  A new method is introduced for making X-ray mass determinations of spherical
clusters of galaxies. Treating the distribution of gravitating matter as
piecewise constant and the cluster atmosphere as piecewise isothermal, X-ray
spectra of a hydrostatic atmosphere are determined up to a single overall
normalizing factor. In contrast to more conventional approaches, this method
relies on the minimum of assumptions, apart from the conditions of hydrostatic
equilibrium and spherical symmetry. The method has been implemented as an XSPEC
mixing model called CLMASS, which was used to determine masses for a sample of
nine relaxed X-ray clusters. Compared to conventional mass determinations,
CLMASS provides weak constraints on values of M_500, reflecting the quality of
current X-ray data for cluster regions beyond r_500. At smaller radii, where
there are high quality X-ray spectra inside and outside the radius of interest
to constrain the mass, CLMASS gives confidence ranges for M_2500 that are only
moderately less restrictive than those from more familiar mass determination
methods. The CLMASS model provides some advantages over other methods and
should prove useful for mass determinations in regions where there are high
quality X-ray data.
