and on Algebra as the Science of Pure Time. 321 
On the Multiples of a given base, or unit-step ; and on the Algebraic Addition, 
Subtraction, Multiplication, and Division, of their determining or multipling 
Whole Numbers, whether positive, or contra-positive, or null. 
13. Let us now apply this general theory of successive and compound steps, from 
any one moment to any others, or of component and compound ordinal relations 
between the moments of any arbitrary set, to the case of an equidistant series of 
moments, 
EGGERE: AUBMB, Busi (29.) 
constructed so as to satisfy the conditions of a continued analogy, 
... B —B = B’—B=RB—A=A—E=E—E =E—E’, &e.; (30.) 
and first, for distinctness of conception and of language, let some one moment a of 
this series be selected as a standard with which all the others are to be compared, and 
let it be called the zero-moment ; while the moments B, B’, &c. which follow it, in the 
order of progression of the series, may be distinguished from those other moments 
E, E, &c., which precede it in that order of progression, by some two contrasted 
epithets, such as the words positive and contra-positive: the moment B being called 
the positive fi'st, or the first moment of the series on the positive side of the zero ; 
while in the same plan of nomenclature the moment B' is the positive second, B’ the 
positive third, © the contra-positive first, © the contra-positive second, and so forth. 
By the nature of the series, as composed of equi-distant moments, or by the condi- 
tions (30.), all the positive or succeeding moments B B’ &c. may be conceived as 
generated from the zero-moment a, by the continual and successive application of 
one common step a, and all the contra-positive or preceding moments E £’ &c. may be 
conceived as generated from the same zero-moment a, by the continual and successive 
application of the opposite step © a, so that we may write 
Bo=a+A, Bo=a+B, B’=a+B, &c., (95.) 
and. 
E=Oa +A, F’'=Oa +E, E =—Oa +E, &C.; (96.) 
while the standard or zero-moment a itself may be denoted by the complex symbol 
© + a, because it may be conceived as generated from itself by applying the null step 
