DETERMINATION OF THE PLACE OF RAPANUI. 155 



four times the Proto-Samoan and the Tongafiti. Conditioned by the 

 fact that between the several members of the Polynesian family there 

 existed no marked diversity of culture attainment, we feel justified in 

 the assumption that the more numerous and more generally extended 

 element of the speech is certainly the senior. Thus again we are brought 

 to the same conclusion which on another basis we have reached in 

 respect of this provincial element. In general in our studies of the 

 South Sea, senior and elder have been found to belong to the Proto- 

 Samoan migration, a fact authentically established as to Nuclear Poly- 

 nesia and reasonably extensible to Southeast Polynesia. Accordingly 

 I have no hesitation in assigning to the province three settlement 

 factors: (i) a Proto-Samoan discovery and first settlement; (2) a col- 

 ony mixed in some possibly intermediate halting-place but with strong 

 Proto-Samoan affiliations; (3) a Tongafiti colony. I shall be the first 

 to acknowledge the degree to which the hypothetical enters into this, 

 but qua hypothesis it is surely a working one. 



We are by no means done with this record. If we compare Table 32 

 with the first of this series of summation tables (Table 28) we see how 

 much is revealed by dissection down to particular features. Yet one 

 more detailed dissection lies within our reach : in Table 30, which is a 

 summation of the extra-Rapanui element, inspection will show that 

 there is a wide variety in the language extent of the several charted 

 items; for instance, in the general Polynesian column 40 items are 

 common to all four languages of the province, 114 to three languages, 

 and so along. This introduces to us an element of quality, whereas 

 heretofore our examinations have been numerical, quantitative. It 

 has seemed to me that it is possible to show forth, still in figures, this 

 qualitative character. For this purpose I have selected a modulus 

 based on the figure representing the number of occurrences of the words. 

 Thus: a word which is found in Tahiti and Proto-Samoan I regard as 

 having 1 for a modulus; if in Tahiti, Mangareva, and Proto-Samoan as 

 having 11 for its modulus, and so on ; where 1 is the modulus the arith- 

 metical percentage based on net stock stands as the index, where 11 is 

 the modulus the percentage is multiplied by two, and so on. In the 

 rigidly provincial element we lose the prime element of the computa- 

 tion. This cuts out all such cases of modulus 1. But in the higher 

 moduli I preserve the modulus parallel with the foregoing; thus a word 

 which appears in all four languages is assigned to modulus iv, just as 

 would be the case if we had an exterior identification. Based upon 

 this arbitrary modulus system and upon real percentages the resultant 

 figure becomes artificial, but it should serve to give us a common system 

 of index figures wherewith we may continue our examination into 

 quality. We shall establish these figures for the whole province (using 

 the sum of the net stocks, 19,000) in order to secure a basis from which 

 to note individual deviation. 



