  We investigate systematic uncertainties in determining the profiles of the
solar sound speed, density, and adiabatic index by helioseismological
techniques. We find that rms uncertainties-averaged over the sun of ~ 0.2%-0.4%
are contributed to the sound speed profile by each of three sources: 1)the
choice of assumed reference model, 2) the width of the inversion kernel, and 3)
the measurements errors. The density profile is about an order of magnitude
less well determined by the helioseismological measurements. The profile of the
adiabatic index is determined to an accuracy of about 0.2% . We find that even
relatively crude reference models yield reasonably accurate solar parameters.
