  In this article, we study the Ising vectors in the vertex operator algebra
$V_\Lambda^+$ associated with the Leech lattice $\Lambda$. The main result is a
characterization of the Ising vectors in $V_\Lambda^+$. We show that for any
Ising vector $e$ in $V_\Lambda^+$, there is a sublattice $E\cong \sqrt{2}E_8$
of $\Lambda$ such that $e\in V_E^+$. Some properties about their corresponding
$\tau$-involutions in the moonshine vertex operator algebra $V^\natural$ are
also discussed. We show that there is no Ising vector of $\sigma$-type in
$V^\natural$. Moreover, we compute the centralizer $C_{\aut V^\natural}(z,
\tau_e)$ for any Ising vector $e\in V_\Lambda^+$, where $z$ is a 2B element in
$\aut V^\natural$ which fixes $V_\Lambda^+$. Based on this result, we also
obtain an explanation for the 1A case of an observation by Glauberman-Norton
(2001), which describes some mysterious relations between the centralizer of
$z$ and some 2A elements commuting $z$ in the Monster and the Weyl groups of
certain sublattices of the root lattice of type $E_8$ .
