Taylor.] ^^^ [Oct. 21, 



scale appears still to prevail. The central tribes of North America show 

 also traces of this digital period ; and they are frequent among the innu- 

 merable languages of Africa. Thus with the Jallolfs, the word for 

 "fiYQ^'—juorom — signifies the "hand." So with the Foulahs, the Jal- 

 lonkas, the Fellups, etc. There are no examples, however, of the num- 

 ber five ever having been used as a true radix of notation ; that is, as a 

 direct ratio of continued progression ; 5 — 5x5 (25) ; — 5X5x5 

 (125), etc. The quinary scale has seldom gone further than 20. 



The Senary scale would require about seventeen places of figures for 

 thirteen of the common scale ; and its notation would therefore have 

 about a one-third greater extent. Though not one of the most desirable 

 scales, it would be much superior to the denary system. The simplifica- 

 tion arising from the reduction of its digits, would much more than coun- 

 terbalance the extension consequent on the increase of its places. Like 

 the denary scale, it admits of but one bisection ; but it possesses the great 

 superiority of admitting at the same time of a trisection. No examples of 

 this scale are to be met with ; although it is said to have been at one time 

 decreed in China, by the caprice of an Emperor, who had conceived 

 some astrologic fancy for the number six. 



The Octonary scale approaches very nearly to the common scale in its 

 capability of expression, as it requires on an average but one-ninth more 

 places of figures to represent any given amount ; that is, ten places of 

 this scale would be equivalent to nine places of the denary. Being de- 

 rived from the third power of the binary scale, it possesses most of the 

 advantages of that system ; though not its admirable simplicity. Like the 

 quaternary, it admits of continued bisection down to unity ; and, of 

 course, of indefinite bisection below 1, by the simple expedient of an in- 

 verted, or negative notation (as in decimal fractions). As a perfect cube, 

 it has peculiar advantages both as a radix of numeration, and as a ratio of 

 progression or of division for weights and measures ; and in the latter 

 respect particularly, there is, perhaps, no other number that would so 

 well express the average range of a convenient metrical multiple. 



The Denary scale* may be said to present a tolerably convenient mean 

 between the prolixity of a very small radix, and the intricacy of a very 

 large one ; besides which, it possesses the immense advantage of a uni- 

 versal establishment. But beyond this, there is nothing to be said in its 

 behalf. Intrinsically, it is one of the most imperfect and troublesome 

 scales which could be selected. Still, the inconveniences of the system 

 should be very serious and very apparent, and the claims of any rival 

 scheme very unquestionable, to justify the advocacy of a change, which 



*The name " Decimal," by which our present system of arithmetic is commonly des- 

 ignated, appears not to have a perfect propriety. The terms " Octaval," "Nonal," 

 " Decimal," " Duodecimal," etc., are derived from the Roman " ordinals," and belong to 

 the series Primal, Secundal, Tertial, Quartal, etc. The idea really involved is not that 

 of relation to a tenth, but of a relation to a grouping by ten^, and would require the term 

 " denal" or " denary "—from the Roman " distributive " numerals, of which the terms 

 "binary," "ternary," etc., commence the series. 



