  We report measurements of the parity-conserving beam-normal single-spin
elastic scattering asymmetries $B_n$ on $^{12}$C and $^{27}$Al, obtained with
an electron beam polarized transverse to its momentum direction. These
measurements add an additional kinematic point to a series of previous
measurements of $B_n$ on $^{12}$C and provide a first measurement on $^{27}$Al.
The experiment utilized the Qweak apparatus at Jefferson Lab with a beam energy
of 1.158 GeV. The average lab scattering angle for both targets was 7.7
degrees, and the average $Q^2$ for both targets was 0.02437 GeV$^2$ (Q=0.1561
GeV). The asymmetries are $B_n$ = -10.68 $\pm$ 0.90 stat) $\pm$ 0.57 (syst) ppm
for $^{12}$C and $B_n$ = -12.16 $\pm$ 0.58 (stat) $\pm$ 0.62 (syst) ppm for
$^{27}$Al. The results are consistent with theoretical predictions, and are
compared to existing data. When scaled by Z/A, the Q-dependence of all the
far-forward angle (theta < 10 degrees) data from $^{1}$H to $^{27}$Al can be
described by the same slope out to $Q \approx 0.35$ GeV. Larger-angle data from
other experiments in the same Q range are consistent with a slope about twice
as steep.
