CAPILLARY ACTION. 



d6 

 Remembering that 0(0) ia a finite quantity, and that ^ = -$(z), we find 



| 



When c is greater than e this ia equivalent to 2// in the equation of Laplace. 

 Hence the tension is the same for all films thicker than c, the range of the 

 forces. For thinner films 



IT 



Hence if ^(c) is positive, the tension and the thickness will increase together. 

 Now 1wmp^(c) represents the attraction between a particle m and the plane 

 tfiir&ce of an infinite mass of the liquid, when the distance of the particle out- 

 side the surface is c. Now, the force between the particle and the liquid is 

 certainly, on the whole, attractive ; but if between any two small values of 

 < it should be repulsive, then for films whose thickness lies between these 

 values the tension will increase as the thickness diminishes, but for all other 

 cases the tension will diminish as the thickness diminishes. 



We have given several examples in which the density is assumed to be 

 uniform, because Poisson has asserted that capillary phenomena would not take 

 place unless the density varied rapidly near the surface. In this assertion we 

 think he was mathematically wrong, though in his own hypothesis that the 

 density does actually vary, he was probably right. In fact, the quantity 4wp-K, 

 which we may call with Van der Waals the molecular pressure, is so great 

 for most liquids (5000 atmospheres for water), that in the parts near the sur- 

 face, where the molecular pressure varies rapidly, we may expect considerable 

 variation of density, even when we take into account the smallness of the 

 compressibility of liquids. 



The pressure at any point of the liquid arises from two causes, the external 

 pressure P to which the liquid is subjected, and the pressure arising from the 

 mutual attraction of its molecules. If we suppose that the number of molecules 

 within the range of the attraction of a given molecule is very large, the part 

 of the pressure arising from attraction will be proportional to the square of 

 the number of molecules in unit of volume, that is, to the square of the 

 density. Hence we may write 



(1), 



