六十黍为圭。(旧云六十四黍,四字衍文,今删之。)
四圭为撮。(三指撮之曰撮,五撮为一龠,一千二百黍也。)
十撮为合。(黄钟律龠,容千二百黍,二龠为合也。)
十合为升。
十升为斗。
(孙子算法,以六粟为圭,十圭为抄,十抄为撮,十撮为勺,十勺为合。此流俗之鄙谈,非先王之
法制,儒者所不道也。)
(即黄帝所设也。周公嘉量、太公旧量并同。)
四豆为区。(四升曰豆。区为一斗六升,三百二十龠。区或作 。)
五区为釜。(八斗也。为一千六百龠。釜或作 ,即所谓斛也。)
倍釜为庾。(十六斗也。庾或作 ,又作逾,又作 。)
五庾为钟。(八十斗也。)
倍钟为秉。(一百六十斗也。)
(此非周制,而与汉制颇同。)
五豆为区。(二斗也,比旧区多四升。)
五区为釜。(十斗也,比旧釜多二斗。)
十釜为钟。(百斗也,比旧钟多二十斗。)
成化十五年奏准铸成斛法,根据宝源局量地尺,斛口外方一尺,内方九寸,斛底外方一尺
六寸,内方一尺五寸,深一尺,浓三分,平秤一百斤。根据古黍度尺,斛口外方一尺二寸八分,
内方一尺一寸五分有奇,底外方二尺零五分,内方一尺九寸二分,深一尺二寸八分,浓四
分。(郑世子曰∶按古人未尝以五斗为斛,五斗为斛,盖自唐宋始也。算法根据宝源局尺量,置斛口内
方九寸自乘,得八十一寸,置底一尺五寸自乘,得二百二十五寸,又以口底相乘,得一百三十五寸,三
宗相并得四百四十一寸,三归得一百四十七寸,以深一尺乘之,得一千四百七十寸,是为铁斛五斗实
积,倍之得二千九百四十寸,是两铁斛即十斗实积。然则今之斛法,非二千五百也。民间俗传算术,
多以二千五百为斛法者,疑术士之杜撰也。)
Sixty grains of millet constitute one *gui* (a small unit of volume). (Old texts stated sixty-four grains; these four characters are considered interpolations and have been deleted.)
Four *gui* constitute one *cuo* (a pinch taken with three fingers). Five *cuo* make one *yue* (a standard measure), which holds one thousand two hundred millet grains.
Ten *cuo* constitute one *he* (a unit of volume). The *yue* of the Huangzhong pitch pipe holds one thousand two hundred millet grains; two *yue* make one *he*.
Ten *he* constitute one *sheng* (a unit of volume).
Ten *sheng* constitute one *dou* (a unit of volume).
(The *Sunzi Suanjing* states that six grains of broomcorn millet make one *gui*, ten *gui* make one *chao*, ten *chao* make one *cuo*, ten *cuo* make one *shao*, and ten *shao* make one *he*. This is a vulgar calculation of common people, not the legal system of the ancient kings, and is not discussed by Confucian scholars.)
(This was established by the Yellow Emperor. The *Jialiang* (standard measures) of Duke of Zhou and the old measures of Jiang Ziya were identical to this.)
Four *dou* constitute one *qu* (a unit of volume). Four *sheng* make one *dou*. One *qu* equals one *dou* and six *sheng*, or three hundred twenty *yue*. The character *qu* may appear in variant forms.
Five *qu* constitute one *fu* (a large vessel for grain). Eight *dou* make one *fu*, which holds one thousand six hundred *yue*. The character *fu* may appear in variant forms, referring to what is called *hu*.
Double one *fu* constitutes one *yu* (a unit of volume). Sixteen *dou* make one *yu*. The character *yu* may appear in variant forms, or be written as *yu* (surpass), or other variants.
Five *yu* constitute one *zhong* (a large unit of volume). Eighty *dou* make one *zhong*.
Double one *zhong* constitutes one *bing* (a unit of volume). One hundred sixty *dou* make one *bing*.
(This is not the Zhou system but is quite similar to the Han system.)
Five *dou* constitute one *qu* (two *dou*; this is four *sheng* more than the old *qu*).
Five *qu* constitute one *fu* (ten *dou*; this is two *dou* more than the old *fu*).
Ten *fu* constitute one *zhong* (one hundred *dou*; this is twenty *dou* more than the old *zhong*).
In the fifteenth year of the Chenghua reign, it was approved to cast standard *hu* measures based on the land-measuring ruler of the Baoyuan Bureau. For the *hu*: the outer side of the mouth is one chi, the inner side is nine cun; the outer side of the bottom is one chi six cun, the inner side is one chi five cun; the depth is one chi, and the wall thickness is three fen. A flat scale weighs one hundred jin. Based on the ancient millet-degree ruler: the outer side of the mouth is one chi two cun eight fen, the inner side is one chi one cun five fen and odd; the outer side of the bottom is two chi zero cun five fen, the inner side is one chi nine cun two fen; the depth is one chi two cun eight fen, and the wall thickness is four fen. (Prince Zheng stated: Examining the ancients, they never used five *dou* as one *hu*. Using five *dou* as one *hu* likely began in the Tang and Song dynasties. According to calculations based on the Baoyuan Bureau ruler: square the inner mouth side of nine cun to get 81 square cun; square the inner bottom side of one chi five cun to get 225 square cun; multiply the mouth and bottom values to get 135 square cun. Summing these three yields 441 square cun; dividing by three gives 147 square cun. Multiplying by the depth of one chi yields 1,470 cubic cun. This is the actual volume of five *dou* in an iron *hu*. Doubling this gives 2,940 cubic cun, which is the actual volume of two iron *hu* (ten *dou*). Thus, the current *hu* standard is not 2,500. Folk arithmetic often cites 2,500 as the *hu* standard; this is suspected to be fabricated by fortune-tellers or mathematicians.)