The Smithsonian far-infrared spectrometer is a remote sensing Fourier transform spectrometer that measures the mid- and far-infrared thermal emission spectrum of the stratosphere from balloon and aircraft platforms. The spectrometer has had nine successful ballon flights from 1987 to 1994, flying a float altitudes of 36--39 km and collecting 131 hours of midlatitudes stratospheric limb spectra. The spectrometer also flew on a NASA DC-8 aircraft, as part of the second Airborne Arctic Stratospheric Expedition (AASE-II), collecting 140 hours of overhead spectra at latitudes ranging from the equator to the north pole. We present here a description of the instrument, a discussion of data reduction procedures, an estimation of both random and systematic errors, an outline of the procedure for retrieving mixing ratio profiles, and an explanation of the method of deriving temperature and pressure from the far- and mid-infrared spectra.