  There are obvious discrepancies among various experimental constraints on the
variation of the fine-structure constant, $\alpha$. We attempt to discuss the
issue in the framework of de Sitter invariant Special Relativity (${\cal
SR}_{c,R}$) and to present a possible solution to the disagreement. In
addition, on the basis of the observational data and the discussions presented
in this Letter, we derive a rough theoretical estimate of the radius of the
Universe.
