  We continue the discussion of our previous paper on writing down gauge
invariant interacting equations for a bosonic string using the loop variable
approach. In the earlier paper the equations were written down in one higher
dimension where the fields are massless. In this paper we describe a procedure
for dimensional reduction that gives interacting equations for fields with the
same spectrum as in bosonic string theory. We also argue that the on-shell
scattering amplitudes implied by these equations for the physical modes are the
same as for the bosonic string. We check this explicitly for some of the
simpler equations. The gauge transformation of space-time fields induced by
gauge transformations of the loop variables are discussed in some detail. The
unintegrated (i.e. before the Koba-Nielsen integration), regularized version of
the equations, are gauge invariant off-shell (i.e. off the {\em free} mass
shell).

High Energy Physics - Theory