  It has been shown that certain $W$ algebras can be linearised by the
inclusion of a spin--1 current. This provides a way of obtaining new
realisations of the $W$ algebras. Recently such new realisations of $W_3$ were
used in order to embed the bosonic string in the critical and non-critical
$W_3$ strings. In this paper, we consider similar embeddings in $W_{2,4}$ and
$W_{2,6}$ strings. The linearisation of $W_{2,4}$ is already known, and can be
achieved for all values of central charge. We use this to embed the bosonic
string in critical and non-critical $W_{2,4}$ strings. We then derive the
linearisation of $W_{2,6}$ using a spin--1 current, which turns out to be
possible only at central charge $c=390$. We use this to embed the bosonic
string in a non-critical $W_{2,6}$ string.

High Energy Physics - Theory