the shower causes deviations from Molière radius scaling. However, roughly 95% of the shower are contained laterally in a cylinder with radius . The mean longitudinal profile of the energy deposition in electromagnetic cascades is reasonably well described by a gamma distribution: where , is the initial energy and and are parameters to be fitted with Monte Carlo or experimental data. Hadronic showers The physical processes that cause the propagation of a hadron shower are considerably different from the processes in electromagnetic showers. About half of the incident hadron energy is passed on to additional secondaries. The remainder is consumed in multiparticle production of slow pions and in other processes. The phenomena which determine the development of the hadronic showers are: hadron production, nuclear deexcitation and pion and muon decays. Neutral pions amount, on average to 1/3 of the produced pions and their energy is dissipated in the form of electromagnetic showers. Another important characteristic of the hadronic shower is that it takes longer to develop than the electromagnetic one. This can be seen by comparing the number of particles present versus depth for pion and electron initiated showers. The longitudinal development of hadronic showers scales with the nuclear interaction length: The lateral shower development does not scale with λ. Theoretical analysis A simple model for the cascade theory of electronic showers can be formulated as a set of integro-partial differential equations. Let Π (E,x) dE and Γ(E,x) dE be the number of particles and photons with energy between E and E+dE respectively (here x is the distance along the material). Similarly let γ(E,E')dE' be the probability per unit path length for a photon of energy E to produce an electron with energy between E' and E'+dE'. Finally let π(E,E')dE' be the probability per unit path length for an electron of energy E to emit a photon with energy between E' and E'+dE'. The set of integro-differential equations which govern Π and Γ are given by γ and π are found in for low energies and in for higher energies. Examples Cosmic rays hit earth's atmosphere on a regular basis, and they produce showers as they proceed through the atmosphere. It was from these air showers that the first muons and pions were detected experimentally, and they are used today by a number of experiments as a means of observing ultra-high-energy cosmic rays. Some experiments, like Fly's Eye, have observed