  It has been known for some time that $W$ algebras can be realised in terms of
an energy-momentum tensor together with additional free scalar fields. Some
recent results have shown that more general realisations are also possible. In
this paper, we consider a wide class of realisations that may be obtained from
the Miura transformation, related to the existence of canonical subalgebras of
the Lie algebras on which the $W$ algebras are based. We give explicit formulae
for all realisations of this kind, and discuss their applications in $W$-string
theory.
