  We show directly in the Lax operator approach how the Virasoro and
W-constraints on the $\tau$-function arise in the $p$-reduced KP hierarchy or
generalized KdV hierarchy. In partiacular, we consider the KdV and Boussinesq
hierarchy to show that the Virasoro and W-constraints follow from the string
equation by expanding the ``additional symmetry" operator in terms of the Lax
operator. We also mention how this method could be generalized for higher KdV
hierarchies.
