《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§2. Units of weight (or mass)

This section introduces Chinese units of weight and gives the conversion rates between them.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
稱之所起、起於黍。 [Of] that which measuring weight beginneth from: beginneth [it] from millet.
  • 稱: measuring weight; or weighing

    稱、平聲、 Cantonese: chʻing1 (post-merger: tsʻing1), Mandarin: chēng
    (but in modern Cantonese, read 去聲 chʻing3 for .)

  • 起: beginneth from; lit. ariseth from
  • 黍: millet

    黍、音暑、 Cantonese: shü2, Mandarin: shǔ

    Shu ().

十黍為一絫、
十絫為一銖、
二十四銖為一兩、
十六兩為一斤、
三十斤為一鈞、
四鈞為一石。
Ten millets make one pile;
ten piles make one dram;
twenty-four drams make one tael;
sixteen taels make one catty;
thirty catties make one quarter;
four quarters make one stone.
  • 絫: pile

    絫、魯水切、 Cantonese: l_ü5, Mandarin: lěi

    Lei (). Difficult to render because Chinese dictionaries simply define it as ten shu (). I have taken "pile" from the interchangeable , "to accumulate/pile/heap".

  • 銖: dram

    銖、 Cantonese: chü1, Mandarin: zhū

    Chu (), of the order two grams. According to Williams' Tonic Dictionary, "a small ancient silver coin", so I have chosen "dram" after the eponymous ancient Greek coin and weight, which is of similar magnitude.

  • 兩: tael

    Liang ().

    One sixteenth of a catty, except in Mainland China where it has been metricised to a tenth, thus ruining the phrase 半斤八兩, "half [a] catty [is] eight taels".

  • 斤: catty

    Kin ().

    Of the order one pound, or half a kilogram.

  • 鈞: quarter

    鈞、音均、 Cantonese: kwan1, Mandarin: jūn

    Kün (). A quarter of the shek () or "stone" below, and of similar weight to the imperial quarter (28 pounds). Difficult to render otherwise since Chinese dictionaries simply define it as thirty catties.

  • Version C erroneously has for .
  • 石: stone

    Shek ().

    This is a literal rendering. The Chinese stone shek () is of the order 120 pounds, making it closer to the imperial hundredweight than the much lighter imperial stone (14 pounds).

Extended commentary

I can't be bothered looking up a reputable source for the precise weight of a kin () or catty when Sun Tzŭ's Computational Classic was first written, but using 600 grams as an estimate, we have:

\begin{alignedat}{3} 1 \unit{millet~(黍)} &={} & \tfrac{1}{38400} & \unit{catties} && \sim 0.02 \unit{g} \\ 1 \unit{pile~(絫)} &={} & \tfrac{1}{3840} & \unit{catties} && \sim 0.2 \unit{g} \\ 1 \unit{dram~(銖)} &={} & \tfrac{1}{384} & \unit{catties} && \sim 2 \unit{g} \\ 1 \unit{tael~(兩)} &={} & \tfrac{1}{16} & \unit{catties} && \sim 40 \unit{g} \\ 1 \unit{catty~(斤)} &={} & 1 & \unit{catty} && \sim 600 \unit{g} \\ 1 \unit{quarter~(鈞)} &={} & 30 & \unit{catties} && \sim 18 \unit{kg} \\ 1 \unit{stone~(石)} &={} & 120 & \unit{catties} && \sim 72 \unit{kg}. \end{alignedat}

By the later part of the Tsʻing Dynasty, one kin () or catty is 1⅓ pounds in Hong Kong, locally called a kan (). As with length units, Ordinance No. 22 of 1844 (PDF) of Hong Kong gives the relevant conversions between the Chinese units themselves (here, candareen and mace are used rather than "piles" and "drams"):

Image of Ordinance Number 22 of 1844, British Hong Kong. Weights. Ten Candareen or 分 Fun, make one 錢 Tseen, (Mace). Ten Mace or 錢 Tseen, make one 兩 Leang, (Tael). Sixteen Taels or 兩 Leang, make one 斤 Kin, (Catty). One hundred Catties or 斤 Kin, make one 担 Tam, (Picul). One and one fifth Picul or 担 Tam, make one 石 Shik, (Stone).

And likewise they are only standardised with reference to English units forty years later, in Ordinance No. 8 of 1885 (PDF) (note the typo in the definition of candareen):

Image of Ordinance Number 8 of 1885, British Hong Kong. Weights. One Fan (candareen) equals 0.133 oz. avoirdupois. One Tsin (mace) equals 0.133 oz. avoirdupois. One Leung (tael) equals one and one third oz. avoirdupois. One Kan (catty) equals one and one third lbs. avoirdupois. One Tam (picul) equals 133 and one third lbs. avoirdupois.

Eventually the kan () or catty is given the almost equivalent definition of 0.60478982 kg, used unto this day in Hong Kong street markets; see Cap. 68 Weights and Measures Ordinance.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §2". <https://yawnoc.github.io/sun-tzu/i/2> Accessed yyyy-mm-dd.