  Motivated by a variety of theories that predict new effects, we tested the
gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using
two different 10-fold azimuthally symmetric torsion pendulums and rotating
10-fold symmetric attractors. Our work improves upon other experiments by up to
a factor of about 100. We found no deviation from Newtonian physics at the 95%
confidence level and interpret these results as constraints on extensions of
the Standard Model that predict Yukawa or power-law forces. We set a constraint
on the largest single extra dimension (assuming toroidal compactification and
that one extra dimension is significantly larger than all the others) of R <=
160 microns, and on two equal-sized large extra dimensions of R <= 130 microns.
Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for
lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are
restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of
large extra dimensions. We also provide new constraints on power-law potentials
V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of
pseudoscalars with m <= 10 meV/c^2.
