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The statistical model of particle production makes definite predictions about «compound-elastic» scattering cross-sections. Such predictions are available in a numerical form for π-N and p-p collisions with primary energy (laboratory-system) between zero and about 20 to 30 GeV. The result is that the «compound-elastic» cross-section for π-N should show the following dependence on the total centre-of-momentum energyE(measured in GeV):wheref(E)is a slowly varying function representing the «inelasticity». Experimental results are compared to this prediction and qualitative agreement is found.