  We start with a brief account of the latest analysis of the Oklo phenomenon
providing the still most stringent constraint on time-variability of the fine-
structure constant $\alpha$. Comparing this with the recent result from the
measurement of distant QSO's appears to indicate a non-uniform time-dependence,
which we argue to be related to another recent finding of the accelerating
universe. This view is implemented in terms of the scalar-tensor theory,
applied specifically to the small but nonzero cosmological constant. Our
detailed calculation shows that these two phenomena can be understood in terms
of a common origin, a particular behavior of the scalar field, dilaton. We also
sketch how this theoretical approach makes it appropriate to revisit non-
Newtonian gravity featuring small violation of Weak Equivalence Principle at
medium distances.

General Relativity and Quantum Cosmology