  We present CS(3-2) and DCO+(2-1) observations of 94 starless cores and
compare the results with previous CS(2-1) and N2H+(1-0) observations to study
inward motions in starless cores. The velocity shifts of the CS(3-2) and (2-1)
lines with respect to N2H+ correlate well with each other and have similar
distributions. This implies that, in many cores, systematic inward motions of
gaseous material may occur over a range of density of at least a factor 4. We
identify 18 infall candidates based on observations of CS(3-2), CS(2-1),
DCO+(2-1) and N2H+(1-0). The eight best candidates, L1355, L1498, L1521F,
L1544, L158, L492, L694-2, and L1155C-1, each show at least four indications of
infall asymmetry and no counter-indications. Fits of the spectra to a 2-layer
radiative transfer model in ten infall candidates suggest that the median
effective line-of-sight speed of the inward-moving gas is ~0.07 km/s for CS
(3-2) and ~0.04 km/s for CS(2-1). Considering that the optical depth obtained
from the fits is usually smaller in CS(3-2) than in (2-1) line, this may imply
that CS(3-2) usually traces inner denser gas in higher inward motions than
CS(2-1). However, it is also possible that this conclusion is not
representative of all starless core infall candidates, due to the statistically
small number analyzed here. Further line observations will be useful to test
this conclusion.
