The transport of solar 584-A photons through the spherical, asymmetric helium geocorona is discussed in detail. The analysis shows that with a favorable geometry and a moderately optically thick atmosphere it is possible to determine the helium abundance from dayglow observations without knowing the incident solar flux or the instrument calibration. comparison of theoretical intensities with 584-A airglow observations made from the STP 72-1 satellite shows that recent satellite-drag and mass spectrometer-incoherent scatter empirical models predict helium densities in shape, but in general are high by as much as a factor of 2 in absolute density. Airglow-determined densities in the polar regions suggest a decrease in the exospheric helium density relative to the empirical model estimates.