A simple analytic model of radiative transfer in two parts of a contra
cting cloud matches a wide range of line profiles in candidate infall
regions and provides a sensitive estimate of V-in, the characteristic
inward speed of the gas forming the line. The model assumes two unifor
m regions of equal temperature and velocity dispersion sigma, whose de
nsity and velocity are attenuation-weighted means over the front and r
ear halves of a centrally condensed, contracting cloud. The model pred
icts two-peak profiles for ''slow'' infall, V-in much less than sigma
and red-shoulder profiles for ''fast'' infall, V-in similar to sigma A
simple formula expresses V-in solely in terms of sigma and of observa
ble parameters of a two-peak line. We apply the model to fit profiles
of high and low optical depth lines observed in a dense core with no s
tar (L1544, V-in = 0.006 km s(-1)), with an isolated protostar (L1527,
0.025 km s(-1)), and with a small group of stars (L1251B, 0.35 km s(-
1)). The mass infall rate obtained from V-in and the map size varies f
rom (2-40) x 10(-6) M(.) yr(-1) and agrees within a factor similar to
2 in each core with the independently determined rate similar to sigma
(3) G(-1) for a gravitationally collapsing isothermal sphere. This agr
eement suggests that the inward motions derived from the line profiles
are gravitational in origin.