An investigation of the relation of frequency to rainfall intensity, by the statistical method, forms the basis of this paper. All the available records of excessive rainfall published by the United States Weather Bureau for nineteen cities were first examined and those exceeding certain rates were tabulated and plotted on semi-logarithmic paper. The graphs were straight lines of marked regularity in their arrangement. Then, the data from ten cities of the original nineteen were tabulated and plotted, thus using about one half the quantity of data first used. A similar regularity and consistency in the curves were found. Finally, the data from fourteen rain-gages in the Chicago (Ill.) District were used for finding curves and formulas for the use of the City of Chicago. The formulas for intensity are rectangular hyperbolas and are plotted on hyperbolic paper as straight lines. The study is limited to excessive storms having durations of 120 min, and less.