TYPES OF COMPOUND STATEMENT. 93 



verses may be evenly distant, when the remaining marks 

 form a group either proper, with its origin, obverse, and 

 pair of mediates, or two pairs of mediates, or else improper, 

 3 types ; or oddly distant, when the remainder form one of 

 the six pure fourfold statements enumerated art. 6. Two 

 marks distant 2 from each other may be distant 11,33 

 or I 3, I 3 from the pair of obverses which are oddly distant 

 from them ; thus each of the six fourfold statements gives 

 3 types of eightfold statement, except the third, which 

 gives 4 ; in all, 19. In the second case the three may be 

 a triad or may contain a pair of obverses. If it is a triad, 

 the five are mediates to one origin and its obverse, and we 

 may add three proximates distant i i 3 or i 3 3 or two proxi- 

 mates distant i i , i 3, or 3 3 with an ultimate distant respec- 

 tively I I or 3 3 from the odd mediate; 6 types. If the 

 three contain a pair of obverses, the five make a proper group 

 with obverse of one mark ; to this we may add the origin and 

 obverse of the group with mediate distant i or 3 from the 

 ultimate, or a pair of obverse mediates with a mediate distant 

 I or 3 as before ; 4 types. In the third case the six must 

 be an origin and five mediates, and we may add two proximates 

 distant i i, i 3, 3 3 from the odd mediate, or a proximate and 

 an ultimate, or two ultimates, distant as before ; 9 types. 

 20. In an eightfold statement with three pairs of ob- 

 verses these may be either all evenly distant, or two o£ them 

 evenly distant and the other oddly distant from both. In the 

 first case they are mediates to a certain origin audits obverse, 

 and we may add the origin with a proximate or ultimate, two 

 proximates, or a proximate and ultimate ; 4 types. In the 

 second case take the oddly distant pair for origin and ob- 

 verse ; then these are associated with two proximates and 

 their obverse ultimates, and we may add the two other 

 proximates, a proximate and an ultimate, a proximate and a 

 mediate (distant i i, 13, 31, 33 from this proximate and 



