Astronomical Instruments in Ancient India

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12thIFToMM World Congress, Besanon (France), June18-21, 2007

Astronomical Instruments In Ancient India

Shekher Narveker*

Agnel Polytechnic,Goa, India

AbstractSome of the measuring instruments made up of

simple mechanisms used for the measurement of length, angle,

and time have been described in ancient Indian literature.

However these instruments have remained unnoticed due to

language constraints. These instruments were put into use by

various ancient Indian astronomers and mathematicians.

This paper is an attempt to interpret and construct these

instruments based on the available ancient Sanskri tliturature.

Some of the applications of this instrument are also included in

this paper. This paper is an attempt to highlight progressive

development of this instruments from 1000 BC to 1507 AD.

Mercury-water wheel mechanism used for time measurement is

also included.

Keywords: unnoticed, progressive development,mercury-water wheel.

I. IntroductionAncient Indian literature that is available today makes it

clear that there were instruments based on simple

mechanisms which were used to measure vertical angle,

horizontal angle, angles in an inclined plane, distances

and height. Similarly time was measured using water

vessels and also with mechanism working with water

head as a potential. These instruments are discussed in the

various sections of the paper. Original Sanskrit script

describing the instrument and its translation is also

included.

Section II deals with Historical review, section III deals

with Instruments developed by mathematician Lalla.

Section IV deals with stick instrument. Section V deals

with disk instrument. Section VI deals with semicircular

disc, plumb bob type instrument. Section VII deals with

star anglar positioning instrument. Section VIII mentions

a type of armilliary sphere. Section IX deals with water

wheel mechanism for time measurement, and section X

concludes the paper.

II. Historical Review.A. Period of Suryashidhanta (1000 BC).

In India people had started the use of the

astronomical instruments before 1000 BC. During this

period one of the prominent books 'Suryasidhanta' was

written for astronomical calculations. The content of this

book is available but its author is not known. The title

'Suryasidhanta' means sun theory and it highlights the

calculations of positions of stars and planets.

*E-mail :[email protected]

Some of the Indian mathematicians later have

developed their own instruments and developed their own

methods to facilitate the theory of 'Suryasidhanta'.

Introduction of zero in mathematics and the decimal

method of calculation is one of such invaluable

contribution.

B. Aryabhatta (476 AD)

In his book named 'Aryabhattium' he has given lot of

references of Suryasidhanta. He had developed

instruments like chakra yantra (disk instrument), Gola

yantra (type of armillery sphere) and shadow instruments.

C. Varahamihira (505 AD)

He has done a valuable job of compilation of five

astronomical theories which were in use before Crist and

suryasidhanta is one of them. This compiled book is

known as 'Panchasidhanta'. He had developed some ringand string instruments.

D. Lalla (700 BC)

He wrote a book 'Shihya Dhi Viddhida'. He was well

known because of twelve instruments which he broughtinto practice. These instruments are dealt later in sec III.

E. Bhaskaracharya (1072 AD)

He was one of the promonent Indian mathematicien

and astronomer, who wrote a book Sidhantshiromani'. In

his book he has documented valuable ancient liturature

and given the references of many of the instruments used

by the astronomers before him. Similarly he has

documented the various methods for the use of these

instruments.

F. Ganesh Dayvatnya (1506 AD)

He has also described the use of the instruments in his

book 'Grahalaghawam'. There is a typical method of star

positioning listed in his book. His star positoning

instrument is dealt later in section IX.Prominent astronomers, their period, books written by

them and instruments used by them are listed in the

table 1. Shadow instruments (gnomon) are not included in

this table.


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Astronomers andtheir period.

Contribution in the form ofbook

Instruments used bythem. Original name

Equivalent name.

(1000 BC) Suryasidhanta

Aryabhata

(476 AD)

Aryabhata Sidhanta

Aryabhatiya

Chakra Yantra

Gola Yantra

Disk instrument.

Spherical instrument

Varahamihira,

(505 AD)

Pancha Sidhanta

Brihatsamhita Brihat Jataka

Chakra Yantra Ring instrument.

Brahmagupta(598 AD)

Brahmasphuta Siddhanta Karmakhandakhadyaka

Lalla

(700 AD)

Shihya Dhi Vriddhida Gola Yantra,

Bhangana Yantra, ChakraYantra,

Dhanu Yantra, Ghati Yantra. Shakat Yantra Kartari Yantra,

Shalaka Yantra,

Yashti Yantra

Spherical instrument.

Ring instrument. Disk instrument.

Bow & arrow instr. Time vessel. Two pivoted sticks Scizzor instrument

Needle instrument.

Stick instrument.

Shripati

(999 AD)

Jyotishratnamala, Shidhantashekhara

Shalaka Yantra Needle instrument

Bhaskaracharya(1072 AD)

Sidhantashiromani Leelavati,

Beejaganitam, Karanakutuhala

Chakra Yantra Chaapa Yantra

Yashti Yantra Gola Yantra

Disk instrument. Semicircular disk instr.

Stick instrument. Spherical inst.

Ganesh Daywanya

(1507 AD)

Grahalaghav, Sudhiranjani, Tarjaniyantram

Jalatnalika Yantra

(method)

Star positioning

instrument

TABLE 1. Astronomers, books written by them and their instruments.

.

Most of above books are available and they form a fair

link from 1000 BC to 1507 AD. Instruments used during

the period of suryasidhanta [1],[3] are mentioned in its

text (fig 1). It tells us about the instruments that were

based on the use of mercury, water, oil, sand, spokes etc.

Fig 1 Script of Suryasidhant stating the instruments.

Script can be read as: Paradara, ambu, sutrani,

shulbataila jalanicha. Bijani, pasava, asteshu prayoga,

stepi durlabha.

Translation : Mercury filled in spokes, water, thread,

with good craftsmenship these instruments are made,

along with oil mixed with water. Also seeds, fine sand, is

used in these applications, these instruments are rare.

III. Units of measurement.A. Angle.

Unit used for the measurement of angle has been

describe [1],[2] in the text of suryashidhant (Fig 2)..

Fig 2 Script of Suryasidhanta stating the units for angular

measurement.

Script can be read as: Vikalanamkalasastya, tat sastya

bhaga, uchate, tantrimsatam bhavedrasi, bhagano

dvadasaiva te.

Translation : Sixty vikala is one kala, sixty units (kala) is

one bhaga, it is said this way that, thirty units (bhaga)makes one rashi, twelve rashi makes one bhagana.

Vikala, kala, bhaga, bhagana are the units of the angle.

In the modern notation vikala, kala and bhaga are

second, minute and degree respectively. Rashi is alsoanother unit used for the measurement of angle.

B. Length.

Unit used for the measurement of length was

Yahodara, Angula, Hatha, Danda, Krosha and Yojanas.

This unit has been described in the book Lilawati. (Fig3).

Fig 3 Units for measurement of length are mentioned in the sript of thebook Lilawati.

Script can be read as:

Yavodaray-raagul-mashashata-sankhay-hasto-angulay

shada-gunitaisacha-turbhihi.

Hasteshacha-trurabhivatiha dandaha, kroshaha sahastra-

dwitayena tesham.


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Sthadhojanam krosha-chatushastayen, tatha karanam

dashaken vansha.

Nivartanam vimshati-vansha-sankhayhi shetram

chaturmishacha bhujay-nirbandham.

Translation :

Eight rice grains (yahodara) makes one fingure width(angula), twentyfore fingures make one hand (hasta),

four hands make one stick (danda), 2000 danda makeone krosha (unit of length).

Four krosha make one yojana (unit of length), ten

hasta make one vamsha (unit of length), one nirwatan

(unit of area) is equal to 400 square vamsha.

C. Time

Unit for the measurement of time was Vipal, Pala,

Gadi, Hora, and Deena. Sixty Vipala makes one pala.

Sixty pala makes one ghati. 150 Pala makes one Hora.

24 Hora (Hours) makes one Deena (a day). Similarly

units for the measurement of weight, temperature are

also described in ancient text.

IV Instruments of Lalla.Astronomer Lalla describes his fomous twevelve

instruments [3],[4] in his book 'Shihya Dhi Viddhida' as

given in fig 4.

Fig 4 Twelve instruments used by Lalla are described in this script..

Script can be read as:Golo, bhagana, chakra, dhanu, ghati, shanku, shakata,

kartaryaha. Pipta, kapal, shalaka, dwadahsa yantrani saha

yastya.Translation:

Sphere, ring, dial, bow, time measuring water vessel.

Gnomon, divider, scissor. Circular seat with central

stick, semicircle with stick, combination of sticks, are the

twelve instuments along with a stick.These twelve instruments are as described below and

some are shown in fig 5.

The Gola yantra is a type of armilliary sphere used to

locate planetary positions. Bhangana is a ring with

angular graduations alonge its circumference, it is a type

of protractor. Chakra is a circular disk with angular

graduations, it is also a type of protractor. Dhanu is a

semicircular disk with angular graduations and a stick

pivoted at the center, it is a type of protractor with aplumb bob arrangement. Ghati is a small vessel with a

hole at the bottom. It was used to measure time. Shanku

is a type of gnomon, a long vertical cone used to identifyEast-West-North-South direction based on shadow of its

tip. A special geometrical construction known a 'Matsya'

was used for this purpose. Altitude of sun and day time

was also measured with this instrument based on the

shadow. Shakata consists of two 'V' shaped sticks,

pivoted at the end. Kartari means a seizer. This

instrument is made up of two sticks both pivoted

together. It was used like a caliper, and also to measure

angle with the help of protractor. Pitha is a horizontal

disk with a vertical stick at its center. It was used to

measure local time based on its shadow, it was used tomeasure the height with the help of special geometrical

contruction. Shalaka is combination of two sticks with astring. Yasti is just a long stick having standard

dimensions, it was used to measure height and distances.

Special geometrical constructions were framed to

facilitate the use of this stick. These proposed

geometrical constructions were to construct the

proportionate triangles with the help of which heights of

terrestrial objects could be calculated.

Fig 5 A sketch of some of the instruments described by Lalla.

V. Stick Machine of Bhaskaracharya.This machine was known as Yasti Yantra. Yasti means

a stick. It is also refered as Dhi Yantra. Dhi Yantra

means a machine to be used with intelegence. This

machine has been also described by mathematicians like

Lalla, Shripati and others but Bhaskaracharya has

developed his unique method to calculate the height of

terrestrial objects like trees and mountains. The principle

and constructional details of this machine are available

in fair detail in 'Shidhantashiromani' of Bhaskaracharya

[7]. His script describing this instrument is given in the

fig 6.

Fig 6 Sript describing the stick instrument of Bhaskaracharya.

Script can be read as:Vansasha mulam pravilokya chagram, tatsavantaram

tatsya samuchayam cha.Yo vetti yastey-va kar-sthaya sow, dhi-yantra vedi vada

kim na vetti.

Translation :

Look at the bottom and top of bamboo tree, simply

looking at it you can find its distance and its height.


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The person who obtains these distance and height with a

stick, such person can calculate many other astronomical

parameters using this stick which is a intelegent machine

(dhi yantra).

This machine (fig 7) has a stick pivoted to a board. Fig

8 shows geometrical construction to calculate the heightof a tree. To use this machine one has to focus the top

and bottom of the object and draw the two lines on theboard. With these two lines, two triangles are

constructed and based on their proportions, height of the

object is calculated. It is to be noted here that there is no

need to measure the distance between the object and the

observer. This instrument was also used for land survey.

Fig 7 Stick machine known a yasti yantra of Bhaskaracharya.

H

2h

h1

l2l1

d

H d2l

h2 l1

h1

+= dHeight =

Fig 8 Stick machine was used to calculate the height of the tree and

other terrestrial objects.

VI Disk Instrument of Bhaskaracharya.This machine is known as Chakra Yantra. It means

dick machine. It appears to be the combination of chakra

yantra, shanku yantra and pitha yantra of Lalla. Its

description is available in the script of Sidhantshiromani

[7] as given in fig 9. This instrument is a type of

protractor used for angular marking, measurements andto obtain astronomical parameters. (Fig 10).

Fig 9 Sript describing disk instrument of Bhaskaracharya known a

chakra yantra.

Script can be read as: Chakram chakrashankam

paridhow slatha-shrunkhala-dika-dhararam.

Dhatri tribh adharat kalpya bhardheatra khardha cha.

Tanmadhe sushmatam shiptawarka-bhimukha-nemikam

dharyam.

Bhumerunnatta-bhagastatra-kshachchyaya bhuktaha.Tatkhardhantacha nataa unnata-lavasangunikrutam

dhrudalam.Dhrudalonnata-shabhaktam nadya stula paire prokta.

Dalikrutam chakra-mushanti chaapa kodandakhandam

khalu turyagolam.

Translation :

A disk with graduations on the cercumference and is

supported with a flexible chain.

Horizoantal line on this disk is named as bhumi (earth),

space above this line is akash (sky), top point of vetical

line is named as khardha.

At its center attach a stick.

Hold this disk in front of sun, stick will cast its shadow.Angle between the ground (horizontal) line and shadow

of stick is named as unnata.

Similarly angle between top point of disk and shadow of

the stick is nammed as natta.

This natta and unnata are used to calculate the local time.

Half of this disk is known as Chaapa Yantra, and half

of this chaapa yantra is named as turya yantra.

On the surface of this disk a special construction is

recomended to mark E-W-N-S direction [7]. This

instrument was used for angular marking of land and

angular positioning of cities. It was also used to measure

time and to measure some astrological parameters like

'natta' and 'unnatta'.

Fig 10. Disk instrument of Bhaskaracharya.

VII. Semicircular disk machine of Bhaskaracharya.This machine is known as chaapa Yantra. Chaapa

means a semicircle. This instrument appears to be the

modified version of Dhanu Yantra of Lalla.Bhaskaracharya has attached a long stick along the

diameter of the semicircular disk [7]. Disk has the

angular graduations and a pivoted chain at the center of

the disk (fig 11), this chain is used in similar way like a

plumb bob. Description of this instrument is also given

in Sidhantashiromani [7] which is already listed in fig 9.

Basically it was used for the measurement of verticalangle.


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Fig 11 Semicircular disk instrument of Bhaskaracharya known as

chaapa yantra.

Height of the terrestrial objects, diameter of earth,

diameter of moon, circumference of earth and distancebetween moon and the earth was calculated by

Bhaskaracharya using this instrument.

To calculate the height of the terestrial object, stick

was focussed at the bottom and top of the object and the

angle was measured. This angle was then used to

calculate the height with the help of jya and cotijya. This

jya and cotijya are similar as sine and cosine resp.

VIII Star positioning instrument of Bhaskaracharya.

This instrument is known a Gola yantra and has beenalso described in the text of 'Sidhantshiromani'. It is

somewhat similar to armilliary sphere. However theterminology used here is not understandable and it is

difficult to construct the instrument in its original form.

Instrument used by Aryabhatta for star positioning

consists of one horizontal disk, positioned in E-W-N-S

direction and another similar disk held perpendicular to

it with a plumb bob arangement [4].

IX. Star positioning Instrument of GaneshDaywatnya.

This instrument is known as Jala nalika yantra. It

means water and tube machine. It is described as a

method of measuring star angle with the help ofhorizontal water surface and a hollow tube. Angle is

measured with the help of constructed triangles as

described in the book Grahalaghawam of Ganesh

Daywatnya. This original script is not in full detail, it is

given as a outline of points as explained below (fig 12).

Its detail explanation is available in other edited

books[2].

Fig 12 Script describing the star angle measuring instrument.

Translation :

A method to measure the angle of the planet through a

tube. In the respective direction, complete the

construction, that is if star is in east then in the easten

side or if star is in west then western side, construct the

further proccedure.

Construct the triangle and mark its base, height and

hypotenuse.

Locate the gnomon, hold the thread, and hold the tube on

top of the gnomon and look at the star.

Keep a plate filled with water and you can observe star

immage through this water.This arrangement consists of a levelled surface

placed in E-W-N-S direction [2]. Triangles areconstructed on this surface to obtain angles. A gnomon

is placed on this surface. A tube is placed on the top of

the gnomon. A plate filled with water is kept on the

surface. Reflected image through water surface of the

star or a planet is observed through the tube and its angle

is measured with the help of constructed triangles. A

thread is used to measure height, base and hypotenuse in

the vertical plane. This instrument was used for mapping

of stars and planets. Instrument used for star angle

measurement is shown in fig 13.

Plate

waterwith

Star

Table

Tube

Gnomon

EyeObserver's

Fig 13 Schematic diagram of star angle measuring instrument.

X. Time measuring machine of Bhaskaracharya.This machine was known as Jala chakra yantra. It

means water wheel machine. It is a time measuring

machine and is described in the book Sidhantsiromani

[7]. Schematic diagram is shown in fig 14, its script is

shown in fig 15, and fabricated model is shown in the fig

16. This mechanism operates with a balance between

mercury in the tubes and the water in the vessels.

This mechanism uses water head as a potential. In theinitial position, containers are empty and mercury is in

lower position on the wheel. As the water gets collected

into one of the container, the wheel starts rotating. A

stage comes when mercury slides from one end of the

tube to the other end of tube and causes an imbalance,

due to which the wheel rotates further. Because of

mercury, wheel rotates in jerks. If four containers are

used then each container rotates the wheel by 90 degrees.

Draining tray

Mercury

Watercollection tank

Wheel

( siphon)

Tube

Copper tubeWater

Container

reservoir

Fig 14 Schematic diagram of time measuring machine.


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Fig 15 Script describing time measuring machine.

Script can be read as:Laghu-daruja-samachakre sama-sushiraraha samantara

nemyam.

Kinchid-wakra yojyaha sushira-syardhe pruthaka tasam.

Rasapurne tachakram dyadhara-shasthita svayam

bhramati.

Tamradi-mayasya-nkusha-rupanalasyambu-poornasya.

Yeka-kunda-jalantardwitiya-magram twadho-mukham

cha bahihi.

Yugapanmuktam chet ka nalena kunda-dwahihi patati.

Nemyam badhadwa ghatika-chakram jalayantrawata

tatha dharyam.

Nalaka-prachuta-salilam patati tatha tad-ghati-madhe.Bhamati tatastat satat purna-ghati-bhihi samakrustam.

Chakra-chutam tadudakam kunde yati pranalikaya.

Translation :

A symetric wheel made of wood with exactly similar and

hollow spokes joined to the rim such that they are

slightly inclined.

Hollow spokes should be half filled with mercury. Wheel

should be supported on the axle to rotate freely.

Copper or other metallic U shaped bent tube, is inverted

and filled with water.

One end of tube is deeped in water tank and other endkept below water level and outside the tank.

If both ends are oppened simultaneously then water

flows outside the tank through the tube.

On the rim attach the vessels, place the whole

arrangement of water wheel below the tube.

Such that the water flowing through the tube falls into

the vessel.

Vessel gets filled with water and wheel starts rotating.

Water gets poured out of the vessel and is collected inthe tank through a channel.

Time period of rotation of this wheel is constant as

long as water flow is constant. It was used to measure

the time which was based on revolutions made by the

wheel.

Fig 16 Time measuring machine of Bhaskaracharya.

V. Conclusion

The concept of measurement of angle, height and time

with the help of instruments and mechanisms was being

practiced in ancient India. It appears that there is aprogressive development of instruments from 1000 BC

to 1507 AD. Measurements were also done with well

defined units for angle, length and time. Similarly

innovative geometrical constructions were used to

facilitate the use of these instruments. A typical time

measuring mechanism using water-mercury was used to

achieves the constant time period of rotation.

Acknowledgement:The author is thankful to Sanskrit Bharati and Bharat

Vikas Parishad for their support and for arranging the

literature. Thanks goes to Mr. Vishavanath G. Joshi for

helping the author to learn Sanskrit language and to

translate the scripts.

References:

[1] Baladevprasadji Mishra. (Ed). Suryasidhant, Khemraj ShrikrishnaPrakashana, pages 234, 1996.

[2] Bramhanand Tripathi, (Ed) Grahalaghavam of GaneshaDayawanya., Choukhamba Surbharati Prakashan, Varanassi, page

109, 1995.

[3] Chinmaya Yuva Kendra, Awakening Indians to India. CentralChinmaya Mission Trust. Page 397, 404, 2003.

[4] Keshav Srusti (Ed), Vijanan Bharati Publication, Mumbai, page

21, 23, 29, 31, 90

[5] Shrikapileshwara Shastri, (Ed), Suryasidhant, ChoukhambaSanskrit Sausthan, Varanassi, Page 264, 270, 2003.

[6] Ramchandra Pandey, (Ed), Lilawati, Kkrishanadas Akadamy,

Varanassi, page 2, 134, 196, 1993.[7] Muralidharachaturvedi, Shrimad Bhaskaracharya Pranit

Sidhantsiromani, Sampurnanand Sanskrit University, Varanassi,page 360-362, 443,470, 1998.

[8] Mohan Apte, Ganitashiromani Bhaskaracharya, Moraya

Publication, Mumbai, page 115-118, 1998.[9] S. R. Narvekar, 'Constant RPM Water wheel Clock', Proceedings

of 12th National Conf. on Machines & Mechanisms 2005, India,.

page236-242,2005.

Astronomical Instruments in Ancient India

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