476 Notices respecting New Books. 



number by means of the powers of 1*1, 1*01, 1*001, &c. entering as 

 factors ; separating these from the ordinary numerals by an arrow | » 

 and from each other by commas. Thus he expresses by 



32 | 2, 1, 3, 4 



what we might write at full length in the ordinary notation of powers 

 as 



32 . (l-l) 2 . (1-01) . (TOOl) 3 . (1-0001) 4 ; 



or, when expanded, as 



39-25036 52125 50568 92246 17678 7172; 



and the expression in his notation 



4 0, 2 



means 



4.(l-01) 2 or4-0804. 



He expresses by 4 j 0, 2 the fraction 

 4.(l'01)~ 2 or 



1-0201 



It will be obvious that the product or sum of any two numbers so 

 represented is expressible at sight, without further labour than the 

 multiplication or division of the numbers lying to the left of the 



symbol A , and the addition or subtraction of the numbers to its 



right. Thus the product of 



16 | 4, 3,0, 1, 9 and s|l, 2,9,7, 2 



is 



128 1 5, 1, 9, 8, 11, 



and their quotient is 



or its reciprocal, 



2 { 3, 5, 9, 6, 7, 



1 | 3, 5, 9, 6, 7; 



the numbers to the right of the arrow being, in fact, indices. 



We must refer to the treatise itself for the mode of expressing 

 ordinary numbers in a notation of this kind, and of comparing dif- 

 ferent expressions of the same number, whether absolute or approxi- 

 mate. It is obvious that every number may be expressed in an infi- 

 nite variety of ways under this notation. For instance, 10*01 may 

 be expressed indifferently as 



10-01, 10 jo, 1, or 9-1 1 1. 



Whether this indeterminate character of the notation be an advan- 

 tage or a hindrance, we have not sufficient experience to decide. 

 The notation just explained appears to be only the preliminary, 



