  We extract densities and eccentricities of 139 sub-Jovian planets by
analyzing transit time variations (TTVs) obtained by the Kepler mission through
Quarter 12. We partially circumvent the degeneracies that plague TTV inversion
with the help of an analytical formula for the TTV. From the observed TTV
phases, we find that most of these planets have eccentricities of order a few
percent. More precisely, the r.m.s. eccentricity is 0.018^{+0.005}_{-0.004},
and planets smaller than 2.5R_\earth are around twice as eccentric as those
bigger than 2.5R_\earth. We also find a best-fit density-radius relationship
\rho ~3 g/cm^3 \times (R/3R_\earth)^{-2.3} for the 56 planets that likely have
small eccentricity and hence small statistical correction to their masses. Many
planets larger than 2.5R_\earth are less dense than water, implying that their
radii are largely set by a massive hydrogen atmosphere.
