A fundamental class of geodesics on any closed surface of genus greater than one

t}rpe of fundamental geodesic and it is with the aid of this representation that the fundamental class of geodesies is studied.The surface 2. The surface defined.The surfaces to be considered are to be twosided, closed surfaces of finite genus p, p greater than unity.They are to be without singularities.More specifically we will suppose that the points in the neighborhood of any point of the surface can be put into one to one continuous correspondence with the points in the neighborhood of some point in a plane, in such a manner, that for the neighborhoods considered, the cartesian coordinates, x, y, and z, of a point of the surface, be continuous functions of the cartesian coordinates, u, v, of the plane, provided with continuous partial derivatives up to the fourth order, while further