towards a Dynamical Theory of Solutions. 23 



on x x and x 2 . The latter term contains the factor pip 2 , and 

 as we shall see that A depends chiefly on a factor pip 2 , ^ ve 

 have u—p x u x —p 2 u 2 nearly containing a factor pjp 2 . This 

 result reminds us that the law of mass action comes in with 

 physical as well as with chemical change. If the closest 

 packing of two sets of molecules is obtained when their 

 numbers stand to one another in the ratio of two small 

 integers, then we should have the two main conditions for 

 chemical combination between them satisfied ; we might, for 

 instance, deduce the existence of hydrates, whose structure 

 indicates the merging of chemical energies into physical, 

 of intramolecular energies into intermolecular, rather 

 than typical chemical combination. It is often forgotten 

 that in a large part of the theory of solutions we are on a 

 border where the separation between chemistry and physics 

 becomes arbitrary, where we need to express ourselves in 

 more general terms that will assume a mutual interdepen- 

 dence between intramolecular and intermolecular phenomena. 

 Chemists have long been confronted with the same need in 

 regard to water of crystallization. Molecular dynamics 

 furnishes the appropriate means of expression. 



2. Detailed Examples of its Application to the Densities of 

 Solutions of Ethyl Alcohol and Acetic Acid in Water 

 and the Contraction whicli occurs in their Formation. 



Here we concentrate oar study upon A and put u=l/p y 

 whereupon (6) becomes 



A + p^/2 = -p lJ)2 p(.r 1 l P2 + ., 2 !p^2 . . . (7) 

 and the immediate subject of investigation is 



(A + /3 A 2 /2)/p lW =-(^2 + ^/f>i)/2 . . (8) 



Here x± and x 2 are not determined separately by means of 

 the values of A for each value of p { . In the following table 

 are given the data for ethyl alcohol and water, with the 

 values of A the contraction calculated from them and also 

 those of (A + pA 2 )/'pip 2 p on the left hand of (8) to serve for 

 the study of — {x l jp 2 -\-x 2 jp-^ on the right. 



