Measurements of the linearly-polarized photon beam asymmetry $\Sigma$ for
photoproduction from the proton of $\eta$ and $\eta^\prime$ mesons are
reported. A linearly-polarized tagged photon beam produced by coherent
bremsstrahlung was incident on a cryogenic hydrogen target within the CEBAF
Large Acceptance Spectrometer. Results are presented for the $\gamma p \to \eta
p$ reaction for incident photon energies from 1.070 to 1.876 GeV, and from
1.516 to 1.836 GeV for the $\gamma p \to \eta^\prime p$ reaction. For $\gamma p
\to \eta p$, the data reported here considerably extend the range of
measurements to higher energies, and are consistent with the few previously
published measurements for this observable near threshold. For $\gamma p \to
\eta^\prime p$, the results obtained are consistent with the few previously
published measurements for this observable near threshold, but also greatly
expand the incident photon energy coverage for that reaction. Initial analysis
of the data reported here with the Bonn-Gatchina model strengthens the evidence
for four nucleon resonances -- the $N(1895)1/2^-$, $N(1900)3/2^+$,
$N(2100)1/2^+$ and $N(2120)3/2^-$ resonances -- which presently lack the
"four-star" status in the current Particle Data Group compilation, providing
examples of how these new measurements help refine models of the
photoproduction process.
