Three methods are presented for measuring the mass of the Martian atmosphere using an orbiting gamma ray spectrometer. With single-line attenuation, atmospheric thickness is measured by the extent to which it modulates a line flux emitted from a surface whose composition is both known and uniform to a depth of a meter or more. Direct determination derives atmospheric concentration of a particular component. Alternatively, if atmospheric thickness is known, concentration may be determined. Differential attenuation utilizes the ratio of paired emission line fluxes and requires adequate energy contrast and line intensities as well as knowledge of the production mechanism. The sensitivity of these methods as a fraction of the atmospheric thickness is nominally 2--5% over the range of 2.5--30 g/cm2 for accumulation times of 100 hours. This precludes the observation of short-period phenomena such a diurnal oscillations but permits the tracking of more gradual variations, particularly the basic seasonal cycle on a regional, zonal, hemispheric, or whole planet basis. The three methods may be combined not only to improve the sensitivity with which atmospheric thickness may be measured but also to provide additional information including the presence of carbon in the regolith, the extent of atmospheric fractionation in south polar regions during winter, and the effect of stratification on surface gamma ray emission. ¿American Geophysical Union 1990