  We test some ideas for star formation relations against data on local
molecular clouds. On a cloud by cloud basis, the relation between the surface
density of star formation rate and surface density of gas divided by a
free-fall time, calculated from the mean cloud density, shows no significant
correlation. If a crossing time is substituted for the free-fall time, there is
even less correlation. Within a cloud, the star formation rate volume and
surface densities increase rapidly with the corresponding gas densities, faster
than predicted by models using the free-fall time defined from the local
density. A model in which the star formation rate depends linearly on the mass
of gas above a visual extinction of 8 mag describes the data on these clouds,
with very low dispersion. The data on regions of very massive star formation,
with improved star formation rates based on free-free emission from ionized
gas, also agree with this linear relation.
