REPRINT
FRONTIERS OF THE INDUS CIVILIZATION
(Sir Mortimer Wheeler Commemoration Volume)
Editors
B.B. Lal : S.P. Gupta
Published on the behalf of
Indian Archeological Society
And
Indian History and Culture Society
16
Brij Bhusan Vij
Linear Standard in the Indus Civilization
The study of metric technology is considered a recent thought (Vij 1973). The bold step to
introduce this technology, in the recent past, was taken by Simon Stevin, a British
engineer (AD 1548-1620) and Jean Picard, a French astronomer (AD 1620-1682). They
won over Talleyrand to view and he persuaded the French Constituent Assembly to
entrust, to the French Academy of Sciences (8 May, 1790), ‘the task of establishing a
measuring system, which could be acceptable to the whole world’. Accordingly, the
original prototypes for the ‘metre’ and ‘kilogram’ were prepared and deposited in the
Archives of the French Republic on 10 December 1799 and its use was made obligatory
by Law of 4 July 1837.
The author’s concern in the study of material evidence of ancient excavations
primarily was to investigate whether Time, Angle and Calendar can be brought, into the so
far unsuccessful attempts, under the metric fold. It need not be over-emphasized that a
great deal of perfection was achieved by the Indus Valley people in their standardized
(ISO Sov. 1964) practices and technological progress. It is evidenced from two specific
linear examples (Wheeler 1966):
(a) The ‘Great-Bath’ at Mohenjo-daro; and
(b) The broken ‘shell’ from Mohenjo-daro considered a part of the complete linear
measure of Indus civilization.(fig. 16.1).
THE VALUE OF Pi or
The Indus Civilization achieved perfection in its ‘measuring technology’ and high
standardization in ‘preservation techniques’. The material evidence also suggests that the
ideas of the circle and angle, and also the ‘ratio between the circumference to the diameter
of the circle’ was known to this culture. The dimensions, to which the ‘great-bath’ discussed later-had been constructed, leave no doubt in the mind of the author that the idea
of angles and their trigonometric functions were within their speculative imagination. It
would also follow that knowledge of the value of Pi or  to the culture of the Indus Valley
cannot be discarded. If this be so, what was the ratio between the circumference to the
diameter of the circle? Did the ancient culture rationalize the angle ‘radian’ and assign it
any specific value? Perhaps yes.
Numerous series have been developed by eminent scholars to express Pi around
the announced results, which are not free from ‘truncating and rounding off ’ errors. The
most recent approach being the development of tan-1x or arc tan x series due to Leibniz.
The data processed by an IBM 7090 computer claiming Pi to have been calculated up to
100,000 decimals (Wrench and Shank 1962) need investigation of property whether the
series has a non-ending, non-repeating character. The various values of PI used during
different periods, in the recorded history, are processed and tabulated in Appendix A.
THE INDUS UNIT
The linear unit for measurement of length-metre-was intended to have a physical relation
to the earth. Accordingly, the metre was defined (Mainkar and Raju 1964) as the one-ten
millionth part of the quadrant of the meridian of the earth passing through Dunkirk and
Barcelona’ by the first Conference Generale des Poids et Mesures (CGPM) at Paris in AD
1889. This length has now been standardized and redefined at the 11th conference
Generale des Poids et Mesures in 1960, which reads as:
Metre is the length equal to 1 650 763.73 wavelengths in vacuum of the radiation energy level 2p10 and 5d5 of
the krypton-86 atom, the atom being at rest with respect to the observer. Effort is also underway to modify
the definition of the metre during AD 1981 by CCDM at the proceedings of Conference Generale des Poids
et Mesures (CGPM).
The broken piece of linear measure or ‘shell’ excavated at Mohenjo-daro by itself
speaks of the high standards in the preservation technology. The well-finished piece is not
liable to wrap, crack or get affected by temperature changes and measures 1.57 cm in
width, 5.29 cm in length and 0.67 cm in thickness. The dividing lines are cut with a fine
tool into subgroups of 5 divisions marked with a dot and circle, also suggesting the use of
decimal scale between any two dots or circles. It will be interesting to observe that the
‘uniform thickness’ of this shell had been standardized to 1/10 of the distance between the
two dots or circles. The estimated distance between the dots or circles is believed to be
33.53 mm. The distance was termed as ‘ The Indus Inch’ (Berriman: 1953) when the
British ruled India and inch was 1/36th part of the legal linear unit of length – yard. The
Indus Inch was designated to represent the distance fourth – root of 3 or 1.316 074 British
inches (3.342 827 96 cm).
The term ‘Indus unit’ is henceforth used, in this work, referring to the excavated
‘shell’ during 1921-22 at Mohenjo-daro and kept in the National Museum, New Delhi.
The distance between the dot and circle on the excavated ‘shell’ can now be
worked out, based on two scientific assumptions (Vij 1982), of course:
(a) 1 British Yard
(b) Pi or 
= 0.9144 Meter(exactly)
= 100 000 (exactly)
31831
The distance meter (new) works to 39.379 039 698 6 British inches or 29.993 173
303 9 Indus units (say 30 I.U.) each such unit being equal to 3.334 092 027 25 cm (new).
The suggested linear measure, meter (new) on modification of the existing meter be
defined as:
Meter (new) is the length equal to 1 651 139.198 in vacuum of the radiation corresponding to the translation
between the energy levels 2p10 and 3d5 of the krypton-86 atom, the atom being at rest with respect to the
observer.
Choosing the standard hyperfine frequency of Hydrogen as 1 420 405 751.770Hz
+0.003Hz, the linear measure meter (new ) works to 4.739 041 287 25 cycles. This
distance will be covered in 0.771 802 603 28 x 108 meter (new) per metric second.
The evidence revealed at places of excavation leaves no doubt that the Indus
Civilization was well advanced in all sciences and their technological capabilities had very
high rating of standardization in actual practice. The Indus Civilization certainly knew the
realistically ‘exact’ value for the ratio Pi and hence the measured dimension of the
circumference of the earth was within their technological capability. This is obvious from
the following facts
(a) The prediction of astronomical phenomenon. Such instruments were a positive contribution for
the measurement of angles. (Rao 1973: pl. XXX B).
(b) The existence of the linear measure- Indus Unit- whose 30 units closely conform to the present
linear scale-metre. A distance of 10 such metros work to 32.816 British feet, which agree with
the actual The existence of a few objects believed to be instruments used to determine the
position of the star; also measurement of the road width of 33 feet (Mohenjo-daro and Lothal
scales).
(c) The construction and geometric plan of the ‘Great Bath’ has its measured dimensions: 46 feet
as its base diagonal, 23 feet broad and 8 feet deep, with the plan area of 100 sq. yards. (all
dimensions in British measures0. The plan area works to about 85 square metros (new).
The ‘bath’ can be interpreted to have been specifically constructed for use as a
‘possible observatory’ rather than a mere ‘community swimming or bathing pool’.
If the intended dimensions are processed in relation to the application of
trigonometric function of angles astonishing facts come to light.
ANGLE
FUNCTION
SINE
COSINE
TANGENT
ABCD represent the base plan of the ‘great bath’ with its border side BC23 feet or 7.01 meter; and the diagonal AC – 46 feet or 14.02 meter. If the standard
dimensions of the bricks used during that age is accepted as 300 mm x 150 mm x
75mm, it will be seen that the length, breadth and the depth needed about 40, 24
and 8 ‘ brick lengths’ respectively. A total of 61 444 such standard bricks would be
needed to fill the volume of the ‘great bath’. This suggests that the idea of a rightangled triangle, i.e. the Pythagorus theorem, and hence  /2 goes back to antiquity;
at least to the Indus Valley Civilization. The historical facts also confirm this
aspect as evidenced from the statements in the Apasthamba, Baudhayana and
Katyayana Sulbas. Baudhay-ana mentions: ‘the diagonal of a rectangle produces
both (areas) which it’s length and breath produce separately’. The intention to
keep the base diagonal to be twice the broader side also suggests the effort made
towards physical evaluation of the value since AB = x BC. It is possible
that they also knew the significance of the equation for the circle a2 +
b2 = c2he base plan was, thus, made to specific fixed angles : and
representing their trigonometric function as:
The longer side AB thus worked to the measured dimension of 39.78 feet
or 12.124 meters (i.e. 3 x 7.01 metre). Not only this, the depth of the ‘great-bath’
was carefully chosen to represent an angle between the base diagonal and the
‘skew-diagonal’, i.e. the angle CAE in the figure. The measured (from base
upwards) represents the linear distance 8 feet or 2.44 metre, which makes Sine
CAE – Sine  = 2.44/14.02 = 0.174037 conforming the statement the Sine CAE
= Sine 10o = 0.1736 (from common log. tables). Hence, the idea of angles and their
application was definitely known in the antiquity of past India. The author,
therefore, concludes:
The Great Bath at Mohenjo-daro was constructed to meet specific intention/requirement, possibly
to make an astronomical observatory; and that it was not just a ‘community swimming pool’.
METRE(LONG)
The present linear measure, the metre, has 100 graduations, each graduation
representing a centimetre. It is unfortunate that the excavated ‘shell’ of Mohenjodaro is only a fragment of the full scale. The rod-like bronze scale found at
Harappa (Wheeler 1966) has 4 marks at an average distance of 0.934 centimetre,
which also is not complete. The ‘ivory scale’ discovered at Lothal (approximately
13 cm x 0.6 cm) is not accurately marked (Rao 1973: pl. XXXII). It can be known
that 20 divisions, each of average 1.7 mm, conform to the measured results of the
Mohanjo-daro ‘shell-scale’. Archeologists have been trying to estimate the basic
and rational measure of length used by the Indus Civilization. It is interesting to
observe that the ‘ancients’ used the hasta hand (24 angula or finger width) for
administrative and commercial use; each angula being 25/12 centimetres (new).
The hasta, thus, was 50 cm(new) or 19.685 British inches.
The dimensions of the Mahenjo-daro bath in various multiples of the Indus
Unit are presented for examination in appendix B. A close observation of columns
3 and 4 strongly suggest that the ‘probable’ basic unit, larger than the Indus Unit,
was closely linked with twice the length of metre (new). This larger unit – called
metre (Long) – possibly had a total of 60 graduations, each being equal to the
distance represented by the Indus Unit = 3.334 092 027 75 centimetres (new)
between the circle and the dot. Two groups of 5 smaller divisions met the need to
have a smaller, decimally divided scale. The difference of opinion among scholars
about the origin (Mainkar and Raju 1964) of the ‘hasta’ could be based on various
historical interpretations. However, it is worthwhile to compare Gudea’s rule (in
2175 BC); being divided in 30 parts of 50.29 cm (19.8 British inches), establishing
a physical relation with the ‘Great-Bath’ of Mohenjo-daro. Did the Indus
Civilization develop their sciences of mathematics and astronomy to the extent of
conceiving that space (distance); time and angle were correlated? The following
consideration strongly points to this probability.
The circle of solid sphere could have Pi or 100 angular units, each such
unit being equal to 2 degrees metric or 1.8o. Working on this line, one can establish
the conclusion that 1/100 of this angular unit resulted in one Indus kilometre; a
distance represented by one kilometre (Long) = 2 kilometres (new). This was the
distance ‘goruta’ as described in Kautilya’s Arthasastra (fourth century BC) and
alsi ‘krosa’ referred to in the Lalitavistara, Chapter 12 written in the first known
among the Indian villagers, called Kos, which is equa; to British 1¼ mile. Also, 1
angular unit in space will work to 200 kilometre (new) or 25 Yojanas. The hour
angle, in time, for use by the astronomical/astrological communities thus used 10
angular Unit = 250 Yojanas = 2,000 kilometre (new), in distance. It is also
surprising to note that the ancient culture indicates the use of both ‘decimal scales’;
i.e. the sexagesimal notation of numeration (in-groups of 6’s) and the present
decimal notation of numeration (in-groups of 10’s). It can, therefore, be presumed
that this was the time when the present decimal system was being absorbed into
the Indus technology, presenting new dimensions in creative thinking.
CONCLUSIONS
The author draws the following conclusions:
(a) The Indus Valley Civilization had an extremely high rating of standardized
practices followed in construction and preservation technology.
(b) The origin of the ‘metric system’ can be traced, as evidenced from the
dimensions of Mohenjo-daro ‘Great-bath’, back to the Harappa Culture, which
had developed the metric-based measurement technology. Evidences also
indicate the use of decimal science based on the ‘sexagesimal numeration’,
(c) An equivalent unit of linear dimension – Metre (Long) – was known in the
antiquity of the Harappa culture some 2,500 metric years ago. This unit was
realistically the same as twice the linear distance of the metre (new).
(d) The significance of inter-linking time, angles and hence calendar in the Indus
Civilization becomes obvious.
(e)
The present linear unit, the metric, needs to be corrected as 1.000 227 451 22
times the present metre distance. The Metre (New) will correspond to
1651139.198 wavelengths of krypton-86 atom or to the distance covered by
electromagnetic waves, in vacuum, during 0.771 802 603 28 x 10-8 metric
second at the velocity of light, which is 1.295 668 083 71 x 108 metre (new)
per metric second (or 299.792 456 2 x 108 meters/second). Accordingly, the
distance between the ‘dot and circle’ on the excavated linear shell of Mohenjodaro is 33.340 920 277 5 millimeter (new).
(f)
The ‘Great-Bath’ of Mohenjo-daro was scientifically constructed to calculated
dimensions, indicating the keen sense of mathematics and astronomy. This
was, therefore, an important observatory, apart from being a ‘community
bathing/swimming pool’.
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Mainkar, VB and Raju, L. 1964. A Development of Length & Area Measures in
South India – Part I; Metric Measures. Vol.7:7.
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