On the Internal Pressure of a Liquid. 193 



the same gravitational terms were given by Rankine in the 

 section on " domes " in his ' Applied Mechanics/ In this 

 case, he professes to deal only with stresses other than those 

 caused by cohesion or elastic reactions, whereas this paper 

 includes general stresses to whatever physical causes they 

 may be due. 



If the conclusions are found to be well based, they may 

 affect structural design and suggest lines of experiment on 

 the strength of materials. 



XV. Note on the Internal Pressure of a Liquid. By W. C. 

 M C C. Lewis, M.A., D.Sc, Physical Chemistry Laboratory, 

 University College, London *. 



RECENTLY (Phil. Mag. September 1910, p. 502, and 

 Kolloidzeitschrift, vol. vii. p. 197, 1910) attention was 

 drawn by the writer to the large discrepancies in the value of 

 the internal pressure K of a liquid according as to whether 



w r e base calculation on van der Waals' equation ( K= — J 



•or take Dupre's value which depends on the internal latent 

 heat of vaporization of unit volume of the liquid. Thus, 

 taking the case of water at ordinary temperature, the value 

 of K from van der Waals' expression is 10,500-11,000 

 atmospheres, while the value given by Dupre's method is 

 23,900 atmospheres. 



To account for the difference in the two sets of values, it 

 was suggested that the density in the surface layer differed 

 .from that in the bulk of the liquid, it being necessary to 

 assume that the average density in the surface is greater than 

 that of the bulk. This entails as a consequence the suppo- 

 sition that the density passes through a maximum as we cross 

 from liquid to vapour. On further consideration of the 

 question, however, the conclusion has been come to that such 

 :a state of things could not represent a permanent equilibrium 

 condition, and that therefore the hypothesis in question is no 

 longer a tenable one. It seems possible that the discrepancies 

 ■observed may be ascribed simply to the fact that molecular 

 forces have a temperature coefficient. Dupre virtually 

 assumed K independent of temperature. Van der Waals 

 assumed (in the simple form of his equation) that K/o 2 is 

 independent of temperature, where p denotes density. Neither 

 •of these is borne out by experience, though undoubtedly 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 22. No. 127. July 1911. O 



