NUMBER AS DETERMINING FORM OF GROUP 2$
elements, only that the empirical relations actualize this division with greater or less exactness. If it has been said of the Ger- man Hundreds that they were intended to express merely an indefinitely large number between the individual and the totality of members, this designates precisely the asserted sociological type. The life of the group demands a middle resort between the One and the All, a bearer of definite functions which neither the One nor the All can discharge, and the structure devoted to these tasks is thus named in accordance with its numerical com- position. The functions do not give the name, because they are manifold and variable. What remains is merely the consolida- tion of an aliquot part of the totality into a unity. How great this part is in each case may be uncertain. The permanent numerical designation shows that the numerical relation in gen- eral was felt to be the essential thing. Therewith appears in the social realm an occurrence whose psychological form is else- where observed. The Russian types of coin are said to have been derived from an old system of weights, and it was of such sort that'every higher type contained tenfold the amount of the lower. As a matter of fact, however, not merely the absolute but also the relative amount of metal in the coins often varied, but at the same time their values, after they were once brought into the numerical order, remained constant. While, therefore, the real proportions of metal value are shifting, the service which they have to render to commerce through the constancy of these nominal relations is marked by the fact that the historically first weight relations give permanent name and symbol for these later relations. In other ways, also, the number becomes the repre- sentative of the thing which it enumerates, and then the essen- tial matter, namely, that the real affair in question is a relation between the whole and the part, is denoted by the fact that the numerical concept of the earlier relation covers all later changes. Thus the tax upon the miners in Spain in the sixteenth century was called the Quinto because it amounted to a fifth of the value, and it retained its name later when the proportion was quite dif- ferent. In the same way the word "tithe" came to have, among the old Israelites and in many other places, the significance of
