﻿Attraction of Unlike Molecules. 1 9 1 



replacement of summation for separate molecules by inte- 

 gration for a continuum ; the step is a piece of approximation 

 whose justification is this, that even if we endeavoured to 

 carry out the process of summation we should have to make 

 arbitrary arrangements of the molecules. If we tried to sum 

 for the molecules of a mixture, our suppositions as to the 

 arrangement of the molecules would be still more markedly 

 arbitrary ; as, for instance, if we tried to represent the space- 

 distribution of the spheres in a mixture of equal numbers of 

 two sets of spheres of different sizes. These considerations 

 seem to me to make the above expression for the surface- 

 tension of a mixture satisfactory enough for present ^ appli- 

 cations. When a higher degree of accuracy is required, it 

 will be an interesting piece of mathematics te^ devise arrange- 

 ments of molecules as in nature and convenient methods of 

 summation. 



In the paper on the Diffusion of Gases we have seen 



reason to believe that X A 2 = GAx 2 A 2 ) ; and as the arithmetical 

 mean of the molecular radii {{m 1 /p 1 )? + (m 2 /p 2 )*\/2 of most 

 pairs of liquids is little different from the geometrical mean 



{(WpOKW/^)*}*? we can wr ^ e approximately 



as the law which rules the surface-tension of mixtures if 

 iA 2 = dA 12 A 2 )*. But equation (6) is the fundamental one to 

 be used in the discussion of the experiments, as it gives 

 directly a value of 1 A 2 /( 1 A 12 A 2 ) 5 , which is the thing sought 

 in these investigations on the attraction of unlike molecules. 



A fair amount of experimental work on the surface-tension 

 of mixtures has been published, but hardly any of it is of 

 immediate use in connexion with the present inquiry. For 

 instance, Traube (Ber. deut. chem. Ges. xvii. ; Ann. der 

 Chem. cclxv. ; Journ. fur prakt. Chem. xxxiv.) has investi- 

 gated the surface-tension of mixtures of water, and a large 

 number of organic liquids such as alcohols, acids, and amines ; 

 but as water and the alcohols and acids are exceptional in 

 their molecular structure in the liquid state, the surface- 

 tensions of these mixtures cannot be appropriately discussed 

 at the outset of this inquiry ; but Traube's numerous experi- 

 ments will doubtless be of great value when the exceptional 

 nature of these substances is under systematic examination. 

 But before Traube, Rodenbeck (Wied. Beibl. iv.) measured 

 the rise in capillary tubes of a certain number of mixtures, of 

 which only one set relates to strictly normal liquids, the 



