  Sagnac interferometry has been employed in the context of gravity as a
proposal for the detection of the so called gravitomagnetic effect. In the
present work we explore the possibilities that this experimental device could
open up in the realm of non--Newtonian gravity. It will be shown that this
experimental approach allows us to explore an interval of values of the range
of the new force that up to now remains unexplored, namely, $\lambda\geq
10^{14}$ m.
