  The exchange of light pseudoscalars between fermions leads to a
spin-independent potential in order g^4, where g is the Yukawa
pseudoscalar-fermion coupling constant. This potential gives rise to detectable
violations of both the weak equivalence principle (WEP) and the gravitational
inverse-square law (ISL), even if g is quite small. We show that when
previously derived WEP constraints are combined with those arisingfrom ISL
tests, a direct experimental limit on the Yukawa coupling of light
pseudoscalars to neutrons can be inferred for the first time (g_n^2/4pi < 1.6
\times 10^-7), along with a new (and significantly improved) limit on the
coupling of light pseudoscalars to protons.
