  We develop a relativistic treatment of interference between light reflected
from a falling cube retroreflector in the vertical arm of an interferometer,
and light in a reference beam in the horizontal arm. Coordinates that are
nearly Minkowskian, attached to the falling cube, are used to describe the
propagation of light within the cube. Relativistic effects such as the
dependence of the coordinate speed of light on gravitational potential,
propagation of light along null geodesics, relativity of simultaneity, and
Lorentz contraction of the moving cube, are accounted for. The calculation is
carried to first order in the gradient of the acceleration of gravity. Analysis
of data from a falling cube gravimeter shows that the propagation time of light
within the cube itself causes a significant reduction in the value of the
acceleration of gravity obtained from measurements, compared to assuming
reflection occurs at the face. An expression for the correction to the
acceleration of gravity is derived and found to agree with experiment.
Depending on the instrument, the correction can be several microgals,
comparable to commonly applied corrections such as those due to polar motion
and earth tides. The controversial "speed of light" correction is discussed.
