Taylor.] ^^8 [Oct. 21, 



with great precision into halves, quaiters, and eighths, while we should 

 have to make repeated trials to divide the same into thirds or fifths, and 

 then attain the result only tentatively and approximately. And lastly, 

 it appears to be the most natural of scales, from the very common use 

 of the two hands in separating objects into pairs.* 



Such being the claims, then, of the binary scale of geometrical progres- 

 sion, and such its obvious advantages over all others, it is not surprising 

 that this should be found to be practically the prevalent mode of distribu- 

 ting the more common weights and measures throughout the world, what- 

 ever may be the multiples or divisions enacted by law. 



The .Roman weights in general use throughout the empire (that is, 

 throughout the civilized world) for some centuries after the Christian era, 

 were by means of intermediate subdivisions (introduced by the common 

 consent of traders) practically distributed upon a binary scale. So with 

 the divisions in universal use at the present day ; we find that a nest of 

 avoirdupois weights comprises ^ oz., ^ oz., 1 oz., 2 oz., 4 oz., 8 oz. and 

 16 oz., or 1 pound, and sometimes a 2-pound weight and a 4-pound weight ; 

 and by this scale of binal progression or division, almost everything is 

 purchased at retail. Our yardsticks are found to be divided not into the 

 legal feet and inches, but into halves, quarters, eighths and sixteenths. 

 Precisely so with the inch, which is never divided into its primitive 

 "three barleycorns," but almost always, like the yard, by the binal scale 

 into eighths and sixteenths, though occasionally divided for particular 

 purposes into twelfths, or into tenths. The operation of this great law is 

 quite as strikingly exhibited in France, where the popular necessities have 

 compelled the introduction of binal divisions, not recognized by the estab- 

 lished decimal scales, nor, indeed, strictly compatible therewith. 



Mr. Peacock, in his admirable treatise on "Arithmetic," in the Encyclo- 

 pedia MetropolUana, thus sums up his review of the French system : 

 " The decimal subdivision of these measures possessed many advantages 

 on the score of uniformity, and was calculated to simplify, in a very 

 extraordinary degree, the arithmetic of concrete quantities. It was 

 attended, however, by the sacrifice of all the practical advantages which 

 attend subdivisions by a scale admitting of more than one bisection, which 

 was the case with those previously in use ; and it may well be doubted 

 whether the loss in this respect teas not more than a compensation for every 

 other gain." This deliberate judgment is from the author of perhaps the 



* " The classification by pairs which nature points out would suggest the simplest mode 

 of reckoning. Counting these pairs again by two, and repeating the procedure, we arrive 

 by progressive steps at the radical terms, 4, 8, 16, etc." {Edinburgh Revinv for May, 1811, 

 Vol. xviii, p. 185). 



The celebrated Leibnitz, so eminent as a mathematician as well as a philosopher, 

 struck with the simplicity and peculiar capabilities of this scale, proposed and strongly 

 urged the introduction of Binary Arithmetic. He showed that the Binary system, in 

 addition to its extreme facility, possessed peculiar value in discovering the properties of 

 numbers, and in constructing tables, etc. He did not, however, recommend it for gene- 

 ral use, from the increased number of figures required to express ordinary amounts. 



