302 Professor Hamitton on Conjugate Functions, 
5. When the foregoing relation between four moments aBcpD does not exist, 
that is, when the pairs aB and cp are not analogous pairs, we may mark this non- 
analogy by writing 
D—C=-B— A; (15.) 
and the two possible cases into which this general conception of non-analogy or di- 
versity of relation subdivides itself, namely, the case when the analogy fails on ac- 
count of the moment pD being too /ate, and the case when it fails because that moment 
p is too early, may be denoted, respectively, by writing in the first case, 
D—C>B—A, - (16.) 
and in the second case, 
D—C<B—A; (17.) 
while the two cases themselves may be called, respectively, a non-analogy of subse- 
quence, and a non-analogy of precedence. We may also say that the relation of 
p to c, as compared with that of B to 4, is in the first case a relation of comparative 
lateness, and in the second case a relation of comparative earliness. 
Alternations and inversions may be applied to these expressions of non-analogy, ead 
the case of p too late may be expressed in any one of the eight following ways, which 
are all equivalent to each other, 
D—C>B—aA, B—A<D—C,} 
D—E>C—A, saseoas (18.) 
c—D<a—B, A—B>C—D, 
B—D<a—C, A—cC>oB—D; 
while the other case, when the analogy fails because the moment p is too early, may 
be expressed at pleasure in any of the eight ways following, 
D—c<B—a, B—A>D—CE, 
pD—B<C —a, C_a>D—B, 
C—D>A—B, A__B<C—D, 
B—D>A—C, A—C<C¢B—D. 
(19.) 
In general, if we have any analogy or non-analogy between two pairs of moments, 
4 B and c D, of which we may call the first and fourth mentioned moments, a and p, 
the extremes, and the second and third mentioned moments, namely, 8 and c, the 
