Units of Length Measurement and Speed of
Light in Ancient India
Dr M R Goyal <mrgoyal@gmail.com>
July 18, 2014
Abstract
An exact value of the unit of length measurement, used in Indus-
Saraswati Civilization, has been determined from the precise scale dis-
covered by Ernest Mackay in the 1930-31 season excavation at Mohenjo-
daro, and further correlated with the present day units of measure-
ment. It has then been calculated and shown that the speed of light as
given in the Vedic literature, when referenced with this erstwhile unit
of length measurement (used in Indus-Saraswati Civilization), works
out to be precisely equal to the speed of light as per modern measure-
ments. The present article is a step-wise process followed to unveil this
equality.
1 The Precise Scale
In his 1930-31 season at Mohenjo-daro, Ernest Mackay discovered a broken
piece of shell bearing 8 divisions of 6.7056mm each, with a dot and circle ve
graduations apart, which suggests a decimal system. However, attempts by
Mackay, to relate such a unit to the dimensions in Mohenjo-daro, were not
very successful(ref Michel Danino [1]) and thus were abandoned.
2 Units of Length in Chanakya's Arthashas-
tra
Chanakya was the political mentor of the legendary Indian monarch Chan-
dragupta Maurya of 4th century BC. He was a man learned in many disci-
plines and wrote the famous book Arthashastra. In Arthashastra, Chanakya
1
mentions two types of Dhanusha s as units for measuring lengths and dis-
tances. One is the ordinary Dhanusha, consisting of 96 Angula s, and the
other Dhanusha is mentioned as Garhpatya Dhanusha and consists of 108
Angulas, used for measurement of roads and distances. Chanakya also men-
tions that a Dhanurgraha consists of 4 Angula s and a Yojana consists of 8000
Dhanusha s.
3 Decoding the Mohenjo-daro Scale
If we keep 10 divisions of the Mohenjo-daro scale to be equal to a Dhanurgraha
or 4 Angula s, the precise length of an Angula works out to be 16.764mm.
A Dhanusha of 96 Angulas = 96 × 16.764mm = 1.609344m (1)
And
A Dhanusha of 108 Angulas = 108 × 16.764mm = 1.810512m (2)
A Y ojana = 8000 Dhanushas(of 108 Angulas each) (3)
= 8000 × 1.810512m = 14.484096km (4)
Further
14.484096km = 9 miles, (exactly!). (5)
Also
1000 Dhanushas of 96 Angulas each = 1 mile (6)
Interestingly, when we look into the history of mile, we nd that the word
mile is derived from mille, which means a thousand.
4 Other Ancient Scales
4.1 The Indus Inch
The Indus civilisation unit of length, widely known as Indus Inch was 1.32
Inches which is exactly equal to 2 Angulas of 16.764mm each.
2
4.2 The Gudea's Rule
The Gudea's rule (2175 B.C.) preserved in the Louvre shows intervals in
Sumerian Shusi of 0.66 inches, which is exactly equal to the Indus-Saraswati
Angula of 16.764mm.
4.3 Temple Wall-Engravings
Two engravings on a wall of the temple at Tiruputtkali (12th Century A.D.)
near Kanchipuram, show two scales[8] one measuring 7.24 metres in length,
with markings dividing the scale into 4 equal parts, and the second one
measuring 5.69 metres in length and markings dividing the scale into 4 equal
parts. It may be observed that each division of the rst scale is precisely equal
to a Dhanusha of 108 Angulas of 16.764mm each. Interestingly, the second
scale is precisely equal to π times Dhanusha i.e. equal to the circumference
of a circle with one Dhanusha as its Diameter.
It is interesting to note here that Mackay reports[9] at Mohenjo-daro, a
lane and a doorway having both a width of 1.42m, which is precisely equal to
one division of the second scale at the Tiruputtkali Temple, indicating that
both the scales were prevalent in Indus-Saraswati Civilization as well as in
South India.
5 Correlation with Dimensions of Ancient Struc-
tures
5.1 Mohenjo-daro's Great Bath
The height of the corbelled drain forming the outlet of Mohenjo-daro's Great
Bath[2, pp. 133-142] is about 1.8m, which is equal to a Dhanusha of 108
Angulas of 16.764mm each.
5.2 Standard Street-Widths
Kalibangam, a city in the Indus-Saraswati Civilization (in Rajasthan, India)
had street widths[3] of 1.8m, 3.6m, 5.4m and 7.2m i.e. built to the stan-
dard dimensions being equal to 1 Dhanusha, 2 Dhanushas, 3 Dhanushas and
4 Dhanushas respectively. Such widths are found at other sites also. Big-
ger streets of Banawali[3] another town in Indus-Saraswati Civilization (in
Haryana, India) measure 5.4m i.e 3 Dhanushas.
3
5.3 The Great Pyramid of Giza, Egypt 3104BC[12]
From accurate measurements of the base of the Great Pyramid, the length of
its north-west-south-east diagonal works out to 325.87 m, which is precisely
equal to 180 Dhanushas of 108 Angulas each, the dierence being only 0.02 m,
which is well within the error of measurement. Clearly the Indus Saraswati
units of length were prevalent in Egypt at that time.
5.4 Taj Mahal
A Persian manuscript Shah Jahan Nama contains a very particular descrip-
tion of three principal buildings of Agra the Taj Mahal, Moti Masjid and
Jamah Masjid. In the Shah Jahan Nama, the dimensions of these three
buildings are given in Gaz. These dimensions were got measured by col. J.A.
Hodgson in December, 1825, in feet and inches. The various (28) dimensions,
in feet and inches, as well as in Gaz, are given by Hodgson in his article[4],
in Table A. The weighted mean length of a Gaz works out to 31.7 inches,
(80.5 cm) from Table A. It is pertinent to mention here that Barraud[5, pp.
108-109, 258-259] in The Complete Taj Mahal and the River front Columns
of Agra, has taken a Gaz as equal to 80.5cm which is precisely equal to half
a Dhanusha of 96 Angulas.
5.5 Mayan City in Mexico (North America)
Drewitt[6] and Drucker[7] made a study of the ancient city of Teotihuacan,
belonging to Mayan Civilization , in Mexico, and hypothesised a unit of
80.5cm, which is precisely equal to half a Dhanusha of 96 Angulas.
6 Speed of light in Vedic Literature
In the commentary on Rig-Veda, Mandal 1, Sukta 50, Mantra 4, Sayanacharya
(14th Century AD) writes:
ta;Ta;a . ca .sma;yRa;tea ...
ya;ea:ja;na;a;na;Ma .sa;h;~å:òea :dõe :dõe Za;tea :dõe . ca ya;ea:ja;nea Á
O;;ke+:na ; a;na;a;ma;Sa;a;DeRa;na kÒ+:ma;ma;a;Na na;ma;ea;~tua .tea Á Á
Meaning. . . Salutations to Thee (the Sun) who approacheth (at
a speed of ) 2202 yojanas in a nimishardha.
Clearly it is the Speed of light(or sunrays) that is mentioned in the shloka.
This shloka is attributed[10, pp. 67] to the son of Kanva Maharshi (5
th
4
mellenium B.C.). Bhatt Bhaskara (10th Century A.D.) also mentions[11]
this shloka, in his commentary on Taittiriya Brahmana.
To put it in mathematical terms, as stated by the above shloka, the speed
of light would be:
Speed Of Light = 2202 Y ojanas/N imishardha (7)
As we have calculated earlier, a Yojana = 14.484096 Km. For the value
of Nimishardha, we refer to Vishnu Purana (Book 1, Chpater 3, shloka 8,9),
wherein it is stated that:
15 Nimisha s = 1 Kashtha
30 Kashta s = 1 Kala
30 Kala s = 1 Muhurta
30 Muhurta s = 1 day & night (A;h;ea:=+a:a;m,a)
Thus
one day & night = 405, 000 N imishas = 810, 000 N imishardhas. (8)
(Literal meaning of Nimishardha being half a Nimisha ).
In Surya Sidhant (Chapter 1, Shloka 12), it is stated that 60 Nadis con-
stitute one Sidereal Day and Night (na;a;[a:a;m,a A;h;ea:=+a:a;m,a). It is also well known
that a Muhurta = 2 Nadi s. It is clear from this that in Astronomical calcu-
lations, the sidereal day was taken as the unit of time. A sidereal day is the
time taken by the stellar constellations to complete one revolution around
the Earth. A sidereal day is equal to 23 hours, 56 minutes and 4.1 seconds,
or equivalently 86,164.1 sec.
Thus. . .
N imishardha = 86164.1/810000 sec = 0.1063754sec (9)
The speed of light as given in the Vedic Literature therefor comes out to
be:
2202 × 14.484096 km
= 2.998 × 105 km/sec (10)
0.1063754 sec
which is precisely equal to the speed of light as per the latest modern mea-
surements.
7 Conclusions
From the above, the following conclusions can be drawn:
5
1. The basic unit of length measurement in the Indus-Saraswati Civiliza-
tion was an Angul of 16.764mm. This unit was used not only in the
Indus-Saraswati Civilization, but also in South India, and other ancient
world Civilizations including Sumerian, Egyptian and Mayan Civiliza-
tions.
2. The modern age concept of globalization was an established way of life
in the Vedic/Indus-Saraswati Civilization era, as proven by the shared
unit of length measurement found across far- ung cultures spread over
Asia, Europe, Africa and America.
3. The Speed of Light as given in the Vedic literature, is precisely equal
to the Speed of Light as per modern measurements, which shows that
during the period 5000 B.C. to 3000 B.C., Science and Technology was
very much advanced, which was somehow lost during the medieval ages.
References
[1] Danino, Michel The Lost River On the Trail of Saraswati, Penguin
Books, 2010.
[2] Jansen, Michael Mohenjo-daro: architecture et urbanisme, Les cités ou-
bliées de lÍndus: Archéologie du Pakistan, 1988.
[3] Lal, B.B. The Earliest Civilization of South Asia, Aryan Books Interna-
tional, New Delhi, 1997
[4] Hodgson, Col. J.A. Memoir on the Length of the Illahi, Guz, Journal of
the Royal Asiatic Society of Great Britain and Ireland., 1840.
[5] Barraud, R.A.The Complete Taj Mahal and the Riverfront Gardens of
Agra (ed. Koch E.) Thames and Hudson. London, 2006.
[6] Drewitt, Measurement Units and Building Areas at Teotihuacan, 1987
[7] Drucker, R. David.Precolumbian Mesoamerican Measurement Systems:
Unit Standards for Length, 1977
Urban Geography and Land Measure-
[8] James Heitzman and S. Rajagopal,
ment in the Twelfth Century : The Case of Kanchipuram, The Indian
Economic and Social History Review. SAGE, 2004
[9] Mackay, E.J.H., Further Excavations at Mohenjo-daro, Govt. of India.
vol. I. republished Munshiram Manoharlal, 1998.
6
[10] Pride of India, Published by Sanskrit Bharati, 2006.
[11] Subhash Kak, The Speed of Light and Puranic Cosmology, 2001.
[12] S.G. Taseos: Back in Time 3104 B.C. to the Great Pyramid, 1990
