o
Sundial, calendar and Khmer temples
 


The Indian Circle

An ancient Vedic method for determining an east-west alignment
าพระวิหาร

     This web-page illustrates by photos the implementation of the Indian Circle (or Vedic Circle) for the construction of a true east-west line, an alignment regarded as auspicious for Vedic Altars in India - and eventually for later Khmer Hindu temples as well.

     Orientation of monumental structures has a history far beyond the invention of the compass. The ancient sages and master-builders were capable of constructing the Pyramids in Egypt and Meso-America very close to the cardinal directions. Harappan cities from northern India used E-W orientations in the second millennium B.C. The lay-out of later Chinese cities also followed a cardinal grid, but with celestial north as auspicious. The construction of the ancient Khmer city, Shrestrapura, was initiated in the first part of the first millennium with a centre line oriented straight E-W, a preference implemented by later Khmer master-builders in most royal palaces.

     The oldest description of the Indian Circle Method is found in the Katyayana Sulba-sutra (400-300 BC) giving instructions for construction of Vedic fire altars: Yano (1986, p. 18) translates the Sanskrit text as follows: ‘‘Driving the gnomon into the leveled (ground), and drawing a circle with the rope whose length is equal to the gnomon (length), one drives two pegs at (the intersections of) the two lines where the shadow of the tip of the gnomon falls . This is the east (-west) line.’’
     Re-written as: Fasten a stick (gnomon) on a water leveled surface and draw a circle with radius identical to the height of the gnomon.  In the morning and in the afternoon and mark where the shadow of the sun crosses the circle: These two marks are orientated east-west.

    Ancient Indian literature on astronomy always refers to a vertical gnomon raised on a water levelled surface.
     The ancient Chinese astronomers used gnomons oriented parallel to the axis of the Earth, thus pointing towards the celestial north - close to the present location of the Polar Star.

     Between the tropics the Sun passes zenith twice a 'year, and the shadow of a gnomon is a point below it. The use of a vertical gnomon results in some practical problems determining the exact location of the solar noon shadow.
     The 'Chinese gnomon' will therefore be implemented in my next sundial. When the sun is at zenith a plump line hanging from the tip of the gnomon will show the exact location of the shadow. The noon shadow on zenith-day is significant as it marks the centre of the Vedic Circle.

 
   

Sunrise and gnomon, 24 October 2007

 

     The gnomon ('shadow pointer') is an ancient astronomical tool and probably the first device used for celestial observations.
     The shadow of the sun will on any given day of the year follow a curved path from west towards east. From spring equinox to autumn equinox the path will curve towards south. From autumn equinox to spring equinox (yellow area above) the curving is northerly. On the two equinox days the shadow will follow the nearly straighy line between the yellow and white areas.

 

     On a coincidental day in late October (right after the rainy season) a circle was drawn around the gnomon with a radius = the length of the gnomon.
     The curving path of the shadow was marked throughout the day. On the photos above the shadow has just passed the circle for the second time. The Indian textbook on astronomy, the Surya Siddhanta, informs us that the  two intersections between the curve and the circle are on an east-west line. The rope passing the two intersections is thereby oriented straight east-west (or rather very close to).

     

     To the ends of the rope there are attached two plumps, which hang down below the terrace and at the same time keep the rope above the terrace floor straight.

     Aligning the two plump lines one can extend the east-west orientation of the the two inter-sections on the Vedic Circle (not described in Indian texts on astronomy).

     In the first millennium the Indian astronomers became aware of that the E-W line described above was only approximate, because the declination of the sun is slightly differing in the morning and the afternoon. Corrections to the method was done in the end of the first millennium and versified in the 11th century.

     An over-looked aspect is the error-margin in reading the shadow of the gnomon. Within the circle on the photos above the shadow of the gnomon is easily readable. Outside - with a longer shadow - the centre of the top of the gnomon is difficult to determine exactly.
     Around the solstices the declination of the sun is practically the same for 3-5 days, which the observer will perceive as the sun follows the same daily path. The solstices therefore seem to be the best days to perform the Vedic Circle with a high accuracy.
     Of the two solstices the summer solstice (in the rainy season!) is the best candidate! On the photo of the solstice floor above the red circle (exact reading) intersects with the summer solstice path where the white area curves the most. Winter solstice is where the yellow part of the sundial floor curves the most. The distance between the summer solstice intersections is clearly much longer than the winter solstice intersections. The longer distance of the summer solstice results in a longer sightline, which gives higher accuracy.

A new series of pictures were taken the 11th of November:

 
Above: The shadow passed the circle at app. 10.00   Above: The shadow at solar noon (11:47)
 
Above: The shadow at solar noon (11:47)   Above: The shadow passed the circle at app. 14.00
 

Above: The Vedic Circle was constructed with thinner lines the day before.

Resume:

1. A circle (red) with radius equivalent to the length of the gnomon was drawn around foot of the gnomon.
2. When the shadow passed the circle in the afternoon the two crossing points were connected by drawing a straight line, which is aligned close to true east-west.
3. Two (blue) lines with radius equivalent to the length of the gnomon were drawn with the crossing points as centres. A lens shaped figure called 'the fish' appeared.
4. The intersections between the two blue circles were connected resulting in a line aligned close to true north-south.

NB: Two curves are marked on the floor: One passes the foot of the gnomon and marks the day when the Sun passed zenith. The second (marked by the shadow above) was drawn when the sun passed nadir at night. The latter date was not done by observation, but by calculation.

See also: Determining celestial north - A method for determining cardinal directions. Dr. Kate Spence. NATURE 2000 Nov.

 

Literature:

Burges, Ebenezer
 
Surya-Siddhanta. A Textbook of Hindu Astronomy. India, 1858.
(From: Journal of the American Oriental Society, Vol. 6, 1959-60. Page 141-498)

Bose, D.M.,  Sen S.N.
& Subbaratapra, B.V.

A Concise History of Science in India, New Delhi, 1971

Lyle, Emily (ed.)
J. Mckim Malville et. al.

Sacred Architecture in the Traditions of India, China, Judaism and Islam, Edinburgh University Press, 1992. COSMOS, The yearbook of the Traditional Cosmology Society.

Malville, John McKim
 
Cosmogony and the Elements...

The Intuition of Cosmos in Science and Myth.

Malville, John McKim
 

Ancient Cities, Sacred Skies, Cosmic Geometries and City Planning in Ancient India. New Delhi, Aryan for Indira Gandhi National Centre for the Arts, 2000,  ISBN 81-7305-189-5.

Yano, Michio
 
Knowledge of Astronomy in Sanskrit Texts of Architecture.
In Indo-Iranian Journal 29, pp. 17-29. 1986.
Yano, Michio
 
Planet Worship in Ancient India, Studies in the History of the Exact Sciences in Honour of David Pingree, Leiden/Boston, 2004, pp. 331-348.

INDEX

12 November 2007 © Asger Mollerup

macsida@thai-isan-lao.com

www.thai-isan-lao.com


โดย อ.ทองคำ