Best. — 31dori Numeration. 159 



It seems probable that tekaii was originally te kau, two 

 ■distinct words ; and it is the opinion of several Alaori scholars 

 that kau represents an original Polynesian word meaning 

 " collection, assemblage." (See Tregear's Dictionary.) 



The late Mr. ^.. S. Atkinson mentions, in a pamphlet pub- 

 lished by him in 1893, that both Archdeacon Maunsell and 

 Bishop Williams — two excellent Maori scholars — agreed in 

 saying that among some tribes ngahuni meant ten, and tekau 

 ■eleven : Bishop Williams saying that they counted by elevens, 

 the eleventh being a tally; and he compares our "baker's 

 dozen." Thompson, in his paper on " Barata Numerals,"^' 

 gives tekau for eleven, but does not quote any authority, 

 except as to spelling. At page 137 he gives the Maori 

 numerals one to ten, where he spells tahi (one) " tahai," toru 

 appears as " torou," ivha as " t'fa," ono as "one," ngahuru as 

 " anga hourou." After that, small wonder that he made 

 "eleven" cf tekau: we should be thankful that he made it 

 •nothing worse. 



At page 61, vol. i, of the "Transactions of the New 

 .Zealand Institute " Mr. Phillips gives tekau ma ngahuru as 

 meaning twenty, which is obviously an error, that term mean- 

 ing thirty in Maori. 



I have not been able to obtain locally any confirmation of 

 the above remark concerning tekau as having been used for 

 ■eleven, or of any system of counting by elevens ; but it is 

 possible that some tribes did so use the term. Many customs 

 •differed to soaie extent among various tribes. 



The Vigesimal System of Enumeration (Table No. 1). 



It appears to me that at some period of their history 

 the Maori must have used a vigesimal numerical method — 

 a system of counting by scores, or twenties. I shall include 

 in this paper a table showing the method so far as I have 

 been able to ascertain it from my local Native friends. It 

 will be observed that there was a special term (tekau) for 

 twenty, but none for thirty ; a special term (hokorua) for 

 •forty, but none for fifty ; a special term [hokotoru) for sixty, 

 but none for seventy ; and so on. Thirty was twenty and 

 ten ; thirty-one was twenty, ten, and one ; and so on to 

 thirty-nine. Forty was again a special term, then forty and 

 ■one, then forty and two, and so on to forty-nine. Fifty was 

 forty and ten ; fifty-one was forty and ten and one, &c. 

 (See Table No. 1.) 



In the " Journal of the Polynesian Society," vol. x, p. 101, 

 Professor Cyrus Thomas gives a short paper on the vigesimal 

 ^system of enumeration. In it he observes that traces of a 



* Trans. N.Z. Inst., vol. v, p. 131. 



