  A quantum Monte Carlo approach, considering all the corrugation effects, was
used to calculate the complete phase diagram of the second $^3$He layer
adsorbed on graphite. We found that a first-layer triangular solid was in
equilibrium with a gas in the second layer. At a surface density $0.166 \pm
0.001$ \AA$^{-2}$, this fluid changes into two first-layer registered phases:
4/7 and 7/12 solids. The 7/12 arrangement transforms into an incommensurate
triangular structure of $\rho = 0.189 \pm 0.001$ \AA$^{-2}$ upon further helium
loading. A recently proposed hexatic phase was found to be unstable with
respect to those commensurate solids.
