  We present the results of spectroscopy of four bright proplyds in the Orion
Nebula obtained at a velocity resolution of 6 km/s. After careful isolation of
the proplyd spectra from the confusing nebular radiation, the emission line
profiles are compared with those predicted by realistic dynamic/photoionization
models of the objects. The spectral line widths show a clear correlation with
ionization potential, which is consistent with the free expansion of a
transonic, ionization-stratified, photoevaporating flow. Fitting models of such
a flow simultaneously to our spectra and HST emission line imaging provides
direct measurements of the proplyd size, ionized density and outflow velocity.
These measurements confirm that the ionization front in the proplyds is
approximately D-critical and provide the most accurate and robust estimate to
date of the proplyd mass loss rate. Values of 0.7E-6 to 1.5E-6 Msun/year are
found for our spectroscopic sample, although extrapolating our results to a
larger sample of proplyds implies that 0.4E-6 Msun/year is more typical of the
proplyds as a whole. In view of the reported limits on the masses of the
circumstellar disks within the proplyds, the length of time that they can have
been exposed to ionizing radiation should not greatly exceed 10,000 years - a
factor of 30 less than the mean age of the proplyd stars. We review the various
mechanisms that have been proposed to explain this situation, and conclude that
none can plausibly work unless the disk masses are revised upwards by a
substantial amount.
