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The Astronomical Observatories of Jai Singh

Between 1724 and 1727, Jai Singh II, a re-gional king under the Mogul empire, con-structed ve astronomical observatoriesin his native territory of west central In -dia. Passionately interested in mathemat-ics and astronomy, Jai Singh adapted andadded to the designs of earlier sight-basedobservatories to create an architecture forastronomical measurement that is unsur-passed. Jai Singh was inuenced primarily by

the Islamic school of astronomy, and hadstudied the work of the great astronomers

of this tradition. Early Greek and Persianobservatories contained elements that JaiSingh incorporated into his designs, butthe instruments of the Jantar Mantar, as

Jai Singhs observatories have come to beknown, are more complex, or at a much

The Jantar Mantar at New Delhi, India. The red wash on the masonry structures stands in

contrast to the lush green of its park-like setting in the midst of downtown New Delhi. A

popular itinerary for foreign as well as national tourists, the sites open space and protected

boundaries also offer the citys residents a quiet place for respite and contemplation.

Architecture in the Service of Science

greater scale than any that had come be-fore, and in certain instances, are com-pletely unique in design and function.

Of the observatories originally built atDelhi, Jaipur, Mathura, Ujjain, and Vara-nasi, all but the Mathura observatory stillexist. The condition of the instrumentsvaries, due to the ravages of weather andlack of maintenance over time, but the ob-servatories at Jaipur and Ujjain have havehad considerable restoration, and repairshave been made from time to time at eachof the sites.

The Astronomical Observatories of Jai Singh II

The Varanasi observatory was built on

the roof of the Man Singh palace, over-

looking the Ganges.

Text and Photographs by Barry Perlus

Photographs and text 2005 Barry Perlus

Illustrations of the principles of the instruments

from Virendra Sharma: Jai Singh and His Astron-

omy , Motilal Banarsidass, publishers - used by

permission.

Site plans and elevation drawings, except where

otherwise noted from G. S. Kaye: The Astronom-ical Observatories of Jai Singh, published by the

Archaeological Survey of India.

Two of the twelve instruments known

as the Rasivalaya Yantras, foreground,

at the Jaipur observatory. Each of the

Rasivalayas refers to one of the signs

of the zodiac, and is designed to direct-

ly measure the latitude and longitude

of a celestial object at the moment that

the sign to which it refers crosses the

meridian.

Above: Part of the Ujjain observatory.

From left to right, the Samrat, Nadiva-

laya, and Digamsa Yantras.

Plan of the Delhi Observatory. The site

occupies an area of approximately ve

acres.


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The Jaipur Observatory

The city of Jaipur is located about 220km south and west of New Delhi, in theState of Rajasthan. It was designed and

built as a new city ca. 1727 by Jai Singh,and incorporated architectural and plan-ning concepts that were advanced fortheir time. The city is also home to thelargest and most elaborate of the ve ob-servatories, located just across from theRoyal Palace.

The observatory at Jaipur, above seen

from atop the gnomon of the Samrat

Yantra (large sundial). The grey area in

the site plan, below, indicates the area

captured in the photograph.

a prominent star. This may be ob-tained from appropriate tables orcalculated from the knowledge thata star returns to the meridian after23 h, 56 min, 4.09 sec, the length ofa sidereal day. The time at nightis measured then by observing thehour angle of the star or its angulardistance from the meridian. Thereadings then may easily be con-verted into the mean solar time. Formeasuring at night, a tube or slit is

used as a sighting device as Jagan-natha suggests. With the quad-rant edge as the vantage point, theobserver looks at a prominent starthrough the device and moves thedevice back and forth along thequadrant edge SQ I (gure 1), untilthe star appears to graze the gno-mon edge AC. The vantage point Von the quadrant edge then indicatesthe hour angle or meridian distanceSV of the star, which after proper

conversion gives the apparent solartime.

Because a Samrat, like any othersundial, measures the local timeor apparent solar time and not theStandard Time of a country, acorrection has to be applied to itsreadings in order to obtain the stan-dard time. The correction for IndianStandard Time is as follows:

Indian Standard Time = LocalTime Equation of Time Longi-tude difference.

Telling Time with the LargestSundial in the World

The Samrat Yantra, picturedfar right andin illustrations, below, is the largest sundialin the world. Its gnomon rises over 73feet above its base, and the marble facedquadrants, 9 feet in width, create an arc

that reaches 45 feet in height. According toPhysicist V. N. Sharma, author ofSawaii

Jai Singh and His Astronomy:

The primary object of a Samrat isto indicate the apparent solar timeor local time of a place. On a clearday, as the sun journeys from east towest, the shadow of the Samrat gno-mon sweeps the quadrant scales be-low from one end to the other. At agiven moment, the time is indicated

by the shadows edge on a quadrant

scale.In order to nd time with the in-

strument at night, one has to knowthe time of the meridian transit of

View of the Samrat Yantra at Jaipur from the North East

Samrat Yantra section and model

Figure 1

Samrat Yantra: Principle and Operation

Site plan of the Jaipur observatory


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cision brought forth a collection of largescale structures for the measurement ofcelestial position and movement thatis unequalled today. Among the manystartling impressions for a visitor to oneof the observatories, is the scale of the in-struments. One is literally enveloped, and

When the surface upon which the sunsshadow falls is formed into a circular arc,and aligned perpendicular to the earthsaxis of rotation, the passage of the sunoverhead casts a shadow which movesacross the surface in equal time incre-ments. This type of dial, known as equi-noctial, was described as early as the7th century and is the design used by JaiSingh for the Samrat Yantra.

Accuracy and Scale

When Jai Singh designed the observa-tories, one of his foremost objectives wasto create astronomical instruments thatwould be more accurate and permanentthan the brass instruments in use at thetime. His solution was to make them large,really large, and to make them of stone andmasonry. This simple yet remarkable de-

The Problem of the

PenumbraWhile the enormous size of the Samrat

Yantra generates large scales with nedivisions, a problem arises due to the factthat the sun is not a single point in thesky, but rather a disc, with nite diameter.Expressed in angular degrees, the sunspenumbra (the edge of the suns shadow)is one-half degree. As a consequence, theshadow edge is not a sharp, abrupt changefrom light to dark, but changes graduallyover a distance of several centimeters.

time with accuracies better than 15seconds. However, when the sun isstrong, the difculty may be elimi-nated and the procedure of mea-suring time made objective. This isdone by superimposing on the pen-umbra the shadow of a thin object

confronted with a space that is both aes -thetic and mathematical. The time scale ofthe Samrat Yantra at Jaipur, for example,includes subdivisions as ne as two sec-onds, and as one watches, the motion ofthe gnomons shadow becomes a palpableexperience of earths cosmic motion.

Virendra Sharma writes:

The rst and foremost factor affect-ing the precision of time measure-ments, and which is inherent in thevery design of the instrument, is thewidth of the penumbra. For largeSamrats, such as those at Delhi and

Jaipur, the penumbra could be sev-eral centimeters wide. The sun, be-cause of the nite width of its disc,casts diffused shadows of objects.As a result, pinpointing the exact lo-cation of the shadow-edge becomesa difcult as well as a subjectivematter. The penumbra at the GreatSamrat of Jaipur, at mid-morning ona clear day, can be as wide as 3 cmor more, making it difcult to read

such as a needle or a string.By holding a one to two cm long

taut string parallel to the shadowedge, about one cm or so above theinstruments surface, and readingthe scale where the strings shad-ow merges with the shadow of thegnomon edge, we could repeat ourreadings with an accuracy of 3 secor better. The author believes that

Time subdivisions on the quadrant scale.

The smallest subdivisions, visible in the

lower right corner, represent intervals of

two seconds.

How Does It Work?

Most of us are familiar with the brasssundials often used as ornaments in gar-dens. These designs, known as horizontaldials, cast the suns shadow from a verti-cally mounted triangular plate across ahorizontal surface scribed with lines in-dicating the hours of the day. Due to theprojection of the suns apparent circularmotion across our sky onto a at plane, thehour divisions are unequal, being moreclosely spaced towards the noon hour.

Figure 2

Samrat Yantra Perspective

The penumbra of the sun is one-half

degree wide. The gure shows a highly

exaggerated version of the effect.

Detail of Quadrant with shadow

Panoramic view of the Samrat Yantra

from ground level at the west quadrant.


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the astronomers of Jai Singh musthave used some device similar tothat of the string for overcoming theproblem of the penumbra.

the object and the hour angle of areference star. From the measure-ments, the difference between theright ascensions of the two is calcu-lated. By adding or subtracting thisdifference to the right ascension ofthe reference star, The RA of the ob-

ject is determined.

Shasthansa Yantra

A secondary instrument, built within thetowers that support the quadrant scales,gives extremely accurate measurementsof the zenith distance, declination, and di-ameter of the sun. Called the ShasthansaYantra, as Virendra Sharma describes, it isessentially:

. . . a 60 degre arc facing south,within a dark chamber. The arc isdivided into degrees and minutes.High above the arc, at its center onthe south wall, is a pinhole to letsunlight in. As the sun passes across

Other Measurements

In addition to marking local time, the

Samrat or Great Yantra was used to de-termine the suns declination and the rightascension (RA) of any celestial object.

According to Virendra Sharma:

to measure the declination of thesun with a Samrat, the observermoves a rod over the gnomon sur-face AC up or down (Figure 1) untilthe rods shadow falls on a quad-rant scale below. The location of therod on the gnomon scale then givesthe declination of the sun. Decli-

nation of a star or planet requiresthe collaboration of two observers.One observer stays near the quad-rants below and, sighting the starthrough the sighting device, guidesthe assistant, who moves a rod upor down along the gnomon scale.the assistant does this until the van-tage point V on a quadrant edge be-low, the gnomon edge above wherethe rod is placed, and the starallthreeare in one line. The locationof the rod on the gnomon scale then

indicates the declination of the star.In this exercise, in addition to twoobservers, a torch bearer may also

be necessary to shine light on therod on the gnomon edge for theprincipal observer near the quad-rants below to see it clearly.

The right ascension or RA of anobject is determined by simultane-

ously measuring the hour angle of

the meridian at noon, its pinholeimage falling on the Shasthansascale below enables the observer tomeasure the zenith distance, declil-nation, and the diameter of the sun.

The gure below shows the principle ofits operation.

of the chamber are home to dozens of batswho gain entrance through ventilationgrills in the upper section of the tower. Aplatform about 12 feet above oor levelprovides access to observe the suns im-age on the quadrants. A bamboo ladder isused to reach the platform.

I visited the Shasthansa Yantra at Jaipurin December 2004 and made time lapsestudies of the suns meridian transit. Thechamber is entered from the north wallof either the east or west tower (there areduplicate instruments, one in each tower).the interior of the chamber is about 15feet wide by 30 feet long, and is open toa height of about 40 feet. The upper areas

Observing the center of the penumbra

Interior of the Shasthansa Yantra

Detail of the Shasthansa quadrant with

the pinhole image of the sun at noon

Figure 1

Samrat Yantra: Principle and OperationThe principle of the Shasthansa Yantra

The Shasthansa Yantra is built withinthe towers that support the great quad-

rant, as seen in this model.


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The Jai PrakashMirror of the Heavens

The Jai Prakash may well be Jai Singhsmost elaborate and complex instrument.It is based on concepts dating to as earlyas 300 B.C. when the Greco-Babylonianastronomer Berosus is said to have made

a hemispherical sundial. Hemisphericaldials also appear in European Church ar-chitecture during the Middle Ages, and atthe observatory in Nanking, China in thelate 13th-century. The Jai Prakash, howev-er, is much more elaborate, complex, andversatile than any of its predecessors.

How it Works

The Jai Prakash is a bowl shaped instru-ment, built partly above and partly below

ground level, as can be seen in the draw-ing below.The diameter at the rim of the bowl is

17.5 feet for the Jaipur instrument, and 27feet at Delhi. The interior surface is di-

Plan and section of one of the Jai

Prakash pairs at the Delhi observatory.

Jai Prakash were built only at Jaipur and

Delhi.

vided into segments, and recessed stepsbetween the segments provide access forthe observers. A taut crosswire, suspend-ed at the level of the rim, holds a metalplate with circular opening directly overthe center of the bowl. This plate serves asa sighting device for night observations,and casts an easily identiable shadow onthe interior surface of the bowl for solar

observation.The surfaces of the Jai Prakash are en-graved with markings corresponding toan inverted view of both the azimuth-al-titude, or horizon, and equatorial coordi-nate systems used to describe the positionof celestial objects. See gure 4, right.

Virendra Sharma gives a detailed de-scription of the design of the Jai Prakash:

In the azimuth-altitude system,the rim of each hemispherical sur-face represents the local horizon andthe bottom most point, the zenith.

Cardinal points are marked on therim, and cross wires are stretched

between them. A great circle drawn between the north and the southpoints and passing through thezenith on the instruments surfacerepresents the meridian. From thezenith point a number of equalazimuth lines are drawn up to the

rim or horizon. Next, a number of

equally-spaced circles with theircenters on the vertical axis passingthrough the zenith are inscribedon their surface. These circles areparallel to the rim and intersect theequal azimuth lines at right angles.

For the equatorial system, a sec-ond set of coordinates is inscribed.For these coordinates, a pooint on

the meeridian, at an appropriatedistance below the south point onthe rim, represents the north celes-tial pole. At a distance of 900 furtherdown, a great circle intersecting themeridian at right angles representsthe equator. On both sides of theequator, a number of diurnal circlesare drawn. From the pole, hour cir-cles radiate out in all directions upto the very rim of the instrument.

On a clear day, the shadow fo thecross-wire falling on the concave

Unwrapped spherical panorama from within the Jai Prakash at the Jaipur observatory. The sighting guide is visible against the sky.

Figure 4

The principle of the Jai Prakash.


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surface below indicates the coordi-nates of the sun. These coordinatesmaay be read either in the horizonor in the equator system as desired.The time is read by the angular dis-tance from the meridian measuredalong a diurnal circle.

Jai Singhs Ingenuity:The Jai Prakash built asComplementary Pairs

As described earlier, the design of the JaiPrakash was based on earlier hemispheri-cal sundials. But Jai Singh modied thisdesign to be able to make night time ob-servations. He did this by removing thearea of the concave surface between alter-nate hour circles and providing steps forthe observer to move around freely to take

readings. Working at night, the observersights the object in the sky through the cir-cular aperture plate at the intersection ofthe cross-wires. With the aid of a sightingdevice attached to the concave surface theposition of the sky object is then read fromthe engraved coordinates.

A second instrument was built next tothe rst, identical in all respects except thatthe hour circles corresponding to the stepsin the rst have a solid, engraved surface,and the hour circles corresponding to the

Plan view of the Jai Prakash at Delhi.

engraved surface of the rst are removedto provide steps. As seen in the plan view,the instruments are exact complements ofeach other, and if the engraved surfaces(tinted red) of one were to be transposed

above the other, they would represent asingle complete surface. In practice, whenthe shadow of the sun cast by the cross-wire, or the coordinates of a celestial bodyobserved at night moves past the edge ofone of the engraved surfaces, the observerwalks to the other instrument and contin-

ues the observation there.

Panoramic view of the interior of the Jai Prakash at Jaipur. At far left is the passageway to the companion instrument, and at far right, exit

steps to the outside. At center is the opening between hour segments of the hemispherical surface, with steps leading down to the center of

the bowl.

Kapala YantraPredecessor to the Jai Prakash

According to maps of the Jaipur ob-servatory dating to the early years of itsconstruction, Jai Singh built two smallhemispheric dials, with a diameter of 11

feet, before constructing the Jai Prakash.These instruments, named Kapala Yan-tras, were built side by side on a masonryplatform. Named Kapala A and KapalaB, the two hemispheric bowls have verydifferent functions. Kapala A has engrav-ings similar to the Jai Prakash, but lacksthe cutaways and size that would permitnight observations. Kapala B serves onlyto transform graphically the horizon sys-tem of coordinates into the equator systemand vice versa. It is the only instrument at

Jaipur not meant for observing.

The Kapala A at Jaipur. The crosswire,

center plate, and its shadow can be

clearly seen in the inset.

The Jai Prakash at Jaipur. The pattern of

alternating areas of surface and void can

be seen by careful comparison.


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Ram Yantra

The Ram Yantra is a cylindrical structurebuilt in pairs like the Jai Prakash. Its pri-mary function is to measure the altitudeand azimuth of celestial objects, includingthe sun. In the Islamic and Hindu schoolsof astronomy there were no insturmentslike the Ram Yantra prior to Jai Singhscreations.

Virendra Sharma gives this descriptionof the principle and operation of the RamYantra:

The cylindrical structure of Ramayantra is open at the top, and itsheight equals its radius. To under-stand the principle, let us assumethat the instrument is built as a singleunit as illustrated in Figure 4. Thecylinder, as illustrated in the gure,is open at the top and has a verticalpole or pillar of the same height asthe surrounding walls at the cen-ter. Both the interior walls and theoor of the structure are engravedwith scales measuring the angles ofazimuth and altitude. For measur-ing the azimuth, circular scales withtheir centers at the axis of the cyl-inder are drawn on the oor of thestructure and on the inner surface ofthe cylindrical walls. The scales aredivided into degrees and minutes.For measuring the altitude, a set of

equally spaced radial lines is drawnon the oor. These lines emanatefrom the central pillar and termi-nate at the base of the inner walls.Further, vertical lines are inscribedon the cylindrical wall, which be-gin at the walls base and terminateat the top end. These lines may beviewed as the vertical extension ofthe radial lines drawn on the oorof the instrument. The radial andthe vertical lines are inscribed withscales for measuring the altitude of

a celestial object, and are graduated

such that the zero mark is at the top,and the 900 mark is at the base of thecentral pillar. If the preference is tomeasure the zenith distance, thenthe markings would have to be re-versed, i.e., the top end would nowdenote a 900 mark and the base ofthe pillar, zero.

is not bright enough, or if one wish-es to measure the coordinates of astar or planet that does not cast ashadow, a different procedure isfollowed. To accomplish this, theinstrument is built in two comple-mentary units.

The two complementary units ofa Rama yantra may be viewed as ifobtained by dividing an intact cy-lindrical structure into radial andvertical sectors. The units are such

that if put together, they wouldform a complete cylinder with anopen roof. The procedure for mea-suring the coordinates at night witha Rama yantra is similar to the oneemployed for the Jaya Prakasa. Theobserver works within the emptyspaces between the radial sectors

or between the walls of the instru-ment. Sighting from a vacant place,he obtains the object in the sky, thetop edge of the pillar, and the van-tage point in one line. The vantagepoint, after appropriate interpola-tion gives the desired coordinates.If the vantage point lies within theempty spaces of the walls, well

above the oor, the observer mayhave to sit on a plank inserted be-tween the walls. the walls haveslots built specically for holdingsuch planks. Because there are nograduations between the emptyspaces, arc lengths of wood or metalto t between the walls are neces-sary for a reading.

Detail of the gnomon surface at the

Delhi Ram Yantra. Weathering has

eroded and stained the engraved angu-

lar markings.

The gnomon (central pillar) of the Ram

Yantra at the Delhi observatory, as seen

through one of the arched openings in

the outer wall. For night observations

an observer can move easily between

the wedge shaped sectors, which are

suspported at chest height by masonry

arches and posts.

Figure 4

Principle of the Ram Yantra, above, and

a plan and elevation of the Ram Yantra

at Delhi, below.

In daytime the coordinatesof the sun are determined byobserving the shadow of thepillars top end on the scales, asshown in the gure. The coor-dinates of the moon, when it is

bright enough to cast a shadow,may also be read in a similarmanner. However, if the moon

Plan view: Ram Yantra pair at Delhi


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and time lapse studies illustrating themovement of the shadow of the sun on thescales of several instruments from the ob-servatories. A collaborative project withSciCentr, an outreach program of CornellUniversitys Theory Center, is creating aninteractive 3D world in the ActiveWorldsEducational Development Universe. Thisproject enables science students fromparticipating middle schools and highschools to interact with a computer basedscale model of the Samrat Yantra at Jaipur,walking around it, climbing its stairs,and observing the methods of establish-ing local time from a simulation of themovement of the suns shadow across itsscales.

The observatories themselves are some-times used for making observations, butmostly serve as tourist attractions, as his-toric monuments and curiosities. Localguides, many of them sanctioned by the

Archaeological Survey of India, which hasauthority over the observatories, presentvisitors with a mixture of truth and ctionas they explain the history and workingsof the instruments.

In contrast, Dr. Nandivada Rathnasree,director of the Nehru Planetarium, usesthe instruments of the Delhi observatoryas a real world classroom to demonstrateprinciples of basic astronomy to students.A group under her direction used the in-struments at Delhi to chart the path of theplanet Venus during its 2004 transit.

Jantar Mantar on the Web

VR Panoramas, 3D Models,Animations, Time Lapse Studies,Interactive Media, and Outreach

One of the objectives of the multimedia

web site www.jantarmantar.org is the cre-ation of a virtual museum to present andinterpret Jai Singhs observatories. At thetime of writing, the web site presents aninteractive tour of the jaipur observatory,employing navigable, immersive, VR pan-oramas, images derived from 3D models,animations illustrating the passage of thesun overhead during the course of a day,

Students and astronomy enthusiasts

under the guidance of Dr. Nandivada

Rathsnasree, (in blue, lower right), use

makeshift crosswires to make solar ob-

servations at the Delhi Jai Prakash.Screen view of the Jaipur World

from Cornell Universitys SciCentr

Rendering from a computer based 3D

model of the Samrat Yantra

Still frame from an animation illustrating

the movement of the suns shadow along

the quadrant of the Samrat Yantra

One of the VR panoramas as it appears

in a web browser. The user can pan and

zoom through a fully spherical 3600.

Above, an unwrapped rendering of a 3600 spherical panorama taken from the top of the

east quadrant of the Samrat Yantra at the jaipur observatory, and above left, an undistorted

wide-angle view from the same location. More about panoramas on the next page.


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More about Panoramas

In 2001 I began to use panoramic pho-tography to interpret the architecture ofthe Jantar Mantar observatories. Advanc-es in technology enabled photographersto capture multiple image panoramas andassemble the images digitally. Free view-ing software made the panoramic images

accessible to anyone with a computer.There are two types of panoramic ren-dering commonly in use: cylindrical andspherical.

In the cylindrical panorama, a series ofoverlappping photographs is taken whilerotating the camera 3600 along the line ofthe horizon. The panoramas vertical an-gle of view is limited by the angular cov-erage of the lens.

The spherical panorama comprises a se-ries of overlapping photographs that cap-ture all areas of a scene, including directlyoverhead and directly beneath the camera.This is usually done with a digital camera,in multiple rows, with the camera point-ed along the horizon for one row, angledupwards for a second row, and angleddownward for the third row.

After the photographs are taken, they aretransferred to a computer and loaded intoa program that assembles the photographsinto a composite simulating the original360 degree scene. Called stitching soft-ware, these programs nd the common

elements in adjacent photographs and usethem to seamlessly recreate the originalview as though it were tted to the insideof a sphere with the viewer at the center.The stitching software evaluates the colorsand brightnesses of adjacent photographsand creates a smooth blend between them.From this stitched image it is possibleto generate many kinds of images, fromimmersive QuickTime VR movies to pla-nar renderings (like conventional photo-graphs) to spherical renderings like theexample above.

Spherical rendering from a 3600 panorama of the Jai Prakash at the Jaipur observatory.

The area along the horizontal centerline corresponds to the equator or maximum circum-

ference of the spherical image, and thus is the least stretched. Areas at top and bottom

show the maximum stretch and distortion. At tthe very bottom, what appears to be a ribbon,

is actually a circular map rose with copyright information. See the photograph, lower right.

As seen in a browser window, the

image appears as a conventinalcamera would render it.

The top and bottom point must be stretched to span the full width of the rectangle

All points around the equator are equally distributed across the centerline of the rectangle

Rendering a spherical image to a 1:2 rectangle

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