  Radul has recently introduced a map from the Lie algebra of differential
operators on the circle to $W_n$. In this note we extend this map to
$W_{KP}^{(q)}$, a recently introduced one-parameter deformation of
$W_{KP}$---the second hamiltonian structure of the KP hierarchy. We use this to
give a short proof that $W_\infty$ is the symmetry algebra of additional
symmetries of the KP equation.
