182 The Contact- Angle of Liquids and Solids. 



the finite contact-angle found for it, notwithstanding its great 

 mobility. 



It must be admitted, however, that the temperature dif- 

 ferences assumed in the preceding explanation are, for some 

 of the liquids, very slight, especially for those, like turpentine 

 and petroleum, for which the results indicate large contact- 

 angles. On the whole, I am inclined to believe that the 

 finite contact-angles indicated are due to the relations among 

 the molecular forces at the line of contact. If this view be 

 accepted, we might assign a limit to the molecular forces 

 between the molecules of glass and those of the liquids for 

 which the finite contact-angle appears, by the help of Gauss's 

 hypothesis as to the similarity in form of the force-functions 

 representing the forces between liquid elements and between 

 liquid and solid elements. Doubt is, however, thrown on 

 that assumption by the values of a 2 obtained for the liquids 

 examined. 



Law of Molecular Force. — The expression for the force 

 between two elements of a liquid is, in Laplace's and Gauss's 

 theories, D 2 f(x)dv 2 , where I) represents the density of the 

 liquid, dv the volume of an element, and f{x) a function of 

 the distance x between the elements. In the operation by 

 which Laplace's capillary constant H = a 2 D is determined in 

 terms of/(#), the only property of this function of which use 

 is made is that it diminishes with extreme rapidity as the 

 distance x increases, and becomes insensible for measurable 

 values of x. No assumption is made as to whether it is the 

 same for all kinds of molecules. In Gauss's discussion of the 

 contact-angle he makes the assumption, to which reference 

 has already been made, that the two functions f(x) and F(#), 

 the one of which is proportional to the force between two 

 elements of the liquid separated by the distance x, and the 

 other proportional to the force between an element of the 

 liquid and one of the solid, are in a ratio independent of x; 

 that is, that they have the same form. If this assumption be 

 true for the relation between these forces, it seems likely that 

 it would be true for the different values of f(x) for different 

 liquids. Indeed, if the molecular force varies inversely as 

 some power of the distance, it seems the most probable sup- 

 position that this power is the same for all liquids. If this 

 were so, the integral \zdzsfr(z) contained in the expression for 

 the capillary constant H, since y/r(z) is a function ultimately 

 depending on /(#), should then be the same for all liquids. 

 Since H equals 27rD 2 §zdzyjr(z), the values of H/D 2 for dif- 



