Helicity of the toroidal vortex with swirl

On the basis of solutions of the Bragg-Hawthorne equations we discuss the helicity of thin toroidal vortices with the swirl - the orbital motion along the torus diretrix. It is shown that relationship of the helicity with circulations along the small and large linked circles - directrix and generatrix of the torus - depends on distribution of the azimuthal velocity in the core of the swirling vortex ring. In the case of non-homogeneous swirl this relationship differs from the well-known Moffat relationship - the doubled product of such circulations multiplied by the number of links. The results can be applied to vortices in planetary atmospheres and to vortex movements in the vicinity of active galactic nuclei.