  The ratio of the proton elastic electromagnetic form factors,
$G_{Ep}/G_{Mp}$, was obtained by measuring $P_{t}$ and $P_{\ell}$, the
transverse and longitudinal recoil proton polarization components,
respectively, for the elastic $\vec e p \to e\vec p$ ~reaction in the
four-momentum transfer squared range of 0.5 to 3.5 GeV$^2$. In the
single-photon exchange approximation, the ratio $G_{Ep}/G_{Mp}$ is directly
proportional to the ratio $P_t/P_{\ell}$. The simultaneous measurement of
$P_{t}$ and $P_{\ell}$ in a polarimeter reduces systematic uncertainties. The
results for the ratio $G_{Ep}/G_{Mp}$ show a systematic decrease with
increasing $Q^2$, indicating for the first time a definite difference in the
distribution of charge and magnetization in the proton. The data have been
re-analyzed and systematic uncertainties have become significantly smaller than
previously published results.
