  The electromagnetic transition moments of the $SU(3)$-flavor baryon octet to
decuplet are examined within a lattice simulation of quenched QCD. The magnetic
transition moment for the $N \; \gamma \to \Delta$ channel is found to be in
agreement with recent experimental analyses. The lattice results indicate
$\mu_{p \Delta} / \mu_p = 0.88(15)$. In terms of the Particle Data Group
convention, $f_{M1} = 0.231(41)$ GeV${}^{-1/2}$ for $p \; \gamma \to \Delta^+$
transitions. Lattice predictions for the hyperon $M1$ transition moments agree
with those of a simple quark model. However the manner in which the quarks
contribute to the transition moments in the lattice simulation is different
from that anticipated by quark model calculations. The scalar quadrupole form
factor exhibits a behavior consistent with previous multipole analyses. The
$E2/M1$ multipole transition moment ratios are also determined. The lattice
results suggest $R_{EM} \equiv -{\cal G}_{E2}/{\cal G}_{M1} = +3\pm 8$ \% for
$p \; \gamma \to \Delta^+$ transitions. Of particular interest are significant
nonvanishing signals for the $E2/M1$ ratio in $\Xi^-$ and $\Sigma^-$
electromagnetic transitions.
