Best. — Maori Numeration. 171 



Although the toi^u or binary system of counting, as given 

 in Table No. 2, was not appHed to persons, yet the double 

 hoko and rau methods were. Tlius hokorua was usually em- 

 ployed to denote forty persons, hokotoru for sixty, and on to 

 hokoiica for 180. The- single hoko system appears to have 

 been sometimes employed when stating an excess over a 

 round number (see Table No. 3 for examples). The single 

 rau, or hundred, seems to have been seldom applied to per- 

 sons, 100 being expressed by hokorima. But 200 was kotahi 

 rail topti — i.e., one hundred doubled, or one hundred pairs. 

 The word tojnc was not actually used, as a rule, but was left 

 to be inferred. Thus 140 was termed a hokoichitu ; 310 was a 

 rau hokoicliitu. 



I have given many terms in Table No. 3, so that the reader 

 may know the exact terms for precise numbers ; but it must 

 be here explained that the Maori usually gave round numbers 

 for persons, and seldom expressed exact numbers between 

 twenties. He would use the term hokorua makere for any 

 number between forty and sixty, and would not specify the 

 excess unless under peculiar conditions — e.g., in answer to a 

 question. In like manner the expression kotahi rau tuvia 

 might be used for any number between 200 and 300, unless 

 he employed the takitahi method, in which case it might 

 stand for any number between 100 and 200. The table shows 

 the forms employed to express the excess numbers, when 

 required. The number 101 might also be expressed by hoko- 

 rima, kotahi te t2t7na ; 102 by hokoritna, tokorua te tuina ; and 

 so on to 119 — hokorima ngahuni ma tahi te tuma (or 2:)«e^jae) ; 

 122 might be given as hokoono, tokorua te tuma, and so on ; 

 130 as hokoono, he ti ugahuru te tuma ; 131, hokoono, ngahuru 

 ma tahi te tuma, and so on. The different terms used to 

 denote a given number are perplexing in the extreme. Pos- 

 sibly different methods, or different expressions, were formerly 

 used among different tribes, and the modern Maori has con- 

 fused them. 



If the single hoko and rau terms are used, then the system 

 of numeration may be termed decimal ; but if the double 

 hoko method be employed (as hokorua = forty, &c., and kotahi 

 rau = 200), then the system is vigesimal. 



Eegarding the numbers eleven to nineteen in Table No. 3, 

 these were given to me by Te Puia, of Tuhoe, as — eleven, 

 ti ngahuru, kotahi; twelve, ti ugaMiru, tokorua; thirteen, ti 

 ngahuru, tokotoru ; nineteen, ti ngahuru, tokoiica. He also 

 gave — fifty-one as hokorua, ngahuru takitahi, kotahi ; fifty- 

 two as hokorua, ngahuru takitahi, tokorua; fifty-three as hoko- 

 rua, ngahuru takitahi, tokotoru ; and so on to hokotoru = sixty. 



The Ngati-Awa Tribe, according to Matutaera Hatua, 



