  We report the results of a direct search for the $^{229}$Th ($I^{p} =
3/2^+\leftarrow 5/2^+$) nuclear isomeric transition, performed by exposing
$^{229}$Th-doped LiSrAlF$_6$ crystals to tunable vacuum-ultraviolet synchrotron
radiation and observing any resulting fluorescence. We also use existing
nuclear physics data to establish a range of possible transition strengths for
the isomeric transition. We find no evidence for the thorium nuclear transition
between $7.3 {eV}$ and $8.8 {eV}$ with transition lifetime $(1-2){s} \lesssim
\tau \lesssim (2000-5600){s}$. This measurement excludes roughly half of the
favored transition search area and can be used to direct future searches.
