  The quantization of a free boson whose momentum satisfies a cubic constraint
leads to a $c=\ha$ conformal field theory with a BRST symmetry. The theory also
has a $W_\infty $ symmetry in which all the generators except the stress-tensor
are BRST-exact and so topological. The BRST cohomology includes states of
conformal dimensions $0,\si,\ha$, together with \lq copies' of these states
obtained by acting with picture-changing and screening operators. The 3-point
and 4-point correlation functions agree with those of the Ising model,
suggesting that the theory is equivalent to the critical Ising model. At tree
level, the $W_3$ string can be viewed as an ordinary $c=26$ string whose
conformal matter sector includes this realisation of the Ising model. The
two-boson $W_3$ string is equivalent to the Ising model coupled to
two-dimensional quantum gravity. Similar results apply for other W-strings and
minimal models.
