Best. — Maori Numeration. 155 



Mohi Turei, of the Ngati-Porou Tribe, that hokorua signified 

 forty, and hokotoru = sixty, but that eighty was hokorua topic. 

 This last ^erm is very singular. Judging from the value of 

 iioko before I'lia and torn, then eighty should be hokowha, as 

 used by the Tuhoe people. It was surely a very strange 

 break, or change, in this system of numeration to jump 

 from hokotoru for sixty to hokorua topu for eighty. I can- 

 not help thinking that this is an error. If, however, it was 

 really the case that hokorua topu — eighty, then it is a 

 proof that hoko really multiplied by twenty the subjoined 

 numeral. Only one local authority has informed me that 

 the hoko system was used in both ways, singly and doubly : 

 as hokorua takitahi — twenty, and hokorua topu = forty, and 

 so on. This would mean that Williams's Dictionary is 

 correct that hoko multiplies by ten, and that hokorua topu 

 simply means ten times two doubled, and not twenty times 

 two. Anyhow, Vaux's statement was correct when he said 

 that hoko was used for multiples often." 



An examination of the Native methods of enumeration 

 given in this sketch will show that several systems were 

 employed — viz., counting singly, and the binary system of 

 counting in pairs. There were also some differences in 

 counting persons, and different words for various by-terms- 

 pertaining to enumeration : for example, the words kehe, 

 taukehe, and tautahi all denoted an odd number. The terms 

 paepae and tmna both mean an odd number in excess, as 

 an incomplete ten or hundred. Tuhoe use the former word, 

 and in this manner : kotahi ran, hokorua te paepae (one 

 hundred, forty the excess) for 140. Tauhara and tauiohara 

 are also terms for an odd number. By "an odd number" 

 I do not necessarily mean the odd numbers three, five, 

 seven, &c. ; the terms are also used to denote (as in preserv- 

 ing birds) an incomplete ten. If eighty-three, or eighty-five, 

 or eighty-six birds were put into a calabash, that vessel 

 would be said to contain Jiokoioha (eighty), ka whakarerea nga- 

 tauivhara (the odd ones are omitted). 



The verb " to count " in Maori is tatau. Counting singly, 

 as we do, would be described as tatau takitahi, and the dual 

 method as tatau topu. Pu and toj^u bear much the same 

 meaning — a pair, couple, brace. Takitahi, as we have seen, 

 means — by ones, singly, once told. 



It is possible that the last migration of Polynesians to 

 New Zealand brought with them a somewhat difterent sys- 

 tem of numeration to that in use among the original peoples, 

 the descendants of Toi and the old-time tribes of these isles. 

 They were certainly more advanced than the latter in some 



* Trans. N.Z. Inst., vol. viii, p. 38. 



