-associating 

 liquids, to deduce the average molecular weights of associating liquids 

 at any given temperature. 



Differentiating equation (1) we obtain 



for non-associating liquids ; or, if we insert a term x, to represent a 

 factor with which the gaseous or normal molecular weight of a liquid 

 should be multiplied in order that the normal value of Jc should result 

 from the equation, we obtain 



(2) - 7 (sM*)t = Jc, ' 



In our first attempts to deduce the true average value of M for 

 associating liquids, equation (2) was expanded, thus : 



(3) aft . 7 (Mi,)! + 7 (M^ . = ft ; 



