  We show that any covariant scattering amplitude of the $W_3$ string will
contain, as part of its integrand, a factor that obeys the differential
equations satisfied by an Ising model correlation function. This factor can
thus be identified with such a correlation function, in agreement with a
previous result of the authors. The $W_3$ string is also shown to contain an
$N=2$ parafermion theory, and hence to contain in addition the non-linear
infinite-dimensional $W$-algebra corresponding to this parafermion theory. The
physical states form a representation of this algebra.
