郑世子曰∶按淮南子谓十二粟而当一分,十二分而当一铢,则一铢者,一百四十四粟
也。汉志谓一千二百黍为十二铢,则一铢乃一百黍也。后汉志注又谓十粟重一圭,十圭重
一铢,则一铢者亦惟百粟耳,更减淮南之数而不相合也。且汉制律度量衡,悉纷乱无纪。
臣家有汉钱数十枚,凡若干种,每种虽度数分寸仿佛,而浓薄轻重不匀。以汉食货志校之,
彼志云∶货泉重五铢,货布重二十五铢,大泉重十二铢,大布重二十四铢。臣以今时等子,
将钱每种或十枚或五枚,总秤之以均其轻重,而用算法求之,合其一两之数,则大泉合今三
钱三分,货泉合今三钱五分,货布合今三钱七分,大布合今三钱八分,此皆汉时一两之数,
而率皆乖异,与宋吕大临考古图之说相同。大率汉之一两,惟有今之三钱半强,是汉三两
为今之一两强。其数与 黍之法不同者,盖因刘歆误以 黍为 ,故律、度、量、衡,四器皆
失之小,其余器皿,率多舛谬矣。又史言晋之秤两,不与古同;梁陈根据古秤;齐以古秤一斤八
两为一斤;后周玉秤四两,当古秤四两半;隋以古秤三斤为一斤;唐量衡与古校,皆三之一。
然史文缺略,今不能的悉其数。唐孙真人千金方曰∶古秤惟有铢两而无分名,今则以十(十当
作百,传写之误。)黍为一铢,六铢为一分,四分为一两,(合今之六钱也。)十六两为一斤,此则神农
之秤也。吴人以二两为一两,隋人以三两为一两,今根据四分为一两秤为定。(此唐秤十斤,正合
今之六斤。)此说足以破其惑。而肘后方鹿鸣山序云∶古方药品分两,灸穴分寸,与今不类,为
古今人体大小或异,血脉亦有差焉。此说非也,宋林亿等千金方凡例曰无稽之言莫此为甚
者是也。又如千金方所载药升之制,上径一寸,下径六分,深八分。此升甚小,不知何代之
量有如此者?又云半夏一升,秤重五两。校之不同。即所云诸药权量,大率类此,姑存其
说,以见度量权衡长短大小轻重之不同耳。隋唐宋元之度量,校之累黍则失于长大;汉魏
南北朝之度量,校之累黍则失于短小。宋儒论乐律者,率舍高而取下,论度量者,又舍大而
取小,夫岂知适中之道哉?今选羊头山 黍中者一千二百粒,实于黄钟之龠无欠无余,以
天平秤之,整有三钱,乃古半两也。两龠之黍,当天平六钱,为古一两。然则古秤一斤,当
天平九两六钱,今之平秤一斤,是古一斤十两,盖三分两之二也。今大明钞尺七尺五寸,适
合黍尺一丈;铁斛三升二合,适合黍量一斗;平秤九斤,适合黍权一秤。(十五斤曰一秤。)虽不
同而实同,虽不用而实用,妙理存乎其间,而人未之知也。臣若不累黍亲验,亦不信有如此
之妙。后世为钟律之学人,不可以其常用而忽之也。
郑世子说:查阅《淮南子》记载,十二粒粟等于一分,十二分等于一铢,那么一铢就是一百四十四粒粟。《汉书·律历志》记载一千二百粒黍等于十二铢,那么一铢就是一百粒黍。后汉《律历志》的注释又说十粒粟重一圭,十圭重一铢,那么一铢也只是一百粒粟罢了,这比《淮南子》的数值更小且互不相合。况且汉代的音律、长度、容量、重量标准,全都混乱无章。我家有汉代钱币几十枚,共有若干种,每种虽然尺寸长短大致相似,但厚薄轻重不均匀。用《汉书·食货志》来核对,该志记载:“货泉”重五铢,“货布”重二十五铢,“大泉”重十二铢,“大布”重二十四铢。我用当时的戥子(小型秤),将每种钱币取十枚或五枚,总加起来称重以平衡其轻重,再用算法推算,折合为一两的数量,则“大泉”折合现在的三钱三分,“货泉”折合现在的三钱五分,“货布”折合现在的三钱七分,“大布”折合现在的三钱八分,这些都是汉代一两的标准,但结果大多差异很大,与宋代吕大临《考古图》的说法相同。大体上汉代的一两,只有现在的三钱半多一点,也就是汉代的三两相当于现在的一两多。这个数值与累黍法不同,大概是因为刘歆错误地将黍当作某种度量基准,导致音律、长度、容量、重量四种器具都偏小,其余器皿也多有误谬。又史书记载晋代的秤两,与古代不同;梁、陈依据古秤;齐代以古秤的一斤八两作为一斤;后周玉秤四两,相当于古秤的四两半;隋代以古秤的三斤作为一斤;唐代的量衡与古代相比,都是三分之一。然而史文简略,现在不能确切知道具体数值。唐代孙思邈在《千金方》中说:古秤只有铢和两,没有分的名称,现在则以一百粒黍为一铢,六铢为一分,四分为一两(相当于现在的六钱),十六两为一斤,这就是神农时代的秤。吴人以二两作为一两,隋人以三两作为一两,现在以四分为一两的秤为标准。(这种唐秤十斤,正好相当于现在的六斤。)这种说法足以破除疑惑。而《肘后方》鹿鸣山序言说:古代方剂的药品分量、灸穴的尺寸,与现在不类似,是因为古今人体大小或许不同,血脉也有差异。这种说法是不对的,宋代林亿等在《千金方》凡例中批评道:“没有根据的话,没有比这更严重的了。”又如《千金方》所载药升的制度,上口直径一寸,下口直径六分,深八分。这个升非常小,不知道是哪个朝代的量具有如此规格?又说半夏一升,称重五两。核算起来不一致。即所谓各种药物的权量,大体都类似这样,姑且保留这种说法,以显示度量权衡长短大小轻重的不同罢了。隋、唐、宋、元时期的度量,用累黍法校核则失之于过大;汉、魏、南北朝时期的度量,用累黍法校核则失之于过小。宋代研究乐律的儒者,往往舍弃高的而选取低的;研究度量的,又舍弃大的而选取小的,他们哪里懂得适中的道理呢?现在挑选羊头山中等大小的黍一千二百粒,放入黄钟之龠(古代容量单位)中,不多不少,用天平称重,整有三钱,这就是古代的半两。两龠的黍,当天平六钱,就是古代的一两。既然这样,古代的秤一斤,相当于天平九两六钱,现在的平秤一斤,相当于古代的十两,大概是古代秤的三分之二。现在大明钞尺七尺五寸,恰好符合黍尺一丈;铁斛三升二合,恰好符合黍量一斗;平秤九斤,恰好符合黍权一秤。(十五斤称为一秤。)虽然形式不同但实际上相同,虽然不常用但实际有效,妙理存在于其中,只是人们不了解罢了。我如果不亲自用黍进行验证,也不会相信有如此精妙之处。后世从事钟律学问的人,不可以因为它是日常所用就忽视它。
The Prince of Zheng stated: According to the *Huainanzi*, twelve grains of millet constitute one *fen* (a unit of weight), and twelve *fen* constitute one *zhu* (a unit of weight); thus, one *zhu* equals 144 grains of millet. The *Book of Han: Treatise on Music and Measures* states that 1,200 grains of broomcorn millet (*Shu*) equal twelve *zhu*; therefore, one *zhu* equals 100 grains of millet. The commentary in the later *Han* treatise further states that ten grains of millet weigh one *gui* (a small unit of weight), and ten *gui* weigh one *zhu*; thus, one *zhu* is also merely 100 grains of millet. This figure is even smaller than that in the *Huainanzi* and does not coincide with it. Moreover, the standards for music pitch, length, volume, and weight during the Han dynasty were chaotic and unregulated. My family possesses dozens of Han dynasty coins of various types. Although the dimensions of each type are roughly similar, their thickness and weight are uneven. Comparing them with the *Treatise on Food and Money* in the *Book of Han*, which records that the *Huoquan* coin weighs five *zhu*, the *Huobu* coin weighs twenty-five *zhu*, the *Daquan* coin weighs twelve *zhu*, and the *Dabu* coin weighs twenty-four *zhu*: using a contemporary balance scale, I weighed ten or five coins of each type in total to average their weight, and calculated the equivalent in modern units. One tael of Han weight corresponds to approximately 3.3 qian of modern weight for the *Daquan*, 3.5 qian for the *Huoquan*, 3.7 qian for the *Huobu*, and 3.8 qian for the *Dabu*. These represent the standard of one Han tael, yet they vary significantly, consistent with the views of Lu Dalin in the Song dynasty's *Kaogu Tu*. Generally, one Han tael is slightly more than 3.5 qian in modern measure; thus, three Han taels exceed one modern tael. This discrepancy from the method of counting millet grains likely arises because Liu Xin erroneously used millet as a standard, causing all four instruments—pitch pipes, rulers, measures, and weights—to be too small, leading to errors in other vessels as well. Historical texts state that Jin dynasty weights differed from ancient ones; Liang and Chen dynasties followed ancient weights; Qi dynasty defined one jin as eight liang of ancient weight; Later Zhou jade weights of four liang equaled four and a half ancient liang; Sui dynasty defined one jin as three ancient jin; Tang dynasty measures and weights were one-third of ancient standards. However, historical records are sparse, making exact figures unknown today. Sun Simiao in the *Qianjin Fang* (Thousand Gold Formulas) stated: Ancient scales only had *zhu* and *liang*, without *fen*; now, 100 millet grains equal one *zhu*, six *zhu* equal one *fen*, four *fen* equal one *liang* (equivalent to six modern qian), and sixteen *liang* equal one *jin*. This represents the scale of Shennong. Wu people used two *liang* as one *liang*; Sui people used three *liang* as one *liang*; currently, the standard is four *fen* per *liang*. (Ten Jin of this Tang scale correspond exactly to six modern Jin.) This explanation suffices to dispel confusion. However, the preface to *Zhouhou Beiji Fang* by Luming Mountain claims that ancient herbal dosages and acupuncture point measurements differ from modern ones due to differences in human body size and blood vessel caliber. This view is incorrect, as criticized by Lin Yi et al. in the Song dynasty's preface to *Qianjin Fang*, who stated that baseless claims are most severe here. Furthermore, the *Qianjin Fang* describes a medicinal sheng (volume unit) with an upper diameter of one cun, lower diameter of six fen, and depth of eight fen. This sheng is very small; it is unclear which era's measure was so tiny. It also states that one sheng of Banxia weighs five liang, which contradicts calculations. Such discrepancies in drug weights and measures are common; these views are retained merely to illustrate the variations in measurement standards across eras. Measurements from Sui, Tang, Song, and Yuan dynasties, when verified by millet counting, appear too large; those from Han, Wei, and Southern and Northern Dynasties appear too small. Song Confucians discussing music pitch often chose lower over higher; those discussing measures chose smaller over larger, failing to understand the principle of moderation. Now, selecting 1,200 medium-sized millet grains from Yangtou Mountain, filling a Huangzhong zhuo (ancient volume unit) perfectly, and weighing them on a balance scale yields exactly three qian, which is the ancient half-ounce. Two zhuo of millet weigh six qian on the balance scale, constituting one ancient liang. Therefore, one ancient jin equals nine liang and six qian on the modern balance scale; one modern jin equals ten ancient liang, representing two-thirds of the ancient standard. Currently, the Ming dynasty paper currency ruler of seven chi and five cun matches the millet ruler of one zhang; the iron hu of three sheng and two ge matches the millet measure of one dou; the balance scale of nine jin matches the millet weight of one cheng (fifteen jin is called one cheng). Though different in form, they are identical in essence; though rarely used, they are practically effective. Profound principles lie within, unrecognized by many. Had I not personally verified this using millet, I would not have believed such subtlety existed. Scholars of bell and pitch-pipe studies in later generations should not neglect this due to its common usage.