  By constructing $d_{x^2-y^2}-d_{z^2}$ two-orbital models from first
principles, we have obtained a systematic correlation between the Fermi surface
warping and the evaluated $T_c$ for various bilayer as well as single-layer
cuprates. This reveals that smaller mixture of the $d_{z^2}$ orbital component
on the Fermi surface leads to both of larger Fermi surface warping and higher
$T_c$. The theoretical correlation strikingly resembles a systematic plot for
the experimentally observed $T_c$ against the Fermi surface warping due to
Pavarini {\it et al.} [Phys. Rev. Lett. {\bf 87}, 047003 (2001)], and the
present result unambiguously indicates that the $d_{z^2}$ mixture is a key
factor that determines $T_c$ in the cuprates.
