PRIMITIVE NUMBER SYSTEM^^. 589 



iiu'iit lo ])r(»v(' tliat the most coiiNtMiienl base is tliat wliicl! will a<liiiit 

 ot (li\isi()ii without a I'cniaiiKh'r by tlic miiiiljci's L*, .'), and I. Ten ctui 

 be (lixided by but one ol" these uuuibcrs without remain(h'r: liciicc (he 

 eoufusion of fi-actions is at once iutioduecd. Twehe, on the otlier 

 hand, is an exaet uuilti])h'of each of the three numbers. It olfers, tlieu, 

 to the mass of mankind an enormous advaiitajic over 10 or any other 

 small number as a base for eom])utation. With the growth of business 

 in its many forms, the civilized world has lon<>' since come to recognize 

 this faet, and in many ways to nuike practical nse of it. The word 

 ''dozen/' and its equivalent in other languages, has been coined as a 

 noun to express the number 11*, and in a very great number of tlie 

 eommercial transactions of the world the dozen and its s(piar(', the 

 gross, are the common units of measui'e. So pali)able are the advan- 

 tages of 12 from this ])oint of view that some writers have gone so tar 

 as to advocate the entir<' abolition of the decimal system and the sub- 

 stitution of a duodecimal system in its place. ( -harles Xlf, of Sweden, 

 may be mentioned as an espeeially zealous advocate of this change, 

 which lu' is said to have had in actual contem])lation for his own 

 dominions at the time of his death. The adoi)tion of the duodecinuil 

 notation would involve the introduction of two new symbols, for 10 and 

 11, respectively. Twelve would then be represented by 10, thirteen by 

 11, fourteen by 1-5, twenty-four l»y 20, one hundred ami forty-four by 

 100, etc. No such change can ever meet with general favor, so lirndy 

 has the deciuial scale become intrenched; but it is more than ])r()bable 

 that the Avorld of trade and commerce will continue to use the dozen, 

 its fractions and its multii)les in many of its transactions in the future, 

 as it has for centuries in the past. It was thus used l>y the Jlomans, 

 and it has been and is used among all TcMitoiiic nations at the picsent 

 day. It is more than probable that the English divisions of weights, 

 measures, and money were intluence<l by the ease with which mental 

 com])iitation is effected when fractional i)arts of 12 are involve<l. The 

 duodecimal is not a natural seale in the same sense as are the decimal, 

 the (piinary and the vigesimal; but it is a system which is brought 

 into use at a later day and at a higher stage of development, solely 

 through its convenience when ai)plied to the everyday transactions of 

 business life. IIund)oldt, in discussing the nund)er s\stems of the 

 various peoi)les he had ^■isited in his travels, remarked Ihat no people 

 had ever used exclusi\el\' that best of bases, 12. A possible exception 

 to this has siiu^e Humboldt's time been noted by IJobert Flegid, in the 

 Aphosof Eenui', who count by simple woids to 12, an<l then ])r()ceed 

 with 12 and 1. 12 and 2, 12 and .'>, etc.* 



Kemarkable as it may at tirst glance seem, the uuml)er 2 has in a 

 few seattei'cd instanc(>s been mad<^ to do duty as the base of number 

 system. Thirion saysi it was thus eniploy(Hl by l\gv|»tian surveyors; 



" .Scliuljt'i't, H., Ill Xeiiin!iy<T's .IiiIiUkikj zn U'ls.fni'iclionHclnii IIcoIkicIiIkiii/ <iiif 

 Iteiseii, ]). 290. 



1 Histoirc de raiithiiu't i(|uc, p. 5. 



