  Calculations are performed to demonstrate the deviations from Gaussian that
occur in the spectral line profiles of a linear maser as a result of the
amplification process. Near-Gaussian profiles are presented for bright,
interstellar 22 GHz water masers obtained from high resolution Very Long
Baseline Array (VLBA) observations of W3 IRS 5. For the profiles to be so close
to Gaussian, the calculations indicate that these masers must originate in
quite hot gas with temperatures greater than 1200 K -- a conclusion that is
supportive of C-type shocks as the origin of these masers. In addition, the
degree of saturation of these masers must be less than approximately one-third,
from which it follows that the beaming angles are less than about 10^{-4} ster
and the actual luminosities are modest. If spectral profiles that are as close
to Gaussian as the profiles presented in this initial investigation are found
to occur widely, they can be valuable diagnostics for the environments of
astrophysical masers.
