  In 1894 M.J.M. Hill published an article describing a spherical vortex moving
through a stationary fluid. Using cylindrical coordinates and assuming the
azimuthal velocity component zero, Hill found a simple solution that described
this flow. A similar modern problem in the MHD framework was put forth in 1987
by A. A. Bobnev and in 1995 by R. Kaiser and D. Lortz who applied the setup to
model a ball lighting. We present a much simpler derivation of Hill's spherical
vortex using the Bragg-Hawthorne equation. In particular, by using the moving
frame of reference, the Euler equations reduce to equilibrium flow which are
equivalent to the static equilibrium MHD equations up to relabelling. A new
generalized version of Hill's spherical vortex with a nonzero azimuthal
component is derived. A physical solution to the static equilibrium MHD
equations is computed by looking at a separated solution to the Grad-Shafranov
equation in spherical coordinates. Finally, the stability of Hill's spherical
vortex is examined by performing an axisymmetric perturbation described; it is
shown that the Hill's spherical vortex is linearly unstable with respect to
certain kinds of small perturbations.
