  We test the methods developed in previous papers for inferring the intrinsic
shapes of elliptical galaxies, using simulated objects from N-body experiments.
The shapes of individual objects are correctly reproduced to within the
statistical errors; close inspection of the results indicates a small
systematic bias in the sense of underestimating both the triaxiality and
short-to-long axis ratio. We also test the estimation of parent shape
distributions, using samples of independent, randomly oriented objects. The
best results are statistically accurate, but on average the parent
distributions are again slightly biased in the same sense. Using the posterior
probability densities for the individual objects, we estimate the magnitude of
the bias to be less than approximately 0.1 in both shape parameters. The
results support the continued use of these methods on real systems.
