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A system of non-linear differential equations, typical of the interior ballistics equations for orthodox guns, is studied. Characteristics of the mathematical pressure curves are obtained for the entire spectrums of the ballistic parameter, burning exponent, and geometric parameter (characteristic of the form function). The mathematical solutions are found to distinguish sharply between regressive and progressive burning geometries, and a constant pressure solution is obtained (a piezometric efficiency of one) for what is defined as the ideally progressive geometry. The approximate validity of isothermal solutions, established by Clemmow for a linear burning law, is extended to the general case. [ABSTRACT FROM AUTHOR]