  We present a measurement of $\sigma \cdot B(W \to e \nu)$ and $\sigma \cdot
B(Z^0 \to e^+e^-)$ in proton - antiproton collisions at $\sqrt{s} =1.8$ TeV
using a significantly improved understanding of the integrated luminosity. The
data represent an integrated luminosity of 19.7 pb$^{-1}$ from the 1992-1993
run with the Collider Detector at Fermilab (CDF). We find $\sigma \cdot B(W \to
e \nu) = 2.49 \pm 0.12$~nb and $\sigma \cdot B(Z^0 \to e^+e^-) = 0.231 \pm
0.012$~nb.
