variable cell size and the range of the variable values to be well described. We show (Section 3) that some of the electron distributions can be described by a number of variables smaller than five, the new variables being a product of the old ones raised to some power. This simplifies a lot the analytical parametrization of the electron distributions found here. In Section 4 we parametrize the simulated distributions by analytical functions and give an estimation of the accuracy of our parametrization. In Section 5 we describe an analytical way of estimation the distortions of the electron angular and lateral distributions caused by the geomagnetic field.\
The universality of the electron distributions in showers provides a new method for reconstructing shower development in the atmosphere with the fluorescence technique (Section 6). The full description of the electron states and its universal character allows one to predict exactly the light fluxes (both fluorescence and Cherenkov) emitted by shower electrons at consequent time intervals (as recorded by telescopes), by adopting only two quantities for a shower: $N_{max}$ and $X_{max}$. Finding their values which fit best the data one can determine quite well the shower primary energy, and from the depth $X_{max}$ 