  A scale invariant model containing dilaton $\phi$ and dust (as a model of
matter) is studied where the shift symmetry $\phi\to\phi +const.$ is
spontaneously broken at the classical level due to intrinsic features of the
model. The dilaton to matter coupling "constant" $f$ appears to be dependent of
the matter density. In normal conditions, i.e. when the matter energy density
is many orders of magnitude larger than the dilaton contribution to the dark
energy density, $f$ becomes less than the ratio of the "mass of the vacuum" in
the volume occupied by the matter to the Planck mass. The model yields this
kind of "Archimedes law" without any especial (intended for this) choice of the
underlying action and without fine tuning of the parameters. The model not only
explains why all attempts to discover a scalar force correction to Newtonian
gravity were unsuccessful so far but also predicts that in the near future
there is no chance to detect such corrections in the astronomical measurements
as well as in the specially designed fifth force experiments on intermediate,
short (like millimeter) and even ultrashort (a few nanometer) ranges. This
prediction is alternative to predictions of other known models.
