300 Professor Haminton on Conjugate Functions, 
annexing, here and afterwards, to these concise written expressions, the side-marks 
(1.) (2.), &c., merely to facilitate the subsequent reference in this essay to any such 
assertion or result, whenever such reference may become necessary or convenient. 
The latter case of relation, namely, the case (2.) of diversity between two moments» 
or of non-equivalence between two dates, subdivides itself into the two cases of subse- 
quence and of precedence, according as the moment 8 is later or earlier than a. To 
express concisely the former sort of diversity, in which the moment B is ater than a, 
we may write . 
B>A; (3.) 
and the latter sort of diversity, in which the moment B is earlier than A, may be ex- 
pressed concisely in this other way, 
B<A. (4.) 
It is evident that 
if B=A, then a=B; (5.) 
if BA, then as ; (6.) 
if B>a, then A<B; (7.) 
if B<a, then a>B. (8.) 
Comparison of two pairs of moments, with respect to their analogy or non-analogy. 
2. Considering now any two other dates c and p, we perceive that they may and 
must represent either the same pair of moments as that denoted by the former pair 
of dates a and B, or else a different pair, according as the two conditions, 
C=A, and p=B, (9.) 
are, or are not, both satisfied. If the new pair of moments be the same with the old, 
then the connecting relation of identity or diversity between the moments of the one 
pair is necessarily the same with the relation which connects in like manner the mo- 
ments of the other pair, because the pairs themselves are the same. But even if the 
pairs be different, the relations may still be the same ; that is, the moments c and p, 
even if not both respectively coincident with the moments a and 3, may still be re- 
lated to each other exactly as those moments, (p to c as B to A;) and thus the two 
pairs, A, B and c, D may be analogous, even if they be not coincident with each other. 
An analogy of this sort (whether between coincident or different pairs) may be ex- 
pressed in writing as follows, 
