The best fitting polynomial descriptions are in Appendix.\
Fig. 9 presents an example of the distribution $F_{\xi} (\xi ; \varphi, s)$ and fitting functions for four values of azimuth angles $\varphi$ and three values of $s$. It can be seen that the description by formula (7) is quite satisfactory (see also Section 4.4).

Estimation of the accuracy of the universal fit
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### General considerations

The analytical description of the electron distributions found in this paper, the universal fit, is not, of course, ideal. Now we aim at estimating how well it describes the actual electron distributions in an arbitrary shower detected by the fluorescence method as it is done e.g. at The Pierre Auger Observatory and any other similar experiment.\
The reasons why the actual distributions and the universal fit may differ are several:

-   the universal fit is meant to describe an average from several simulated proton and iron initiated showers with primary parameters somewhat arbitrarily chosen; whereas a measured shower has a single primary energy $E_0$, primary mass and zenith angle arising from the distributions of these parameters in the sample registered by the experiment;

-   the simulated distributions have been fitted with possibly simple analytical functions, 