Abstract
SUMMARY. — Newton had classed phenomena involving capillary action amongst those suitable for mathematical treatment. Inspired directly by the methods of celestial mechanics, Laplace carried out this treatment in two stages. Firstly, he analysed the phenomenon at the level of elementary particles in accordance with a gravitational model. Then, he obtained a partial differential equation presumed to regulate the shape of the surface of the liquid phase. The equation of 1805 remains the fixed point of contemporary works on surface phenomena. The intention of this paper is to account for this scansion of the Laplacian model for mathematical physics, by attempting to separate the strictly physical inspiration from the very brilliant progress of the analytical calculation.
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