SYNOPSIS This is the ninth of a series of papers on the rainfall of the world, and the second on the application of Schuster's Periodogram. In the last application of this method, published in the Monthly Weather Review of October, 1924, periods longer than nine years were investigated. In this one, periods are examined between nine and two and one-sixth years. In the next paper, which is already mostly computed, still shorter periods will be considered. The aim of these investigations is to examine typical sections systematically, so that all facts concerning rainfall periodicities, which are inherently possible in data at the present time, may be established. It is believed by the author that this question requires such a method as the periodogram, through which periodicities and probabilities are shown, entirely free from the personal bias which must affect the judgment when almost any other method is used. At present, it is his belief, the great need is for such a careful examination of data, rather than for theorizing regarding causes. It is only through thus establishing accurate quantitative relationships that the theories regarding causes can be given the sound footing which they require. Naturally a knowledge of causes is the final goal of all research, but any short cut to theories regarding them is too dangerous to use. The following summarizes the principal results obtained so far. (a) Rainfall periods certainly do exist. (b) There is, in all sections of the world examined, a very marked bias toward harmonics of the sun-spot period, too much so to be merely accidental. (c) It is impossible to say at present whether these periods are constant or varying in length, however, the bulk of the evidence favors the former. (d ) It would be too unsafe to make agricultural predictions on the basis of results so far obtained. However, some sections of the world indicate quite strongly that this may be possible in the future. (e) The more nearly a climate approaches a pure marine the more nearly does its periodogram give us definite results.