134 THE SOCIAL THEORY OF GEORG SIMMEL
third modifies it entirely, but also by the fact that a further
 extension is not followed by a modification of corresponding
 degree. The dyadic group is the first in the numerical
 scale to show a unity and synthesis, but it also
manifests an internal antithesis and opposition. The entrance
 of a third element causes considerable modification.
On the one hand it makes for a superindividual unity,
and on the other hand it changes the direct and immediate
reciprocity. Added to the direct relationship there is now
an indirect relationship which both reinforces and interferes
 with the immediate reciprocity. The new group is
less dependent on the immediate participation of the elements
 than the dyadic group. It absorbs less of the total
personality and can continue its existence if one element
drops out.
The function of the third and the configurations of
triadic groups are herewith largely indicated. The dyadic
group showed synthesis and antithesis. The entrance of a
third element means transition, conciliation, renunciation
both of the immediate reciprocity and of the direct opposition.
 But it can also create oppositions formerly absent.
The triadic group can therefore manifest three characteristic
 formations which are impossible in dyadic groups and
which are likewise excluded from larger groups. Two of
these configurations are known by the title of the third
person, namely, the non-partisan arbitrator or mediator
on the one hand, and the tertius gaudens on the other hand.
The third configuration is usually indicated by the motto
Dimde et impera.
In the first instance, the non-partisanship of the third
element serves the group as a whole. The conciliator or arbitrator
 aims to prevent a disruption of the existing unity
between the opposing elements.
The non-partisan can. however, also use his advanta-