  We find experimentally that the optical sheet conductance of graphite per
graphene layer is very close to $(\pi/2)e^2/h$, which is the theoretically
expected value of dynamical conductance of isolated monolayer graphene. Our
calculations within the Slonczewski-McClure-Weiss model explain well why the
interplane hopping leaves the conductance of graphene sheets in graphite almost
unchanged for photon energies between 0.1 and 0.6 eV, even though it
significantly affects the band structure on the same energy scale. The f-sum
rule analysis shows that the large increase of the Drude spectral weight as a
function of temperature is at the expense of the removed low-energy optical
spectral weight of transitions between hole and electron bands.
