POLYNESIAN AND MALAYAN. 151 
These forms in Melanesia and Indonesia are so obscure that it will 
require more abundant data before they may be studied with a sense of 
security. I should not be surprised if it were necessary to segregate 
several stems here interlaced. Our present task is to extricate from 
this material whatever evidence may establish the filiation of the Subanu 
pa and the Polynesian word for foot or leg. The Niué v@ may be con- 
sidered as a direct mutant of vae through Tongan vee with crasis, an 
interpretation supported by direct but scanty evidence in that speech. 
On the other hand we encounter a we in Melanesia and again in Indo- 
nesia; therefore this may be regarded as an ancient stem. The Viti 
yava may not be regarded as a derivative from vae; in The Polynesian 
Wanderings at page 319, I have given exhaustive study to the y-initial 
of Viti; the presence of an alternative avae in Tahiti points to the 
existence of an early ava which has become yava in Viti and in the 
eastern island has become colored by the greater prevalence of vae; for 
a primal ava we have Melanesian affiliates in ape and afe. Inthe same 
area we pass readily to baz, which may be comprehended as the primal 
va colored by the neighboring frequency of ae. Having abundant 
reason to regard Viti in Polynesia and Subanu-Visayan in Indonesia as 
preserving archetypal forms of speech, we need have no hesitation in 
establishing a primal va, with which pa readily affiliates. 
98. pasa to speak; Visayan basa to read aloud. P. W. tg1. 
pasa Nukuoro. vasa Sesake. 
paha Mangareva. bosa Negela. 
visau Fotuna. baha Tavara, Awalama. 
vosa_ Viti. — 
ae basa Malay, Tagalog, Visayan. 
At intervals I have deemed it better to interrupt the foregoing 
alphabetic series in order that I might discuss in conjunction a group of 
ten similar vocables. In all that has gone before I have been by no 
means chary of directing our attention upon the psychological factors 
which function these linguistic problems. ‘This group of ten vocables, 
lying in the Polynesian content of Melanesia as well as of Indonesia, must 
in the highest degree involve the psychology of the arithmetic of the 
savage, the mathematics of fingers and toes of the bare man. ‘The 
physical association of the mathematics and the mathematician is a 
matter of observation and record: 
In counting any objects that can not be held in the hand or placed in a 
row the Kayan (and most of the other peoples) bends down one finger for each 
object told off or enumerated, beginning with the little finger of the right hand, 
passing at six to that of the left hand, and then to the big toe of the right foot, 
and lastly to that of the left foot. (Hose and McDougall, The Pagan Tribes 
of Borneo, vol. 2, page 210.) 
There we have the basis of all such arithmetic as we are to study 
in this work, fingers, one hand, two hands, the whole man—quinary, 
decimal, and vigesimal numeration. ‘Through a black mass of igno- 
