108 PROCEEDINGS OF THE AMERICAN ACADEMY. 



tion between ^•olume and pressure is the same for every temperature. 

 The only way in which temperature has an effect in Case II is with 

 regard to the critical temperature which determines when Case II 

 passes into Case III. The pressure for a given volume in Case III 

 ultimately becomes less than we would have expected it to be if we 

 extrapolated by the formula of Case I. In other words, the substance 

 is more compressible than we should expect it to be from its behavior 

 at low pressures. This reminds us of the formulas of Tumlirz and 

 Tammann. It should be said however, that the mathematical analy- 

 sis applied to Case III cannot continue to have physical significance 

 indefinitely, for it was assumed that the springs obey Hooke's law, 

 which is true only for small displacements. The characteristic equa- 

 tion given above for Case III predicts the vanishing of the volume 

 at a finite pressure. 



Something similar to the action of the model must take place in a 

 liquid. At any instant there are collisions taking place, some free 

 collisions similar to those of Case I, some collisions with interference 

 like Case III, and some contacts between molecules like Case II, 

 which are not properly called collisions at all. The momentum com- 

 putation of pressure applies only to Case I. At low pressures, by 

 far the greater number of collisions is of type I, but as the volume 

 decreases and pressure increases, collisions of type II and III become 

 increasingly predominant, until at infinite pressure we may suppose 

 type II only to be present. Under these conditions, the momentum 

 effect has absolutely no connection with pressure. 



The ordinary conception of internal pressure must obviously be 

 modified in a similar way. There are many different meanings at- 

 tached to "internal pressure." One way of defining internal pressure 

 is by constructing an imaginary surface in the interior of a liquid, 

 and finding the momentum of all the molecules which cross this 

 surface in unit time. This process evidently fails to have physical 

 meaning when there are molecules in the liquid in contact with each 

 other for any length of time. The modification of the definition 

 necessary to meet these new^ conditions would be very complicated. 

 It seems better under the circumstances to give up this conception of 

 internal pressure altogether. Other conceptions may still be useful 

 at high pressures; such, for example, as to regard the internal pressure 

 as the external pressure plus the unbalanced attractive effect of the 

 molecules at the surface of the liquid. But it is a difficult matter to 

 define internal pressure in such a way as to have a physical meaning 

 for one of Maxwell's demons inhabiting the interior of a liquid. 



