  In this third paper in a series on stable magnetic equilibria in stars, I
look at the stability of axisymmetric field configurations and in particular at
the relative strengths of the toroidal and poloidal components. Both toroidal
and poloidal fields are unstable on their own, and stability is achieved by
adding the two together in some ratio. I use Tayler's (1973) stability
conditions for toroidal fields and other analytic tools to predict the range of
stable ratios and then check these predictions by running numerical
simulations. It is found that while the poloidal field can account for no more
than approximately 80% of the total energy, it can account for a very small
fraction of the energy, i.e. that the toroidal field can be -- and is likely to
be -- significantly stronger than the poloidal. Furthermore, the weaker the
field, the weaker the poloidal component can be in relation to the toroidal.
The implications of this result are discussed in various contexts such as the
emission of gravitational waves by neutron stars, free precession, and a
`hidden' energy source for magnetars.
