592 primitivp: number systems. 



Eifiks, and two tribes visited by Stanley; the Ki yaiis and tlie Ki- 

 Nyassas.* These and a nnmber of otliers nse practically a pure quinary 

 scale. The Dinkas, the Fulbes, the Pi<;inies,t and otliers use a mixed 

 quinary and decimal scale, while the ISTupes and one or two other tribes 

 employ a quinary vigesimal system. Among the Australasians and 

 Polynesian islands abundant traces are found of quinary number sys- 

 tems, but they are in almost all cases nothing more than traces. 

 Throughout that i)art of the world the <iuinary system has been suy)er- 

 seded by the decimal. This has been widely spread through the islands 

 of the Pacific and Indian Oceans by the Malays, who in turn obtained 

 it from the Hindus. But the home i^ar excellence of the quinary, or 

 rather of the quinary vigesimal scale, is America. It is practically 

 universal among the Eskimo tribes of the Arctic regions. It jtrevailed 

 among a considerable portion of the North American Indian tribes, and 

 Avas almost universal with the native races of Central and South Amer 

 ica. So numerous are the examples which might be given, that mention 

 will be made rather of the exceptions, that is, of those using the decimal 

 base. It is interesting to note also that a considerable number of lan- 

 guages show that the quinary system was once in use among pet)ples 

 which, with the development of civilization, discarded that system for 

 the decimal. The Greeks of Homer's time used a system in which 

 traces of the quinary base are observable. The common lloman nota- 

 tion shows clearly that the ancient Komans made at least a limited use 

 of the same base, as did also the Persians. 



The exclusive use of 5 as a number base is never tbund in any sys- 

 tem of any considerable extent. Whenever the ([uinary system is ex 

 tended beyond the narrowest limits it invariably runs into either tlie 

 decimal or the vigesimal. Touching- this point Ilankel says It that no 

 race, even though it began its number system on the quinary base, ever 

 expressed 10 by 5-2 or 2-5, but always by a simple word ; and hence that 

 the system passes immediately into the decimal. This statement is 

 only partially correct. The quinary in many instances runs into the 

 vigesimal, no trace whatever of a decimal base appearing. Further 

 more, even though 10 is never expressed by 5-2 or 2-5, it is often ex 

 pressed by "two hands" or "both hands." Mungo Park observed tliis 

 among the Yolofs and Foulkas of Africa; Humboldt and others among 

 the Omaguas, the Zarmiscas, the Tainanacs, the Tonpmambos, and 

 many more of the South American tribes; and Russian explorers 

 found the same method common among the native Siberian races. 

 Hence the statement as the (lerman historian makes it needs imjior 

 tant qualification. 



Vigesimal-number systems are less common than quinary, but as 

 the two are so persistently interwoven together it is difficult to sepa- 

 rate them from each other, llie use of a base as large as 20 must 

 necessarily be cumbersome, and it can constitute no ground for sur 



* Stanley, Through the Dark Continent, ii, p. 486. 



t Op. eit. II, p. 492. tt Gescliithte der Mathematik, p. 20. 



