  Many structures in nature are invariant under the transformation
(p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis
affirms that this invariance extends to the entire Hamiltonian and equations of
motion. We investigate this idea for atomic physics and galactic motion, where
one is basically dealing with a 1/r potential and the observations are very
accurate, so as to determine the scale $b = m\Omega$. We find that an $\Omega
\sim 1.5\times 10^{-15}$ Hz has essentially no effect on atomic physics but
might possibly offer an explanation for galactic rotation, without invoking
dark matter.
