present examples of the distributions $F_{\varphi} (\varphi ; \chi, s =1 )$ in the log-lin scale. The distributions look more or less like a fraction of a cosine function. Thus, we look for a function of the form $$log\, F_{\varphi}=A+Bcos(a\,\varphi +b)\;\textnormal{,}$$ where the parameters $A, B, a$ and $b$ have to be fitted for different values of $\chi$. We fit the distributions $F_{\varphi} (\varphi ; \chi, s)$ for various $\chi$ in bins $\Delta \varphi =10^{\circ}$. The best fitting polynomial descriptions, taking into account the dependence on $s$, are given in Appendix.\
In Fig. 8 the histogrammed distributions $F_{\varphi} (\varphi ; \chi, s =1 )$ refer to various values of $\chi$ for one $10^{17}$ eV iron shower. The smooth lines represent function (6) with the parameters described in Eq. A3-A4.\

Parametrization of the distributions of the polar angles $F_{\xi} (\xi ; \varphi , s)$
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We fit the distributions $F_{\xi} (\xi ; \varphi, s)$ for various $\varphi$ in bins $\Delta \varphi =10^{\circ}$, with the function $$F_{\xi}(\xi; \varphi, s)=\frac{C\xi}{(d+e^{\xi/2})^{\gamma}} \, \textnormal{.}$$ The parameters $d$ and $\gamma$ depend on $\varphi$, as it is obvious from Fig. 7. Parameter $C$ normalizes the integral $\int F_{\xi} ( \xi ; \varphi,s) d \xi $ to unity. 