Quick Answer: How Was Land Measured in Ancient China?
Ancient Chinese land measurement combined observations of a plot with rules for calculating area and recording it. In early mathematical texts a bu (步, bù) can be a unit of length, while a mu (亩, mǔ) measures land area. Administrators could record the resulting area together with boundaries and names.[1][2][4]
- Measure: Record the relevant lengths of a plot.
- Calculate: Apply a rule suited to the shape and convert the area into local units.
- Register: Identify the plot so officials can refer to it for land administration and tax.
The size of a unit and the contents of a register depend on the period and the source.
A field can appear as several lengths in a problem, an area in a tax record and an outline in a register. Those are related records with different purposes. Reading an old land figure starts by deciding which of those jobs it was doing.
Distance, Area and the Meaning of a Mu
The Nine Chapters on the Mathematical Art uses bu when giving a field’s width and length. In the multiplication result, the same written unit can denote a square bu. Its rule gives 240 square bu to one mu and 100 mu to one qing (顷, qǐng). The quantity being measured tells the reader how to interpret the unit.[1][2]
Historical sources give more than one standard for the mu. A study comparing the Book of Lord Shang with a land statute from the state of Qin distinguishes earlier small and larger measures. The statute shows that the larger standard was in use in Qin by 309 BCE, before the later unified Qin dynasty. To convert an old entry into modern area, you need to know both the number of square units in a mu and the length represented by the underlying unit.[3]
From Measured Sides to an Area
One problem in the Nine Chapters gives a width of 15 bu and a length of 16 bu. Multiplying them gives 240 square bu, which the text’s rule converts to one mu. Another rectangular example gives dimensions of 12 and 14 bu. Its answer is 168 square bu, less than a full mu in the same system.[1][2]
The field chapter also gives different rules for other shapes. For a trapezoid, it averages the two parallel widths and multiplies by the perpendicular distance between them. In the text’s example, widths of 20 and 5 and a distance of 30 give 375 square bu. The example shows why a set of recorded sides needs to be read with the calculation rule. A field problem models a shape so the reader can compute its area, while a survey register records land for use by an office.[2]
How Survey Results Entered Land Registers
During the Ming dynasty, officials used fish-scale registers (鱼鳞图册, yúlín túcè) to document land. Plots could have outlines, numbers, names of people associated with them and records of their boundaries. The name evokes the appearance of adjoining plots, whose outlines could resemble a pattern of fish scales on the page.[4][5]
A register in the National Museum of China comes from the 1581 survey. Its entries run through 2,142 numbered plots in the locality represented. They give shapes, boundaries and owners’ names. The item records one locality in a much wider survey. It gives a concrete example of how an office could match an entry to a place, even where plots did not have simple shapes.[4]
How to Read a Historical Land Figure
Identify the date and locality before converting a number. Then check whether the record describes a side or an area. Ask how the record was created. A mathematical problem explains a rule. A statute can prescribe a standard. A land register identifies parcels in a particular jurisdiction. County gazetteers provide another kind of local evidence, which can help establish the context for a number quoted on its own.[1][2][3][4][5]
Recorded area and tax due answer different questions. The area identifies a quantity of land within a system of units. Determining a levy requires evidence of the rules and classifications applied to that land.[5]
FAQs About Ancient Chinese Land Measurement
Was a mu the same size in every dynasty?
Historical standards varied. Establish the period, place and underlying units before converting a recorded mu to modern area.
Did a fish-scale register show exact survey geometry?
The outline helped identify the parcel. The area, boundaries and names are important evidence in their own right, and the accuracy or scale of a drawing needs separate confirmation.
Is a recorded land area the same as the amount of tax?
A register can support tax administration, but the number for area does not by itself give a tax amount. The assessment rules and other classifications matter.
Sumber
[1] Academia Sinica, Digital Culture Center. Nine Chapters on the Mathematical Art, nine juan
[2] Nine Chapters on the Mathematical Art. Chapter on Field Measurement
[3] Early China, Cambridge University Press. Dating a Pre-Imperial Text: The Case Study of the Book of Lord Shang
[4] National Museum of China. Fish-Scale Survey Register of the Ninth Year of Wanli
[5] National Bureau of Statistics of China. Ming Fish-Scale Registers and the Development of Land Statistics