  $^{192}$Pt is produced solely by the slow neutron capture (\textit{s})
nucleosynthesis process and hence an accurate ($n$,$\gamma $) reaction rate for
this nuclide would allow its use as an important calibration point near the
termination of the \textit{s}-process nucleosynthesis flow. For this reason, we
have measured neutron capture and total cross sections for $%
^{192,194,195,196,nat}$Pt in the energy range from 10 eV to several hundred keV
at the Oak Ridge Electron Linear Accelerator. Measurements on the other Pt
isotopes were, in part, necessitated by the fact that only a relatively small
$^{192}$Pt sample of modest enrichment was available. Astrophysical $%
^{192,194,195,196}$Pt($n,\gamma $) reaction rates, accurate to approximately
3%--5 %, were calculated from these data. No accurate reaction rates have been
published previously for any of these isotopes. At \textit{s}-process
temperatures, previously recommended rates are larger (by as much as 35%) and
have significantly different shapes as functions of temperature, than our new
rates. We used our new Pt results, together with $^{191,193}$Ir(n,$% \gamma $)
data, to calibrate nuclear statistical model calculations and hence obtain an
improved rate for the unmeasured \textit{s}-process branching-point isotope
$^{192}$Ir.
