Metrology in Artha-sastra
by Lalit Tiwari & D.P. Agrawal
Trade and administration is an essential part of urban societies. Both require standardization of weights and measures. This science is called metrology. Even in the third millennium BC the Harappans (Indus Civilization) had developed a standard system of weights and measures. At Lothal, a Harappan site in Gujarat, they found a scale with 17.7 mm divisions, which compares well with the Artha-sastra’s angula. Their measure of length had only a mean error of 0.003 inches.
For the weight they followed a binary system (1,2,4,8,……. up to 12800). This binary system was followed till recently in Indian coins (rupee 1=16annas) and in weights (1seer=16 chattacks). The Harappans had a unit of weight of 13.625 gm. As the Harappans traded with West Asia, it was necessary to have a simple and convenient conversion systems. The West Asian unit of weight was shekel, 60 shekels=1 mina. The Dilmun shekels of 13.68 grams were almost like the Harappan units (13.625 gm). One hundred Dilmun shekels were equal to 160 Mesopotamian shekels and 175 Eblaite-Carcemish shekels.
The Artha-sastra was written by Kautilya (321-296 BC), who is supposed to be a courtier of the Mauryan King. Kautilya’s Artha-sastra is a great scientific treatise, which deals with a variety of topics including agriculture, animal husbandry, mining, trade etc. Artha-sastra also gives a detailed standardized system of weights and measures. As the linear measures are based on the width of a finger (angula) there have been slightly divergent values given by different translators. We give below the values of the weight and measure systems of Artha-sastra mainly based on the translation by Dr. R. Shamasastry (1961) of Mysore.
Kautilya, popularly known as Chanakya, was a great master of science, philosophy and economics. Basically the Artha-sastra is the ‘science of economics’, including organization of productive enterprises, taxation, revenue collection, budget and accounts.
Kautilya describes the standardised measuring and weighing methods and parameters in his Artha-sastra. Basically the measuring and weighing methods are related to trade. Kautilya developed the standard weights and measures for merchants. To ensure fair trade, it was necessary to periodically stamp weights and measures for the merchants. Use of unstamped measures and weights was a punishable offence.
Kautilya’s Measuring Concepts
Linear Measures: The basic linear measure is the ‘angula‘. The angula is defined as the middle-most joint of the middle finger of a man of average height and girth. Kautilya subdivided angula to anus, particles, likshas and yukas(defined below).
Subdivision of angula:
|8 anus||1chariot wheel particle|
|8 particles||1 liksha (nit)|
|8 likshas||1 yuka (louse)|
|8 yukas||1 barley middle (width of a grain of barley at its widest)|
|8 barley middles||1 angula|
|Thus, 1 angula = 32,768 anus.|
Multiples of angula:
|4 angulas||1 dharnurgraha (bow grip)||3in|
|8 angulas||1dhanurmushti (fist with thumb raised)||6in|
|12 angulas||1 vitasti (span-distance between the tips of a person’s thumb and little finger when stretched out)||9in|
|2 vitastis||1 aratni (cubit)||18in|
|4 aratnis||1 danda or 1 dhanus or 1 nalika or 1 paurusha||6ft|
Measures for long distance:
Kautilya describes the following measures for long distances:
|10 dandas||1 rajju||60ft|
|2 rajjus||1 paridesa||120ft|
|2000 dhanus||1 goruta or krosa||4000yds|
|4 gorutas||1 yojana||9 miles|
Kautilya describes some special measures of length which were used in professional and surveying works like:
|Sama, sala, pariraya||used for battle arrays||10.5in|
|hasta||used for balances and for surveying pastures||21in|
|kisku, kimsa||for carpenter’s sawing, for forts, camps and royal property||31.5in|
|vyama, paurusha||for ropes, surveying, digging of moats||43in|
|dhanus||for roads and city walls||6’9in|
|for placing archers in battle||7’6in|
|danda||for making gifts to Brahmins and guests||12ft|
Measures of capacity: Kautilya categorized measures of capacity into four standards. This was to enable the collection of the vyaji (transaction tax) in kind without having to calculate the tax separately. Each successive measure was 6.25% smaller than the previous one, the highest being the measure for receipts into the Treasury and the lowest for payments towards royal personal expenditure.
- Revenue measure – the standard for receiving payments into the Treasury.
- Trade measure – 6.25% less then the above (or 93.75% of standard measure).
- Payment measure – For payments out of the Treasury 12.5% less than the standard (87.25% of the standard).
- Palace measure – For payments for royal expenditure 18.75% less than the standard (81.25% of the standard).
Measures of Weight: According to Artha-sastra the basic weight was a dharana, which was the weight of 640 masha (black beans), 320 gunja (berries) or 14080 white mustard seeds. A rough estimate is that one dharana is equivalent to 3.5 grams.
10 dharanas = 1 pala =1¼ oz. =35 grams
100 palas = 1 tula =7¾ lbs. = 3.5 kilos
20 tulas = 1 bhara = 154 lbs. = 70 kilos
Kautilya describes two different types of weighing instrument:
Standard officially stamped weights were in subdivision of a pala and multiples of palas (1,2,3,4, and 10).
1. Tula (the balance with two pans): No doubt it was similar to the modern machine; the machine had a pointer, which indicated when the beam came to the horizontal level.
2. Samavritta (moving fulcrum steel-yard): It was different from the modern steel-yard weighing machines, which work on the basis of a beam with unequal arms and a fixed fulcrum with the object to be weighed suspended at the end of the shorter arm and a counterpoise moved along with a graduated scale.
- Metal beam to weigh from ¼ pala to 100 palas.
- A counterweight of 5 palas suspended at the one end.
- Metal beam, with a counterweight of 5 palas, to weigh from 100-200 palas.The scale with two pans (tula) could only use two weight quantities up to 10 palas and steel-yard (Samavritta) was used for weighing higher quantities.
3. Wooden Weighing Machine: In this machine, the main beam was made of hardwood, of 12ft length. Machine had two posts, set 1 to 2 ft apart, with a top beam from which the balancing beam was to be suspended.
According to Artha-sastra, the stamping fee should be 1 kakani (for each weight, capacity measure or balance) for each day (of use) since the last stamping. Penalty for using unstamped weight measure of capacity or balance should be 27¼ panas.
There is no doubt that Kautilya’s Artha-sastra is a remarkable text in the context of history of science and administrative knowledge of the Indians. It was Kautilya who set the standardised guidelines for measuring and weighing practices. The concept of Kautilya’s weighing machine was similar to the modern machines.
Lamberg-Karlovsky, C.C. 2001. Converting currencies in the Old World. Nature 41:437.
Rangarajan, L. N. 1992. Kautilya: the Arthasthastra. Penguin Book India Private Limited: New Delhi.
Shamasastry, R.1961. Kautilya’s Arthasastra. Seventh Edition. Mysore: Mysore Printing & Publishing House.