NUMERICAL RELATIONS OF SOCIAL FORMS 141 pendent of any specific number. Certain specific numbers have, however, usually been chosen for such subdivisions, namely, the number ten and its derivatives. This is un- doubtedly due to the fact that the number of the fingers of the hands suggests itself easily as an appropriate mag- nitude for numerical groupings of elements into units. Many secret societies have consisted of organizations of groups of five. In the older civilizations, many organiza- tions shaped themselves as combinations of groups of ten with special duties and responsibilities. Of the larger de- rivatives, the classical example is the hundred. It was the numerical magnitude for subdivisions, not only in early German and Anglo-Saxon times, but also in the ancient American civilizations.! Minimum and Maximum Qualifications i] The second instance in which the numerical magnitude becomes of importance for the external relations occurs in case the group manifests specific characteristics only below or above a certain size. The distinction between the gen- eral character of the external relations of small and large groups has been referred to previously. But the same ques- tion can be asked in detail for the relation between certain specific characteristics and certain well-defined magni- tudes. In the last analysis the internal relations of the group elements will be the basis for the character of the group as a whole, but in this case the interest is not in these internal relations, but in the group as a unit. The facts which point to the existence of a special significance of the size for the group as a whole all belong to one category. They are the legal prescriptions with regard to maximum and minimum membership for groups which are to be sub- ject to specific rights and duties. 1 Soz., pp. 126-30.