98 
the second case we have five mediates of an origin or its 
obverse, to which we may add 2 proximates distant 11, 13 
or 33 from the odd mediate, or a proximate and an ultimate 
distant 11, 13 or 33 respectively from the odd mediate; 6 
types. 
If the seven»fold statement subdivide into four and three, 
the two pairs may be both in the four, or one in the four 
and one in the three. In the former case we have a triad, 
to which may be added the origin and obverse and a pair of 
mediates, or two pairs of mediates ; two types. In the latter 
case the four consist of an origin and obverse and two 
mediates ; we must add a pair consisting of a proximate and 
an ultimate, which may be distant 11, 33 or 13, 13 from 
*• 
the two mediates, and then another proximate or ultimate 
which may be distant 11, 13, or 33 from the two mediates ; 
6 types. 
16. Three pairs of obverses in a seven-fold statement may 
be all evenly distant, or two evenly aud the other pair 
oddly distant from each. If they are all evenly distant 
they are the mediates to a certain origin or its obverse, and 
the seventh mark may be the origin or a proximate, 2 types. 
In the other case we have an origin obverse and pair of 
mediates together with a proximate and its obverse ultimate ; 
we may add a proximate or a mediate, 2 types. 
17. A pure eight-fold statement must consist of two 
groups, either both proper or both improper, or one of each. 
Two proper groups may have their origins distant 1 or 3 ; 
two types. To an improper group we may add a proper 
group made of one origin and three obverses, or of three 
origins and one obverse ; or an improper group made of 
four origins or four obverses, or two origins and two 
obverses; five types; altogether there are seven types of 
pure eight-fold statement. 
18. An eight-fold statement with one pair of obverses 
must subdivide into four and four, or into five and three. 
