  We present a detailed investigation of scattering processes in $W_3$ string
theory. We discover further physical states with continuous momentum, which
involve excitations of the ghosts as well as the matter, and use them to gain a
better understanding of the interacting theory. The scattering amplitudes
display factorisation properties, with states from the different sectors of the
theory being exchanged in the various intermediate channels. We find strong
evidence for the unitarity of the theory, despite the unusual ghost structure
of some of the physical states. Finally, we show that by performing a
transformation of the quantum fields that involves mixing the ghost fields with
one of the matter fields, the structure of the physical states is dramatically
simplified. The new formalism provides a concise framework within which to
study the $W_3$ string.
