Static Friction. 209 



solid integrated through the depth of the layer, whilst the 

 stability o£ a layer of a given thickness is a function of 

 the differential coefficients of the interracial energy taken 

 with reference to the thickness. 



The integral is the work done by the cohesive forces acting 

 between lubricant and solid when the layer of the former is 

 interposed between the faces of the latter. This may be 

 expressed in terms of a tension, and thereby become mea- 

 surable, if one solid lace alone is considered. Let t be the 

 work in ergs done per unit area in removing a layer from 

 the surface of a mass of fluid, the layer being so thin 

 that the fluid composing it is not in mass ; t will then also 

 be the tension of the free layer. Now apply the layer to the 

 solid face. The forces of attraction between the two will do 

 work. Let this be t' per unit area. The tension T of the 

 composite surface so formed will then be 



where T s is the tension of the solid. 



For the difference between the tension of two composite 

 surfaces formed on the same solid but with different fluids 

 a and b we have 



T a -T b = (t a -t b ) + (t b '-t a '). 



If we assume that t a bears the same ratio to t b as do the 

 tensions of the fluids in mass and choose for the purpose 

 of experiment two fluids whose surface tensions are equal, 

 the term (t a — t b ) will vanish, and the left-hand side of the 

 equation be positive or negative according as the term 

 {ta —tb) is positive or negative. 



In an earlier paper (this journal, ser. 6, vol. xxxviii. p. 49 

 (1919)) I described how films of insensible thickness form on 

 a plate of glass about drops of certain fluids, and how the 

 drops are moved over the surface of the plate by the con- 

 tractility of the films. This property may be utilized to 

 measure the sign of the term (t a ' — t b ). Let one drop of 

 each of two fluids a and b be placed on the plate : there will 

 form about each a composite surface of tensions T« and T 

 respectively. If T a is greater than T b the drop a will move 

 away from drop b and the latter will pursue it and, if the 

 surface tensions of the fluids are equal, such movement will 

 show that the adhesion of the film of b to the surface is 

 greater than that of a. 



Benzene and propionic acid are a pair of fluids whose 

 surface tensions are practically equal, while the former 



