Theory of Surface Forces. 463 



fluid spreads itself indefinitely upon the interface of the first 

 and third fluids. 



The experimenters who have dealt with this question, 

 Marangoni, Van der Mensbrugghe, Quincke, have all arrived 

 at results inconsistent with the reality of Neumann's triangle. 

 Thus Marangoni says* : — "Die gemeinschaftliche Oberflache 

 zweier Fliissigkeiten hat eine geringere Oberflachenspannung 

 als die Differenz der Oberflachenspannung der Fliissig- 

 keiten selbst (rait Ausnahme des Quecksilbers)." Three pure 

 bodies (of which one may be air) cannot accordingly remain 

 in contact. If a drop of oil stands in lenticular form upon a 

 surface of water, it is because the water-surface is already 

 contaminated with a greasy film. 



On the theoretical side the question is open until we intro- 

 duce some limitation upon the generality of the functions. 

 By far the simplest supposition open to us is that the functions 

 are the same in all cases, the attractions differing merely by 

 coefficients analogous to densities in the theory of gravitation. 

 This hypothesis was suggested by Laplace, and may con- 

 veniently be named after him. It was also tacitly adopted by 

 Young, in connexion with the still more special hypothesis 

 which Young probably had in view, namely that the force in 

 each case was constant within a limited range, the same in all 

 cases, and vanished outside that range. 



As an immediate consequence of this hypothesis we have 

 from (3) 



K = KX, (44) 



T = 1V, (45) 



where K , T are the same for all bodies. 



But the most interesting results are those which Young f 

 deduced relative to the interfacial tensions of three bodies. 

 By (12), (43), 



T' 12 = <7 lO - 3 T ; (46) 



* Pogg. Ann. cxliii. p. 348, 1871 (1865). It was subsequently shown 

 by Quincke that mercury is not really an exception, 

 t Works, vol. i. p. 463. 



