147 Harappan Stone Weights From Mohenjo-daro and Harappa, 500 Miles Apart, Fit One Series Built on a Unit of About 0.86 Gram

In the official account of the Mohenjo-daro excavations, published in 1931, A. S. Hemmy, a former principal of Government College, Lahore, reported the results of weighing the small stone blocks found at Mohenjo-daro and Harappa. Of 159 blocks in good enough condition to give a reliable weight, 147 fell into one series of steps built on a single unit of about 0.857 gram. The unit came out at 0.856 gram from Mohenjo-daro and 0.860 gram from Harappa, and Hemmy wrote that there was no local variation between two cities about 500 miles (800 km) apart.

Later studies have tested the same idea on larger samples and more sites, among them Dholavira in Gujarat, and have changed some of the details. The sources do not agree on every number, and this piece sets out which figure comes from whom.

Small blocks of banded stone, none of them marked

Hemmy’s chapter describes the objects as small rectangular blocks, mostly of a tawny or light grey banded chert (a hard, fine-grained stone) and a few of other hard rocks such as gneiss. Most are cubes and a few are cylinders. They are well finished and polished, and none bears an inscription or mark that gives a value.

Ernest Mackay, the excavator who wrote the volume’s chapter on household objects, says the cube-shaped type was by far the commonest. The cubes were roughly flaked into shape, then ground, then polished, and an unfinished one survives from Mohenjo-daro. The smallest cube measures 0.3 by 0.3 by 0.25 inch, about 8 mm across.

Mackay noted that weights turned up in small houses as well as large ones, and not in any one place that might be a workshop. He found the number remarkable, writing that he did not think any ancient site outside India had produced so many. He also noted that the cubes were quite unlike the shapes used in Babylonia.

T. G. Bibby, writing in the Danish journal Kuml in 1970, cites Mackay’s later analysis of 297 weights from Mohenjo-daro and 34 from Harappa, and compares Bahrain with a sample of 331 Indus weights. In that sample 262 were cubical, 14 spherical and 8 of steatite (a soft stone).

How a pile of grey cubes gave up a unit

Hemmy’s method was plain. He assumed that no single weight was more accurate than the rest and that the chance of error was the same for all. He then sorted the blocks into groups whose masses stood in simple ratios, gave the smallest group the value of one, divided each group’s mean by its ratio, and averaged the results, so that every specimen counted equally.

At Mohenjo-daro 113 of the 120 weights he selected fit the table, and at Harappa 34 of 39. Combined, the ratios of the groups run 1, 2, 4, 8, 16, 32 and 64, then jump to 160, 200, 320, 640 and 1,600. There is one extra group, whose two members weigh a third of the group at ratio 8. Hemmy remarked that the system shows no trace of the sexagesimal (base 60) counting used in Mesopotamia: every ratio is binary or decimal, apart from that single third.

At the top of Hemmy’s table, the heaviest group sits at about 1,375 grams, or 1.37 kilograms. At the bottom, the unit is a block weighing under a gram.

Hemmy was open about the scatter. Specimens of the same nominal weight could differ by as much as 10 per cent, he wrote, though the mean deviation within a group hardly ever exceeded 2 per cent. He set the loss from chipping or wear at rarely more than 3 parts in 1,000, small beside that scatter.

Why the sources quote different units

Readers who look this up find figures that differ by a factor of 16 or 2, and the reason is which step each author calls the base.

In Hemmy’s table the 16th step, group F, has a calculated value of 13.71 grams. The figure of about 13.6 grams quoted in many accounts belongs to that step, not to the unit. Chandrakant Doshi’s 2019 summary of the Dholavira excavation report gives 13.625 grams for the standard Harappan system, which is the same step.

Mackay’s later analysis, as Bibby reports it, put the basic weight at 1.714 grams. That matches Hemmy’s second step, group B, whose calculated value is 1.71 grams.

MacTutor’s overview of Indian mathematics describes the Harappan weights as two decimal-based series, in which each value is multiplied and divided by two, with a main series at 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200 and 500 times a base. The overview does not say where that ladder comes from, and it differs from Hemmy’s 1931 table. What the sources share is the idea of fixed steps related by doubling and, higher up, by tens. They differ on the exact ladder.

From Mohenjo-daro to Dholavira

Dholavira, the Harappan city in the Rann of Kutch that UNESCO inscribed on its World Heritage List on 27 July 2021, lies far from both Hemmy sites. The Press Information Bureau’s release on the listing dates the city to the third to mid-second millennium BCE. For the story of its water works, see our piece on Dholavira.

Doshi’s blog post, which summarises the Dholavira excavation report by R. S. Bisht of the Archaeological Survey of India, says the report lists 996 weight specimens in 20 shapes and 44 materials. Cuboids are the commonest shape at 387, followed by 124 spheroids. Bisht identified three weight systems at the site, and one of them is the standard Harappan system with the 13.625-gram step. Doshi plots the weights that fit it and finds chert gives the clearest staircase pattern.

Doshi also records a case that does not fit. The heaviest Dholavira weight, a limestone piece of 35,700 grams, sits about 31 per cent away from the nearest nominal value. The post is a secondary summary, and the report’s own tables are the place to check these counts.

Beyond the cities themselves, Bibby argued in 1970 that seven weights from early Dilmun, on Bahrain, agree in shape and weight with those of the Harappan cities. He added that seven is too few to carry much weight as proof.

For scale, a paper in PLoS ONE in 2010 says the civilisation covered about a million square kilometres between 2600 and 1900 BCE. Sinha, Yadav and Vahia, in a 2011 arXiv paper, describe a surprising degree of uniformity in measurement units across the widely dispersed centres. For the Gujarat port that sits within the same culture, see our article on Lothal.

The rulers: an Indus inch and an ivory scale

MacTutor reports a decimal length scale with a unit of 1.32 inches (3.35 cm), which it calls the Indus inch, and a bronze rod marked in units of 0.367 inch. It adds that measurements of excavated ruins show these lengths were used accurately in construction. Its authors call the accuracy of the markings surprising.

A well-known find is the ivory scale from Lothal, excavated by S. R. Rao. Sinha, Yadav and Vahia describe it as 27 uniformly spaced lines over 46 mm, indicating a unit of about 1.70 mm. Subhash Kak’s essay on ancient Indian space and time gives the same data, 27 graduations in 46 mm, as 1.76 mm each. The two figures differ because of how the lines are counted: 27 lines enclose 26 gaps, and 46 divided by 26 is about 1.77 mm. Anyone quoting the Lothal unit should say which counting they used.

Kak also summarises Michel Danino’s analysis of the dimensions of Dholavira, which proposes a length unit of 190.4 cm. Danino links it to a measure named in the later Arthashastra, and Kak draws a continuity from there. That is the authors’ proposal and not an excavator’s reading of an object, and it should be weighed as such.

How tight the standard was, and who enforced it

The cubes do not settle how tightly the system was held. Hemmy’s own figures show an error of up to 10 per cent between specimens and about 2 per cent on average within a group, which is tight for hand-ground stone but not a modern tolerance.

The question of control is argued. Kenoyer’s chapter in The Archaeology of Measurement begins from the older view that the uniform proportions of baked bricks and the similar sizes of weights across the Indus valley reflect standardisation imposed by city rulers. The chapter treats that as a premise to test, using detailed measurements from Harappa to ask how standardised the Indus systems were and how much they varied by region.

Mackay offered a reading in the same 1931 volume. He thought the careful making and the hard stone suggested that the authorities kept some watch on manufacture, and added that false weights may have been a penal offence. He gave this as a possibility, and no text from the civilisation records a rule of that kind. The script is undeciphered.

What the cubes weighed

Hemmy cited a hypothesis of Ridgeway’s that weighing was first limited to the more precious objects bartered in small quantities. That would lead one to expect the smaller weights to be the more accurate, he wrote, yet his tables show much the same percentage consistency across the whole scale.

Mackay thought the smallest blocks were probably used by jewellers for precious metals. He added that no scales had been found at Mohenjo-daro, and that if they were made of wood, as seemed likely, they would have perished long ago.