  The thermodynamics and mechanics of the surface of a deformable body are
studied here, following and refining the general approach of Gibbs. It is first
shown that the 'local' thermodynamic variables of the state of the surface are
only the temperature, the chemical potentials and the surface strain tensor
(true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A
new definition of the surface stress is given and the corresponding surface
thermodynamics equations are presented. The mechanical equilibrium equation at
the surface is then obtained. It involves the surface stress and is similar to
the Cauchy equation for the volume. Its normal component is a generalization of
the Laplace equation. At a (body-fluid-fluid) triple contact line, two
equations are obtained, which represent: (i) the equilibrium of the forces
(surface stresses) for a triple line fixed on the body; (ii) the equilibrium
relative to the motion of the line with respect to the body. This last equation
leads to a strong modification of Young's classical capillary equation.
