The steeply falling end of the cosmic ray spectrum now extends up to ≈ 3 × 10 eV (see Ref. [1] for a recent survey), three orders of magnitude higher than the highest energy achieved by hadron colliders. Direct measurements using sophisticated equipment on satellites or high altitude balloons are limited in detector area and in exposure time. Ground-based detectors with large apertures make such a low flux detectable after a magnification effect in the upper atmosphere. Namely, the incident cosmic radiation interacts with atomic nuclei of the air molecules and produces extensive air showers which spread out over large areas. This indirect method of detection bears a number of serious difficulties in the interpretation of the recorded data. In particular, since many variables are involved the processes describing the shower development are intrinsically complicated, numerical simulation of the giant cascades has to be performed. The most important source of fluctuations in Monte Carlo simulations such as corsika [2] and aires [3] are the depth and characteristic of the first few inter-
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