  We propose a new method of searching for the composition-dependent dilatonic
waves, predicted by unified theories of strings. In this method, Earth's
surface-gravity changes due to translational motions of its inner core, excited
by dilatonic waves, are searched for by using superconducting gravimeters. This
method has its best sensitivity at the frequency of $\sim$ 7 $\times$ 10$^{-5}$
Hz, which is lower than the sensitive frequencies of previous proposals using
gravitational-wave detectors: $\sim$ 10 to 1000 Hz. Using available results of
surface-gravity measurements with superconducting gravimeters and assuming a
simple Earth model, we present preliminary upper limits on the energy density
of a stochastic background of massless dilatons at the low frequency. Though
the results are currently limited by the uncertainty in the Earth model, this
method has a potential of detecting dilatonic waves in a new window.
