Section 2. CHINESE NUMERALS. THE numerals of the Chinese in the complex, simple, and contracted forms, with their pronunciation in the court, Canton, Shanghai, and Amoy dialects, are as follows: The first three characters in the first column properly denote their respective numbers, but the others are selected from their similarity in form and sound to represent the proper numerals in the second column, and are all used chiefly in bills, promissory notes, and other documents as a security against alterations. The figures in the third column are used in accounts and ordinary papers where less formality and more compactness are wished. The Chinese, like the ancient Greeks, do not reckon above a myriad, but they have, through the Budhists, learned to use a few characters for the higher numbers, as yih for 100,000; cháu for 1,000,000; king for 10,000,000; hái for 100,000,000; tsz' for a billion; yang for ten billions; and even higher than these. Numbers above a myriad are expressed by reproducing those below it, as sán-peh-vu-shih-gih wán, th wán, sán tổ ien, ling luh-shih-vi = 五十一萬六萬三千零六十五 is 35,163,065. The character ling, or a circle, denotes a cypher; twenty is written 廿 jih; and 30 is contracted to H sán, which are merely + shih combined twice and thrice; but the common way to express or all num bers above ten is by combining the digits and reading them off, as shihgih, 11 ; shih-sán, 13; sán-shih-gih, 31 ; gih-peh ling’rh, 102 ; &. The decimals are not called tenths, hundredths, &c., as in the Arabic notation, but each progressive place has its own name. The first five places are called fun a tenth; 分 li Ja hundredth; Special characters are used for numerals by particular trades, in order to keep their prices and rates secret, whose value is not known by other persons. The characters of the Thousand Character Classic are not unfrequently used as numerals, beginning 天地黄宇宙洪荒 tien tí hiuen huáng, gi chau hung háng, &e, which correspond to 1, 2, 3, &c. The ten stems, ZT kiph yuch ping ting, &c. are also similarly employed. In bills and accounts, the character hau is used for dimes by natives at the open ports, and the characters szor sin-sz 先絲 for cents; at Canton, sán ko yin tsien, sz' hau, yih sz denotes $3.41. This usage enables foreigners to understand accounts better, and furthermore obviates the confusion that might ensue by using fun and li for the decimals of both taels and dollars. The Chinese use a kind of abacus, called swán-pán or counting-board, in making calculations. It consists of a shallow frame divided into two unequal parts by a bar running lengthwise, through which are inserted parallel wires or sticks, from 9 to 18 or more, according to its uses; on each wire are seven balls, five in the lower compartment, and two (sometimes only one) in the upper. The principle on which calculations are made is decimal, and is simply this: that a single ball in the lower part being placed against the bar and called unit, is increased towards its left, and decreased on its right, by tens, hundreds, thousands, &c. A ball in the upper division denotes a value five times that of a ball opposite to it in the lower, and the two equal the single ball in the next higher place below the bar. Thus, if opposite to one, it stands for five, and the two balls make 6; if opposite to ten, fifty, and the two balls make 51; and so also, if opposite to a hundredth part, it stands for ths, and the two balls makeths. The machine is an imperfect assistant in doing calculations, though practice makes the Chinese very expert in common sums; it enables them to note the steps in their mental arithmetic, but if the result is doubtful or erroneous, the whole must be reckoned over again. When writing their numbers, the Chinese follow the order of the balls in the abacus, and accordingly place the figures after each other from left to right in the same order as in the Arabic numerals. For this 13,209.243; the characters for myriad and thousand being written underneath those places to indicate the highest number of the sum, and thereby rendering it needless further to mark the decimals. The Arabic notation C.G. 37 has been tried in some works on mathematics issued by foreigners; there is no difficulty in thus using the Chinese numerals, but as long as the language is written perpendicularly, they cannot be employed in that way. The Chinese abacus and numerals are both in general use throughout the Chinese-language nations, none of whom have hitherto adopted the Arabic notation. Of these denominations of weights, the first three and the yin, kiun, and shih, are nominal, though the last is frequently used as synonimous with a tán or picul. Subdivisions of the liáng are expressed by the decimals given in the table of money weights on page 274; and so are parts of the catty, when weighing coarse things. The use of the word tán for picul is a modern term, and was once confined to Canton; the progress of foreign trade has extended its use to the other ports, and by the recent treaties, its weight in all transactions with foreigners is fixed at 1334 lbs. av. Chinese weights and grain measures, and the linear, long, and land measures, all vary in different parts of the country; but as a general rule they are the largest and longest in the southern provinces. The kin decreases in weight, the chih in length, the mau in area, and the tau in quantity, as one approaches the capital, though exceptions are 1.19047 cwt., or 1 cwt. 21 lbs. The Chinese use three instruments for weighing, to wit, balances, steelyards, and money-scales. The balance, or tien pingi. e. heaven's level, is made of brass of different sizes; the large ones will The steelyards or dotchin (a word derived from toh-ching weigh upwards of 200 taels without injury to the pivot; those of smaller size will detect tenths of a grain. The workmanship of the balance is usually very good, and as it is almost exclusively used for weighing gold, silver, jewelry, pearls, bird's-nests, baroos camphor, medicines, and such like valuable articles, the weights and pans are wrought with great accuracy. The weights, called sz' ma 司碼 or ma ts: 碼子, are made of brass, and shaped somewhat like a dumb-bell. to weigh) is made of wood, and is in general use in the markets, shops, and boats; it was known in China in the Chau dynasty, as early as B.C. 1100. The largest size can weigh 6 or 8 piculs; common ones have a beam about 18 inches long, and weigh from a tael up to a picul; the weight is made of brass, iron, or stone. There are usually two hooks for the fulcrum, and each side of the beam is marked to correspond, so that the instrument can weigh more or less, according to the fulcrum used. It is in the hands of every body; no native hardly goes marketing or shopping, without a dotchin to weigh his purchase, and hang it on when bringing it home. At the open ports, Fairbank's scales are coming into use to weigh heavy produce. The money scales, called li-tangare made on the same principle as the dotchin, but weigh only 2 or 3 taels. The beam, 9 or 10 inches long, is made of ivory or horn, and graduated to mills; the thing is put up in portable cases, so that persons can verify their exchanges of silver and copper. The hesitation to trust another man's scale and weights, which prevails among the Chinese, arises partly from a consciousness of the tricks common in all trades, and partly from the want of a common standard throughout the country, so that one can never be sure how much he gets for his money. Moreover, each trade has its own usages in respect of weights, and prices are regulated accordingly. M. Rondot furnishes many curious data respecting the weights of the tael and catty, showing that they have altered in different periods, and that even now, they present many discrepancies in parts of China remote from each other In 1769, Père Amiot wrote, "The weight of the fú (a certain measure) is 288 modern ounces and 480 ancient; and I have ascertained that 288 modern Chinese ounces equal 320 oz. in our balances," This proportion to the old French ounce gives 0.719 oz. for the ancient tael, and 1.199 oz. for the modern. In 1648, the Government made cubes of gold, silver, copper and lead, each measuring one tsun; they were found to weigh-gold, 16.8 taels; silver, 9 taels; copper, 7.5; and lead, 9.9; but the question is, what length was the tsun? If that of the Hiá dynasty be taken as the standard, the average weight of the tael would be 0.68 oz.; but as the standard chih of the present dynasty is more likely, it would give the weight of the tael at 1.327 ounces avoirdupois. The expedient of weighing ancient Chinese coins in order to ascertain the value of the catty was tried by Biot, who deduced from them its weight during the Chau dynasty (B. c. 600) to be only 5.85 oz.; during the Han to be 8.9 oz.; increasing under the Tang (A. D. 700) to 19.4 oz., and as high as 22.09 oz. under the Sung. M. Rondot has pursued this examination further than M. Biot was able to do, and gives the results of weighing a great number of coins. From one of the time of Tsin Chí-hwangtí, (called pwán liángi. e. half tael,) he infers the weight of the catty to have been 10.83 oz. In the time of Wang-mang of the Han dynasty, (A. D. 14) it seems to have increased to 11.35 oz., which is almost the same as that given by Amiot a century ago, as the ancient weight of the catty; but some coins of emperors earlier in the same dynasty (B. c. 140), give only 8.83 oz., showing that the emperors of China have resorted to the same means of paying their debts by depreciating the coinage that western monarchs have found convenient. The mean weight of 15 copper coins of the Tang dynasty, gives 21.18 oz. for the catty during three centuries; while the average of 168 cash cast during the Sung dynasty gives as much as 26.11 oz.; or only 24.7 oz., if the mean of 67 coins cast between A. D. 960 to 1031 be taken. The discrepancies, therefore, of weights in various periods of Chinese history, are as great as those of measures and lengths; though the results to be deduced from the weight of ancient coins must be considered uncertain. It appears that the weight of the tael at Canton in 1710 was 1.32 oz. av.; and in 1770 the E. I. Company's supercargoes agreed with the hong-merchants to fix its weight at 21 drs. av., the catty at 213 oz., and the picul at 133 lbs. This continued to be the standard as long as the Company existed, and became the commercial usage at Canton. It was therefore adopted by the framers of the treaties, and will gradually extend to all ports of the empire. By the Prussian treaty, a picul is made equal to 120 zollpfund, 27 loth, and 1186 quent; or 60 kilogrammes and 453 grammes French. The difference in the values of the weights above a tael, as fixed by the treaties, and those in common use in China, are as follows: The terms tán and shih are often indiscriminately applied by the natives among themselves to a large weight of anything, somewhat as the words load and stone would be among ourselves; and consequently their values vary. At Amoy, brown sugar is sold at 94 kin, sugar candy at 95 kin, indigo at 110 kin, and rice at 140 kin, the picul. At Fuhchau, a picul of rice weighs 100 lbs. av. At Shanghai, the largest measure by which rice is sold contains 180 kin, yet it is also called a picul. At Tientsin, a shih of 360 catties is used only in weighing peas; but a weight of 160 catties of wheat is also called a shih. At Niu-chwang, the shih of rice and peas weighs 320 catties, though the latter is often only 300 catties; oil and indigo are weighed by a picul of 91 catties. M. Rondot furnishes a table of 59 items, giving the weights of the tael and catty at different times and places, and by different trades. The highest values are 1.372 oz. for the tael, and 21.952 oz. for the catty, which is that of 16 taels 3 mace used by Shantung merchants; the lowest is that of Timkowski at Peking, which are respectively 1.129oz. and 18.064 oz. At Shanghai, the catty was found to contain 16.3 taels, |