  The $Q^2$ dependence of the ratio of the cross sections with and without
proton spin flip, as well as the polarization asymmetry in the process $e
\vec{p} \to e \vec{p}$ has been numerically analyzed using the results of JLab
polarization experiments on the measurements of the ratio of the Sachs form
factors in the $\vec{e} p \to e \vec{p}$ process. The calculations have been
made for the case where the initial (at rest) and final protons are fully
polarized and have a common spin quantization axis, which coincides with the
direction of motion of the final proton. The longitudinal polarization transfer
to the proton has been calculated in the case of the partially polarized
initial proton for a kinematics used in the experiment reported in [A. Liyanage
et al. (SANE Collaboration), Phys. Rev. C 101, 035206 (2020)], where the double
spin asymmetry was measured in the $\vec{e} \vec{p} \to e p$ process. A
noticeable sensitivity of the polarization transfer to the proton to the form
of the $Q^2$ dependence of the ratio $\mu_p G_E/G_M$ has been found. This
sensitivity may be used to conduct a new independent experiment to measure this
dependence in the $ e \vec{p} \to e \vec{p}$ process. A criterion to assess the
reliability of measurements of the ratio of Sachs form factors using the
Rosenbluth technique has been proposed and used to analyze the results of two
experiments.
