  On the basis of the Poincare-Weyl gauge theory of gravitation, a new
conformal Weyl-Dirac theory of gravitation is proposed, which is a
gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field
representing the dark matter model. A static approximate axially symmetric
solution of the field equations in vacuum is obtained. On the base of this
solution in the Newtonian approximation one considers the problem of rotation
velocities in spiral components of galaxies.
