Abstract: A series of base functions has been proposed for global analytical approach to the firing table on cannons and guns. Numerical tests on the firing table of a gun of specific model prove that it is satisfactory; showing that these functions should also be useful to approach to the firing table of firearms of other models.Methods of extension and invariability analysis developed for obtaining the base functions in question should be of value as a reference to global analytical approach to a great many other numerical functions.

Key words: periodic solutions, Duffing equations, Leray-Schauder principle