  In our previous work [PSSW], we showed that the Ricci flow on S^2 whose
initial metric has conical singularities \sum_{j=1}^k \beta_j[p_j] converges to
a constant curvature metric with conic singularities (in the stable and
semi-stable cases) or to a gradient shrinking soliton with conical
singularities (in the unstable case). The purpose of this note is to show that
in the unstable case, that is, the case where \beta_k>\beta_k'=\s_{j<k}\beta_j,
that the limiting metric is the unique shrinking soliton with cone singularity
\beta_k[p_\infty]+\beta_k'[q_\infty]. This verifies the prediction made in
[PSSW].
