Observations of cosmic-ray electrons and positrons have been made with a new balloon-borne detector, HEAT (the High-Energy Antimatter Telescope), first flown in 1994 May from Fort Sumner, NM. We describe the instrumental approach and the data analysis procedures, and we present results from this flight. The measurement has provided a new determination of the individual energy spectra of electrons and positrons from 5 GeV to about 50 GeV, and of the combined all-electron intensity (e+ + e-) up to about 100 GeV. The single power-law spectral indices for electrons and positrons are alpha = 3.09 +/- 0.08 and 3.3 +/- 0.2, respectively. We find that a contribution from primary sources to the positron intensity in this energy region, if it exists, must be quite small.
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