Taylor.] ^^^ [Oct. 21, 



magnitude, but beyond all rational requirement of any real calculations 

 we can devise. There is, in the law of continued georaelrical progression, 

 even on its lowest scale, a power so overwhelming, that we feel we have 

 no extra wonder or admiration left to spare, upon these "infinites of 

 higher order," and confess to a predilection not to travel at such dizzying 

 speed. 



The world has had some centuries of experience in the denary arithme- 

 tic. We are all familiar with the laborious and tedious discipline by 

 which its practice is acquired ; and we are all conscious of the exertion of 

 thought demanded to perform a lengthy operation in figures. When we 

 consider the amount of time bestowed in training youth in this branch of 

 learning (and yet the fact that not one-half so trained are really expert in 

 calculation), we must record it as our deliberate conviction, that the denal 

 radix is too large. We believe that a lower figure would give the true de- 

 sideratum — the minimum of labor. Nay, as between the scale of ten and 

 that of six, we incline to the opinion that the latter would be found the 

 more convenient notation. Its labor, both of acquisition and of exercise, 

 would certainly be far less than half, while its figures in use would be 

 only about a third more. A priori, we might expect that a scale estab- 

 lished in rude and inexperienced times (were it not that it was really de- 

 termined by an arbitrary and extraneous circumstance) would be too large 

 in its ratio of progression — rather than too small ; and that a more en- 

 lightened age would find it convenient to reduce it ; just as we have seen 

 to occur with the vicenary and the denary scales, in their early history. 



The second essential that should be demanded in a radix is that it must 

 admit of indefinite bisection, or, in other words, that it must be found 

 among the powers of two ; namely, 4, 8, or 16. As 4 is probably too 

 small, and 16 certainly too large, we have the octonary scale alone left to 

 satisfy our most vital two conditions of a medium size, and a complete divisi- 

 bility. The concurrence of these qualities in any one scale, and in that 

 one alone, is sufficient to establish its claims against all competitors. 

 There is but one scale which could have any pretensions to be consid- 

 ered a rival, or which would be likely to find intelligent advocates ; and 

 that is the duodenary. Much stress has been laid upon the number of 

 its aliquot parts. That this quality is a higlily useful one, we frankly 

 acknowledge, but yet, as we maintain, not nearly so useful as that other 

 quality this radix lacks, the facility of successful halving. The number 

 12 is not a power ; the number 8 is a cube ; an important advantage in 

 several respects, but particularly in the application of this scale to a 

 system of metrology, from the simple relations thereby established be- 

 tween the measures of length and those of volume — by which both 

 weights and measures of capacity are determined. All that has been said 

 on the subject of the denary being too large a scale, applies with much 

 greater force against the duodenary. And, finally, we believe that a large 

 majority of the mathematicians would give their vote unhesitatingly in 

 favor of the octonary arithmetic. It appears to combine advantages of 



