It lies principally on finding the latitude of the vertex ψ_m to solve the problem of finding azimuths or length of a geodesic of which quantities are entirely unlimited, giving the positions of its both ends-the second problem on the geodesic. In 1953 Bodemuller for the first time solved the problem by his own way of repeating the cyclic approximation between ψ_m and the longitude-difference on the auxiliary sphere. Later in 1959 Moritz thought the direct solution of ψ_m, however, it is felt that it implies rather complex computations. The author derived a formula connecting ψ_m with the vertex of the elliptic arc, which is the intersection of the surface of the spheroid with the plane determined by both ends of the geodesic and the center of the spheroid. By the aid of this formula he could obtain ψ_m by repeating the cyclic approximation between these two vertices. It was found that the proposed method is superior in convergency than Bodemuller's method at least for the same numerical example as he gave.