  In the first part to this paper\cite{part1} it was shown how a simple
Magnetohydrodynamic model could be used to determine the stability of a Tokamak
plasma's edge to a Peeling (External Kink) mode. Stability was found to be
determined by the value of $\Delta'$, a normalised measure of the discontinuity
in the radial derivative of the radial perturbation to the magnetic field at
the plasma-vacuum interface. Here we calculate $\Delta'$, but in a way that
avoids the numerical divergences that can arise near a separatrice's X-point.
This is accomplished by showing how the method of conformal transformations may
be generalised to allow their application to systems with a non-zero boundary
condition, and using the technique to obtain analytic expressions for both the
vacuum energy and $\Delta'$. A conformal transformation is used again to obtain
an equilibrium vacuum field surrounding a plasma with a separatrix. This allows
the subsequent evaluation of the vacuum energy and $\Delta'$. For a
plasma-vacuum boundary that approximates a separatrix, the growth rate $\gamma$
normalised by the Aflven frequency $\gamma_A$ is then found to have
$\ln(\gamma/\gamma_A)=-{1/2} \ln (q'/q)$. Consequences for Peeling mode
stability are discussed.
