  Linear cases of Bragg-Hawthorne equation for steady axisymmetric
incompressible ideal flows are systematically discussed. The equation is
converted to a more convenient form in a spherical coordinate system. A new
vorticity decomposition is derived. General solutions for 16 linear cases of
the equation are obtained. These solutions can be specified to gain new
analytical vortex flows, as examples in the paper demonstrate. A lot of
well_known solutions like potential flow past a sphere, Hill's vortex with and
without swirl, are included and extended in these solutions. Special relations
between some vortex flows are also revealed when exploring or comparing related
solutions.
