Weights found in excavating the settlement at Allahdino.

© J. M. Kenoyer. Courtesy Dept. of Archaeology and Museums, Gov't of Pakistan.

From eosnap, courtesy Chelys srl.

The Harappan culture flourished in the Indus valley between 2600 and 1900 bce. Excavations have recovered a number of balance weights in the shape of cubes, often of chert, some from sites as early as 2800-2600 bce. Around 2200 bce, weights also began to be made in the form of spheres with two flat spots on opposite sides, but the cubic weights continued to be produced until about 1900 bce.

The discovery of impressive cities from a previously unknown ancient culture electrified archeologists in the 1920's. In analyzing weights recovered in the first excavations at Mohenojo-daro, A. S. Hemmy discovered a regular pattern¹: the smaller weights increased by a factor of two, and the larger were a decimal multiplier times one of the seven smaller weights.

Hemmy described the system in terms of multiples of the smallest weight, around 0.87 gram. Later researchers² took as the basic unit the weight of about 13.65 grams, because it is the one most commonly found, because the 13.65 g unit has a decimal relationship to the first “heavy”unit, and because units of about this size were later the basic units in South Asia.

multiples of the smallest unit |
1 | 2 | 4 | 8 | 16 | 32 | 64 | |||

multiples of the 13.65 g unit |
1/16 | 1/8 | ¼ | ½ | 1 | 2 | 4 | |||

Idealized Weight |
0.85 g |
1.75 g |
3.45 g |
6.85 g |
13.65 g |
27.35 g |
54.65 g |
|||

Larger by a factor of 10 |
160 | 200 | 320 | 640 | ||||||

10 | 12.5 | 20 | 40 | |||||||

136.5 g |
170.6 6 |
273.5 g |
546.5 g |
|||||||

Larger by a factor of 100, 100 unit increments |
1600 | 3200 | 6400 | 8000 | 12,800 | |||||

100 | 200 | 400 | 500 | 800 | ||||||

1.365 kg |
2.73 kg |
5.46 kg |
6.83 kg |
10.92 kg |

The Harappan's written language (if that is what the symbols found on Harappan seals are) has not been deciphered, so we do not know their names for these units.

Later excavations uncovered weights both larger and smaller than those Hemmy first worked with, but they are relatively rare. A few incorporate subdivisions by thirds.

Any process for producing standard weights has some tolerance, and the
tolerances in 2200 bce were of course larger than they are today. To add
to that, as Hendrickx-Baudot^{3} says, “We have to bear in mind not only the normal
statistical spreading and standard deviation, but also the unknown from
detrition or crumbling and chemical alteration.” Numerous workers^{4} have analyzed
statistically the spread of weights around central values. As a rough estimate,
taking all the weights from all sites, the measured mass generally comes within
6% of the ideal mass.

The tolerances are smaller if the weights of each city are analyzed separately.
Probably each city's weight-makers worked from that city's prototype, and the
prototypes themselves could be compared only with the precision of the day's
balances. The astonishing thing is not that their tolerance was larger
than ours, but that it is so small and that this probably pre-literate culture
maintained the same tight standards for over seven centuries. Indeed, several scholars^{5} have thought that, though the use of cubical weights ceased, the system of weights continued.
It appears again around 600 bce, when cities began to be built in northern India,
and is reflected in units of weight used in South Asia today.

Kenoyer has speculated^{6} that the weights were primarily used in collecting
taxes or tariffs, since finds are concentrated near the gates of cities, but he
also feels that traders were instrumental in maintaining the standard. Weights of the same age, calibrated to the Harappan standard, have been found at distant trading centers, including Mesopotamia
(Ur), Dilmun (modern Bahrain) and Magan (modern Oman).^{7}

1. A. S. Hemmy.

Systems of Weights at Mohenjo-Daro.

in

J.
Marshall, editor.

*Mohenjo-Daro and the Indus Civilization*. Vol. 2

London: A. Probsthain, 1931.

—

System of Weights.

in

E. J. H. Mackay.

*Further Excavations at Mohenjo-Daro, being an official account of
archaeological excavations at Mohenjo-daro carried out by the government of
India between the years 1927 and 1931.* Vol. 1.

Delhi: Manager of Publications, 1938.

The first excavation of a city of the Indus civilization. For a reproduction of Hemmy's list of the weight in grams of the weights found in the 1920's and 1930's, see www.safarmer.com/Indo-Eurasian/weightchart.jpg

2. Ardelia R. Hall.

The Cube Weights in Boston.

in

Ernest J. H. Mackay.

*Chanhu-daro Excavations, 1935-36.*

New Haven, CT: Pub. for American
School of Indic and Iranian Studies and Museum of Fine Arts, Boston, by American
Oriental Society, 1943.

3. M. P. Hendrickx-Baudot.

The weights of the Harrapa-culture.

*Orientalia Lovaniensia Periodica*, vol. **3**, pages 5-34 (1972).

4. For example,

S. Iwata.

On the standard deviation of the weights of the Indus civilization.

*Bulletin of the Society of Near Eastern Studies in Japan*, volume **27**,
number 2, pages 13-36 (1974).

5. For example,

V. B. Mainkar.

Metrology in the Indus Civilization.

in

B. B. Lal and S. P. Gupta, editors.*Frontiers of the Indus Civilization.*

New Delhi: Books and Books, 1984.

6. J. Mark Kenoyer.

Measuring the Harappan world: Insights into
the Indus order and cosmology.

in

Ian Morley and Colin Refrew, editors.

*The Archaeology of Measurement. Comprehending Heaven, Earth and Time in
Ancient Societies.*

Cambridge: Cambridge Univ. Press, 2010.

7. For a list of Harappan weights found elsewhere, see Table 1 of

Shereen Ratnagar.

Theorizing Bronze-Age intercultural trade: the evidence of
the weights.

*Paléorient*, vol. **29**, no. 1 (2003).

Jonathan Mark Kenoyer.*Ancient Cities of the Indus Valley
Civilization.*

Karachi: Oxford U. Press and American Institute of Pakistan
Studies, 1998.

Jane R. McIntosh.*The Ancient Indus Valley. New
Perspectives.*

Santa Barbara, CA: ABC-Clio, 2008.

From a series intended for a wide audience, *Understanding
Ancient Civilizations. *Contains extensive bibliographies.

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Last revised: 20 March 2012.