  Paircorrelations and the magnetic susceptibility of electrons in a spherical
cavity are studied both for grand canonical and the canonical ensemble. The
coupling constant of the $BCS$ Hamiltonian is adjusted to experimental values
of the gap parameter. The gap parameter is found to increase for small grains
as a consequence of the pronounced shell structure in the spectrum of the
spherical cavity. The sharp phase transition at $T_c$ is smeared out for the
canonical ensemble. The strong paramagnetic susceptibility of the normal
electrons in the cavity is reduced by the superconductivity, but it remains
positive.
