  We investigate experimentally the dissolution of an almost spherical
butyramide particle during its sedimentation, in the low Reynolds high P\'eclet
regime. The particle sediments in a quiescent aqueous solution, and its shape
and position are measured simultaneously by a camera attached to a translation
stage. The particle is tracked in real time, and the translation stage moves
accordingly to keep the particle in the field of the camera. The measurements
from the particle image show that the radius shrinking rate is constant with
time, and independent of the initial radius of the particle. We explain this
with a simple model, based on the sedimentation law in the Stokes' regime and
the mass transfer rate at low Reynolds and high P\'eclet numbers. The
theoretical and experimental results are consistent within $20\%$. We introduce
two correction factors to take into account the non-sphericity of the particle
and the inclusions of air bubbles inside the particle, and reach quantitative
agreement. With these corrections, the indirect measurement of the radius
shrinking rate deduced from the position measurement is also in agreement with
the model. We discuss other correction factors, and explain why there are
negligible in the present experiment. We also compute the effective Sherwood
number as a function of an effective P\'eclet number.
