Notation. partial differential equations in infinite media. boundary conditions at a plane surface separating two media -- Vibrating sphere in an infinite homogeneous medium. definition of the point source II. initial conditions -- The method of integration -- Determination of the exponential coefficients determination of the,transmission factor B(t) -- Study of the transmission factor B(t) -- Solution of the other integral equations. behavior of the ensemble of different wave fronts. definitive justification of the solution. importance of the conical wave fronts -- The static problem: the limiting case -- The particular case of the harmonic steady state -- The progressive wave when the second medium is a vacuum. kinematic discontinuities. primary terms -- The rayleigh wave -- The second surface wave -- The spherical distortional pseudo-wave -- The case in which the second medium is a fluid. further consideration of the case of two solid media.