are nine curves, referring to combinations of three electron energies: $E=23$, $70$ and $200$ MeV and three lateral distances: $log ( r / r_M )=-1.25$, $-0.85$ and $-0.45$ for $s=0.7$ and $log ( r / r_M )=-1.05$, $-0.65$ and $-0.25$ for $s=1.3$. The different sets of the lateral distances reflect the fact that in older showers the lateral distribution becomes flatter. It is seen that the distributions are essentially independent of energy, lateral distance or the polar angle once the value of $\xi$ is fixed.\

Analytical parametrization of the universal angular distributions
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![Comparison of simulated (histograms) and parametrized (lines) distributions $F_{\varphi}(\varphi;\chi,s=1)$ of azimuth angles $\varphi$ for five equidistant values of $\chi$ from 3 to 15 (top to bottom at the right side). One $10^{17}$ eV iron shower. []{data-label="fig8"}](fig8N.eps){width="4.7in"}

![Comparison of the actual (histograms) and parametrized (lines) distributions $F_{\xi}(\xi;\varphi,s)$. One iron shower with $E_0=10^{17}$ eV (without thinning). []{data-label="fig9"}](fig9N.eps){width="4.8in"}

Having established the character of the universal distributions of the azimuth angles $F_{\varphi}(\varphi;\chi, s)$ and the distributions of the polar angles $F_{\xi} (\xi ; \varphi , s)$, we undertake the task of finding their analytical descriptions.

Parametrization of the distributions of the azimuth angles $F_{\varphi}(\varphi;\chi, s)$
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The histograms in Fig. 8 