It is evident that the forms of the Serian digit “seven” are variants from a common source, and it is equally apparent that the numeral “two” is the basis for the term. The several examples of this numeral are ghá`kum, kahom, kaχ´kum, kookχ´, in which the final -um, or -om appears to be a suffix; in the term for “twenty” Professor MeGee writes ŭntçkō´k; in which the final kō´k is the term denoting “two”, and in which the final -um or -om is wanting, which probably indicates that it is a flexion. Now, it is seen that this numeral “seven” terminates in the syllable -wūū, -ue, and -ui, in direct contrast with, the termination of the digit “two”. The material at hand is too limited to determine whether this final syllable should be -wūū, -ue, -ui, or -kwūū, -kue, -kui. It apparently signifies “added, over, plus”, or some equivalent term. To attain economy of utterance the term denoting “five” was omitted from the original statement, “two added to five”, as the expression of the number seven, and so “two added” became the name of the number “seven”. An initial tom, tum, tŭn, or diŭn occurs in the names for 7, 17, 70, and 700. An evident derivative from the name for “hand”, it denotes “five”. It is a cognate of ŭnt in ksókhŭnt “nine”, literally “four-five”, and also with tanchl in Mr Bartlett’s numbers 12-19; the correct form for “seven”, it would seem, should have been tan`l kaχkue, etc., “five-two-added-on”; its initial t is identical with thet in t-aul (t-anl?), “ten”. The difference in the endings of this prefix—the difference between an m and an n—may easily be explained. In the several vocabularies it is seen that one collector fancied he heard an m sound, while another, equally careful, heard an n sound. The fact appears to be that it is an obscure nasal sound, which may readily be taken either for an m sound or an n sound by the heteroglot. In Bartlett’s list of numerals tan-tasó-que signifies “eleven”, wherein tasó- is the numeral “one”, as given by both M Pinart and Sr Tenochio, tan- the prefix under discussion, and -que the suffix mentioned above, which was regarded as signifying “added, more, plus”.

The first eight terms of the Yuman list are clearly modified forms of a single original combination, which is apparently still retained nearly unchanged in the Yavapai (18) of Corbusier, hěwakě-spé. The signification and function of the final -spé have been discussed in the remarks on the probable derivations and meanings of the Yuman names for “six”. The given conceptual element is evidently the term hěwakě-, “two”. And -spé, as has been ascertained, signifying “added, more, plus”, etc., the expression literally means “two added”, i. e., to five, which is here understood, but unnecessary, since “two added” has acquired the meaning “seven”, originally expressed by the entire proposition. The Kiliwee (23) term ẖooak-eleepai, “seven”, has literally the same meaning as the terms last under discussion. It will be seen that the conceptual element is the term ẖooak;, “two”, which is only another form of hěwakě, treated above. Now, it is mathematically certain that if “two” be an element of the concept “seven”, it must be added to some preceding number that will produce the result sought, and this number is of course five. So it is presumptively certain that the element -eleepai must mean “added, laid onto, superadded, subjoined”. The Hummockhave (8) maik-kewik-enaich is composed of the conceptual element kewik, “two”, the prefix maik- meaning “more, over”, and the suffix -enaich (or -kenaich), which seems to be an ordinal or distributive flexion. So that “two over, added”, is here likewise the expression for the numeral “seven”. The next form, the Diegueño (14) of Dr Loew is another example of the use of the numeral “two” with different flexions, to express the number “seven”. An examination of this Diegueño list of numerals shows that in such a form as nio-khoak, “seven”, the initial nio- is a prefix signifying “added, in addition to”, etc., while the khoak is a form of the numeral “two”. The next ten forms, while apparently derivative from a common source, are difficult of explanation from the material at hand. The same may be said of the last four, three of which are evidently cognate and are very probably shortened forms of the original represented by the first group in the list. Take, for example, a form like (22) hawake-zpé, and drop the final -zpé, as is done in some of the terms in the “eight” list, and also the initial ha-, and the result is a form wake, which in the dialects (6) and (9) would become viiga, víka, which is the form of the digit “two” in these dialects. The form (7) bee-eeka is also merely the digit “two” of this dialect without any index to show that it is not “two” rather than “seven”. The same thing is to be noticed in the Serian lists, in which the form for thirteen is in all respects the same as that for the numeral “eighteen”, both apparently meaning merely “three added”.

EIGHT

Serian
A.páhkwūū
B.phraque
C.kshoχolka, p’χakχue
D.osrojoskum (osχ´oχoskum?)
Yuman
23.ẖamiak-eleepai
10.hamúge-shbe-k
22.hamuke-zpé
18.hěmukě-spé
18.hěmukě-spé
11.hmaga-spe
1.humuga-spe
2.moge-shbe
19.múkě-shpë
9.móka
7.moo-ooka
6.muugá
16.chip-hoke
12.chip-hóok
21.hipp-óka
3.sep-hoke
13.seepa-hook
4.sepp-óque
5.sep-χúk
15.sepp-ôck
17.shepa-hook
20.siip-jóc (j=χ)
25.tcěp-hōk
26.tcěp-hōk
8.maike-homok-enaich
14.nio-khamuk
24.pakai-hin-awach
I.nyakivamivapai

The Serian numeral “eight” is expressed by two different terms. The first is based on the numeral three, and the second on the digit four. The former is the remaining factor of an original expression which signified by uttered elements “three added to five (=the full hand)”, but the need for economy of expression led to the suppression of the uttered element denoting “five”, as soon as the shorter “three added” acquired the usual signification of “eight”. The basis of the digit is kō´pka or kapχ´a, “three”, with the suffix -kwūū (-kχue, -que), presumably denoting “added, plus”. This represents the usual method of forming this digit. The second term, kshoχolka, is that which is presumably based on the numeral “four”. This is the form given by M Pinart. But Sr Pimentel, citing Sr Tenochio, writes this osrojoskum, which at first sight appears to be quite different from the other; yet the r of the latter evidently stands for a modified χ and the j for a χ, and making these substitutions the term becomes osχ´oχoskum, which is approximately the form in which Professor McGee and Mr Bartlett wrote this digit in the numeral “eighty”. Now, it is self-evident that if the element “four” constitute a factor in the combination denoting “eight”, it must be added to itself by addition or multiplication, and the result will be the same in either event. The final -olka appears also as -otkŭm, -olchkom, and -oskum, in these Serian vocabularies, either in the numeral “four” or its multiples. The origin and signification of this ending are not clear; but taking into consideration the great variations in the spelling of its recorded forms, especially in so far as the consonant sound preceding the k-sound is concerned, it may not be presumptive to adopt the s-sound (though sχ´ may be more correct) as that which represents approximately at least the true sound, for it varies from l, t, lch, to s. And it has been seen that the final -um is a flexion denotive of serial or consecutive counting and so not a part of the stem. Then it is seen that -s-k- (the last two hyphens representing uncertain vowels) is the termination requiring explanation. Now, it is probable that this termination is identical in meaning and origin with the -sūk, -shoχ, -sho, -schoch, and -shroj (= -shχ´oχ) terminating the forms of the digit “six”. If this identification be correct (and there is no present reason to doubt it), it signifies “repeated, again, duplicated”, as was suspected and stated in the discussion of the forms of the numeral “six”. So granting this derivation to be correct, kshoχolka, then, signifies “four repeated”, which of course denotes “eight”.

In the Yuman list, the first eleven forms are evidently composed of the numeral “three” and a suffix signifying “added, plus, more than”, but the last three of the group want this suffix, a fact due perhaps to the fault of the collector rather than to linguistic development. The terminations -eleepai and -shbe-k and its variants have already been explained when treating of the numeral “seven”. And the twelve forms beginning with chip-hoke (16) are variants from a common original composed of the numerals “two” and “four”. It will be readily seen that chip- in such a form as chip-hoke is a contraction of a form such as tchibabk (14), “four”, chepap (24), “four”, as may be seen in the Yuman list of terms for the digit “four”. Now, the next portion of the term is -hoke, which is but a slightly disguised numeral “two”, as may be seen by reference to the schedules of the numeral “two”. Compare ẖooak (23), huáka (19), uake (2), and hěwáki (18), all signifying “two”. Now, the next term, maike-homok-enaich (8), is a combination of maike, “above, over, more than”, homok, “three”, and the ending -enaich (or -kenaich), which may be either an ordinal or a distributive flexion. The form nio-khamuk (14) is a combination of the prefix nio-, signifying “added, above, or more than”, and the conceptual term khamuk, “three”, the expression signifying “three over, or added to”. The next two examples are evidently irregular, if not spurious. The form pakaikhin-awach is composed of pakai, “seven”, khin-, “one”, and the suffix -awach, “added to”. Now, the last, the Cochimi nyaki-vamivapai, appears to be erroneous. It contains the term nyaki for ginyaki, “hand”, but the remainder of the expression is composed of elements that are not comparable to anything in the meager material at present accessible. The Serian and the Yuman terms herein show no relationship.

NINE

Serian
A.ksókhŭnt, ksókh-ŭnt
B.sohántl, soh-ántl
C.soχanthe, soχ-anthe, ksovikanlχ´
D.ksobbejoaul (j=χ)
Yuman
9a.hailyuthu
1.halathuya
11.halathúya
10.halathúig
22.halesúwi
19.halěsúyi
2.halseye
18.húlěthúyi
3.hamhinmoke
13.hoomhoomook
17.hoomhoomook
15.humhummôck
4.humhummóque
12.humhamóok
21.hŭmhummúka
20.jumjamúç (umχamúk?)
5.χemχemúk
8.muke
16.n’yimhummoke
26.nĭmhŭmmōk
23.m’sigk-tkmat
14.nitchibab, (ni(o)tchibab)
6.paaya
7.paeeya
9b.páia
I.quac̲h̲era-vampai

The first three Serian terms for “nine” are evidently forms of a common original, signifying “four added to five”. It is evident that ksō´kh- in (A) ksō´kh-ŭnt is the same element as -ksō´k in ūnçtksō´k, “forty”, and -kschō´k in ŭnz-untçkŭkschō´k, “400”. The element -ŭnt here is a name for “five”. Its literal meaning is “hand”, which may be gathered from the following citations: ŭnol´k=“hand”; mĭ´noŭl´t=“arm”; ŭnulte-mŭ´ka`p=“middle finger”, in which ŭnulte means “finger (or hand)”. These are from the vocabulary of Professor McGee. Then M Pinart records innolχ´, “arm”, intlash “hand”, inol’tis, “finger, index finger”, inol’tip “ring finger”. And Mr Bartlett writes inoyl, “arm”, inossiskersk, “hand”, inosshack, “fingers”. This -ŭnt will be further treated when the numeral “ten” is under discussion.

While it is evident that the first eight forms of the Yuman list are but variants from a common original, it is not, however, so clear what the original signification of the combination was. But as there can not be any question of relationship between these and the Serian terms, this fact will not affect the result of this study. The next terms of the Yuman list are variants of an entirely different combination of elements. The forms (15) humhum-môck and (12) humhamóok may be taken as characteristic of these terms. Now, it is plain that there is here duplication of the stem hum- or ham-, “three”, making the literal sense of the combination to be “three threes”, which of course gave the required meaning. The Cochimi (23) m’sigk-tkmat contains the element m’sig, “one”, and the final tkmat, which appears to mean “lacking, wanting, or less”. And in the Diegueño (14) nitchibab for niotchibab a still different method of expressing “nine” is found. In discussing the numeral “seven” and “eight” the signification of the initial nio- was ascertained to be “added to, over, plus”, and tchibab is of course the numeral “four”. The original expression, then, was “four added to five”, producing the required number, “nine”. The next three forms, though evidently cognate, are, like the first group, not analyzable from the data to be obtained from the meager material at present accessible. The last form is doubtful. These analyses show no relationship between the Serian and the Yuman terms.