MODELING AND INTEGRATION OF THE RISE AND FALL OF CAPILLARY ACTION BY POISSON (Mathematical aspects of nonlinear waves and their applications)

Abstract

We discuss the mathematical theory of deduction of the capillary action by Laplace, Gauss, Poisson. These share the common concept of attraction and repulsive force on continuum, which is realized with two constants. The former two deduces to the equations of the capillary surface, and the latter, Poisson [10] confirms the formulae, in another model and analytical problems. In the latter half, we introduce Poisson's applications of Legendre's elastic functions to the capillary model owing to the theory and table by Legendre in 1825-6ish [7], which Poisson gives up the self made theories based on the same elliptic functions including tables.