  We use particle image velocimetry to measure the sedimentation dynamics of a
semi-dilute suspension of non-Brownian spheres at Reynolds numbers, $0.001\le
Re\le 2.3$, extending from the Stokes to the moderately inertial regime. We
find that the onset of inertial corrections to Stokes sedimentation occurs when
the inertial screening length $l=a/Re$ becomes similar to the Stokes
sedimentation length $\xi_0$, at $Re_c= a/\xi_0\approx 0.05$. For $Re>Re_c$,
inertial screening significantly reduces both the magnitude and spatial extent
of the particle velocity fluctuations. A modified Hinch force balance model
connects the fluctuation magnitudes $\sigma_V/V$ to the correlation sizes
$\xi$.
