  Some general properties of perturbed (rational) CFT in the background metric
of symmetric 2D sphere of radius $R$ are discussed, including conformal
perturbation theory for the partition function and the large $R$ asymptotic.
The truncated conformal space scheme is adopted to treat numerically perturbed
rational CFT's in the spherical background. Numerical results obtained for the
scaling Lee-Yang model lead to the conclusion that the partition function is an
entire function of the coupling constant. Exploiting this analytic structure we
are able to describe rather precisely the ``experimental'' truncated space
data, including even the large $R$ behavior, starting only with the CFT
information and few first terms of conformal perturbation theory.
