Laplace,derived the theory of capillary phenomena from the principle of possible speeds.
In 1831, Poisson published his Nouvelle theorie del'action capillaire, also based on the assumption of partial interactions. In this work, consideration was given to the rapid change in density that must necessarily exist relative to the liquid particles lying on the surface. Various questions of the theory were examined and studied by Poisson with such completeness that the whole theory seemed exhausted in his labour. All that remained was to connect this theory with the general theory of equilibrium of liquids using the principle of possible speeds. This task was completed by August Yu. Davidov[1] in his dissertation related to this subject. A. Yu. Davidov studied the theory of capillarity with the general rules of analytical mechanics, and also took into account physical circumstances that are significantly related to this subject.
In 1859, Paul du Bois-Reymond[2] defended his dissertation in Berlin, which is also devoted to thermal capillarity. Having laid out with particular care the theory of the potential of capillary forces, he then gave in his dissertation a number of preparatory formulas[3] representing the formation of certain integrals extended to the surface, through integrals extended to its contour. Some of these curious formulas can be
