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placed horizontally in the formal, and vertically in the common, notation. The liuliiiTi and Arabic figures—the originals of the European — are obviously cursive or connected forms ol similar symbols, and it is curious that in the Indian— from which the Arabic are supposed to have been derived—the strokes are horizontal, while in the Arabic they are ■vertical, from which we may perhaps infer that verticul symbols were at one time partially current in India also, or that considerable license prevailed in their position. But the Arabic are so much closer to the vertical Chinese than to the Indian, that it appears most probable they were directly borrowed from that system. A comparison of alphabets shows that written symbols are very apt to be turned iii all directions, right or left, up or down, in their progress amongst rude tribes, prior to the adoption ol unilorm materials for writing. Leaves, bark, hard bauibu, cloth, coarse paper that blots, styles, reeds, quills, brushes, paint, ink &c, all influence the form and position of the symbols. The Chinese symbol for 4 appears anciently to have been, in its rudiments, 4 strokes, a horizontal with two dependent vertical, and a smaller horizontal carried out from the bottom of the right one. It has been complicated by adding two large vertical lines at the sides and one at the bottom, forming with the upper horizontal line an enclosing square which wonld itself represent 4. In the common figure the four lines are obtained by a simple crossing of two curved strokes. The Indian symbol is a similar cross, but with the bottoms of the curved strokes joined and rounded, that is, the figure is written without lifting the pen, and the two strokes run into one symbol, as with the IndqArahic2 and 3. In the Chinese 0 the symbol lor 4 is sometimes looped in the same way. The ancient Chinese 5 appears to have consisted rudimentally of 3 horizontal, crossed by 2 vertical, strokes. The common figure is a very remarkable one. It consists of a body precisely resembling the Indian form ol 4 (chat is, a cross converted into a loop by writing it ■without lilting the pen or brush), and a short stroke carried up from the left point, or it is a stroke with the symbol tor 4 affixed (i. e. 4, 1). It appears to be a rounded, cursive, unilinear modification of the ancient symbol for 5. The Indian, Arabic and European figures lor 5 vary greatly, but some strongly resemble the Chinese symbol The Zend is evidently this symbol curtailed of the loop. The Devanagri, Muhratta and European are also close to it. The common figures for 6, 7, 8 and 9 are quinary, that is, they are the figures for 1, 2, 3, and 4 with a i-hurt vertical stroke to represent 5, or distinguish them Irom the lower series. In 9 it rests on a horizontal stroke, the figure 4 having no stroke of the kind to support it, as in 1, 2 and 3. The formal symbols are probably less simple compounds ol a similar kind. The upper part of 6 is the common figure, (equivalent to 6, 1). The nomenclature was also probably quinary. The ancient 8 and 9 appear to be related. 9 is 4 without the three enclosing lines, and with the left vertical stroke prolonged above the horizontal Jine to represent 5. The Indian, Arabian and European symbols for the higher numbers vary greatly, and the same figure has different powers in different systems, but, like the Chinese, they appear to have been originally formed from the lower ones. Thus the Devanagri 6, is 8 reversed, with the addition of a small curve at the top. 7 is, in general, two strokes like the letter v, but variously placed, sometimes curved in'both or one of the strokes and frequently resembling 1, The 7 of Devanagri and one variety of Arabic resemble the Arabic and European 9, which is also the Indian 1, the Arabic anil European preserving the simple Chinese form. The Devanagri uses the sane symbol lor 9 with the loop on the right side. The same symbol serves for 6 in Arabic with the loop below but on the left side; while iu Maliratta with the loop on the right, as in our 0, it is the symbol lor 7. The figure lor 8 is rudimentally a simple inversion of that for 7. In some systems it appears to be formed irom 4 (as the name is in s>me systems, i. e. 8 is 4 dual). In general 9 is a modification ol 6, as th.it in some forms is of 3, thus corresponding with the tiinal nomenclature, 3, 3 dual, 3 triual.
It may be Inferred from the above that the Chinese and the various Indian figures are ultimately referable to one original, whether in China, India, or S. W. Asia. Some ot the rudimentary symbols, as well as the principle of combining and modifying them, are common to all the systems. The Chinese mode ot symbolising numbers above 10 is ruder than the Indian. They have distinct gymb <ls for 10, 100, 1000, and 10,000, so that their n >tatian exactly corresponds with the oral expression. Thus the figures lor'236 consist of the symbols for 100, 10 and 6, with the symb >l lor 2 over the 100 and that tor 8 over the 10, and it is real off "Two hundred, three ten, six." The ciriamstauca of the figures feeing placed or read from lett to right, instead of from top to bottom or right to left like the symbols of the ancient numerals and the ordinary characters, appears to show that the Chinese system h.is been influenced by the Indian and European. But its general character is that which the latter probably presented in its earliest stages. It is not likely that the idea of value from place alone preceded the use of figures, while a loreign civilised nation which had adopted the Chinese methods would be moro ready to discover that the symbols lor 10,100, &c. might be dispensed with or understood, and to reject them, than the Chinese themselves. The rudiiuentsofthe Indo-Arabic notation are preserved iu Chinese, and probably originated with that race.
•The Tibetans and most of the Barma-Himalayan tribes follow the Chinese iu their mode ot naming the numerals above 10. But there arc many exceptions aud irregularities, occasioned by the mixture of systems and terms, and by languages mutually borrowing. Fur example even the Luopa has not only the Tibetan term for 20, mji she 2, 10, but a hybrid term khechik in which the Tibetan chik 1, is suffixed to khe which must be 20 or " score"; 30 is khe-pheda-ni, 40 kite ni (score-2), 60 khr-phedang-sam, 100 khe nga (score 6). In Lepcha /. he is kha, 20 kha-kat, 30 kha-kat-sa kati (score one and ten), 40 kha nyet (score two), 60 kha nyet sa kati (score two and ten), 100 kha kha ngon (score Jive). In Sun war wo find 20 khalka (score), 30 sasi san (10,3) ; 40 khak neshi (score 4); 60 khak nishisasika (score 4 aud 10 one i. e. scores 4 and tens 1).
* In the terms for 108 Chinese and Tibetan differ. The former has ¥*\ te'tP'i equivalent to pak. The latter has gya. The Tibetan term appears to be unknown in Ultraindia. The Chinese is foun I in tiro Naga dialoet»,-/>u</u. The ancient Tamil paka has an accidental concideu.ee with the i hinese term. But the root fa may be ultimately
s£§T i'iie two paragraphs marked. * should have folio wed "Ten" j>. 27. referable to a similar source with the Chinese. Both the Chinese and Tibetan terms have some appearance ot being flexions «i the terms tor '8. ''hincsc 8 pat, 100 pah; Tibet 8 hre/gtu/, gye, 100 hrnya. aya. If the scale is based on a binary one, as is probable, the itsuumiunce it real. In some ot the Mon-Anan languages the same root is lound expressing 2, 8, and 100.
Addendum (p. 18.)
a. A. dang, L tang, M dan, ga-lan, K, ialanti (T. U.)
b. K. chira da.
«t A. ngaba (? Boclo, Dhioaal lama, dama Tib.)