  The specific heat and susceptibility data for $^3$He on Grafoil are analyzed
in the framework of the Landau Fermi liquid theory. The dominant interaction
between $^3$He quasiparticles is found to be in the p-wave channel for most
experimentally accessible areal densities of $^{3}$He. This interaction is
attractive and gives rise to the p-wave transition temperature which for
moderate areal densities is estimated to be on the scale of several
millikelvin. The relevance of these results to the anomaly in the specific heat
observed at $ T_k = 3.2 \, \mbox{mK} $ is discussed.
