  The Gamma-RAy Polarimeter Experiment (GRAPE) is a concept for an astronomical
hard X-ray Compton polarimeter operating in the 50 - 500 keV energy band. The
instrument has been optimized for wide-field polarization measurements of
transient outbursts from energetic astrophysical objects such as gamma-ray
bursts and solar flares. The GRAPE instrument is composed of identical modules,
each of which consists of an array of scintillator elements read out by a
multi-anode photomultiplier tube (MAPMT). Incident photons Compton scatter in
plastic scintillator elements and are subsequently absorbed in inorganic
scintillator elements; a net polarization signal is revealed by a
characteristic asymmetry in the azimuthal scattering angles. We have
constructed a prototype GRAPE module containing a single CsI(Na) calorimeter
element, at the center of the MAPMT, surrounded by 60 plastic elements. The
prototype has been combined with custom readout electronics and software to
create a complete "engineering model" of the GRAPE instrument. This engineering
model has been calibrated using a nearly 100% polarized hard X-ray beam at the
Advanced Photon Source at Argonne National Laboratory. We find modulation
factors of 0.46 +/- 0.06 and 0.48 +/- 0.03 at 69.5 keV and 129.5 keV,
respectively, in good agreement with Monte Carlo simulations. In this paper we
present details of the beam test, data analysis, and simulations, and discuss
the implications of our results for the further development of the GRAPE
concept.
