  We show that the leading $SU(3)$-breaking corrections to the $\Delta S = 1$
$f_1$ vector form factors of hyperons are $O(m_s)$ and $O(m_s^{3/2})$, and are
expected to be $\sim 20$--$30\%$ by dimensional analysis. This is consistent
with the Ademollo--Gatto theorem, in a sense that we explain. We compute the
$O(m_s)$ corrections and a subset of the $O(m_s^{3/2})$ corrections using an
effective lagrangian in which the baryons are treated as heavy particles. All
of these corrections are surprisingly small, $\sim 5\%$; combining them, we
obtain $\sim 5$--$10\%$ corrections. The pattern of corrections is very
different than that predicted by quark models.
