But he soon felt obliged to make a less radical change. In his successful model of double refraction, the displacement of the medium was constrained to be tangential to the wavefront, while the force was allowed to deviate from the displacement and from the wavefront. Hence, if the vibrations were perpendicular to the plane of polarization, then the plane of polarization contained the wave-normal but not necessarily the ray. In his "Second Memoir" on double refraction, Fresnel formally adopted this new definition, acknowledging that it agreed with the old definition in an isotropic medium such as air, but not in a birefringent crystal.