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 }, }, y3 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. order which for ages had been in use above it. The ancient Egyptian and the still-used Roman and Chinese numeration are indeed founded on savage picture-writing,1 while the abacus and the swan-pan, the one still a valuable schoolinstrument, and the other in full practical use, have their germ in the savage counting by groups of objects, as when South Sea Islanders count with coco-nut stalks, putting a little one aside every time they come to 10, and a large one when they come to 100, or when African negroes reckon with pebbles or nuts, and every time they come to 5 put them aside in a little heap.2 We are here especially concerned with gesture-counting on the fingers, as an absolutely savage art still in use among children and peasants, and with the system of numeral words, as known to all mankind, appearing scantily among the lowest tribes, and reaching within savage limits to developments which the highest civilization has only improved in detail. These two methods of computation by gesture and word tell the story of primitive arithmetic in a way that can be hardly perverted or misunderstood. We see the savage who can only count to 2 or 3 or 4 in words, but can go farther in dumb show. He has words for hands and fingers, feet and toes, and the idea strikes him that the words which describe the gesture will serve also to express its meaning, and they become his numerals accordingly. This did not happen only once, it happened among different races in distant regions, for such terms as 'hand' for 5, 'handone' for 6, 'hands' for 10, 'two on the foot' for 12, 'hands and feet' or 'man' for 20, 'two men' for 40, &c., show such uniformity as is due to common principle, but also such variety as is due to independent working-out. These are 'pointer-facts' which have their place and explanation in a development-theory of culture, while a degeneration-theory totally fails to take them in. They are distinct records of development, and of independent deve 1 6 Early History of Mankind,' p. 106. 2 Ellis, Polyn. Res.' vol. i. p. 91; Klemm, C. G. vol. iii. p. 383. lopment, among savage tribes to whom some writers on civilization have rashly denied the very faculty of selfimprovement. The original meaning of a great part of the stock of numerals of the lower races, especially of those from 1 to 4, not suited to be named as hand-numerals, is obscure. They may have been named from comparison with objects, in a way which is shown actually to happen in such forms. as 'together' for 2, 'throw' for 3, 'knot' for 4; but any concrete meaning we may guess them to have once had seems now by modification and mutilation to have passed out of knowledge. Remembering how ordinary words change and lose their traces of original meaning in the course of ages, and that in numerals such breaking down of meaning is actually desirable, to make them fit for pure arithmetical symbols, we cannot wonder that so large a proportion of existing numerals should have no discernible etymology. This is especially true of the 1, 2, 3, 4, among low and high races alike, the earliest to be made, and therefore the earliest to lose their primary significance. Beyond these low numbers. the languages of the higher and lower races show a remarkable difference. The hand-and-foot numerals, so prevalent and unmistakable in savage tongues like Esquimaux and Zulu, are scarcely if at all traceable in the great languages of civilization, such as Sanskrit and Greek, Hebrew and Arabic. This state of things is quite conformable to the development-theory of language. We may argue that it was in comparatively recent times that savages arrived at the invention of hand-numerals, and that therefore the etymology of such numerals remains obvious. But it by no means follows from the non-appearance of such primitive forms in cultured Asia and Europe, that they did not exist there in remote ages; they may since have been rolled and battered like pebbles by the stream of time, till their original shapes can no longer be made out. Lastly, among savage and civilized races alike, the general framework of numeration stands throughout the world as an abiding monument of primæval culture. This framework, the all but universal scheme of reckoning by fives, tens, and twenties, shows that the childish and savage practice of counting on fingers and toes lies at the foundation of our arithmetical science. Ten seems the most convenient arithmetical basis offered by systems founded on handcounting, but twelve would have been better, and duodecimal arithmetic is in fact a protest against the less convenient decimal arithmetic in ordinary use. The case is the not uncommon one of high civilization bearing evident traces of the rudeness of its origin in ancient barbaric life. CHAPTER VIII. MYTHOLOGY. Mythic Fancy based, like other thought, on Experience-Mythology affords evidence for studying laws of Imagination-Change in public opinion as to credibility of Myths-Myths rationalized into Allegory and History -Ethnological import and treatment of Myth-Myth to be studied in actual existence and growth among modern savages and barbarians -Original sources of Myth-Early doctrine of general animation of Nature-Personification of Sun, Moon, and Stars; Water-spout, Sandpillar, Rainbow, Waterfall, Pestilence-Analogy worked into Myth and Metaphor-Myths of Rain, Thunder, &c.-Effect of Language in formation of Myth-Material Personification primary, Verbal Personification secondary-Grammatical Gender, male and female, animate and inanimate, in relation to Myth-Proper Names of objects in relation to Myth-Mental State proper to promote mythic imagination-Doctrine of Werewolves-Phantasy and Fancy. AMONG those opinions which are produced by a little knowledge, to be dispelled by a little more, is the belief in an almost boundless creative power of the human imagination. The superficial student, mazed in a crowd of seemingly wild and lawless fancies, which he thinks to have no reason in nature nor pattern in this material world, at first concludes them to be new births from the imagination of the poet, the tale-teller, and the seer. But little by little, in what seemed the most spontaneous fiction, a more comprehensive study of the sources of poetry and romance begins to disclose a cause for each fancy, an education that has led up to each train of thought, a store of inherited materials from out of which each province of the poet's land has been shaped, and built over, and peopled. Backward from our own times, the course of mental history may be traced |