Trace gases measured by the Atmospheric Trace Molecule Spectroscopy (ATMOS) instrument during three Atmospheric Laboratory for Applications and Science (ATLAS) space-shuttle missions, in March/April 1992 (AT-1), April 1993 (AT-2), and November 1994 (AT-3) have been mapped into equivalent latitude/potential temperature (EqL/&thgr;) coordinates. The asymmetry of the spring vortices results in coverage of subtropical to polar EqLs. EqL/&thgr; fields of long-lived tracers in spring in both hemispheres show the net effects of descent at high EqL throughout the winter, reflecting strong descent in the upper stratosphere, decreasing descent at lower altitudes, and evidence of greater descent at the edge of the lower stratospheric vortex than in the vortex center; these results are consistent with trajectory calculations examining the history of the air measured by ATMOS in the month prior to each mission. EqL/&thgr; tracer fields, the derived fields CH4-CH4* (CH4* is the expected CH4 calculated from a prescribed relationship with N2O for fall) and NOy-NOy* (analogous to CH4*), and parcel histories all indicate regions of strong mixing in the 1994 Southern Hemisphere (SH) spring vortex above 500 K, with the strongest mixing confined to the vortex edge region between 500 and 700 K, and mixing throughout the Northern Hemisphere (NH) spring vortex in 1993 below about 850 K. Parcel histories indicate mixing of extravortex air with air near the vortex edge below 500 K in the SH but not with air in the vortex core; they show extravortex air mixing well into the vortex above ~450 K in the NH and into the vortex edge region below. The effects of severe denitrification are apparent in EqL/&thgr; HNO3 in the SH lower stratospheric spring vortex. The morphology of HNO3 in the Arctic spring lower stratospheric vortex is consistent with the effects of descent. EqL/&thgr; fields of ATMOS NOy-NOy* show decreases consistent with the effects of mixing throughout the NH lower stratospheric vortex. The EqL/&thgr;-mapped ATMOS data thus indicate no significant denitrification during the 1992--1993 NH winter. Examination of H2O+2CH4 shows that dehydration in SH spring 1994 extended up to ~600 K; it also suggests the possibility of a small amount of dehydration in the NH 1993 spring vortex below ~465 K. Ozone depletion is evident in the spring vortices in both hemispheres. Differences in autumn EqL/&thgr; tracer fields between the missions reflect the fact that each succeeding mission took place ~2 weeks later in the season, when the vortex had developed further. There was greater average descent and greater isolation of air in the developing vortex during each succeeding mission, consistent with progressively larger downward excursions of long-lived tracer contours observed in the upper stratosphere at high EqL. ¿ 1999 American Geophysical Union