and Electronic Potential Energy. 259 



the energy is expressed in ergs for a gram-molecule, having 

 the value 



1,014,000 x 22430/273 = 83 x 10 6 , 



and N = 2-77xl0 19 x 22430. 



Thus «(M/p) 2 / 3 = l-46(T c -T) (13) 



This is the relation discovered by Eotvos (Wied. Ann. 

 xxvii. 1886, p. 448) by means of the princple of correspond- 

 ing states enunciated by van der Waals. In his experiments 

 Eotvos found 2*23 to be the numerical coefficient in place of 

 the 1'46 just found. For 36 normal compounds Ramsay and 

 Shields found 2*121 to be the mean value of this constant of 

 Eotvos. For Cl 2 it is 1*91, 2 1'66, and N 2 1*53 (Boltzmann 

 Festschrift, p. 384). The agreement between the theoretical 

 coefficient, and these experimental values is sufficiently close 

 to justify the reasoning of this section and the assumption 

 1 R 2 3 = m'jp c in elements, and =m\2*p c (\ -\-p\p c )% in compounds, 

 or in other words that at the passage from the surface layer 

 of the liquid to the surface layer of the vapour the criiical 

 density prevails in elements, and a closely related density in 

 compounds. The chief reason for the difference between 

 1*46 and 2*12 is that in our reasoning, by confining our 

 attention to the kinetic energy and the attractional potential 

 energy, we have neglected the energies associated with the 

 external pressure and with the collisional forces, that is, the 

 energies corresponding with the virials Spvj2 and 3RTt'/2 (v—-b) 

 or 3RT2/t/2(r + /<;). These approximately neutralize one 

 another so long, as we can use the equation pv=HT approxi- 

 mately, and that is why we have been able to reason success- 

 fully as if the molecules were planets and comets free from 

 external force and free from collisions. At the critical point 

 and near it the approximation pv = RT is too rough, whence 

 the discrepancy between 1'46 and 2*12, It would lead us 

 too far from the present subject to discuss the inclusion of 

 these two neglected terms. The chief object of the present 

 section is to show how the classical statical theory of surface 

 tension, developed by Laplace, Young, and Gauss, in the 

 days before the kinetic theory of matter, is connected with 

 the more recent discoveries made in the light of that theory. 

 Closely connected with the discovery of Eotvos is that made 

 by Cailletet and Mathias (Comptes Rendus, cii. 1886, p. 1202) 

 which I have discussed in the Boltzmann Festschrift. With 

 temperature as abscissa and density as ordinate they plotted 

 the densities of liquid and saturated vapour right up to the 

 critical point, forming two branches of a curve which merged 



