Taylor.] 



332 



[Oct. 21, 



134,217727— and for the last overtaking, from 1000,000000 to 1073,741823. 

 After this long-continued chase, the octonary scale at the next figure, or 

 1073,741824 (Under-Kaly) loses a place which is never regained. It 

 may not be uninteresting to add, that this scale does not obtain an excess 

 o? three places until it reaches the enormous number of 9 trillions, 223372 

 billions, 036854 millions, 775808, these 19 figures being expressed by (_, 

 and 21 ciphers. This amount diminished by a single unit, or by the last 

 figure 8 being exchanged for a 7, is expressed in the octonary system by 

 21 Ms (0) which would be an excess of only hco places of figures. 



Turning from this comparison of the relative powers of the two scales, 

 to their relative simplicit}^ as exemplified by the octonary multiplication 

 table, we shall find the contrast here as striking as was their parity on the 

 other hand remarkable. 



Multiplication Table. 



The mere inspection of this table is sufl3cient to' show, that the time 

 and labor of acquiring it would not be half that required for committing 

 to memory our received form ; and this facility of acquisition would in- 

 clude almost a corresponding degree of readiness in its use. Figures, like 

 furniture stored in the chambers of the brain, require a constant attention 

 and arranging, to be kept in state for use ; and the amount of care and 

 trouble unconsciously bestowed upon them, must be proportioned to the 

 number of the pieces after which we have to look. It is no idle boast, 

 therefore, to say that a child could be taught a thorough knowledge of the 

 four great rules of arithmetic, and a ready skill in their practical applica- 

 tions, through the octonary system, in one-half the time required for 

 obtaining an equal knowledge and skill by the common system. Nor is 

 this simplification of arithmetical operations its only merit. The danger 

 of error increases rapidly with the increasing complexity of the numeric 



