  The Bose-Einstein condensation of a dilute gas of rubidium-87 atoms was
achieved by cooling a small number of atoms in a magnetic trap. The effective
potential of the trap is to lowest order harmonic and under these conditions we
estimate the critical temperature and the heat capacity of an ideal gas of Bose
particles. Previously this has been estimated within the semiclassical
approximation. However, because of the small number of atoms, the resulting
$T_c$ deviates slightly from our result obtained by exact numerical
calculations. For the gap of the heat capacity at the transition point the
deviation is $20\%$.
