BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 89 



removed from the dilatation of iron, being about 20 times greater. 

 The difference between compressibiHty and dilatation is further 

 accentuated by the fact that the compressibility of iron is nearly as 

 low as that of any solid, while there are a number of solids with a 

 smaller dilatation. There seems, therefore, to be more difference 

 between a solid and a liquid with respect to thermal expansion than 

 with respect to compressibility. 



Pressure Coefficient. — No diagrams have been given for this 

 c^uantity, but it is nevertheless worth some discussion, because of 

 the part it has played in previous theoretical discussions. This 

 so-called "pressure coefficient" is the thermodynamic quantity 



( T~ ) > the change of pressure when the temperature is raised one 



degree at constant volume, and is mathematically equivalent to the 



. . ,., • •, .,• fdp\ ^ /dv\ Udv\ ^ 



ratio of dilatation to compressibility 1"^J ~ — l^j ['^ j ' ^^ 



has been proposed as an empirical law by Ramsay and Young that 

 the pressure coefficient is a function of the volume only. That is, 

 if the pressure coefficient is plotted against volume, the curves for 

 different temperatures will fall together. The experiments of Ramsay 

 and Young covered a wide temperature range, but a comparatively 

 low pressure range, since their chief concern was with the relations 

 between a liquid and its vapor, and their pressures seldom exceeded 

 the critical pressure, a matter of a few hundred atmospheres. Amagat, 

 in his discussion of his own results for liquids up to 3000 atmos., has 

 devoted considerable attention to the pressure coefficient. One of 

 his results was that the pressure coefficient is approximately inde- 

 pendent of temperature at constant volume, but does nevertheless 

 show small consistent variations, which Amagat was unwilling to 

 ascribe to experimental errors. The coefficient of different substances 

 may increase or decrease with rising temperature, or show still more 

 complicated variations. The coefficient increases with decreasing 

 volume, that is with increasing pressure. Tammann, however, in 

 his recent empirical theory of liquids for high pressures, has con- 

 cluded from an examination of Amagat 's work that the variations 

 which Amagat found in the pressure coefficient do not exceed the 

 possible experimental errors. Tammann has accordingly taken as 

 one of the fundamental hypotheses of his theory the assumption that 

 the pressure coefficient is a function of the volume only. 



The discussion of the pressure coefficient to be given here has for 

 its only purpose to show that at high pressures, whatever the facts 



