  We study the BKP hierarchy and its $n$--reduction, for the case that $n$ is
odd. This is related to the principal realization of the basic module of the
twisted affine Lie algebra $\hat{sl}_n^{(2)}$. We show that the following two
statements for a BKP $\tau$ function are equivalent: (1) $\tau$ is is
$n$--reduced and satisfies the string equation, i.e. $L_{-1}\tau=0$, where
$L_{-1}$ is an element of some `natural' Virasoro algebra. (2) $\tau$ satisfies
the vacuum constraints of the $BW_{1+\infty}$ algebra. Here $BW_{1+\infty}$ is
the natural analog of the $W_{1+\infty}$ algebra, which plays a role in the KP
case.
