256 The N.Z. Journal of Science and Technology. [Jan. 
amount of confusion existed or might easily be caused. We have seen 
this in the case of the Paumotu Group, where both the decimal and vigesimal 
systems seem to have been employed, and where counting in fours were 
also practised. Again, we know that both the single and binary modes 
were employed hi New Zealand and elsewhere, while other discrepancies 
and irregularities have been noted in the foregoing pages. The different 
terms for ten in Samoan provide another illustration of lack of precision. 
The counting in fours alluded to above seems to have been used among 
the Tuhoe Tribe of Maori when tallying such small birds as the tui and 
parakeet. We encounter singular oddities in numeration throughout the 
Polynesian area. Thus, in counting eels, the Maori folk of the Waikato 
district proceeded as follows — 
44 eels —- one kaui or tui (string). 
5 kaui = 220 eels — kotahi rau (one hundred). 
10 kaui = 440 eels = kotahi mano (one thousand). 
Karaka Tarawhiti, of Huntly, states that in counting by the binary 
method the procedure was as follows :— 
Ka tahi pu — one brace 2 
Ka rua pu — two brace .. 4 
Ka torn pu three brace .. 6 
&c. 
Ka iwa pu = nine brace . . 18 
Ka tekau = the whole, or tally . . 20 
whereas some communities employed the expression ngahuru pu — ten 
brace = twenty. 
As to the value of the prefixes in the word under discussion, but little 
can be said. The nga of ngahuru is the definite article plural in Maori, but 
may not bear that meaning in that position ; moreover, we have the 
longer form hanga in some cases. The se of the Samoan sejulu also repre¬ 
sents the indefinite article in that dialect, but in many cases we have little 
or no data on which to base an examination of the various forms of prefixes 
noted above. Good work might yet be done in the Pacific isles in the way 
of collecting material for vocabularies and other matter pertaining to native 
customs and beliefs, especially in the isles of Melanesia. 
In his Primitive Culture, Professor Taylor has much to say concerning 
what he terms “ hand numerals ” or “ digit numerals.” He also speaks 
of, and illustrates, the “philological mystification” caused by different 
systems of numeration in Polynesia. Again, he remarks, “ The numerical 
systems of the world, by the actual schemes of their arrangement, extend 
and confirm the opinion that counting on fingers and toes was man’s original 
method of reckoning, taken up and represented in language. To count the 
fingers of one hand up to five, and then to go on with a second five, is a 
notation by fives, or, as it is called, a quinary notation. To count by the use 
of both hands to ten, and thence to reckon by tens, is a decimal notation. 
To go on by hands and feet to twenty, and thence to reckon by twenties, 
is a vigesimal notation. . . . Pure vigesimal is not usual, for the 
obvious reason that a set of independent numerals to twenty would be 
inconvenient, but it takes on from quinary, as in Aztec ... or from 
decimal, as in Basque [and Maori] . . . the childish and savage prac¬ 
tice of counting on fingers and toes lies at the foundation of our arithmetical 
science.” 
