  The radiation from a relativistic charged particle uniformly moving through
the centre of a dielectric ball is investigated. Analytical expressions for
spectral and spectral-angular distributions of the radiated energy are derived
and numerical results for the spectrum of radiation are given. It is shown,
that the spectral distribution of Cherenkov radiation generated by the
relativistic particle inside a dielectric ball at specified frequencies is
strongly influenced by the ballvacuum boundary.
