and on Algebra as the Science of Pure Time. 299 
PRELIMINARY AND ELEMENTARY ESSAY 
ON ALGEBRA AS THE SCIENCE oF PURE TIME. 
Comparison of any two moments with respect to identity or diversity, subsequence or 
precedence. 
1. If we have formed the thought of any one moment of time, we may afterwards 
either repeat that thought, or else think of a different moment. And if any two 
spoken or written names, such as the letters a and B, be dates, or answers to the 
question /Vhen, denoting each a known moment of time#they must either be names 
of one and the same known moment, or else: of two different moments. In each 
case, we may speak of the pair of dates as denoting a pair of moments ; but in the 
first case, the two moments are coincident, while in the second case they are distinct 
from each other. ‘To express concisely the former case of relation, that is, the case 
of identity between the moment named B and the moment named a, or of equivalence 
between the date B and the date a, it is usual to write 
B=A; (1.) 
a written sentence or assertion, which is commonly called an equation : and to express 
concisely the latter case of relation, that is, the case of diversity between the two mo- 
ments, or of non-equivalence between the two dates, we may write 
BA; (2.) 
VOL. XVII. 3N 
