bins of the multidimensional variable space are about 6$\%$, determining the minimum uncertainty needed for parametrization of the universal distributions. An analytical way of estimation of the effect of the geomagnetic field is given.\
    Thanks to the universality of the electron distributions in any shower a new method of shower reconstruction can be worked out from data of the observatories using the fluorescence technique. The light fluxes (both fluorescence and Cherenkov) for any shower age can be exactly predicted for a shower with any primary energy and shower maximum depth, so that the two quantities can be obtained by best fitting the predictions to the measurements
author:
- Andrzej Śmiałkowski
- Maria Giller
title: |
    Universality of electron distributions\
    in extensive air showers
---

Introduction
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Cosmic rays of the highest energies, $E_0 >10^{17}$ eV, can be detected and studied only by registering their effect produced in the atmosphere, i. e. the extensive air showers, cascades of particles (mainly electrons of both signs) and photons reaching the ground. Thanks to the fluorescence technique it is also possible to gain information about the state of a shower developing in the atmosphere at higher altitudes than the ground. Shower particles cause the 