BRIDGMAN. — TIIKRMODYNAMIC PROPERTIES OF WATER. 349 



to indicate the possibility of a iiiaxiimini and a reversal of direction 

 at higher pressures. The pressure for a niaxiniuin, however, if there 

 is one, is much beyond the reach of any at present attainal)l<>. Within 

 the pressure range of these measurements, the attraction between the 

 molecules still remains the dominant feature, so that the work done 

 by the attractive forces and liberated as heat much more than suffices 

 to overbalance the mechanical work of compression. 



The internal energy of a substance is one of those quantities which 

 depend only on the properties of the mass of the substance at interior 

 points and do not involve the action of the surface layer. Change of 

 energy plotted against volume shows in the first place that the change 

 of internal energy is much more nearly a linear function of the volume 

 than it is of the pressure. The average slope of the isothermal lines 

 of energy increases rapidly- with rising temperatiu'c for the lower 

 temperatures, but the two curves for 60° and 80° run nearly parallel 

 to each other for their length. Abnormalities are shown at the upper 

 ends of the 0°, 20° and the 40° curves, and the 0° curve shows the same 

 maximum as it does when plotted against pressure. The origin, of 

 course, for the curves at different temperatures does not coincide as 

 it does for the same quantities when plotted against pressure. 



One other quantity may be simply determined in terms of the 

 compressibility and the thermal dilatation alone, the so-called pres- 

 sure coefficient, that is, the change of pressure following a rise of 

 temperature when the temperature is raised by 1° at constant volume. 

 This quantity is given immediately in terms of the compressibility 

 and the thermal dilatation by the well known formula, 



^dr/y KdTjpl \dpjr 



It is shown plotted in Figure 9. The curves for 0° and 20° show 

 anomalies, as is indicated by the unexpected direction of curvature. 

 The other curves for the higher temperatures seem to be regular 

 enough, though of course it cannot be told whether the course of these 

 curves is the same as that which would be shown by a normal liquid or 

 not. At the upper ends of the high temperature curves, the curva- 

 ture is in such a direction that if they were continued far enough the 

 pressure coefficient would decrease instead of increasing with rising 

 pressure. 



This quantity, the pressure coefficient, has been made the basis 

 of theoretical speculation. It has been enunciated as a law, approxi- 

 mately true, by Ramsay and Shields, that the pressure coefficient 



