172 Transactions. 



objected to applying the topu system of counting to persons 

 because it interfered with their kaiva tajJii. Probably this 

 was on account of food-supplies being counted by the topic 

 or binary system. As almost all local authorities agree that 

 persons were counted singly, and not by the tatau topu, I feel 

 certain that the double hoko and ran methods (Jiokorua — forty, 

 &c. ; kotahi rau — 200) are not viewed by Natives as being 

 binary in their nature, but that that expression is applied only 

 to the system of counting in pairs, as given in Table No. 2 ; 

 and, moreover, that the vigesimal (or double hoko) method was 

 a system of numeration known to, and used by, the Poly- 

 nesian peoples in times long past away. Thus, the reader 

 will bear in mind that the vigesimal system, as given in Table 

 No. 3, seems to have been that in common use for enumerating 

 persons. The variant forms, as kotahi rau takitahi for 100, 

 kotahi rau ma rua and kotahi rau, hokorua takitahi te paepae, 

 for 120, &c., do not seem to have been so much used, at least 

 according to evidence now obtainable. 



In regard to Table No. 1, it seems probable from the evi- 

 dence of many Natives that the terms hokorua viakere, hoko- 

 toru makere, and so on, were also much more commonly used 

 than a perusal of that table would lead one to suppose. I 

 have given the definite terms between twenties, in order to 

 place my notes on record, and to render the table complete ; 

 but a Native would very often say hokorua viakere for any 

 number from forty-one to fifty-nine inclusive. This is equi- 

 valent to our system of counting by scores, when w^e say, 

 " Three score odd," &c. 



A singular form obtains among some of the Waikato 

 Natives, of expressing the numbers twelve to nineteen in the 

 numeration of persons, as — tekau ma tokorua, for twelve ; 

 tekaii ma tokotoru, for thirteen ; and tekau ma tokoiiva, for 

 nineteen. 



Puihi Maru-tawhao, an old man of Tuhoe, has given me 

 the following notes lately : The pu hoko (see ante) consisted, 

 in this district, of six birds. These were, presumably, con- 

 sidered equal to two pigeons or kaka. Both the single and 

 double hoko systems were formerly used here — e.g., hokorua 

 takitahi stood for twenty, and hokorua topu for forty. He 

 says that hokotahi was not here used. Fish, as well as birds, 

 were counted in pairs — i.e., the binary method was employed; 

 but baskets of kumara, &c., were counted singly. 



And here endeth such notes as we have collected anent 

 the systems of enumeration employed by the Tuhoe Tribe in 

 days of old. They are not remarkable for clearness, but re- 

 present, nevertheless, much work in collection, and close 

 questioning of many persons. 



