BRIDGMAN. — WATER UNDER PRESSURE. 553 



XXXIII. The difference between adiabatic and isothermal compressi- 

 bility increases to a maximum and then decreases. The rise of temper- 

 ature produced by the application of 1 kgm. pressure also increases 

 and then decreases again. The normal behavior of both these quanti- 

 ties, as shown by mercury, is a continuous decrease, so that here again, 

 we have an effect of the transition from abnormal to normal. 



The quantities involved in the change of state from one form to 

 another are shown collectively in the folder at the end, where the 

 equilibrium curves, the change of volume curves, and the latent heat 

 curves are plotted on the same scale for all the modifications. The 

 fundamental question as to the change of state liquid-solid may be 

 stated much more definitely than any fundamental question for the 

 theory of liquids. This fundamental question is as to the ultimate 

 behavior of the liquid-solid curve. Does it end abruptly, indicating a 

 critical point for the transition solid-liquid as many have maintained, 

 or does it rise to a maximum and then descend, as Tammann has 

 claimed in combating the idea of a critical point, or does it merely 

 continue rising indefinitely to infinite pressures and temperatures? 

 Evidently none of these things have happened within the domain of 

 the present diagram for water, nor have they happened in the low 

 range up to 3000 or 4000 used before for any other liquid. The only 

 hold we get on this question is by an extrapolation. In this we are 

 very greatly helped by the behavior of the latent heat and the change 

 of volume, for evidently an extrapolation of the equilibrium curve 

 alone is absolutely incompetent to decide whether it is going to stop 

 abruptly or not. But if this curve has an end or a maximum, then the 

 latent heat and the change of volume must behave in a definite manner 

 with respect to each other. At a critical point, the latent heat and 

 the change of volume must vanish together, while at a maximum, the 

 change of volume becomes zero, the latent heat remaining finite. 



Tammann's argument for the probable existence of a maximum 

 comes from observing the general trend of the latent heat and the 

 change of volume on the equilibrium curve. Tammann could not make 

 any very accurate measurements of the change of volume, but they 

 were accurate enough to show that for the substances tried up to 2000 

 or 3000 kgm. the change of volume becomes less at high pressure, but 

 the latent heat remains nearly constant. The change of volume is 

 approximately linear with temperature on the equilibrium line. Whence 

 by an extrapolation, Tammann concluded that the change of volume 

 would pass through zero before the latent heat, and that therefore the 

 equilibrium curve has a maximum. He has calculated the probable 

 position of this maximum for a number of substances, assuming the 



