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Suppose that there are two collections or groups of objects-coins, trees, beans, or aircraft-and we do not know how many objects there are. Suppose further that for some reason we cannot count the number of objects in either group. Still, some property of each group makes it possible for a person to say that one of these groups is greater-than, lessthan, or equal-to the other group. It is this property of a collection of objects that we define as numerousness.l We might say that numerousness is that property of a group of objects which we can discriminate, without counting, under instruction to judge how many objects the group contains. We shall wish to modify this definition later as a result of the experiments reported in this paper, but it is adequate for the present discussion of the problem. The judgment of 'numerousness' may be made in several different ways: (a) it may be comparative-more numerous or less numerous, larger or smaller, etc.; (b) or it may be 'absolute.' There is one special form that the absolute judgment of numerousness can take. It is called the direct reporting of number. In this method of reporting, a numeral is assigned to represent how many things there are in any given collection of objects. After a brief look-so brief that counting is impossible-we say 10, 23, or 250 to indicate that we estimate that the group contained 10, 23, or 250 members.