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Metrology in Arthasastra
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 Arthasastra'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 EblaiteCarcemish shekels.
The Arthasastra was written by Kautilya (321296 BC), who is supposed
to be a courtier of the Mauryan King. Kautilya's Arthasastra is a
great scientific treatise, which deals with a variety of topics including
agriculture, animal husbandry, mining, trade etc. Arthasastra 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 Arthasastra 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 Arthasastra 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 Arthasastra. 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 middlemost 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:
1 angula 

3/4in 
4 angulas 
1 dharnurgraha (bow grip) 
3in 
8 angulas 
1dhanurmushti (fist with thumb raised) 
6in 
12 angulas 
1 vitasti (spandistance 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 
Other measures:
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 Arthasastra 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
Weighing Machines
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 steelyard): It was different from
the modern steelyard 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 100200
palas.
The scale with two pans (tula) could only use two weight quantities
up to 10 palas and steelyard (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.
Stamping Fee
According to Arthasastra, 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.
Conclusion:
There is no doubt that Kautilya's Arthasastra 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.
Main Sources:
LambergKarlovsky, 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.

