594 PRIMITIVE NUMBER SYSTEMS. 



The very word '• score," and one or two happily i:>reserved expres- 

 sions, as "three score and ten," show that an unconscious flavor of the 

 vigesimal scale was to be found in the England of a few centuries ago. 

 The Danish and other Tentonic languages contain words and expres- 

 sions which indicate that the same was true of other north European 

 countries. Bnt here the reckoning by 20's seems always to have been 

 restricted to material objects rather than applied to pure number; so 

 that the Teutonic number systems can not be said ever to have been 

 vigesimal systems. Ancient Palmyra possessed a number system of 

 great extent which was almost purely vigesimal. But scanty traces of 

 it remain however. 



We have last of all to consider the decimal scale. However great 

 the number of examples that may be given of races that have used 

 or now use the quinary or the vigesimal scale, the fact remains that 

 by far the greatest number of uncivilized people perform their reckon- 

 ing by tens; and that, with five or six exceptions, all civilized peoples 

 have done the same. The decimal scale is universal in Europe; in 

 Africa it is almost universal ; in Polynesia the same is true; in Asia 

 all civilized peoples and the great majority of the uncivilized tribes 

 count with this base; in Korth America it is used by the greater num- 

 ber of the Indian tribes; and in South America it is sometimes found, 

 though the prevailing base is quinary or quinary-vigesimal. The sim- 

 ple and undoubtedly the correct explanation of the origin of this sys- 

 tem is the laying aside of the counter, or the scoring of one mark on 

 the completion of each tale of 10 on the lingers. This develops into a 

 perfect decimal system, and needs only the device of characters for the 

 representation of number to become a written number system like the 

 Eoman; or with value of place like the Arabic system of the present 

 day. That it is jireferable to either the ({uinary or the vigesimal scale 

 is a fair inference to be deduced from the numerous instances in which 

 it has superseded the one or the other. As a number base 5 is too 

 small and 20 is too large. Probably no single-number scale would 

 serve the ueeds of mankind better than the decimal with the single ex- 

 ception of the duodecimal. P)Ut the advantages of 12 as a base never be- 

 come apparent until the arithmetic of a people has reached a degree of 

 development such that a change in the scale used would be attended 

 with difficulties so great as to render such a thing altogether impracti- 

 cable. Civilization is a[)parently wedded to the decimal system; and 

 though it may continue to barter by 12's and to perlbrm its astronomi- 

 cal computations by (JO's, it Avill always continue to use the arithmetic 

 of lO's in preference to any other. It seems probable also that the deci- 

 mal scale, already in use among all civilized nations and among the 

 native races of so large a portion of the world, will tend more and 

 more to displace the quinary and the vigesimal scales, and to become at 

 last in reality what it was in the minds of the ancients, the universal 

 number scale (,»f the world. 



