  Spin-spin relaxation time ($T_2$) and magnetic susceptibility ($\chi$) of the
second layer $^3$He adsorbed on Grafoil, exfoliated graphite, preplated with a
monolayer $^4$He are studied by pulsed-NMR in a density range of $0.68 \leq
\rho \leq 5.28$ nm$^{-2}$. The temperature dependence of $\chi(T)$ and $\chi(T
= 0)$ show Fermi fluid behaviour and no evidence of self-condensation are found
even at the lowest density $\rho = 0.68$ nm$^{-2}$. Density dependence of $T_2$
at $f = 5.5$ MHz shows a broad maximum of 5.7 ms around $\rho = 3$ nm$^{-2}$.
Since the decrease of $T_2$ in dilute side can not be expected in the ideal 2D
fluid, it can be understood as the relaxation caused by a small amount of solid
$^3$He at heterogeneity of the substrate. We also measured the Larmor frequency
dependence of $T_2$ at $\rho = 5.28$ nm$^{-2}$. $1/T_2$ has a $f$-linear
dependence similarly to the earlier study on a first layer solid $^3$He. From a
comparison between our result and the earlier one, this linearity is almost
independent of the particle motion. Now, it could be caused by a microscopic
magnetic field inhomogeneity arisen from the mosaic angle spread and
diamagnetism of the graphite substrate.
