12th IFToMM World Congress, Besançon (France), June18-21, 2007
Astronomical Instruments In Ancient India Shekher Narveker* Agnel Polytechnic, Goa, India Abstract—Some 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, mercury-water wheel.
progressive
development,
I. Introduction Ancient 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 :
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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 ring and string instruments. D. Lalla (700 BC) He wrote a book 'Shihya Dhi Viddhida'. He was well known because of twelve instruments which he brought into 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.
12th IFToMM World Congress, Besançon (France), June18-21, 2007 Astronomers and their period. (1000 BC) Aryabhata (476 AD) Varahamihira, (505 AD)
Contribution in the form of book Suryasidhanta Aryabhata Sidhanta Aryabhatiya Pancha Sidhanta Brihatsamhita Brihat Jataka
Brahmagupta (598 AD) Lalla (700 AD)
Brahmasphuta Siddhanta Karmakhandakhadyaka Shihya Dhi Vriddhida
Shripati (999 AD) Bhaskaracharya (1072 AD)
Jyotishratnamala, Shidhantashekhara Sidhantashiromani Leelavati, Beejaganitam, Karanakutuhala Grahalaghav, Sudhiranjani, Tarjaniyantram
Ganesh Daywanya (1507 AD)
Instruments used by them. Original name
Equivalent name.
Chakra Yantra Gola Yantra Chakra Yantra
Disk instrument. Spherical instrument Ring instrument.
Gola Yantra, Bhangana Yantra, ChakraYantra, Dhanu Yantra, Ghati Yantra. Shakat Yantra Kartari Yantra, Shalaka Yantra, Yashti Yantra Shalaka Yantra
Spherical instrument. Ring instrument. Disk instrument. Bow & arrow instr. Time vessel. Two pivoted sticks Scizzor instrument Needle instrument. Stick instrument. Needle instrument
Chakra Yantra Chaapa Yantra Yashti Yantra Gola Yantra Jalatnalika Yantra (method)
Disk instrument. Semicircular disk instr. Stick instrument. Spherical inst. 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.
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 also another 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).
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.
Fig 3 Units for measurement of length are mentioned in the sript of the book Lilawati.
Script can be read as: Yavodaray-raagul-mashashata-sankhay-hasto-angulay shada-gunitaisacha-turbhihi. Hasteshacha-trurabhivatiha dandaha, kroshaha sahastradwitayena tesham.
12th IFToMM World Congress, Besançon (France), June18-21, 2007
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 make one 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.
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 to measure the height with the help of special geometrical contruction. Shalaka is combination of two sticks with a string. 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.
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 a plumb 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 identify East-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,
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.
12th IFToMM World Congress, Besançon (France), June18-21, 2007
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 height of a tree. To use this machine one has to focus the top and bottom of the object and draw the two lines on the board. 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
h1 h2 l2
l1
d
h
l2 Height = H = d h 1 + d 2 l1
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 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 and to obtain astronomical parameters. (Fig 10).
Fig 9 Sript describing disk instrument of Bhaskaracharya known a chakra yantra.
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 vertical angle.
12th IFToMM World Congress, Besançon (France), June18-21, 2007
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 distance between 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 been also described in the text of 'Sidhantshiromani'. It is somewhat similar to armilliary sphere. However the terminology 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 Ganesh Daywatnya. 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 of horizontal 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].
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 are constructed 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. Observer's Eye
Star
Plate with water
Tube Gnomon
Table
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 the initial 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. Copper tube ( siphon)
Water reservoir
Tube Container
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.
Mercury
Draining tray
Wheel
Water collection tank
Fig 14 Schematic diagram of time measuring machine.
12th IFToMM World Congress, Besançon (France), June18-21, 2007
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 end kept 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 in the 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 a progressive 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 Shrikrishna Prakashana, pages 234, 1996. [2] Bramhanand Tripathi, (Ed) Grahalaghavam of Ganesha Dayawanya., Choukhamba Surbharati Prakashan, Varanassi, page 109, 1995. [3] Chinmaya Yuva Kendra, Awakening Indians to India. Central Chinmaya 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, Choukhamba Sanskrit 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.
