For a catholic seasonal adjustment method for monthly economic time series, the general linear model and mutually independent random disturbances with zero mean and constant variance, in the special case with components consisting of twelve seasonal polynomials in t (time) of low degree and a nonseasonal polynomial in t of higher degree have been employed. A cogent set of test results consisting of best (minimum-variance) linear seasonal estimations and adjustments for the common logarithms of the monthly economic time series, "Shipments of Portland Cement in the United States, 1957-61," indicates that this is a theoretically and computationally promising approach now that large-capacity, high-speed electronic computers are available. The author has been attempting since 1959 to validate empirically the feasibility of this model. The history of statistical theories of seasonal adjustment is also briefly reviewed.