76 PROCEEDINGS OF THE AMERICAN ACADEMY. 



The fact that the ratio is approaching unity shows that the atoms 

 are approaching the behavior suggested above, but if they ever reach 

 it, it can only be at pressures considerably beyond those reached here. 



In Table XVII are given the average volumes of the twelve liquids 

 between 20° and 80°. This table corresponds to the diagrams for the 

 average between 20° and 80° of the other thermodynamic properties; 

 it will prove useful in plotting any of the average properties against 

 volume, which may in some cases give more significant results than 

 when pressure is used as the independent variable, as here. 



Thermal Expansion. — The mechanism ordinarily assumed in 

 explanation of thermal expansion is as follows. Any liquid is con- 

 tinually striving to expand, because of the thermal agitation of its 

 molecules. The tendency to expand is resisted by two forces, the 

 external pressure, and the forces of attraction between the molecules. 

 An increase in temperature means an increase in the expanding force, 

 which results in an increase of volume. This increase of volume 

 would be expected to be greater if the force preventing expansion 

 were less. Now the force preventing expansion becomes less as 

 the volume becomes greater, because the cohesional forces decrease 

 as the volume, or the distance apart of the molecules, becomes greater. 

 The result is that the thermal dilatation increases with increasing 



fdh\ 

 temperature, that is with increasing volume. In other words, ( ^j ) 



is positive. Furthermore, as pressure increases, the force resisting 

 expansion increases because of the decreased distance apart of the 

 molecules, so that we are to expect a decreased dilatation at the 

 higher pressures. 



An examination of the curves for dilatation against pressure shows 

 that these expectations are much more nearly fulfilled as regards the 

 behavior of the dilatation with respect to pressure than with respect 

 to temperature. 



The general tendency of the dilatation of the separate liquids 

 (Folder I, Figures 20 to 31) is to decrease with rising pressure. The 

 decrease is very much more rapid at the lower than at the higher 

 pressures. But beyond this general fact the curves give only an 

 impression of bewildering complexity, crossing and recrossing in 

 apparent disorder at the higher pressures. It is possible to find many 

 instances where the dilatation increases with rising pressure over a 

 range of several thousand kilograms, ultimately, however, to decrease 

 again. One of the most striking examples of this is the 20° curve for 

 carbon bisulphide; other well marked examples are afforded by ace- 



