and on Algebra as the Science of Pure Time. 393 
THEORY OF CONJUGATE FUNCTIONS, 
OR ALGEBRAIC COUPLES. 
On Couples of Moments, and of Steps, in Time. 
1. When we have imagined any one moment of time A,, which we may call a 
primary moment, we may again imagine a moment of time 4,, and may call this a 
secondary moment, without regarding whether it follows, or coincides with, or pre- 
cedes the primary, in the common progression of time; we may also speak of this 
primary and this secondary moment as forming a couple of moments, or a moment- 
couple, which may be denoted thus, (A,, A,). Again, we may imagine any other two 
moments, a primary and a secondary, B, and B,, distinct from or coincident with each 
other, and forming another moment-couple, (B,, By); and we may compare the latter 
couple of moments with the former, moment with moment, primary with primary, 
and secondary with secondary, examining how B, is ordinally related to a,, and how 
B, is ordinally related to a,, in the progression of time, as coincident, or subsequent, 
or precedent ; and thus may obtain a couple of ordinal relations, which may be thus 
separately denoted B,—A,, B,—A., or thus collectively, as a relation-couple, 
(8; a iT Ap). 
This couple of ordinal relations between moments may also be conceived as consti- 
tuting a complex relation of one moment-couple to another ; and in conformity with 
this conception it may be thus denoted, 
(Bi, B,) — (A, Aa)s 
