  Most planet pairs in the Kepler data that have measured transit time
variations (TTV) are near first-order mean-motion resonances. We derive
analytical formulae for their TTV signals. We separate planet eccentricity into
free and forced parts, where the forced part is purely due to the planets'
proximity to resonance. This separation yields simple analytical formulae. The
phase of the TTV depends sensitively on the presence of free eccentricity: if
the free eccentricity vanishes, the TTV will be in phase with the longitude of
conjunctions. This effect is easily detectable in current TTV data. The
amplitude of the TTV depends on planet mass and free eccentricity, and it
determines planet mass uniquely only when the free eccentricity is sufficiently
small. We proceed to analyze the TTV signals of six short period Kepler pairs.
We find that three of these pairs (Kepler-18,24,25) have TTV phase consistent
with zero. The other three (Kepler-23,28,32) have small TTV phases, but ones
that are distinctly non-zero. We deduce that the free eccentricities of the
planets are small, < 0.01, but not always vanishing. Furthermore, as a
consequence of this, we deduce that the true masses of the planets are fairly
accurately determined by the TTV amplitudes, within a factor < 2. The smallness
of the free eccentricities suggests that the planets have experienced
substantial dissipation. This is consistent with the hypothesis that the
observed pile-up of Kepler pairs near mean-motion resonances is caused by
resonant repulsion. But the fact that some of the planets have non-vanishing
free eccentricity suggests that after resonant repulsion occurred there was a
subsequent phase in the planets' evolution when their eccentricities were
modestly excited, perhaps by interplanetary interactions.
