Theory of Surface Forces. 461 



and this we may think of as applicable in two dimensions 

 (fig. 6) to each unit of length. When = 0, (41) reduces to T. 



The term T cos in the expression for the 

 total pressure appears to have its origin in 

 the curvature of the surface, only not disap- 

 pearing when the curvature vanishes, in conse- 

 quence of the simultaneous increase without 

 limit of the area over which the pressure is 

 reckoned. If we consider only a distance A B, 

 which, though infinite in comparison with the 

 range of the attraction, is infinitely small in comparison 

 with the radius of curvature, Tcos 6 will disappear from the 

 expression for the pressure, though it must necessarily remain 

 in the expression for the attraction. The pressure acting 

 across a section A B proceeding inwards from a plane surface 

 A E of a fluid is thus inadequate to balance the attraction of 

 the two parts. It must be aided by an external force per- 

 pendicular to A B of magnitude T cos ; and since the 

 imaginary section A B may be made at any angle, we see 

 that the force must be T and must act along AE. 



An important class of capillary phenomena are concerned 

 with the spreading of one liquid upon the surface of another, 

 a subject investigated experimentally by Marangoni, Van der 

 Mensbrugghe, Quincke, and others. The explanation is 

 readily given in terms of surface-tension ; and it is sometimes 

 supposed that these phenomena demonstrate in a special 

 manner the reality of surface-tension, and even that they are 

 incapable of explanation upon Laplace's theory, which dealt 

 in the first instance with the capillary pressures due to curva- 

 ture of surfaces*. 



In considering this subject, we have first to express the 

 dependence of the tension at the interface of two bodies in 

 terms of the forces exercised by the bodies upon themselves 

 and upon one another, and to effect this we cannot do better 

 than follow the method of Dupre. If T 12 denote the inter- 

 facial tension, the energy corresponding to unit of area of the 

 interface is also T 12 , as we see by considering the introduction 

 (through a fine tube) of one body into the interior of the other. 

 A comparison with another method of generating the interface, 

 similar to that previously employed when but one body was 

 in question, will now allow us to evaluate T 12 . 



The work required to cleave asunder the parts of the first 



* Van der Mensbrugghe, " Essai sur la Theorie Mecanique de la Tension 

 Superficielle, &c." Bulletins de I 'Acad. roy. de Belgique, 3 me serie, t. ix, 

 no. 5, 1885, p. 12. AY oythiugton, Phil. Mag- Uet. 1884, p. 364. 



