90 
complementary class. The number of such changes is called 
the distance of the two marks. Thus in the example given 
the distance is 2. In two similar compound statements 
the distances of the marks denied must be the same ; but 
it does not follow that when all the distances are the same, 
the two statements are similar. There is, however, as we 
shall see, only one example of two dissimilar statements 
having the same distances. When the distance is 4, the two 
marks are said to be obverse to one another, and the state- 
ments denying them are called obverse statements; as 
ABCD, abed; or, again, AhQd, aBcD. When any one 
mark is given (called the origin), all the others may be 
grouped in respect of their relations to it as follows. Four 
are at distance one from it, and may be called proximates ; 
six are at distance tivo, and may be called mediates ; four 
are at distance three, and may be called ultimates. Finally, 
the obverse is at distance four. 
aBCD 
ABCc? ABCD A&CD 
ahCD 
ABcD 
Abed 
abcD——od)cd dBcd 
ahCd 
origin and 4 proximates. fi mediates. obverse and 4 ultimates. 
It will be seen from the above table that the four proxi- 
mates are respectively obverse to the four ultimates, and 
that the mediates form three pairs of obverses. Every 
proximate or ultimate is distant I and 8 respectively from 
such a pair of mediates. Thus each proximate or ultimate 
divides the mediates into two classes ; three of them are at 
distance 1 from it, and three at distance 3. Two mediates 
which are not obverse are at distance 2. Two proximates, 
or two ultimates, or an ultimate and a proximate which are 
not obverse, are also at distance 2. 
This view of the mutual relations of the marks is the basis 
of the following enumeration of types. 
