  The recent ideas that the gravitational and gauge interactions become united
at the weak scale lead to Yukawa-type corrections to the Newtonian
gravitational law at small distances. We briefly summarize the best constraints
on these corrections obtained recently from the experiments on the measurement
of the Casimir force. The new constraints on the Yukawa-type interaction are
derived from the latest Casimir force measurement between a large gold coated
sphere and flat disk using an atomic force microscope. The obtained constraints
are stronger up to 19 times comparing the previous experiment with aluminum
surfaces and up to 4500 times comparing the Casimir force measurements between
dielectrics. The application range of constraints obtained by means of an
atomic force microscope is extended.
