  In the fluorescence detection of ultra high energy (> 10**18 eV) cosmic rays,
the number of emitted fluorescence photons is assumed to be proportional to the
energy deposited in air by shower particles. We have performed measurements of
the fluorescence yield in atmospheric gases excited by electrons over energies
ranging from keV to hundreds of MeV in several accelerators. We found that
within the measured energy ranges the proportionality holds at the level of few
%.
