  We measured $^{23}$Na-NMR spectra and nuclear spin-lattice relaxation rates
$^{23}(1/T_1)$ of superconducting and non-superconducting bilayer hydrate
$Na_xCoO_2-yH_2O$ (x ~ 0.3, y ~ 1.3). The central resonance frequency shows a
small but various shift due to the difference in the shielding effect by
intercalated $H_2O$ molecules. The different shielding effect also gives a
large difference in the magnitude of $^{23}(1/T_1)$.
