Theory of Surface Forces. 525 



The surface of RDQESR is given by ^"(pi—p^dh and 



presents the value o£ the constant of Laplace. Now 



(see above) the pressure p for the point F at which fi=/^i 



1 C 2 

 has the same value as the average pressure jp= - I p 2 dh in 



the capillary layer. Hence 'vi 



surface RDQESR = ( Pl —p) h, . . . (25) 



where li denotes the thickness of the capillary layer. 

 The equations (20) and (21) give further by addition : 



J 'T=°-^ ^ 



Now for the point Q in fig. 7, which corresponds with the 

 point F in fig. 4, we have At = /^ 1 , and the equation (4) gives 

 therefore for the point Q in fig. 7, 



Y=-2ap. 



If p denotes the pressure of the isotherm in the point F, 

 we have : 



6 = p + ap\ 



The equation (26) becomes therefore for the point F in fig. 4 

 or the point Q in fig. 7 : 



Further, 2irf\*=a* ; hence p = pl ^. 



By substitution of this value of p in the equation {25), 

 we find : 



surface RDQESR = i( Pl -p 2 ) h = \ surface RUVSR. 



If, however, we would bring the properties of the theoretical 

 isotherm into connexion with those of the capillary layer, we 



must find the relation between p 2 anc ^ v ( = ) • Therefore 



we depart from the equation (26) and make use of the 

 equation of state- of van der Waals, which gives for the 

 thermic pressure : 



6 = T , and thus r r/ = — — . . l2t) 



v — b 2 v—b 4a 



* Phil. Mag. for December 1906, p. 56±. 

 Phil. Mag. S. 6. Vol. 14. No. $2. Oct. 1907. 2 N 



