Embedding of the bosonic string into the W$_{3}$ string

We construct new realisations of the W_3 algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with c=102 and c=100 to build non-critical and critical W_3 BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with c=28-2, together with a Kugo-Ojima topological term. Consequently, the new realisations provide embeddings of the Virasoro string into non-critical and critical W_3 strings