  The TRACER instrument (``Transition Radiation Array for Cosmic Energetic
Radiation'') has been developed for direct measurements of the heavier primary
cosmic-ray nuclei at high energies. The instrument had a successful
long-duration balloon flight in Antarctica in 2003. The detector system and
measurement process are described, details of the data analysis are discussed,
and the individual energy spectra of the elements O, Ne, Mg, Si, S, Ar, Ca, and
Fe (nuclear charge Z=8 to 26) are presented. The large geometric factor of
TRACER and the use of a transition radiation detector make it possible to
determine the spectra up to energies in excess of 10$^{14}$ eV per particle. A
power-law fit to the individual energy spectra above 20 GeV per amu exhibits
nearly the same spectral index ($\sim$ 2.65 $\pm$ 0.05) for all elements,
without noticeable dependence on the elemental charge Z.
