To notice this state of things among savages and children raises interesting points as to the early history of grammar. W. von Humboldt suggested the analogy between the savage notion of 3 as 'many' and the grammatical use of 3 to form a kind of superlative, in forms of which 'trismegistus,' 'ter felix,' 'thrice blest,' are familiar instances. The relation of single, dual, and plural is well shown pictorially in the Egyptian hieroglyphics, where the picture of an object, a horse for instance, is marked by a single line if but one is meant, by two lines if two are meant, by three lines | || if three or an indefinite plural number are meant. The scheme of grammatical number in some of the most ancient and important languages of the world is laid down on the same savage principle. Egyptian, Arabic, Hebrew, Sanskrit, Greek, Gothic, are examples of languages using singular, dual, and plural number; but the tendency of higher intellectual culture has been to discard the plan as inconvenient and unprofitable, and only to distinguish singular and plural. No doubt the dual held its place by inheritance from an early period of culture, and Dr. D. Wilson seems justified in his opinion that it 'preserves to us the memorial of that stage of thought when all beyond two was an idea of indefinite number.'1

When two races at different levels of culture come into contact, the ruder people adopt new art and knowledge, but at the same time their own special culture usually comes to a standstill, and even falls off. It is thus with the art of counting. We may be able to prove that the lower race had actually been making great and independent progress in it, but when the higher race comes with a convenient and unlimited means of not only naming all imaginable numbers, but of writing them down and reckoning with them by means of a few simple figures, what likelihood is there that the barbarian's clumsy methods should be farther worked out? As to the ways in which the numerals of the

1 D. Wilson, 'Prehistoric Man,' p. 616.

superior race are grafted on the language of the inferior, Captain Grant describes the native slaves of Equatorial Africa occupying their lounging hours in learning the numerals of their Arab masters.1 Father Dobrizhoffer's account of the arithmetical relations between the native Brazilians and the Jesuits is a good description of the intellectual contact between savages and missionaries. The Guaranis, it appears, counted up to 4 with their native numerals, and when they got beyond, they would say 'innumerable.' 'But as counting is both of manifold use in common life, and in the confessional absolutely indispensable in making a complete confession, the Indians were daily taught at the public catechising in the church to count in Spanish. On Sundays the whole people used to count with a loud voice in Spanish, from 1 to 1,000.' The missionary, it is true, did not find the natives use the numbers thus learnt very accurately-'We were washing at a blackamoor,' he says.2 If, however, we examine the modern vocabularies of savage or low barbarian tribes, they will be found to afford interesting evidence how really effective the influence of higher on lower civilization has been in this matter. So far as the ruder system is complete and moderately convenient, it may stand, but where it ceases or grows cumbrous, and sometimes at a lower limit than this, we can see the cleverer foreigner taking it into his own hands, supplementing or supplanting the scanty numerals of the lower race by his own. The higher race, though advanced enough to act thus on the lower, need not be itself at an extremely high level. Markham observes that the Jivaras of the Marañon, with native numerals up to 5, adopt for higher numbers those of the Quichua, the language of the Peruvian Incas. The cases of the indigenes of India are instructive. The Khonds reckon 1 and 2 in native words, and then take to borrowed

1 Grant in 'Tr. Eth. Soc.' vol. iii. p. 90.

2 Dobrizhoffer, 'Gesch. der Abiponer,' p. 205; Eng. Trans. vol. ii. p. 171. 3 Markham in 'Tr. Eth. Soc.' vol. iii. p. 166.

Hindi numerals. The Oraon tribes, while belonging to a race of the Dravidian stock, and having had a series of native numerals accordingly, appear to have given up their use beyond 4, or sometimes even 2, and adopted Hindi numerals in their place. The South American Conibos were observed to count 1 and 2 with their own words, and then to borrow Spanish numerals, much as a Brazilian dialect of the Tupi family is noticed in the last century as having lost the native 5, and settled down into using the old native numerals up to 3, and then continuing in Portuguese.2 In Melanesia, the Annatom language can only count in its own numerals to 5, and then borrows English siks, seven, eet, nain, &c. In some Polynesian islands, though the native numerals are extensive enough, the confusion arising from reckoning by pairs and fours as well as units, has induced the natives to escape from perplexity by adopting huneri and tausani. And though the Esquimaux counting by hands, feet, and whole men, is capable of expressing high numbers, it becomes practically clumsy even when it gets among the scores, and the Greenlander has done well to adopt untrîte and tusinte from his Danish teachers. Similarity of numerals in two languages is a point to which philologists attach great and deserved importance in the question whether they are to be considered as sprung from a common stock. But it is clear that so far as one race may have borrowed numerals from another, this evidence breaks down. The fact that this borrowing extends as low as 3, and may even go still lower for all we know, is a reason for using the argument from connected numerals cautiously, as tending rather to prove intercourse than kinship.

At the other end of the scale of civilization, the adoption

1 Latham, 'Comp. Phil.' p. 186; Shaw in 'As. Res.' vol. iv. p. 96;

'Journ. As. Soc. Bengal,' 1866, part ii. pp. 27, 204, 251.

2 St. Cricq in 'Bulletin de la Soc. de Géog.' 1853, p. 286; Pott, 'Zählmethode,' p. 7.

3 Gabelentz, p. 89; Hale, 1.c.

of numerals from nation to nation still presents interesting philological points. Our own language gives curious instances, as second and million. The manner in which English, in common with German, Dutch, Danish, and even Russian, has adopted Medieval Latin dozena (from duodecim) shows how convenient an arrangement it was found to buy and sell by the dozen, and how necessary it was to have a special word for it. But the borrowing process has gone farther than this. If it were asked how many sets of numerals are now in use among Englishspeaking people in England, the probable reply would be one set, the regular one, two, three, &c. There exist, however, two borrowed sets as well. One is the well-known dicingset, ace, deuce, tray, cater, cinque, size; thus size-ace is '6 and one,' cinques or sinks, 'double five.' These came to us from France, and correspond with the common French numerals, except ace, which is Latin as, a word of great philological interest, meaning 'one.' The other borrowed set is to be found in the Slang Dictionary. It appears that the English street-folk have adopted as a means of secret communication a set of Italian numerals from the organ-grinders and image-sellers, or by other ways through which Italian or Lingua Franca is brought into the low neighbourhoods of London. In so doing, they have performed a philological operation not only curious, but instructive. By copying such expressions as Italian due soldi, tre soldi, as equivalent to 'twopence,' 'threepence,' the word saltee became a recognized slang term for 'penny, and pence are reckoned as follows:

One of these series simply adopts Italian numerals decimally. But the other, when it has reached 6, having had enough of novelty, makes 7 by 'six-one,' and so continues. It is for no abstract reason that 6 is thus made the turning-point, but simply because the costermonger is adding pence up to the silver sixpence, and then adding pence again up to the shilling. Thus our duodecimal coinage has led to the practice of counting by sixes, and produced a philological curiosity, a real senary notation.

On evidence such as has been brought forward in this essay, the apparent relations of savage to civilized culture, as regards the Art of Counting, may now be briefly stated in conclusion. The principal methods to which the development of the higher arithmetic are due, lie outside the problem. They are mostly ingenious plans of expressing numerical relation by written symbols. Among them are the Semitic scheme, and the Greek derived from it, of using the alphabet as a series of numerical symbols, a plan not quite discarded by ourselves, at least for ordinals, as in schedules A, B, &c.; the use of initials of numeral words as figures for the numbers themselves, as in Greek II and ▲ for 5 and 10, Roman C and M for 100 and 1,000; the device of expressing fractions, shown in a rudimentary stage in Greek y', d', for 3, 1, yo for ; the introduction of the cipher or zero, by means of which the Arabic or Indian numerals have their value according to their position in a decimal order corresponding to the succession of the rows of the abacus; and lastly, the modern notation of decimal fractions by carrying down below the unit the proportional

1 J. C. Hotten, 'Slang Dictionary,' p. 218.