NUMBER AS DETERMINING FORM OF GROUP 189
of political parties by a government not less than in competitive struggle in which, for instance, the three elements opposed to each other are a very powerful financier or manufacturer, and two less important but disagreeable, and in comparison with each other unequal, competitors. In this case, the first mentioned, in order to prevent the coalition of the other two against him- self, will enter into an agreement about prices, or amount of production, with the stronger of the two, an agreement which assures to him actual advantages, and through which the weaker is embarrassed. So soon as this has taken place, that more powerful opponent may throw off his previous ally, who has no longer any recourse, and he may annihilate him by underbidding or other methods.
I now pass to a quite different type of those sociological formations which are determined by the numerical definiteness of their elements. In the case of the dyad and triad configura- tions, we had to do with that inner group-life, with all its dif- ferences, syntheses, and antitheses, which develops with this minimum or maximum number of members. The question did not concern the group as a whole, in its relation to others, or to a larger group of which it is a part, but the immanent reciprocal relationship of its elements. If, now, on the con-J trary, we ask about the significance which the numerical preci-/ sion betrays in external relations, its most essential function is/ that it makes possible the subdivision of a group into minoij groups. The teleological meaning of this is, as already indi- cated above, the more ready visibility and docility of the total group, frequently the first organization and proper mechaniza- tion of the same. In purely formal respect, the possibility is thereby given of preserving the formation, character, arrange- ments of divisions of the whole, independent of the quantitative development of the whole. The component parts with which its administration reckons, remain qualitatively always the same sociological factors, and the increase of the whole changes only their multiplier. This is, for example, the enormous advantage of the numerical division of armies ; their increase proceeds thereby with relative technical ease because it follows as a
