Theory of Surface Forces. 471 



be a simple function of the distance, such as those considered 

 above in illustrative examples, the thickness of the layer 

 diminishes constantly with increasing height. The limit is 

 reached when the thickness vanishes, and the potential attains 

 the value due simply to the solid wall. This potential is 

 cr'K , the intrinsic pressure within the wall being er' 2 K ; so 

 that if we compare the point above where the layer of fluid 

 disappears with a point below upon the horizontal surface, 

 we find 



gpz = <r{o> -*)*<, (60) 



By this equation is given the total head of liquid in contact 

 with the wall ; and, as was to be expected, it is enormous. 



The height of the meniscus itself in a very narrow tube 

 wetted by the liquid is obtained from (57), (58). If R be 

 the radius of curvature at the centre of the meniscus, 



m =2T/U; (61) 



and B, may be identified with the radius of the tube, for 

 under the circumstances supposed the meniscus is very ap- 

 proximately hemispherical. 



The calculation of the height by the method of energy 

 requires a little attention. The simplest displacement is an 

 equal movement upwards of the whole body of liquid, in- 

 cluding the layer above the meniscus. In this case the w T ork of 

 the cohesive forces depends upon the substitution of liquid for 

 air in contact with the tube, and therefore not merely upon 

 the interfacial tension between liquid and air, as (61) might 

 lead us to suppose. The fact is that in this way of regarding 

 the subject the work which compensates that of the cohesive 

 forces is not simply the elevation against gravity of the 

 column (z), but also an equal elevation of the very high, 

 though very thin, layer situated above it. The complication 

 thus arising may be avoided by taking the hypothetical dis- 

 placement so that the thin layer does not accompany the 

 column (z). In this case the work of the cohesive forces 

 depends upon a reduction of surface between liquid and air 

 simply, without reference to the properties of the walls, and 

 (61) follows immediately. 



Laplace's integral K was, as we have seen, introduced 

 originally to express the intrinsic pressure, but according 

 to the discovery of Dupre * it is susceptible of another 

 and very important interpretation. " Le travail de des- 

 agregation totale d'un kilogramme d'un corps quelconque 



* Theorie Mecanique de la Chaleur, 1869, p. 152. 



Van der Waals gives the same result in his celebrated essay of 1873. — 

 German Translation, 1881, p. 31. 



