  I study the Ward identities of the $w_\infty$ symmetry of the two-dimensional
string theory. It is found that, not just an isolated vertex operator, but also
a number of vertex operators colliding at a point can produce local charge
non-conservation. The structure of all such contact terms is determined. As an
application, I calculate all the non-vanishing bulk tachyon amplitudes directly
through the Ward identities for a Virasoro subalgebra of the $w_\infty$.
