  We have calculated the first and second sound modes of a dilute interacting
Bose gas in a spherical trap for temperatures ($0.6<T/T_{c}<1.2$) and for
systems with $10^4$ to $10^8$ particles. The second sound modes (which exist
only below $T_{c}$) generally have a stronger temperature dependence than the
first sound modes. The puzzling temperature variations of the sound modes near
$T_{c}$ recently observed at JILA in systems with $10^3$ particles match
surprisingly well with those of the first and second sound modes of much larger
systems.
