﻿566 Dr. G. Bakker on the 



dV 

 Let us substitute this value in (9a), and replace -p by 



— ; (9a) finally becomes : 



Thus the constant of Laplace or the surface-tension H 

 depends only on the thermic pressure 6, and consequently on 

 its connexion with the density p. If we accept for 6 the 

 formula 



JRT ETp 

 ~~ « — b 1 — bp 



given by van der Waals, the formula of H is complicated 

 enough. 



Observation. — It is interesting to observe that the surface- 

 pressure (molecular pressure) K can be expressed, on the 

 contrary, very simply by means of the thermic pressure 6. 

 K, being the force by which the unit of surface of the 

 capillary layer is attracted towards the liquid, must be in 

 absolute value also the difference between the thermic pres- 

 sures of the liquid and of the vapour : 



K = 6 2 — 6 1 ; 

 whence, observing that 



Pi — &i—api 2 , and p 2 =Pi = 6 2 — ap2 2 , 

 we see 



K=a(p/-^) (7) 



§ 7. A property of the surface-tension. — If we assume f(r) 

 to represent the force acting between two liquid particles, 

 and put 



/*» / 00 



I f(r)dr = <j)(r), and — I r 2 cj)(r) dr— 



J r J r 



f(r). 



we shall have as the potential energy of a volume v : 



W = 2^(0) p 2 v (Gauss), 



p being the density. 



Now I have demonstrated that for a homogenic agent the 

 virial of the forces of cohesion B is equivalent to the potential 

 energy W multiplied by — §*; 



then one has: 2B + 3W = (17) 



* G. Bakker, " Theorie der VloeistofTen en dampen " (1888), and 

 u Ueber die potentieile Energie und das Virial der Molekdarkrafte," 

 Zeitschr. filr phys. Chem. (1896) ; L. Boltzmann, " Vorlesungen liber 

 Gastheorie, II." (1898), p. 152. 



