  Sum rules are used to calculate the corrections to the hydrodynamic
collective frequencies of a harmonically trapped Bose gas at T=0, due to finite
size effects. We show that, with logarithmic accuracy, the relative corrections
behave like $(a_{ho}/R)^4\log(R/a_{ho})$, where $R$ is the Thomas-Fermi radius
of the condensate and $a_{ho}$ is the oscillator length. Results are given for
both spherical and axi-symmetric trapping.
