  We report the results from our first-generation experiment to measure the
magnetic-dipole transition moment (M1) between the $6S_{1/2}$ and $5D_{3/2}$
manifolds in Ba$^{+}$. Knowledge of M1 is crucial for the proposed
parity-nonconservation experiment in the ion \cite{Fortson93}, where M1 will be
a leading source of systematic error. To date, no measurement of M1 has been
made in Ba$^{+}$, and moreover, the sensitivity of the moment to
electron-electron correlations has confounded accurate theoretical predictions.
A precise measurement may help to resolve the theoretical discrepancies while
providing essential information for planning a future PNC measurement in
Ba$^{+}$. We demonstrate our technique for measuring M1 - including a method
for calibrating for stress-induced birefringence introduced by the scientific
apparatus - and place an upper bound of $\mathrm{M1} < 93 \pm 39 \times 10^{-5}
\mu_{B}$.
