  We perform a numerical calculation of the total cross section $\sigma(e^+e^-
\rightarrow W^+W^-)$ as a function of energy, taking into account the finite
width of the $W$ and the most important radiative corrections. We present these
results, in tabular form, for several values of $M_W$. Using these results, we
investigate running strategies for integrated luminosities that might be
available at LEP~200 and estimate the accuracy to which it will be possible to
determine the mass of the $W$ by measuring this cross section near threshold.
With an integrated luminosity of $100\ {\rm pb}^{-1}$ it should be possible to
achieve a precision of $100\ {\rm MeV}$, and with an integrated luminosity of
$500\ {\rm pb}^{-1}$, a precision of $60\ {\rm MeV}$.
