towards a Dynamical Theory of Solutions. 53 



calories per gramme of mixture when p 2 = 72. For the 

 other three acids H is for the most part negative ; that is, 

 there is an absorption of heat on mixing, except that when 

 p l = O m lS for acetic, 0*17 for propionic, and 0*10 for butyric 

 acid, H becomes positive and remains positive for smaller 

 values of p x . Here we meet a similar contrast between formic 

 acid and the others to that we found in c—piCi—p 2 c 2 . I have 

 found the following empirical relation to hold for the four 

 aci(is as well as for alcohol except when p 1 =zO'S36 for formic 

 and 0*869 for acetic acid : 



H.—a(c—p 1 c 1 -p 2 c 2 ) = b(p—p 1 p 1 —p 2 p 2 ) . . (11) 



with the following values for a and b : — 



Acid.. 

 a 



. Formic. 

 ... 30 



Acetic. 

 -50 



-83 



Propionic. 

 -140 



-39G. 



Butyric. 

 -210 



-549 



Alcohol, 

 -95 



b 



... 76 



- 5 



It will be noticed that the successive differences in a for 

 the acids are 80, 90, and 70, while for b they are 159, 313, 

 and 153. Thus the formula (11) links up the complicated 

 phenomena for the four acids and alcohol in a way that shows 

 the chemical structure of the substance added to water to 

 have a definite influence on the energy changes it produces 

 in the water, for I take the term b(p—p 1 p i —p. 2 p 2 ) to be a 

 rough measure of a change of potential energy. For the 

 general study of potential energy in our mixtures we would 

 need a kinetic theory of liquids. With surface energy, 

 measured by surface tension, we can make some progress 

 at once. 



Surface Energy. 



In "The Mol. Const, of "Water " it is shown that from 

 0° 0. to 10° the surface film of water in contact with air or 

 its own vapour consists of trihydrol. There is evidence that 

 at temperatures above 60° the diminution of the surface 

 tension allows some dihydrol to exist in the surface layer. 

 At temperatures near 15° C. then in the surface layer the 

 problems of surface tension reduce to those of a binary 

 mixture, unless the substance added to water has the power 

 of transforming the trihydrol of the surface film into dihydrol 

 or hydrol. The best and simplest assumption to begin with 

 is that in the surface of a mixture the tension enables the 

 trihydrol to exist just as in the surface of pure water. If this 

 assumption were sufficient, then the surface tension of our 

 mixtures would not be exceptional, it would conform to the 



