Frequency Equations

IN the article on simultaneous equations published in AIRCRAFT ENGINEERING, Vol. XI, May, 1939, pp. 199–200, the author exploited the powerful process of iteration. In the present article he deals similarly with an iterative method for finding the roots of a determinantal equation. Such a method was first given by Duncan and Collar in their paper “On a Method for the Solution of Oscillation Problems by Matrices” (Phil. Mag. Vol. 17, p. 865, 1934), and embodied in the book, “Elementary Matrices,” by Frazer, Duncan and Collar (Cambridge, 1938), reviewed in AIRCRAFT ENGINEERING, Vol. XI, February, 1939, p. 55. The particular treatment here adopted has the advantage that it is founded on elementary algebraic principles.