  We relate possible cosmological variations in the mass ratio mu \equiv
m_p/m_e and the fine structure constant alpha to long-range
composition-dependent forces mediated by a scalar field. The differential
acceleration eta in Eotvos-type experiments is bounded below by 10^{-14},
except in cases where one or more scalar couplings vanish. We consider what
values for these couplings could arise from unified theories. By considering
the contribution of the scalar field to the cosmological energy density we use
bounds on eta to put upper bounds on the current rate of change of mu and
alpha.
