24 A SHORT HISTORY OF SCIENCE 



foot/ Next follows 16, 'one to the other foot/ and so on to 20, 

 twin itoto, 'one Indian;' 21, itacono itoto jamgnar bona tevinitpe, 

 ' one to the hands of the other Indian ' ; 40, acciache itoto, ' two In- 

 dians/ and so on for 60, 80, 100, ' three, four, five Indians/ and be- 

 yond if needful. South America is remarkably rich in such evidence 

 of an early condition of finger-counting recorded in spoken language. 



The Zulu counting on his fingers begins in general with the little 

 finger of his left hand. When he comes to 5, this he may call edesanta 

 ' finish hand ; ' then he goes on to the thumb of the right hand, and 

 so the word tatisitupa 'taking the thumb' becomes a numeral for 6. 

 Then the verb komba 'to point,' indicating the forefinger, or 

 ' pointer/ makes the next numeral, 7. Thus, answering the question 

 ' How much did your master give you ? ' a Zulu would say ' U kom- 

 btte' 'He pointed with his forefinger' i.e. 'He gave me seven/ 

 and this curious way of using the numeral verb is shown in such an ex- 

 ample as 'amahashi akombile' 'the horses have pointed' i.e. 'there 

 were seven of them/ In like manner, kijangalobili 'keep back 

 two fingers/ i.e. 8, and kijangalolunje 'keep back one finger' i.e. 9, 

 lead on to kumi, 10 ; at the completion of each ten the two hands with 

 open fingers are clapped together. 



The most instructive evidence I have found bearing on the forma- 

 tion of numerals, other than digit-numerals, among the lower races, 

 appears in the use on both sides of the globe of what may be called 

 numeral-names for children. In Australia a well-marked case occurs. 

 With all the poverty of the aboriginal languages in numerals, 3 being 

 commonly used as meaning ' several or many/ the natives in the Ade- 

 laide district have for a particular purpose gone far beyond this narrow 

 limit, and possess what is to all intents a special numeral system, extend- 

 ing perhaps to 9. They give fixed names to their children in order 

 of age, which are set down as follows by Mr. Eyre: 1, Kertameru; 

 2, Warritya; 3, Kudnutya; 4, Monaitya; 5, Milaitya; 6, Marru- 

 tya; 7, Wangutya; 8, Ngarlaitya; 9, Pouarna. These are the male 

 names, from which the female differ in termination. They are given 

 at birth, more distinctive appellations being soon afterwards chosen. 



The mathematical advantage of 12 as a base conveniently 

 divisible has often been pointed out, but the choice unfortunately 

 had to be made long before its real significance could possibly 

 be apprehended, and the difficulty of subsequent change would be 



