  Charging of a clean two-dimensional island is studied in the regime of small
concentration of electrons when they form the Wigner crystal. Two forms of
electron-electron interaction potential are studied: the pure Coulomb
interaction and the exponential interaction corresponding to the screening by a
pair of close metallic gates. The electrons are assumed to reside in a
parabolic external confining potential. Due to the crystalline symmetry the
center of the confinement can be situated at distinct positions with respect to
the crystal. With the increasing number of electrons $N$ the center
periodically hops from one such a location to another providing the lowest
total energy. These events occur with the period $\sim N^{1/2}$. At these
moments in the case of the pure Coulomb interaction the charging energy of the
island has a negative correction $\approx 15%$. For the case of the exponential
interaction at the moments of switching the capacitance becomes negative and
$\sim N^{1/4}$ new electrons enter the island simultaneously. The
configurations of disclinations and dislocations in the island are also
studied.
