angles. One $10^{19}$ eV proton shower.[]{data-label="fig7"}](fig7bN.eps){width="3.8in"}

Studying the electron angular distributions in multidimensional space of polar and azimuth angles, lateral distances, energies and ages of showers, allows us also searching for a possible internal type of universality. This means that the angular distributions may depend on a combination of some of the five independent variables rather than on each of the variable separately. Such a universality would simplify the description of the angular distributions by diminishing the number of necessary variables. A similar successful search was done earlier while describing the lateral distributions of electrons with various energies independent of their angles [@gsw]\

Variable $\chi$
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We have found that introducing a new variable $$\chi=(E/1\,\textrm{MeV})\cdot r/r_M  \;\textnormal{,}$$ the distributions $F_{\varphi} (\varphi ; \chi, s )$, where $F_{\varphi} (\varphi ; \chi, s )d\,\varphi$ gives the fraction of the number of electrons with angles $(\varphi, \varphi +d\,\varphi)$ at level $s$, with $E\cdot r/r_M=\chi$, with respect to the total number of them with any $\varphi$, have almost universal shapes. Thus, the function $f_{\varphi} (\varphi ; r / r_M , E , s )$ reduces to a function $F_{\varphi} (\varphi ; \chi, s )$ of three variables: $\chi , \varphi$ and $s$. We have 