  The recent measurement of the nuclear anapole moment of 133Cs has been
interpreted to yield a value of the weak pion-nucleon coupling H_pi^1 which
contradicts the upper limit from the 18F experiments. We argue that because of
the sensitivity of the anapole moment to H_rho^0 in the odd proton nucleus
133Cs, there is a combination of weak meson-nucleon couplings which satisfies
both experiments and which is (barely) in agreement with theory. In addition,
the anapole moment measurement in 205Tl gives a constraint which is
inconsistent with the value from 133Cs, calling into question the theory of
nuclear anapole moments. We argue that measurements of directional asymmetry in
n+p-->d+gamma and in the photo-disintegration of the deuteron by circularly
polarized photons, combined with results from pp scattering, would determine
H_pi^1 and several other weak meson-nucleon couplings in a model-independent
way.
