A general expression for the impedance of acoustical horns and analogous devices is derived by considering a manifold of uniform structures. The impedance of the manifold is obtained by complete mathematical induction and the impedance of a smoothly varying tapered structure is obtained by a limiting process. With the expressions established here the impedances of acoustical horns having mouth to throat area ratios ranging from 0.125 to 8 can be calculated with less than 10% error at zero frequency.