The two examples now given are cases of the _conjugative_ kind. The relationship is a conjugative one and the relations are conjugative relations. The distinguishing characteristic of a conjugative case is the fact essentially involved of the mediation between relational elements by another certain element, or in other words the bringing of diverse relational elements into relation by the function of another relational element. Without the mediation or function of this conjugating element neither the relationship nor the conjugative relations can exist. There is reason to believe that all conjugative cases can be certified as cases of three relational elements or as compounds of a number of such sets of three. To ordinary uncritical thought which is largely constrained by the trammels of ordinary language the most abundant sort of relations appears to be of that sort that are taken to involve only two relational elements. These are cases of what are called _dual_ relationships and the relations that arise out of them are called _dual_ relations. Such are those like father, son, husband, wife, etc. Strictly viewed they ought to be regarded as _degenerate_ relationships and relations just as a pair of lines is regarded as a degenerate conic. VIII. CAUTIONS AND APPLICATIONS. Now besides the error of confounding relations with relationship, it is a very common fault to think and speak of a relation as being _between_ two or more terms. This imports into thought the thoroughly misleading idea of an intervening independent existence for relations. Relations are attributive predicates of terms and each one of them pertains strictly to its proper term or combination of terms, in the same sense for this turn (_pro hac vice_) that qualities are held to pertain to their so-called substances. And yet relations so pertain to their proper terms not in virtue of such terms separately but in virtue of their membership in the plural fact which obtains as the _relationship_ or _foundation_. The notion of a relation as a “betweenness” has perhaps been fostered by the exact coincidence of relations pertaining to the several members of the same relationship. When on contemplating the connection, say of two points, we observe that the distance of one from the other is apparently indistinguishable from the distance of the other from the one, we naturally overlook the fact that we are truly to regard the connection as the coincidence of two really distinct relations, and regarding the pair of relations as one thing and finding it not attributable to one point more than to the other we dissociate it from both. But when we consider a pair of relations that are converse to one another and that arise out of a dual relationship like that of husband and wife we may see that there is _no_ betweenness, no single relation that interlies, but two relations, one the relation of husband and the other the converse relation of wife.