  In the framework of the compactified closed bosonic string theory with the
extra spatial coordinates being circular with radius $R$, we perform both the
zero-slope limit and the $R \rightarrow 0$ limit of the tree scattering
amplitude of four massless scalar particles. We explicitly show that this
double limit leads to amplitudes involving scalars which interact through the
exchange of a scalar, spin 1 and spin 2 particle. In particular, this latter
case reproduces the same result obtained in linearized quantum gravity.
