﻿564 Dr. G. Bakker on the 



If our reasoning is correct the value of H must be identical 

 with that obtained in equation (9). Indeed, if represents 

 the thermic pressure and S the cohesion, we should have 

 in every direction p = 6 — $. 



Hence 



p 1 _p 3 =6i^S 1 -(^-S 2 ) = S 2 -S 1 , 



whence 



n = \\p 1 -p 2 )dh = \ 2 (s 2 -$ 1 )dh. . . (io) 

 t/i *, i 



JFor the cohesion S x in the direction o£ the lines of force 

 (that is to say in the direction normal to the surface of the 

 membrane) we have 



s --^/( R2 -5> 



For the cohesion S 2 perpendicular to the lines of force (or 

 parallel to the membrane) we have found 



=— f 



whence 



which is exactly the formula (9) for H. 



The reasoning based on fig. 1 is absolutely general and 

 the formula for H, 



n = (\s 2 -s l )dj h (io) 



is independent of the function of force adopted, if 6 is a 

 quantity independent of the direction. I have succeeded in 

 demonstrating that formula (10) gives always the expression 

 found by Rayleigh *. 



§ 6. Calculation of the surface-tension by means of the 

 thermic pressure. — I have found for the surface-tension H : 



H =^J 1 2 (:f J dh > « 



which becomes on putting lirfX^—a (p. 561) 



„ X' C-(dVV „ \ 2 ndVdVj ' 



B - = Ya)\dk) dh = Ta) i dkT p d P- ■ -( 9a > 



* Rayleigh, "On the Theory of Surface Forces, II." Phil. Mag. Feb. 

 1892, p. 218, formula' (22). See Zeitschr. fur phys. Chemie, xxxiii. 4. 

 p. 409 (1900). 



