1S87.] ^-' [Taylor. 



the very first importance, and those impossible in any other scale. While 

 perfectly adapted to the highest requirements of science, it is as exactly 

 suited to the- trivial wants and petty occasions of our daily life. It pos- 

 sesses a degree of simplicity the most attainable without a sensible in- 

 crease of figuring. The simple suppression of the largest two digits of 

 our common system (8 and 9) throughout every place of figures, would 

 be found to reduce the working labor by at least one-half. In choosing 

 between a radix of a second power (as 4), and one of a third power (as 

 8), the latter would for several reasons be preferred. It would undoubt- 

 edly be advantageous for it to be at the same time both a square and 

 a cube. But unfortunately we can meet with no such favored number, 

 until we reach the period 64. Our octonary radix is, therefore, beyond all 

 comparison the "best 2^ossible one" for an arithmetical system. 



After this somewhat tedious preparatory exposition, we now propose to 

 briefly develop the scale of numeration thus selected ; and to derive from 

 it an ideal sj'stem of measures, based throughout upon the leading ideas of 

 the French system ; availing ourselves, as we believe, of every beauty and 

 refinement offered by it, and avoiding every difficulty and defect inherent 

 in it. Let us attempt to employ our proposed scale of number in the first 

 place, by putting it in an intelligible form. Although we might readily 

 discriminate between the octonary and the denary notation by the simple 

 expedient of using a somewhat different tyj:)e, of our common figures 

 (suppressing the 8 and the 9), j'et even with this device, the association 

 of local value is so strong that it would not be easy to avoid confusion 

 of idea in attempting to read and understand the unfamiliar conversion. 

 It will be found much easier, therefore, to devise a set of characters for 

 the octonary scale ; which should be entirely distinct both from the letters 

 of the alphabet, and from our ordinary figures. To assist us still more in 

 reading them, these characters might be made significant symbols, by the 

 number of lines employed in the construction of each, though this would 

 be a matter of very little importance in a form of character that should be 

 permanently adopted. The characters should all be simple ; they should 

 all have the same size, for the obvious convenience of typographic 

 "dress;" and they should be so distinctive, that no one could easily be 

 mistaken for anotlier. Let us then represent one by L; tico by C; tliree by 

 6; four bj'' P; five by P; six by B; and seveti hy B; the cipher having no 

 intrinsic value, may very well continue to be still represented by Q- Onr 

 eight dirjits, then (if we must still use so barbarian and unmathematical 

 a designation),* would stand thus : 0LC6FPGB. 



In reading these octonary numbers, a distinctive name for each, as 



* It has been sometimes remarked by advocates of the octonary arithmetic, that if our 

 stupid ancestors had only used their thumbs as the counters of the digits, they would 

 have found that they had but eight fingers, and we should then have had the octaval 

 period—" founded in nature." It may be supposed from the preceding discussion of this 

 subject, that we attach but little importance to such a consideration. 



