This article explores the ingenuity of ancient Vedic scholars in extracting the vast astronomical information with the help of very simple instruments.
Here we propose to explain the method of erecting a ‘Vedic Sundial’ as described in the Narada Purana (II.50.125-131), believed to be one of the ancient classics compiled around 1700 BC, and the Surya Siddhanta, one of the most important Indian astronomical classics.
The erection of the ‘Vedic Sundial’
Select a flat smooth stone or prepare a cemented surface, and level it with water. Draw an even circle having a radius of 12 units of any measurement. In the centre of this circle fix a cylindrical shaft, called ‘Shanku’. The Shanku is divided in twelve equal parts and has a height equal to the radius of the circle.
The classics refer to the unit of measurement as angula or ‘a finger’s-breadth’. The Shanku should be two angulas in diameter, uniformly circular (cylindrical), twelve angulas in height and made of strong wood. If according to this measurement a Shanku of twelve angula is formed, it will have a height of about nine inches.
Knowing the directions
Mark the two points on the circle where the extremity of the Shanku’s shadow touches the circle, once in the forenoon and again in the afternoon. Please refer to the diagram below. Points A and B represent the forenoon and the afternoon points respectively.
Considering these two points as the centre, draw two bisecting arcs a and b, forming the shape of a ‘fish’. Draw a line passing through the ‘mouth’ and ‘tail’ of this fish. This line is the north-south direction line. The line will pass through the centre of the circle O and touch the circle at two points N and S, indicating the north and south points. This line also indicates the meridian of the place.
Again form a ‘fish-figure’ on the north-south line by drawing two bisecting arcs n and s keeping the north and south points as their centres. A line formed by joining the ‘mouth’ and ‘tail’ will be perpendicular to the north-south line and is known as the east-west line. The east-west line passes through the centre of the circle and cuts the circle at two points E and W indicating the east and west points. The east-west line, is also called the prime vertical. The point O, the point of intersection of the north-south and east-west lines, which is also the centre point of the circle where the base of the Shanku lies, is the zenith point.
Thus, after knowing the four directions, by forming similar ‘fish-figures’ (bisecting arcs) between the two points of the directions, find out the four intermediate directions and mark them appropriately.
Draw a circumscribing square, having its sides equal to the diameter of the circle and the four corners of the square touching the four cardinal direction lines NE, SE, SW, NW. The east and west sides of this square are each divided into twenty four parts to form a linear scale. Its use is to aid in ascertaining the length of any given shadow.
Find the position of the Sun
The Indian system of astronomy primarily does the calculations in the Sayana (tropical) system. To convert the planetary longitudes to Nirayana (sidereal), subtract ayanamsha for the given moment from the Sayana position.
Mid-day shadow: When the shadow of the Shanku coincides with the north-south line, the Sun is exactly on the meridian of the place. At that time it is local noon or mid-day of that place. The shadow thus formed is referred to as the mid-day shadow.
Equinoctial shadow: When the Sun is either on the vernal equinox or on the autumnal equinox, the shadow of the Shanku thus formed on the mid-day is termed as Palabha or equinoctial shadow.
Equinoctial line: Mark the extremity of the mid-day shadow on the day when the Sun is at the equinox. Draw a line parallel to the east-west line, touching this point. The line is called the equinoctial line. Refer to the diagram on the right.
North declination line: On the day of the summer solstice, when the Sun is at its maximum declination north, mark the extremity of the midday shadow and draw a line touching this point, parallel to the east-west line and mark it summer solstice line or north declination line.
South declination line: Again on the day of the winter solstice, when the Sun is at its maximum declination south, mark the extremity of the midday shadow. Draw a line parallel to the east-west line passing through this point and mark the line as the winter solstice line or south declination line.
In the above paragraphs we have referred to summer and winter solstice as applicable to persons in the earth’s northern hemisphere. For people in the southern hemisphere, for example Australia, Sun’s maximum northern declination is referred to as winter solstice and Sun’s maximum southern declination as summer solstice.
Now we have got three lines: north declination line, equinoctial line and south declination line. The equinoctial line will be in between the two maximum declination lines of the Sun. On the north-south line, divide the distance between the north declination line and the equinoctial line in three parts, and the distance between the equinoctial line and south declination line also in three parts. On the left side of these six divisions mark vertically from top to bottom 9, 8, 7, 6, 5 and 4. On the right side of these six divisions again mark from top to bottom 10, 11, 12, 1, 2 and 3. These numbers represent the rashis. If the person is located near the equator, these divisions will be uniformally spaced out. But if the person is located far north of the equator, the divisions for signs Libra to Pisces would be more spaced out compared to the divisions for Aries to Virgo. Reverse would be the case for a person located far south from the equator. For persons located at higher latitudes, north or south, it is best to mark the extremity of shadows on the days of Sayana Sankranti (entrance of Sun in Sayana rashis) either of the six rashis of Uttarayana (Capricorn to Gemini) or Dakshinayana (Cancer to Sagittarius).
Observe the extremity of the midday shadow of the Shanku on any day of the year on the scale. When the Sun is in its southward course, the shadow point on the scale indicates the position of the Sun among six rashis from Karka (Cancer) to Dhanu (Sagittarius). When the Sun is in its northward course, the midday shadow point on the scale indicates the position of the Sun among six rashis from Makara (Capricorn) to Mithuna (Gemini).
How to find Latitude of a place using the Vedic Sundial
The diagram below shows the Earth and the rays of the Sun falling on the surface of the Earth. When the Sun is situated at the equinox, the rays of the Sun will be parallel to the equator of the Earth. The Shankus A, B and C are located at three different locations on the surface of the earth at, say, 0, 15 and 35 degrees north latitude.
There will be no mid-day shadow formed by the Shanku A since it is located at the equator and the Sun will be exactly overhead at that moment. S1 is the shadow formed by Shanku B and S2 is the shadow formed by Shanku C. Observe the difference between the lengths of the shadows S1, and S2 at latitude 15 and 35 degrees. The length of the shadow of the Shanku formed at higher latitude will be longer than the length of the shadow at the lesser latitude.
In the diagram above, the Shanku, the shadow of the Shanku and the line joining the top of the Shanku and extremity of shadow forms a right angle triangle where the height of the Shanku is the perpendicular (p), length of the shadow is the base (b) and the line joining the top of the Shanku and the extreme point of the shadow is the hypotenuse (h). If the two arms (perpendicular and base) of a right angle triangle are known, the third (hypotenuse) can be found out by the formula: h = √p2+b2
Latitude of a place is the north or south angular distance between the equator and the place. In the above diagram, angle w indicates the latitude of the place where Shanku C is located. Angle x will also be equal to angle w since the equator and the rays of the Sun are parallel when the Sun is at the equinox.
To find out the latitude of any place, (angle x) measure the midday shadow of the place when the Sun is at the equinox. Multiply the radius by the equinoctial midday shadow and divide by the hypotenuse of the shadow to get R sine of the latitude of the place. Divide the arc of the R sine of the latitude by 60 to get the latitude in degrees.
The above three diagrams show the variations in formation of the midday shadow of the Shanku as observed by persons located at different latitudes on the surface of the earth. Point ‘E’ is the equinoctial midday shadow (Sun at equinox); Point ‘S’ is the south declination shadow (Sun at max. South declination); and Point ‘N’ is the north declination shadow of the Shanku (when the Sun is at max. north declination). Observe the differences in the distances between the points S-E and E-N at different latitudes. At 0 degree latitude S-E and E-N will be equal. At 15 degree north latitude, S-E is marginally longer than the E-N and at 35 degree north latitude, S-E is nearly double the E-N.
© Rajeev Jhanji, Vedic Astrology