1887.] ^-^^ [Taylor. 



the hundred, prevailed ; and from these nations it was derived by the 

 Celtic languages, in all of which its remains are still found. Among the 

 Scandinavians, also, is found a vicenary numeration. The Greenlanders, 

 having counted fingers and toes in periods of five, designated the num- 

 ber 20 by the word innuk, which signifies a " man." If they have occa- 

 sion to proceed higher, the expression for 4Q is innuk arlak — "two men" — 

 etc. A similar method existed among the Aztecs of ancient Mexico ; as 

 well as among the tribes of South America. The Teutonic races retain 

 in their languages the traces of the ancient "score," and in parts of 

 England, counting by scores, or twenties, is still quite usual. The trans- 

 lators of our Bible have frequently (though by no means uniformly) in- 

 troduced this mode of enumeration. Thus we have "three-score and 

 ten" (Ps. xc, 10) — "three-score and twelve'' (Numb, xxxi, 38) — "three- 

 score and fifteen" (Acts vii, 14) — "three-score and seventeen" (Judges 

 viii, 14), etc., etc. The mode of numbering still in common use in 

 Fiance also exhibits a very remarkable retention of the antiquated vice- 

 nary system.* 



This scale is not, as might be supposed, an extension of, and attempted 

 improvement upon, the decimal system. On the contrary, it almost uni- 

 versally preceded it ; and its employment belongs to the very earliest and 

 rudest stage of barbarian society. It betrays a period of human intelli- 

 gence, so destitute of all resource, that fingers and toes must all be pressed 

 into service, to meet the common wants of number ; and when these have 

 been exhausted, there has been found among some tribes, no power of 

 thought or word or symbol for aught beyond. It indicates a period long 

 before a conception of any expedient for numerical expressions had 

 dawned upon the savage brain ; and hence there is no example of the 

 vicenary scale having ever been extended even as far as to the second 

 place of figures, or to 20 times 20 ; nor probably even beyond one hun- 

 dred. It is evident that when the necessity for expressing larger num- 

 bers began to be felt, the cumbrous scale of added "toes." must soon be 

 dropped, and the range restricted to the more manageable mechanism of 

 the ten "fingers." And, accordingly, we find the imperfect vicenary to 

 be always overlaid by the denary, with glimpses of the former still appear- 

 ing through its supplanter. 



The Sexagenary scale deserves notice only from its historical interest in 

 having been from a very remote antiquity employed for particular pur- 

 poses among the people from whom we derive our arithmetical notation — 



* " The French nomcDclature is for the most part purely decimal. The decuual sys- 

 tem is observed from twenty {vingt) to sixty (aoixante); here we find a vestige of an old 

 vicenary scale. Seventy, instead of being neptunle, as the decimal system would require, 

 is soixante-dix (sixty-ten); seventy one, soixatitc-onze, (sixty-eleven); seventy-two, sou:ante- 

 doitze (sixty -twelve), etc. Eighty, instead of being octon^e, is quatrc-vingl, or four twen- 

 ties, and ninety is quatre-vingl-dix (four twenties ten); ninety-one, quatn-vingt-onze (four 

 twenties eleven), etc. Thus twenty becomes the. radix of the system from sixty to a 

 hundred." {Lardner's ArUhmellc, page 11.) 



