sides' (i.e. both hands), 20 as sa re ngome, one man,' &c.; thus in John v. 5 which had an infirmity thirty and eight years,' the numeral 38 is expressed by the phrase, 'one man and both sides five and three.'1 In the MalayoPolynesian languages, the typical word for 5 is lima or rima, 'hand,' and the connexion is not lost by the phonetic variations among different branches of this family of languages, as in Malagasy dimy, Marquesan fima, Tongan nima, but while lima and its varieties mean 5 in almost all Malayo-Polynesian dialects, its meaning of 'hand' is confined to a much narrower district, showing that the word became more permanent by passing into the condition of a traditional numeral. In languages of the Malayo-Polynesian family, it is usually found that 6, &c., are carried on with words whose etymology is no longer obvious, but the forms lima-sa, lima-zua 'hand-one,' 'hand-two,' have been found doing duty for 6 and 7.2 In West Africa, Kölle's account of the Vei language gives a case in point. These negroes are so dependent on their fingers that some can hardly count without, and their toes are convenient as the calculator squats on the ground. The Vei people and many other African tribes, when counting, first count the fingers of their left hand, beginning, be it remembered, from the little one, then in the same manner those of the right hand, and afterwards the toes. The Vei numeral for 20, mō bánde, means obviously a person (mo) is finished (bande),' and similarly 40, 60, 80, &c. 'two men, three men, four men, &c., are finished.' It is an interesting point that the negroes who used these phrases had lost their original descriptive sense -the words have become mere numerals to them.3 Lastly, for bringing before our minds a picture of a man counting upon his fingers, and being struck by the idea that if he describes his gestures in words, these words may become an

1 Gabelentz, Melanesiche Sprachen,' p. 183.

2 W. v. Humboldt, 'Kawi-Spr.' vol. ii. p. 308; corroborated by 'As. Res.' vol. vi. p. 90; 'Journ. Ind. Archip.' vol. iii. p. 182, &c.

3 Kölle, 'Gr. of Vei Lang.' p. 27.

actual name for the number, perhaps no language in the world surpasses the Zulu. The Zulu counting on his fingers begins in general with the little finger of his left hand. When he comes to 5, this he may call edesanta 'finish hand;' then he goes on to the thumb of the right hand, and so the word tatisitupa 'taking the thumb' becomes a numeral for 6. Then the verb komba 'to point,' indicating the forefinger, or 'pointer,' makes the next numeral, 7. Thus, answering the question 'How much did your master give you?' a Zulu would say 'U kombile' 'He pointed with his forefinger,' i.e., 'He gave me seven,' and this curious way of using the numeral verb is shown in such an example as 'amahasi akombile' the horses have pointed,' i.e., 'there were seven of them.' In like manner, Kijangalobili 'keep back two fingers,' i.e. 8, and Kijangalolunje 'keep back one finger,' i.e. 9, lead on to kumi, 10; at the completion of each ten the two hands with open fingers are clapped together.1

The theory that man's primitive mode of counting was palpable reckoning on his hands, and the proof that many numerals in present use are actually derived from such a state of things, is a great step towards discovering the origin of numerals in general. Can we go farther, and state broadly the mental process by which savage men, having no numerals as yet in their language, came to invent them? What was the origin of numerals not named with reference to hands and feet, and especially of the numerals below five, to which such a derivation is hardly appropriate? The subject is a peculiarly difficult one. Yet as to principle it is not altogether obscure, for some evidence is forthcoming as to the actual formation of new numeral words, these being made by simply pressing into the service names of objects or actions in some way appropriate to the purpose.

People possessing full sets of inherited numerals in their

1 Schreuder, 'Gr. for Zulu Sproget,' p. 30; Döhne, 'Zulu Dic.'; Grout, 'Zulu Gr.' See Hahn, 'Gr. des Herero.'

own languages have nevertheless sometimes found it con-
venient to invent new ones. Thus the scholars of India,
ages ago, selected a set of words from a memoria technica in
order to record dates and numbers. These words they chose
for reasons which are still in great measure evident; thus
'moon' or 'earth' expressed 1, there being but one of
each; 2 might be called 'eye,' 'wing,' 'arm,' 'jaw,'
as going in pairs; for 3 they said Rama,' 'fire,' or
'quality,' there being considered to be three Ramas, three
kinds of fire, three qualities (guna); for 4 were used ‘veda'
'age,' or 'ocean,' there being four of each recognized;
'season' for 6, because they reckoned six seasons; 'sage'
or vowel' for 7, from the seven sages and the seven
vowels; and so on with higher numbers, sun' for 12,
because of his twelve annual denominations, or zodiac'
from its twelve signs, and ‘nail' for 20, a word incidentally
bringing in a finger notation. As Sanskrit is very rich in
synonyms, and as even the numerals themselves might be
used, it became very easy to draw up phrases or nonsense-
verses to record series of numbers by this system of arti-
ficial memory.
The following is a Hindu astronomical
formula, a list of numbers referring to the stars of the lunar
constellations. Each word stands as the mnemonic equi-
valent of the number placed over it in the English trans-
lation. The general principle on which the words are
chosen to denote the numbers is evident without further
explanation :-

'Vahni tri rtvishu gunendu kritâgnibhûta
Bânâsvinetra çara bhûku yugabdhi râmâh
Rudrâbdhirâmagunavedaçatâ dviyugma
Dantâ budhairabhihitâh kramaço bhatârâh.'

i.e., Fire, three, season, arrow, quality, moon, four-side of die,

5

fire, element,

2

1

2 5
1 4 4 3
Arrow, Asvin, eye, arrow, earth, earth, age, ocean, Rama,

Rudra, ocean, Rama, quality, Veda, hundred, two, couple,

32

Teeth by the wise have been set forth in order the mighty lords.'1

It occurred to Wilhelm von Humboldt, in studying this curious system of numeration, that he had before his eyes the evidence of a process very like that which actually produced the regular numeral words denoting one, two, three, &c., in the various languages of the world. The following passage in which, more than sixty years ago, he set forth this view, seems to me to contain a nearly perfect key to the theory of numeral words. If we take into consideration the origin of actual numerals, the process of their formation appears evidently to have been the same as that here described. The latter is nothing else than a wider extension of the former. For when 5 is expressed, as in several languages of the Malay family, by "hand” (lima), this is precisely the same thing as when in the description of numbers by words, 2 is denoted by "wing." Indisputably there lie at the root of all numerals such metaphors as these, though they cannot always be now traced. But people seem early to have felt that the multiplicity of such signs for the same number was superfluous, too clumsy, and leading to misunderstandings.' Therefore, he goes on to argue, synonyms of numerals are very rare. And to nations with a deep sense of language, the feeling must soon have been present, though perhaps without rising to distinct consciousness, that recollections of the original etymology and descriptive meaning of numerals had best be allowed to disappear, so as to leave the numerals themselves to become mere conventional terms.

1 Sir W. Jones in 'As. Res.' vol. ii. 1790, p. 296; E. Jacquet in Nouv. Journ. Asiat.' 1835; W. v. Humboldt, 'Kawi-Spr.' vol. i. p. 19. This system of recording dates, &c., extended as far as Tibet and the Indian Archipelago. Many important points of Oriental chronology depend on such formulas. Unfortunately their evidence is more or less vitiated by inconsistencies in the use of words for numbers.

The most instructive evidence I have found bearing on the formation of numerals, other than digit-numerals, among the lower races, appears in the use on both sides of the globe of what may be called numeral-names for children. In Australia a well-marked case occurs. With all the poverty of the aboriginal languages in numerals, 3 being commonly used as meaning 'several or many,' the natives in the Adelaide district have for a particular purpose gone far beyond this narrow limit, and possess what is to all intents a special numeral system, extending perhaps to 9. They give fixed names to their children in order of age, which are set down as follows by Mr. Eyre: 1. Kertameru; 2. Warritya; 3. Kudnutya; 4. Monaitya; 5. Milaitya; 6. Marrutya; 7. Wangutya; 8. Ngarlaitya; 9. Pouarna. These are the male names, from which the female differ in termination. They are given at birth, more distinctive appellations being soon afterwards chosen.1 A similar habit makes its appearance among the Malays, who in some districts are reported to use a series of seven names in order of age, beginning with 1. Sulung ('eldest'); 2. Awang ('friend, companion'), and ending with Kechil (little one'), or Bongsu (youngest '). These are for sons; daughters have Meh prefixed, and nicknames have to be used for practical distinction. In Madagascar, the Malay connexion manifests itself in the appearance of a similar set of appellations given to children in lieu of proper names, which are, however, often substituted in after years. Males; Lahimatoa ('first male'), Lah-ivo ('intermediate male'); Ra-fara-lahy (last born male'). Females; Ramatoa (eldest female'), Ra-ivo (intermediate'), Rafara-vavy (last born female'). The system exists in

1 Eyre, 'Australia,' vol. ii. p. 324: Shürmann, 'Vocab. of Parnkalla Lang,' gives forms partially corresponding.

2 Journ. Ind. Archip.' New Ser. vol. ii. 1858, p. 118 [Sulong, Awang, Itam ('black'), Puteh ('white'), Allang, Pendeh, Kechil or Bongsu]; Bastian, 'Oestl. Asien,' vol. ii. p. 494. The details are imperfectly given, and seem not all correct.

3 Ellis, Madagascar,' vol. i. p. 154. Also Andriampaivo, or Lahi-Zan