1887.] 



131 



[Taylor. 



advantage, not only in being more systematic, but in giving greater pre- 

 cision of expression and idea. Instead of using the same word to indicate 

 both a place, or local value (as the "ten-place") and a specific number, 

 we are furnished with two distinct words — "Ty" designating the place 

 and "Unty" specifying one in the ty-place, as "Dutj^" specifies 

 two in the ty-place. All that is needed to carry out this system is to add 

 a table of places. 



Notation Table. 



The Unkaly is the eighth (or untieth) power of Unty. Its value is 

 16,777216; and it requires but one more figure to express this large 

 amount, than is required by the denarj"- scale. A second place of figures 

 is not lost by our new system — that is, its notation does not exceed that 

 of the common system by two places, until the number 8589,934593 is 

 reached ; these 10 figures requiring 12 (namely \j and eleven ciphers) in 

 the octonary scale to represent their value. If this should appear sur- 

 prising to any, it must be remembered, that although at 8, and at 64, an 

 additional figure is required by the octonary system, yet after 10, and 100, 

 the denary also requires this additional figure ; and considering this, we 

 shall find that the two scales are equal in the number of places occupied — 

 from 1 to 7, inclusive — from 10 to 63, inclusive — from 100 to 511 — from 

 1000 to 4095— from 10.000 to 32,767— from 100,000 to 262,143— from 

 1,000000 to 2,097151— from 10,000000 to 10,777215— from 100,000000 to 



