Astronomy and Cosmology at Angkor Wat

7/30/2019 Astronomy and Cosmology at Angkor Wat

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Astronomy and Cosmology at Angkor WatAuthor(s): Robert Stencel, Fred Gifford, Eleanor MornSource: Science, New Series, Vol. 193, No. 4250 (Jul. 23, 1976), pp. 281-287Published by: American Association for the Advancement of ScienceStable URL: http://www.jstor.org/stable/1742346

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23 July 1976, Volume 193, Number 4250 S C = I ENC1iE

of the sun, moon, planets, or stars. Inthisinstance, both alternatives were mergedin an integrated design, combining func-tion and belief.

Astronomy and Cosmologyat Angkor WatMeasurements of the temple are related to practical

astronomy and religious symbolism.Robert Stencel, Fred Gifford, Eleanor Mor6n

The temple of Angkor Wat in north-central Cambodia was a favorite touristattraction in Southeast Asia until warisolated the Angkor region. At present, itis inaccessible to anyone outside Cam-bodia. Nevertheless, secondary sourcessuch as detailed plans and photographshave provided sufficient data for a numer-ical and astronomical analysis of thetemple. Numerically, Angkor Wat con-tains calendrical, historical, and mytho-logical data coded into its measure-ments. Astronomically, it has built-in po-sitions for lunar and solar observation.The sun itself was so important to thebuilders of the temple that even thecontent and position of its extensive bas-reliefs are regulated by solar movement.It is not surprising that Angkor Wat in-tegrates astronomy, the calendar, andreligion since the priest-architects whoconstructed the temple conceived of allthree as a unity. To the ancient Khmers,astronomy was known as the sacred sci-ence.

Physical Aspects of Angkor WatAngkor Wat was originally dedicatedto the worship of Vishnu. The temple wasbuilt during the reign of Suryavarman II,A.D. 1113to about 1150, and is his majorclaim to greatness. Basically, it is a seriesRobert Stencel is a graduate student in the Depart-ment of Astronomy, Fred Gifford is a student major-ing in the philosophy of science, and Eleanor Mor6nis a graduate student in the Department of the Histo-ry of Art at the University of Michigan, Ann Arbor48109.

23 JULY 1976

of five concentric rectangular walls andgalleries, which extend for 1500 metersfrom west to east and 1300 meters fromnorth to south. Figures I to 4 illustrate theprincipal architectural aspects of thetemple.Once the visitor has crossed the west-ern entrance bridge, he passes throughthe front gateway of the temple, a longvaulted entrance capped by towers. Hethen descends to a causeway that leadshim forward for 350 meters. At the end ofthe causeway is a large cruciform terraceand the first of three concentric galleries.These galleries mark the main stages inthe slow vertical rise toward the massivecentral tower of Angkor Wat. During thelong walk to the sanctuary within thecentral tower, the visitor would certainlynot be aware of the extraordinarily accu-rate measurements of the temple.The sets of west-east walls in the cen-tral galleries were measured from thecenter of the chamber marking the end ofeach gallery (I, plan XI) and they werefound to be essentially identical inlength. The northern and southern wallsof the outer gallery both measure 202.14meters. The northern and southern wallsof the middle gallery measure 114.24 and114.22 meters, respectively. The fourwalls of the topmost gallery vary between47.75 and 47.79 meters. This astoundingdegree of accuracy (the differences areless than 0.1 percent) could mean that thetemple was precisely measured becauseof religious concerns. It could also meanthat the physical structure of the templewas carefully aligned with the movements

Solar and Lunar AlignmentsIn 1969 Nafilyan published more than100 detailed plans and diagrams of Ang-kor Wat, the result of 2 years of very

thorough surveying (2). His work pro-vides all the accuracy and detail neces-sary for a complete numerical analysisand measurement of the temple. From(1) we find that the west-east axis of thetemple is diverted 0.75? south of east(and 0.75? north of west) while the north-south alignments show no deviationwhatever (3). The top of the central tow-er of Angkor Wat forms an angle ofalmost 6? with the horizon when ob-served from the western entrance gate.At the latitude of Angkor Wat (13?27'N)the celestial equator is shifted 1.4? southof due east at 6?of altitude. On the day ofthe spring equinox, an observer standingat the southern edge of the first projec-tion on the causeway (just in front of thewestern entrance gate) can see the sunrise directly over the top of the centraltower of Angkor Wat (4). Three dayslater, the sun can be seen rising exactlyover the top of the central tower from thecenter of the causeway, just in front ofthe western entrance gate. Since theCambodian calendar was based on lunarand solar cycles, this precise observationof the sun at the spring equinox is ex-tremely important. The spring equinoxmarks the beginning of the sun's annualjourney, regardless of the exact date ofthe lunar-solar new year (5). Whetherthis crucial alignment was intended forpractical observation or religious orienta-tion or both is impossible to determine.There is no question, however, that thissolar alignment was important to thetemple of Angkor Wat.It is interesting to note that there arealso two solstitial alignments from thewestern entrance gate of Angkor Wat.These two added alignments mean thatthe entire solar year was divided into itsfour major sections by alignments fromjust inside the entrance of Angkor Wat.From this western vantage point, the sunrises over Phnom Bok on the day of the

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summer solstice (6, 7). Phnom Bok is amajor hill on the plain of Angkor and islocated 17.4 kilometers northeast ofAngkor Wat (Fig. 5). The western en-trance gate of the temple also has a wintersolstice alignment with the temple ofPrasat Kuk Bangro, 5.5 kilometers to thesoutheast (8).

Given these three major alignmentsfrom the western entrance gate, it wouldseem that Angkor Wat had to face west ifits primary purpose (in regardto its orien-tation) was to demarcate the solar calen-dar. This would be a rational explanationfor one of the most unusual aspects ofthe temple, a characteristic that has been

/S3/gS /mS?S~::i'~~::~:? E- Li:?i'~~~:~,~i~~~j:i:?.i;W ::.a LS-; . R2 -: ;--S W-Fig. 1. View of AngkorWat romthe causewaynearthe westernentrancegate.At equinoxthesun can be seen rising over the central tower when viewed from just inside the western entrancegate. [Courtesy of H. C. Mills]

difficult to understand. Of the hundredsof temples located at the site of Angkor,there may be only one or two minortemples that face west, such as thesingle-celled temple called Edifice C inthe Prasat Kok Po groupjust north of thewestern edge of the West Baray. EdificeC dates from the 9th century. Virtuallyall monuments at Angkor face east andare entered from the east. Some of thesemonuments were the repositories for theashes or bodies of dead rulers or minis-ters (9, 10) just as Angkor Wat couldhave been the repository for the remainsof Suryavarman II. Therefore, the argu-ment that Angkor Wat faces west be-cause it is a "funerary temple" (11, 12)hardly accounts for its orientation. Wesubmit that the westward orientation ofAngkor Wat can be explained by thesolar alignments.There are also various positions forlunar observation within the temple com-pound. As shown in Table 1 and Fig. 6, aand b, the projections along the cause-way could have been used to keep arecord of the movements of the moon,which is necessary for the prediction ofeclipses. According to the writings ofChou Ta-kuan, a Chinese merchant whovisited Angkor in A.D. 1296, just as in

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China ". . .there are people who under-stand astronomy and can calculate theeclipses of the sun and the moon" (10, p.22).

Determination of AlignmentsWe have utilized Nafilyan's plans of

Angkor Wat to search for significant as-tronomical alignments in the archi-tecture. Positions of the tops of towersand points along the cruciform terraceand the western causeway, as well as atthe libraries and the western entrancegate, were measured with respect to anorth-south rectangular coordinate gridcentered on the ground level of the cen-tral tower. Given two spatial points (thatis, their x, y, and z coordinates in me-ters), we computed the apparent altazi-muth orientation of one point as seenfrom the other, and further related thesighting line to a particularcelestial decli-nation. This was done with the classicalformula (13) for the celestial declination(6)

sin6 = sin)sinh + cosocoshcosAwhere 4 is 13?27'Nlatitude, h is altitude,and A is azimuth. Forty-six sightingpoints for the observation of the centraltower, the four towers of the first gallery,and the two towers on the western sideof the second gallery were considered.More than 300 observable declinationswere computed. We looked for solarequinoctial and solstitial declinations (0?and +23.5?, epoch A.D. 1110). Since theapparent lunar motion carries the moonwithin +5? of the ecliptic, the declinationextrema of ?5?, 19?, and 29? would besignificant as well. Measurement errorsand eroded tower tops require at least?0.5? uncertainty, depending on thebase length. Several sighting linesmatched all these angles, and these arelisted in Table 1. In addition, severalsolstitial and highly precise north-southalignments for the entire site of Angkorare given in Table 1. These alignmentswere first published by Paris (6, pp. 317,319-321, 323) after a survey of the site(14).We recognize that a few isolated sight-ing lines do not justify an astronomicalinterpretation, especially since most ofthe 322 computed alignments appear tobe almost randomly oriented, but fromthe aggregate we find several interestingtendencies.

1) An angular frequency histogram ofall computed lines reveals peaks [at 2standard deviations (S.D.) from themean] in the distribution at angles 0?,+ 5?, +23?, and +29?.23 JULY 1976

ANGKORTHOMWest Baray

1 lTa Prohm .r SamreJIBez PreRup....... '"' -' --'~'- " "" ! ....- anteay Kdei------------------------------------ Bakheng- ---. < -.. ---. ---------------------------

N tJ ;s S emreapANGKORAT , ..... IKilometers

0 1 2 3123Fig. 5. The site of Angkor lourishedor morethan 500years. It containshundredsof temples,of whichonly a few are shown here. The two Baraysare huge reservoirswhich suppliedthewater for rice irrigation.A few of the longeralignmentsof AngkorWat are illustratedby thedotted ines(alsosee Table1).

2) The angular frequency histogram ofthe points along the causeway showsrelative peaks (3 S.D.) at ?5?. This, inaccord with the six projections along thecauseway, suggests that lunar observa-tion may have been its function.

3) All major points on the ground planhave associated alignments which con-

strain the overall dimensions and ar-rangement of the structure. As can beseen from the alignments in Table 1,there are important sighting points on thenorthern and western steps of the cruci-form terrace. We suggest that these twopoints helped to determine the dimen-sions of the terrace.

Table 1. Computedastronomicalalignmentsat Angkor Wat. Alignments1 to 18 are thosederived n this study.Alignments19 to 22 were derived n 1941,alongwith the three cardinalalignments.Alignments8 to 13correspond o the pointsat which five successive projectionsmark he causeway.The easternmostprojectionhas no computed alignments.Majorcardinalalignments regivenin(21).Align-ment Observer's ocation

1. Northsteps,cruciformerrace2. Weststeps,cruciformerrace3. Weststeps,cruciform errace4. Secondgallery,south ibrary5. Secondgallery,north ibrary6. Causeway,north ibrary7. Causeway,196m fromcentraltower(westernedgeof cruci-form errace)8. Causeway,313m fromcentraltower(fifthprojection)9. Causeway,368 m fromcentraltower(fourthprojection)10. Causeway,368m fromcentraltower fourthprojection)11. Causeway,423m fromcentraltower(thirdprojection)12. Causeway,478 m fromcentraltower(secondprojection)13. Causeway,530m fromcentraltower firstprojection)

14. Westgate,542mfromcentraltower(porch)15. Westgate,542mfromcentraltower(porch)16. Westgate,30mnorthof gate(doorway)17. Westgate, 106mnorthof gate(northernporch)18. Westgate, 107msouthofgate(southernporch)19. Northwestcornerof AngkorWat20. Westgate, AngkorWat21.22. Southentrance,AngkorWatWestgate,AngkorWat

Tower(topobserved)Central owerFirstgallery,southwesttowerSecondgallery,southwest owerCentral owerSecondgallery,northeast owerFirstgallery,northwest owerFirstgallery,southwest owerFirstgallery,northwest owerSecondgallery,southeast owerFirstgallery,northwest owerSecondgallery,southeast owerSecondgallery,northeastowerSecondgallery,southwest owerCentral owerSecondgallery,southwesttowerFirstgallery,northwest owerSecondgallery,northeast owerSecondgallery,southeast owerNortheastcornerof east Barayand unnamed emple o northeastSummit,PhnomBok(17.4kmnortheast)PrasatTopPrasatKukBangro

Decli-nation+0?01-5056'- 19014'+2907'+23011'-0o18,+501'+5056'-5042'+4054'+507'+5017'-5"12'+004'-505,-5032'-5?12'+ 547'+23030'+23030'+23030'-23030'

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4) Although alignments of 0? and +5? While these numerical investigations Numerical Analysis and Time Cyclesare found most frequently with the are to be regarded as preliminary, wepoints observed within the three con- believe that they further our understand- So far we have suggested that the pre-centric galleries, we feel that this results ing of the designer's intention at Angkor cise measurements of Angkor Wat facili-somewhat from selection effect due to Wat and introduce astronomy as a practi- tated the practical pursuits of astrono-the limited number of points being cal function of the architectural format of my. However, that is not their sole pur-considered. the temple. pose. When the principal measurements

Table 2. Major solar and lunar measurements at Angkor Wat. The measurements here are derived from the plans of Angkor Wat published byNafilyan (1). They are accurate to 1 millimeter on a plan with a scale of 1 : 50, or 5 centimeters on the ground.Measurement

Description cPlan Dimension On ground Cosmological interpretation(scale) plan(cm) Meter HatDistance betweeninterior bottom

steps of centralsanctuaryInterioraxial lengthsof nine chambersin central tower

Exterior axial lengthsof central tower(including base)

Interior axial lengthsof four axial en-trances on upperelevation

Interioraxial lengthsof the four cornerpavilions on thetopmost elevation

Exterior axial lengthsof the topmostelevationInterioraxial lengthsof the libraries,second gallery

Exterior axial lengthsof the libraries,second gallery

Distance betweenfloor of north andsouth libraries ofsecond gallery andsacred deposit oftempleHeight of libraries ofsecond gallery fromlevel of terrace onwhich they stand(estimated bysurveyors)

XXII West-east axis(1 : 50) North-south axis

XXII Total, west-(1: 50) east axisTotal, north-south axis

XXII West-east axis(1 : 50) North-south axisTotalXIV(1: 100)

WestEastNorthSouth

10.35 5.175 11.88 At 12hat each and 24 hat together, the in-10.55 5.275 12.11 terior axes of the central sanctuary sym-bolize the 12months in a solar (or lunar)year. There are 24 lunarhalf-months inthe lunar calendar, individually named.24.5 12.25 28.13 At 27 and 28 hat, the combined interioraxial lengths of the central tower provide23.7 11.85 27.21 the alternate numbers of constellations

along the ecliptic in Hindu astronomy, aswell as the alternate number of days themoon is visible each month.39.65 19.825 45.5339.45 19.725 45.3090.8320.0519.7519.0519.90

XXV West-east axis(1 : 50) North-south axisTotalXIV West-east axis(1 : 50) North-south axisXC West-east axis(1 : 50) North-south axiswithout doorwayindentationNorth-south axiswith doorwayindentationXC West-east axis(1 : 50) North-south axis

XIIt

XCI(1: 50)

NorthSouth

20.0519.7519.0519.90

46.0445.3643.7545.70

13.35 6.675 15.3313.35 6.675 15.33122.64*82.1 82.1 189.0076.80 76.80 176.37

At 90.83 hat, the exterior axes of the cen-tral tower approach the average num-ber of days between the solstices andequinoxes (91.31 days average).With an approximate total of 180hat, theinterior axes of the four axial entranceson the upper elevation symbolize one-half of a divine year of the gods (360 earthyears long), as well as the number of de-grees traversed by celestial bodies acrossthe sky.The total of all the interior axes of all thechambers on the upper elevation is358.83 hat,t approaching the lengthof a divine year of the gods.The two exterior axes of the upper eleva-tion total 365.37 hat, almost theexact length of a solar year (365.25 days).

13.8 6.9 15.85 The alternate lengths of the north-south9.7 4.85 11.14 axis produce alternate totals of 27 and28 hat for the interior axes of eachlibrary. The moon passes through each of10.6 5.30 12.11 the 27 and 28 Hindu constellations eachmonth.

38.3 19.15 43.9824.6 12.30 28.25

12.86 29.5312.89 29.60

These numbers have lunar significancewhen converted into thephyeam unit,the only other numerically meaningfulmeasure at Angkor Wat; 4 hat -1phyeam. There are 11 lunargods (karana)and 7 days in a lunar week.The length of one lunar month is exactly29.53 days.

20.8 10.4 23.88 There are 24 lunar half-months in one lunaryear. The days are counted from 1to15 for the first half and 1 to 14 or 1 to15 for the second half, depending on themonth.

*30.66 + 4. t122.64 hat + 28.13 and 27.21 hat from the second set of measurements above + 180.85 hat from the fourth set of measurements above. 1.65 madded to the numbers on the plan to produce the level of the sacred deposit.SCIENCE, VOL. 19384


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T\^ b Na N Celestial bi , Jd r.. _ nt 0 -| _______-__,rJ. - - , -declination

yim I.nsL I+23r

4 ' i--... - --- -J?--

are listed in Table 1.re listed in Table 1.

of Angkor Wat are translated from me-ters into the unit used in the constructionof the temple, very diverse and completedata on the calendar emerge. The origi-nal unit of measure (the Cambodian hator cubit) was determined by deriving thecommon denominator for the broadestrange of measurements at the temple.We then found that 0.43545 m producedthe greatest number of integral multipleswhen divided into approximately 200measurements within the temple (15, 16).During this process, we determined thatexterior measurements invariably ex-tended from the edges of the projectingbases of all superstructures. Interiormeasurements excluded all thresholdsand steps. Therefore, interior measure-ments could be adjusted to the largersystems of exterior dimensions by usingthe number and width of steps withineach chamber. In addition, a wide rangeof measurements, rounded off to wholenumbers, were related to numbers in theHindu calendar and in Hindu mythology(17). Table 2 shows ten of the most basicsolar and lunar measurements at AngkorWat, perhaps the most outstanding beingthe number 365.37 (Fig. 7).Numbers related to cosmology andmythology are particularly recorded inthe bridge, the central tower and its foursurrounding towers, and the west-eastaxis of the temple. We have chosen thelatter as an illustration of the ways inwhich cosmological numbers were incor-porated into architectural units (18).In Hindu cosmology, there are fourmajor periods of time, which succeedeach other in one great time cycle. Theseperiods begin with the Krita Yuga or"golden age" of man and proceedthrough the Treta Yuga, Dvapara Yuga,and Kali Yuga, the last being the mostdecadent age of man. Their respectivedurations are 1,728,000; 1,296,000;864,000; and 432,000 years. The elon-gated west-east axis of Angkor Wat is a23 JULY 1976

perfect vehicle for recording numbers aslarge as 1,728 hat (Fig. 8). The straightand slender causeway is also an appropri-ate visual analogy for the long, linearpassage of time. The architects who con-structed Angkor Wat certainly believedin the auspicious and inauspicious na-tures of these yugas. Assuming that theirbeliefs were also inextricably woven intothe design of the temple, then it musthave been their intent to place the twoworst yugas (Kali and Dvapara) farthestfrom the sacred central sanctuary. The

Table3. CorrespondencebetweendimensionsWatanddurations f Hinduyugas.

beneficent Krita and Treta yugas arecloser to the central sanctuary and theyoverlap the two inauspicious yugas, per-haps to mitigate their unlucky symbol-ism. The axial lengths measured at Ang-kor Wat show a striking correspondenceto the durations of the yugas, as shownin Table 3.

The discrepancies between the dura-tions of the yugas and the lengths re-corded in the axis of Angkor Wat (Table2) are within the range of human error(19). The largest error is found in the

measuredalongthe west-east axis of AngkorDimension . DurationMeasurement (hat) Period (years)

Width of moat 439.78 Kali Yuga 432,000Distance from first step of western entrance 867.03 Dvapara Yuga 864,000gateway to balustrade wall at end of causewayDistance from first step of western entrance 1,296.07 Treta Yuga 1,296,000gateway to first step of central towerDistance from first step of bridge to 1,734.41 Krita Yuga 1,728,000geographic center of temple

N

Abl CD E?G

LJP LPEJ 1-JM-- Fig. 7 (left). When the lengths of the exteriors axes (N-S and W-E) of the upper elevation ofAngkor Wat are added together, they total 365.37 hat. The upper elevation has many otherexamples of solar symbolism (see Table 2). Fig. 8 (right). The four Hindu time cycles, calledyuga periods, are recorded in the west-east axis of Angkor Wat. They comprise the Kali Yuga(B-C), the Dvapara Yuga (D-E), the Treta Yuga (D-G), and the Krita Yuga (A-F). Theirlengths in years are 432,000; 864,000; 1,296,000; and 1,728,000, respectively. The axial lengthsin hats are 439,78; 867.03; 1,296.07; and 1,734.41.285


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width of the moat, which measures191.50 meters between the edges of itsmasonry borders. Part of this error maybe due to centuries of erosion, whichhave left the borders slanted and slightlysunken. At the same time, we are not cer-tain that we have measured the properdistance. For example, the width of themoat at the level of the water approaches432 hat much more closely. Further re-search might clarify this problem.In summary, we propose that the pas-sage of time is numerically expressed bythe lengths corresponding to yugas alongthe west-east axis. Astronomically, thepassage of time is measured along thesame axis by a dozen positions for lunarand solar observation. Finally, time isvisually and symbolically expressed bythe long, linear form of the axis itself.This full integration of astronomy, nu-merology, and architectural form is char-acteristic of the temple.

The Role of the SunWe have indicated that the sun was a

determining factor in the westward orien-tation of Angkor Wat. In reality, the sunhas a multifaceted role in the temple.Angkor Wat is dedicated to Vishnu, themember of the Hindu trinity who pre-sides over all the solar-related deities inthe Hindu pantheon. The posthumoustitle of Suryavarman II was Para-mavishnuloka, or the "one who has goneto the supreme world of Vishnu," relat-ing the king directly to the god and in-directly to the sun. The name Suiryavar-man itself translates as "protected by thesun."

A further indication of the importanceof the sun in the rituals of the temple isthe direction of the bas-reliefs on theinner wall of each side of the third gal-lery. These bas-reliefs constitute thelongest series of continuous reliefs in theworld-more than 500 m in total length.Even though they are a major part of thetemple, it was never fully resolvedwhether they proceeded from left to rightor right to left, or indeed whether theyhad a direction (11, pp. 305-309). How-ever, when they are "read" in relation tothe annual and diurnal movements of thesun, it seems certain that their directionis counterclockwise.In Hindu astronomy, the apparent an-nual movement of the sun is conceivedas counterclockwise. Beginning with thespring equinox (east), the sun progressesto the summer solstice (north), thensouthward to the autumn equinox (west).From that point, it continues on to thewinter solstice (south) and then returnsto its eastern starting point.

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In fact, the subject matter of the bas-reliefs corresponds exactly to the coun-terclockwise motion of the sun. On theeast wall of the gallery of bas-reliefs,there is a scene of the "churning of thesea of milk," a cooperative venturewhich produced the elixir of immortality.The scene epitomizes the concept of cre-ativity and new life. On the side of thesetting sun and autumn equinox, themost destructive battle ever fought inHindu mythology is depicted, the battleon the plains of Kurukshetra (from theIndian epic Mahabharata). The northwall is the only section of bas-reliefwhich depicts all of the Hindu gods to-gether. The day of these gods (who re-side at the north pole, on the cosmicmountain called Mount Meru) lasts forthe 6 months between the spring andautumn equinoxes. Although the sundoes not shine fully on the north wallduring those 6 months because of its13\27' southward trajectory as it ap-proaches the zenith, it is the only appro-priate direction for the placement of thegods. The night of the gods correspondsto the 6 months between the autumn andspring equinoxes. During those 6months, the north wall remains in dark-ness. The same 6 months initiate the dryseason, when trees and plants either dieor become dormant. During that time,the kingdom of Yama, the god of death,is illumined on the south wall. Thus, theplacement of these important bas-reliefsis not haphazard or meaningless. In allcases, their content is directly related tothe solar calendar or the rising and set-ting sun.

ConclusionsThe importance of astronomy, the cal-endar, and the sun in the architectureand bas-reliefs of Angkor Wat is just

beginning to be understood. The resultsof the study of the temple so far aresummarized as follows:1) The rising sun was aligned on the

equinox and solstice days with the west-ern entrance of Angkor Wat.2) The movements of the moon wereobserved from a variety of positionswithin the temple, and lunar cycles wererecorded in the three pairs of libraries.3) The bas-reliefs of the third gallerycan be understood in relation to themovements of the sun, which establishestheir counterclockwise direction.4) The measurements of the templerecord calendric and cosmological time

cycles.In the introduction to the Silpa Pra-kasa, a treatise on Orissan temple archi-tecture between the 9th and 12th cen-

turies, Boner has summed up the impor-tance of astronomy for the Hindu temple(20).. . . thetemplemust, n tsspace-directions, eestablishedin relation to the motion of theheavenlybodies. Butinasmuchas it incorpo-rates n a singlesynthesis he unequalcoursesof the sun, the moon andthe planets, it alsosymbolizesall recurrent ime sequences:theday, the month,the yearandthe widercyclesmarkedby the recurrence f a complete cycleof eclipses, when the sun and the moon arereadjusted n their original positions, a newcycle of creationbegins.

Although the role of astronomy in Hin-du temple architecture has been widelyrecognized, our understanding of it hasremained quite imprecise and undefined.We hope that future research will revealwhether the astronomical relations thatcharacterize the architecture of AngkorWat also apply to other major temples inIndiaand Southeast Asia.References and Notes

1. G. Nafilyan, AngkorVat, DescriptionGraph-ique du Temple (Ecole Francaised'Extreme-Orient,Paris, 1969).2. There are 113plans n (1). Measurementsweretakenseveral imesalonga widevarietyofdiago-nals and axes. Any disagreement etweenmea-surementswasresolvedby remeasurement;ur-ther checks wereprovidedbygeometrical naly-ses andphotographs f theareassurveyed.Thefinaldrawingswere done on a polyesterpaper,which does not expandor contractwith varia-tions ntemperaturerhumidity.3. North-southalignments refromplanXI in (1),drawn o a scale of 1: 250.There s not 1milli-meterof deviationn the north-southxeson thisplan. Nafilyanused the north-south xis of thewestern side of the first (upper) gallery for thenorth-southlignments n hisplans.Aside fromactual measurementn situ, there is no othersource ordeterminingheangleof thewest-eastaxis of AngkorWat.4. This was estimatedfrom plan II in (1), scale1: 5000.The distance rom he central owertothe center of the projection ust in front of thewesternentrancegatewas calculatedas 530 m.Theheightof the central ower s 57m from hecauseway evel or 55.5 m (approximately)romeye level. The tower, seen from ust in front ofthe western entrancegate, thus subtends analtitudeangleof 5.9?. Basedon an axial shift of0.75? south of due east, the observed celestialdeclination over the tower top is +0.7?. Thesouthernand northernedges of the projectionare 6.9 mfrom the center ine of the causeway.From these two edges, the observed celestialdeclinationsare -0.1? fromthe northernposi-tion and + 1.4? rom the southernposition.TheAmerican Ephemerisand Nautical Almanac(Government Printing Office, Washington,D.C., 1971) ists the change n solar declinationat the equinoxto be about 0.4?per day. TheKhmers could then, in principle,have moni-tored the solar declinationquiteexactlyfrom0?to 1.5? north over a 3- to 4-day period. Thismonitoringwouldpermitaccuratedeterminationof thespringandautumn quinoxes.5. F. G. Faraut, Astronomie Cambodgienne(Schneider,Saigon,1910),pp. 113-117.6. P. Paris, Bull. Ec. Fr. Extr. Orient 41, 323(1941).7. Thisalignmentncludes he easternentranceofBanteayKdei,constructed t the endof the 12thcentury.PhnomBok rises 160m fromgroundlevel. An observerwouldhaveto be high up onthe towerin orderto observethe sun riseoverPhnom Bok on the summersolstice day. Thealignments very important,whetheractualob-servations took place or not.8. See the plan of the site annexed to the article in(6) and p. 323 (t'). The date of Prasat KukBangro has not been published.9. According to Chou Ta-kuan (10, p. 24), "thesovereigns themselves are buried in the towers,but I do not know if one buries their bodies ortheir bones."10. Chou T.-K., Memoires sur les Coutumes du Cam-bodge du Tcheou Ta-kouan, P. Pelliot, Transl.SCIENCE, VOL. 193


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(Librairie d'Amerique et d'Orient, Paris, 1951).11. G. Coed&s, Bull. Ec. Fr. Extr. Orient 33, 305(1933).12. It has been postulated that temples entered onthe west were primarilyfunerary in intent where-as temples entered on the east were simply usedin the worship of the Hindu gods. In reality, thequestion is more complex since many temples inIndia have no other explanation for their orienta-tion except geographical convenience.13. W. Campbell, Practical Astronomy (Macmillan,New York, 1913), p. 8, Eq. 4.14. Twelve east-west alignments, 16 north-southalignments, and 26 solstitial alignments havebeen traced at the site of Angkor.

(Librairie d'Amerique et d'Orient, Paris, 1951).11. G. Coed&s, Bull. Ec. Fr. Extr. Orient 33, 305(1933).12. It has been postulated that temples entered onthe west were primarilyfunerary in intent where-as temples entered on the east were simply usedin the worship of the Hindu gods. In reality, thequestion is more complex since many temples inIndia have no other explanation for their orienta-tion except geographical convenience.13. W. Campbell, Practical Astronomy (Macmillan,New York, 1913), p. 8, Eq. 4.14. Twelve east-west alignments, 16 north-southalignments, and 26 solstitial alignments havebeen traced at the site of Angkor.

15. E. Mor6n, thesis, University of Michigan(1974).16. The basic unit of measure was first derived in1973. There are approximately 45 measurementsof independent architectural parts of the temple,35 of which are related to astronomy or cosmolo-gy in a direct manner.17. E. Mor6n paper presented to the College ArtAssociation, Detroit, January 1974.18. J. Cohen and B. Kalman, Angkor: Monumentsof the God-kings (Abrams, New York, 1975),pp. 98-99. The text contains a brief discussion ofthe yugas as proposed by E.M.19. It is possible that the original plan of the yugaswas much more accurate (15).

15. E. Mor6n, thesis, University of Michigan(1974).16. The basic unit of measure was first derived in1973. There are approximately 45 measurementsof independent architectural parts of the temple,35 of which are related to astronomy or cosmolo-gy in a direct manner.17. E. Mor6n paper presented to the College ArtAssociation, Detroit, January 1974.18. J. Cohen and B. Kalman, Angkor: Monumentsof the God-kings (Abrams, New York, 1975),pp. 98-99. The text contains a brief discussion ofthe yugas as proposed by E.M.19. It is possible that the original plan of the yugaswas much more accurate (15).

20. R. Kaulacara, Silpa Prakdsa, A. Boner and S.Rath garma, Transls. (Brill, Leiden, 1966), p.xxxiii.XXIll .21. The major cardinal alignments at Angkor Wat areas follows. The northern side of the moat ofAngkor Wat is along a 27.6-km line between WatKhnat and Wat Trach (about 10 km north ofRoluos). The eastern edge of the moat of AngkorWat is aligned with the east wall of Preah Khanand the outer wall of Angkor Thom. The north-south meridian of the topmost elevation of Ang-kor Wat terminates at Prasat Einkosei 4 km tothe south; 5.5 km to the north it joins the earthenridge west of the western side of the moat ofPreah Khan.

20. R. Kaulacara, Silpa Prakdsa, A. Boner and S.Rath garma, Transls. (Brill, Leiden, 1966), p.xxxiii.XXIll .21. The major cardinal alignments at Angkor Wat areas follows. The northern side of the moat ofAngkor Wat is along a 27.6-km line between WatKhnat and Wat Trach (about 10 km north ofRoluos). The eastern edge of the moat of AngkorWat is aligned with the east wall of Preah Khanand the outer wall of Angkor Thom. The north-south meridian of the topmost elevation of Ang-kor Wat terminates at Prasat Einkosei 4 km tothe south; 5.5 km to the north it joins the earthenridge west of the western side of the moat ofPreah Khan.

In the field of nuclear dynamics a cen-tral theme has been the struggle to findthe proper place for the complementaryconcepts referring to the independentmotion of the individual nucleons andthe collective behavior of the nucleus asa whole. This development has been acontinuing process involving the inter-play of ideas and discoveries relating toall different aspects of nuclear phenome-na. The multidimensionality of this devel-opment makes it tempting to go directlyto a description of our present under-standing and to the problems and per-spectives as they appear today. How-ever, an attempt to follow the evolutionof some of the principal ideas may beinstructive in illustrating the struggle forunderstanding of many-body systems,which have continued to inspire the de-velopment of fundamental new con-cepts, even in cases where the basicequations of motion are well established.Concepts appropriate for describing thewealth of nuclear phenomena have beenderived from a combination of many dif-ferent approaches including the explora-tion of general relations following fromconsiderations of symmetry, the study ofmodel systems, sometimes of a grosslyoversimplified nature, and, of course,the clues provided by the experimentaldiscoveries which have again and againgiven the development entirely new di-rections (1).The situation in 1950, when I firstcame to Copenhagen, was characterizedby the inescapable fact that the nucleus23 JULY 1976

In the field of nuclear dynamics a cen-tral theme has been the struggle to findthe proper place for the complementaryconcepts referring to the independentmotion of the individual nucleons andthe collective behavior of the nucleus asa whole. This development has been acontinuing process involving the inter-play of ideas and discoveries relating toall different aspects of nuclear phenome-na. The multidimensionality of this devel-opment makes it tempting to go directlyto a description of our present under-standing and to the problems and per-spectives as they appear today. How-ever, an attempt to follow the evolutionof some of the principal ideas may beinstructive in illustrating the struggle forunderstanding of many-body systems,which have continued to inspire the de-velopment of fundamental new con-cepts, even in cases where the basicequations of motion are well established.Concepts appropriate for describing thewealth of nuclear phenomena have beenderived from a combination of many dif-ferent approaches including the explora-tion of general relations following fromconsiderations of symmetry, the study ofmodel systems, sometimes of a grosslyoversimplified nature, and, of course,the clues provided by the experimentaldiscoveries which have again and againgiven the development entirely new di-rections (1).The situation in 1950, when I firstcame to Copenhagen, was characterizedby the inescapable fact that the nucleus23 JULY 1976

sometimes exhibited phenomena char;teristic of independent-particle moti(while other phenomena, such as the Ision process and the large quadrup(moments, clearly involved a collectibehavior of the whole nucleus.It was also clear from the workRainwater that there was an importcoupling between the motion of the invidual particles and the collective def(mation; and one was thus faced with tproblem of exploring the propertiesa dynamical system involving sucoupled degrees of freedom (2-5)H = Hvib + Hpart + HcouplHvib = C A I aXfi 2 + Dx IxA?

Heoupi = k(r}p) a,,. YAG0p?'p)P /Xj.where ax, are the amplitudes of the rclear deformation expanded in sphericharmonics and (r,, ,,, Op)are the coonnates of the particles considered. Tcoupling term represents the effect of tdeformation on the one-particle potetial.I remember vividly the many liv

Astronomy and Cosmology at Angkor Wat

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