  The space of positively curved hermitian metrics on a positive holomorphic
line bundle over a compact complex manifold is an infinite-dimensional
symmetric space. It is shown by Phong and Sturm that geodesics in this space
can be uniformly approximated by geodesics in the finite dimensional spaces of
Bergman metrics. We prove a stronger C^2-approximation in the special case of
toric (i.e. S^1-invariant) metrics on CP^1.
