Law of Molecular Force. 175 



of the mercury in them was observed, and also the height of 

 each of the columns of liquid C0 2 ; the density of the liquid 

 was then obtainable in terms of these measurements, and the 

 determined density of the saturated vapour. The vapour-den- 

 sities were determined from — 23° C. to 30°, and the liquid- 

 densities from —34° to 22°; and both sets of densities were 

 then represented graphically in one diagram with temperatures 

 for abscissae and densities for ordinates. The two branches of 

 the curve ought to pass into one another at the critical tem- 

 perature i Cailletet and Mathias, completing the curve for the 

 small portion thatwas not determined by experiment, according 

 to the obvious tendencies of the determined portions, found the 

 critical temperature to lie between 31° and 32°. Thus, again, 

 we meet a determination of the critical temperature in discord 

 with Regnault's work. Probably most of the discord can be 

 traced to the determination of the vapour-densities in capillary 

 tubes, in which it has been shown that the density of satura- 

 tion near the critical temperature may be very different from 

 the density of saturation of the vapour in contact with a 

 plane surface of the liquid and at the same pressure. The 

 form of Cailletet and Mathias's curve would have to be consi- 

 derably altered if 42°*8 is the true critical temperature of C0 2 ; 

 but how far a change in the density of the liquid would have 

 to contribute to this alteration of form we cannot say. 



Thus, then, with the experimental evidence at present 

 available, we cannot construct any equation which will bridge 

 over the discontinuity between the liquid and gaseous states 

 satisfactorily ; because, if it represents the results of some 

 experiments, it will fail to represent others of equal weight. I 

 can only draw attention to the fact that Thilorier, whose deter- 

 minations of pressure agree excellently with Regnault's, found 

 densities differing by as much as 15 per cent, from those of 

 Cailletet and Mathias. There is certainly occasion for an 

 experimental inquiry (and much promise of interesting results 

 to those who have the facilities for making one) into the effect 

 of extent of surface in contact with solid and curvature of 

 surface on the compressibility and dilatability of fluids. There 

 ought to be a physical effect corresponding to each term in the 

 equation of Gauss for the energy of a fluid enclosed in a solid. 



Before passing on to consider the equation in its thermo- 

 dynamic aspect, it may be well to give an idea of its corre- 

 spondence with experiment at low pressures and high tempe- 

 ratures. Amagat has given ( Comptes Rendus, xciii., 1881) the 



following values of the ratio ~~, at different temperatures 



where p' is about 2*85 metres of mercury and v = 2v', and the 



