Continuous absorption in the atmospheric window near 2400 cm-1 has been analyzed from infrared solar occultation spectra recorded by the Atmospheric Trace Molecule Spectroscopy (ATMOS) Fourier transform spectrometer at 0.01 cm-1 spectral resolution during its 4 shuttle flights between 1985 and 1994. The spring and autumn measurements were recorded over a wide range of temperatures and sulfate aerosol loadings. We used the ratio of the transmissions in microwindows at 2415 cm-1 and 2501 cm-1 as a measure of the underlying continuum absorption in the spectra. This ratio decreases from 1.0 to 0.0 as the tangent point density increases from 5 ¿ 1017 to 100 ¿ 1017 molecules cm-3 (altitudes ~10--30 km). Attenuation in both microwindows is due to overlapping absorptions by the fundamental N2 collision-induced band and distant sub-Lorentzian wings of CO2 lines from the strong ν3 fundamental band. Optical depths for both N2 and CO2 absorption are proportional to the square of the air density at constant temperature. These microwindows provide high sensitivity to density and low sensitivity to temperature in the lower stratosphere. Stratospheric transmission ratios from all 4 missions are fitted with a single parameter as a function of tangent point density with a root-mean square residual of ~1%. Corresponding densities from this fit agree with ATMOS version 3 densities to ~2.3% in the region of good sensitivity at 2 ¿ 1018 to 8 ¿ 1018 molecules cm-3 (~12--20 km altitude). The measured transmission ratio versus density relation has been compared with calculations from temperature-dependent laboratory measurements for both the N2 and CO2 continua. Simulation of the ATMOS spectra based on these laboratory measurements also predict a globally compact relation between the transmission ratio and density but differs from the empirically-determined relation by up to 7% in the lower stratosphere.