  Strong - weak coupling duality in string theory allows us to compute physical
quantities both at the weak coupling end and at the strong coupling end.
Furthermore perturbative string theory can be used to compute corrections to
the leading order formula at both ends. We explore the possibility of
constructing a smooth interpolating formula that agrees with the perturbation
expansion at both ends and leads to a fairly accurate determination of the
quantity in consideration over the entire range of the coupling constant. We
apply this to study the mass of the stable non-BPS state in SO(32) heterotic /
type I string theory with encouraging results. In particular our result
suggests that after taking into account one loop corrections to the mass in the
heterotic and type I string theory, the interpolating function determines the
mass within 10% accuracy over the entire range of coupling constant.
