Natural structure is unique and galaxies are natural structure. In our previous work, we showed that rational structure is unique. In this paper, the unique two-parameter rational structure is used to model barred galaxies. The model fits to galaxy images satisfactorily and the prediction on galaxy arms is consistent with observation. Today the accepted theory applied to galaxies is Newton's universal gravity which, however, fails to galactic observation generally. Accordingly, dark matter was introduced but has never been observed. A simple glimpse of the images of edge-on spiral galaxies suggests that Newton's concept of action at a distance should be rejected. It is hard to imagine that the stars far away from the galaxy center suffer an instant force from the center. In our previous work we suggested a new universal gravity which generalizes Newton's one and is uniquely determined by rational structure. The new gravity results from local curvature of Darwin surfaces and simply explains the kinematic phenomenon of constant rotation curves. In this paper, a preliminary study on the new gravity with Poisson's equation is presented which verifies the phenomenon.