  Galaxy formation and evolution are regulated by the feedback from galactic
winds. Absorption lines provide the most widely available probe of winds.
However, since most data only provide information integrated along the
line-of-sight, they do not directly constrain the radial structure of the
outflows. In this paper, we present a method to directly measure the gas
electron density in outflows (ne), which in turn yields estimates of outflow
cloud properties (e.g., density, volume filling-factor, and sizes/masses). We
also estimate the distance (r) from the starburst at which the observed
densities are found. We focus on 22 local star-forming galaxies primarily from
the COS Legacy Archive Spectroscopic SurveY (CLASSY). In half of them, we
detect absorption lines from fine structure excited transitions of Si II (i.e.,
Si II*). We determine ne from relative column densities of Si II and Si II*,
given Si II* originates from collisional excitation by free electrons. We find
that the derived ne correlates well with the galaxy's star-formation rate per
unit area. From photoionization models or assuming the outflow is in pressure
equilibrium with the wind fluid, we get r ~ 1 to 2 * rstar or ~ 5 * rstar,
respectively, where rstar is the starburst radius. Based on comparisons to
theoretical models of multi-phase outflows, nearly all of the outflows have
cloud sizes large enough for the clouds to survive their interaction with the
hot wind fluid. Most of these measurements are the first-ever for galactic
winds detected in absorption lines and, thus, will provide important
constraints for future models of galactic winds.
