  It has been observed that impurity doping and/or ion-beam-induced damage in
high $T_{c}$ superconductors cause a metal-insulator transition and thereby
suppress the critical temperature. Based on our recent theory of the weak
localization effect on superconductivity, we examine the variation of $T_{c}$
with increasing of impurity concentration $\rm (x)$ in
$\rm{La_{1.85}Sr_{0.15}Cu_{1-x}A_{x}O_{4}}$ systems, where A $=$ Fe, Co, Ni,
Zn, or Ga. We find that the doping impurity decreases the scattering matrix
elements for electron-electron attractions, such as
  $V_{nn'}=-V[1-{2\over \pi k_{F}\ell} ln(L/\ell)]$, where $L$ and $\ell$ are
the inelastic and elastic mean free paths, respectively. Using the mean free
path $\ell$ determined from resistivity data, we find good agreements between
our calculated values for $T_{c}$ and experimental data except for Ni-doped
samples, where Ni impurities may enhance the pairing interaction.
