  We calculate high energy massive scattering amplitudes of closed bosonic
string compactified on the torus. For each fixed mass level with given
quantized and winding momenta ((m/R),(1/2)nR), we obtain infinite linear
relations among high energy scattering amplitudes of different string states.
For some kinematic regimes, we discover that linear relations with N_{R}=N_{L}
break down and, simultaneously, the amplitudes enhance to power-law behavior
instead of the usual expoential fall-off behavior at high energies. It is the
space-time T-duality symmetry that plays a role here. This result is consistent
with the coexistence of the linear relations and the softer exponential
fall-off behavior of high energy string scattering amplitudes as we pointed out
prevously. It is also reminiscent of our previous work on the power-law
behavior of high energy string/domain-wall scatterings.
