  The low-energy electronic structure of the trilayer cuprate superconductor
Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ near optimal doping is investigated by
angle-resolved photoemission spectroscopy. The normal state quasiparticle
dispersion and Fermi surface, and the superconducting d-wave gap and coherence
peak are observed and compared with those of single and bilayer systems. We
find that both the superconducting gap magnitude and the relative
coherence-peak intensity scale linearly with $T_c$ for various optimally doped
materials. This suggests that the higher $T_c$ of the trilayer system should be
attributed to parameters that simultaneously enhance phase stiffness and
pairing strength.
