BRIDGMAN. — THERMODYNAMIC PROPERTIES OF WATER. 343 



molecules on the average throughout the mass, and not one depend- 

 ent on the surface layer. There are only a few such quantities de- 

 pending on the state of the liquid at interior points. Any quantities 

 in\'()lving in any way the constancy of i)ressure or of entropy, for ex- 

 ample, do depend on the complieated action of the surface layer. One 

 of the quantities which is independent of this surface layer, however, is 

 the volume. In many theoretical considerations the use of the vol- 

 ume as an independent ^•ariable is known to produce simplifications. 



If the volume, instead of the pressure is taken as the independent 

 variable for the compressibilit\', curves are obtained of the same 

 general appearance as when the pressure is used for the variable. 

 The compressibility falls with decreasing volume, and the curvature 

 is in the same direction as when the pressure is the independent vari- 

 able. The same general characteristics are also shown if the relative 

 compressibility instead of the compressibility is plotted against the 

 volume. The two sets of curves, for the compressibility and the 

 relative compressibility, do show one feature in common, however, 

 different from the curves when the pressure is used as the variable. 

 This is the fact that the compressibility is always lower for the same 

 volume at the higher temperature. This is true throughout the ejitire 

 range of volume used; there is no crossing of the curves indicating 

 abnormalities, such as is the case when the pressure is used as the 

 variable. This is what one would expect on the kinetic theory. A 

 liquid, at two different temperatures but at invariable volume, differs 

 only in the violence of the motion of its molecules. At the higher 

 temperature, the kinetic pressure due to the motion is greater, and so 

 the resistance offered to change of volume under a given increase of 

 external pressure is greater when the temperature is higher. 



Fig. 5 shows the thermal dilatation as a function of pressure at 

 various temperatures. The thermal dilatation plotted in the figure 



is the expression ( ~ ) instead of the expression - ( — ) , which is some- 

 \otJp V \dtjp 



times used as the dilatation. The usage adopted here for the dilata- 

 tion is analagous to that explained above for the compressibility. 

 The values listed in the figure were obtained from the table of volumes 

 in the manner already described. The curve at 0° was obtained from 

 the data of the previous paper for the low temperatures, but in that 

 paper the mean value of the thermal expansion for the range 0°-20° 

 was given, whereas here the instantaneous value at 0° is given instead. 

 The substitution of the instantaneous for the mean dilatation produces 

 no change in the general character of the curves, however. 



