  In [SWW], S. Seto, L. Wang and G. Wei proved that the gap between the first
two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as
large as that for an associated operator on an interval with the same diameter,
provided that the domain has the diameter at most $\pi/2$. In this paper, we
extend Seto-Wang-Wei's result to convex domains in the unit sphere with
diameter less than $\pi$.
