sufficient system size is. However, the average curve between the two curves formed of the points of both kinds of shell states is expected to be a highly probable approximation to the bulk limit and the model with $t'=0$ is also probable to drive SC, although more extensive calculation with large lattices is needed to remove the room for doubt. Incidentally, for $\rho = 0.68$, no finite energy gain was obtained although the shell is open.

In Fig. 1 of the precursive work of Giamarchi et al. \[\] we find a corresponding value for the SC energy gain per site. It is for $\rho = 0.8125$ on the $8 \times 8$ lattice with $U = 10$ and $t'=0$. Our value for $\rho = 0.80$ on the $10 \times 10$ lattice with $U = 8$ and $t'=0$ should be close to the value. The shell structure for $\rho=0.8125$, or $N_e=52$, on the $8\times 8$ lattice is closed; so is the case with $\rho = 0.80$ on the $10 \times 10$ lattice is closed. However, our value is $3.38 \times 10^{-4}$, being about 1/3 of the above-mentioned value, and if we put it in their figure it is located in the lower 