In this paper by the fundamental Gauss' principle of least constraint we obtain the impulse-dynamical equations of a non-holonomic system. We consider in particular the impulse-motion of a solid which rolls without slipping on a fixed plane and we apply this to the case of the sphere and to the case of a solid with gyroscopic structure which rolls along a projecting circular ridge having the gyroscopic axis for axis; the second case may be reduced to that of the circle.