The matching conditions across a hypersurface representing the evolution of a layer of matter are derived from Einstein's equations and from Lichnerowicz' matching conditions by a limiting process which consists in letting the thickness of a volume distribution of dust tend to zero, and are shown to give, in the newtonian approximation, the classical matching conditions for the derivatives of the newtonian potential across a layer of matter. The point of view adopted here is distinct from the ones adopted by Lanczos and Papapetrou & Treder in dealing with the same problem.