CAPILLARY ACTION. 547 



condition when worked out gives not only the equation of the free surface in 

 the form already established by Laplace, but the conditions of the angle of 

 contact of this surface with the surface of a solid. 



Gauss thus supplied the principal defect in the great work of Laplace. 

 He also pointed out more distinctly the nature of the assumptions which we 

 must make with respect to the law of action of the particles in order to be 

 consistent with observed phenomena. He did not, however, enter into the ex- 

 planation of particular phenomena, as this had been done already by Laplace. 

 He points out, however, to physicists the advantages of the method of Segner 

 and Gay-Lussac, afterwards carried out by Quincke, of measuring the dimen- 

 sions of large drops of mercuiy on a horizontal or slightly concave surface, 

 and those of large bubbles of air in transparent liquids resting against the 

 under side of a horizontal plate of a substance wetted by the liquid. 



In 1831 Poisson published his Noiivelle Theorie de I' Action Capillaire. 

 He maintains that there is a rapid variation of density near the surface of a 

 liquid, and he gives very strong reasons, which have been only strengthened 

 by subsequent discoveries, for believing that this is the case. He then pro- 

 ceeds to an investigation of the equilibrium of a fluid on the hypothesis of 

 uniform density, and he arrives at the conclusion that on this hypothesis none 

 of the observed capillary phenomena would take place, and that, therefore, 

 Laplace's theory, in which the density is supposed uniform, is not only insuffi- 

 cient but erroneous. In particular he maintains that the constant pressure K, 

 which occurs in Laplace's theory, and which on that theory is very large, 

 must be in point of fact very small, but the equation of equilibrium from 

 which he concludes this is itself defective. Laplace assumes that the liquid 

 has uniform density, and that the attraction of its molecules extends to a 

 finite though insensible distance. On these assumptions his results are certainly 

 right, and are confirmed by the independent method of Gauss, so that the 

 objections raised against them by Poisson fall to the ground. But whether 

 the assumption of uniform density be physically correct is a very different 

 question, and Poisson has done good service to science in shewing how to 

 carry on the investigation on the hypothesis that the density very near the 

 surface is different from that in the interior of the fluid. 



The result, however, of Poisson's investigation is practically equivalent to 

 that already obtained by Laplace. In both theories the equation of the liquid 

 surface is the same, involving a constant H, which can be determined only by 



692 



