  We studied the temperature dependences of the optical spectra for optimally
and underdoped Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+z}$ single crystals. Similarly to
the other cuprates' cases, a gap-like conductivity suppression was observed
with reducing the temperature from above $T_{\mathrm{c}}$, creating a peak in
the conductivity spectrum. The conductivity peak energy was insensitive to the
doping level, namely $T_{\mathrm{c}}$, which suggests that this gap is not a
superconducting gap but is related to the pseudogap. Comparing the data of
various mono-, double-, and triple-layer cuprates, we found a clear correlation
between the optimal $T_{\mathrm{c}}$ of each material and the pseudogap-related
conductivity peak energy.
