Observations from the Ram Yantra

The basic working of this instrument is discussed here.

On the 29th March 2004, the observations at Ram Yantra started around 11:45 AM. An initial explanation was given to students and visitors present, about the usage of the instrument. Visitors were asked to visualize local (observer centered) co-ordinates of objects in the sky in the manner described here.

The instrument is beautifully designed, precisely to measure such local co-ordinates - Altitude and Azimuth - with ease. The floor of the Ram Yantra building is divided into 30 sectors and 30 gaps (of the same dimensions as the sectors). Each of the sectors is marked with six radial lines - so that each marking corresponds to a degree of Azimuth. The gnomon itself is marked with sections (see photograph below) corresponding to these degree Azimuth markings. The edge of one of the sectors is aligned to the North. This is marked as 360 degrees (in Hindi) on the Gnomon markings. Once the center of the gnomon shadow (this is not so straightforward and is discussed later) is determined and marked with pencil - one can jus read off the Azimuth - by starting with the edge marked as 360 degrees and counting the number of sectors and gaps and individual degree markings upto the center of the shadow. A little trick here, though - the shadow marks a position exactly 180 degrees away from the actual position of Sun in the sky - and therefore 180 degrees would need to be added to the Azimuth reading obtained by counting the sectors and degree lines. More accuracy than within a degree can be obtained by using tape measure to read the distance from the nearest degree marking and dividing it by the length (at that point) of one complete degree marking and adding this fraction to the number of degrees read, by directly counting the sectors, gaps and degree markings to reach the shadow location.

And now for Altitude measurements. These are the measurements that really bring out the care taken by Jai Singh in building this instrument. One could read out the altitude of the Sun in the sky at any time by placing a gnomon (a cricket stump or a kho kho pole would do) in the ground  and marking the edge of its shadow. The Tan of the altitude of the Sun is simply the height of the gnomon/ length of the shadow. By measuring the height of the gnomon and the length of the shadow, taking their ratio and calculating the inverse Tan, one could obtain the Altitude of Sun in the sky. The smaller one's gnomon, the more the errors in this estimation - although, initially, it does seem that the uncertainties in locating the center of the shadow, the uncertainties in differentiating between the Umbra and Penumbra of the shadow - seem easier with a smaller gnomon. This was in fact the rationale behind Jai Singh's construction of such  magnificent masonry instruments - that the large size would easily compensate for the errors in estimation of the center of the shadow.

Here we have a majestic gnomon - whose height is exactly equal to the length of the sectors - that is, the distance between the outer circumference of the gnomon and the inner circumference of the wall. This immediately tells us that at Altitude of 45 degrees the shadow should fall at the junction of the walls and the floor - making the gnomon height equal to the shadow length. At Sunrise - the shadow should fall at the top of the instrument - exactly coincident with the horizontal rim of the cylindrical structure. From the top to the floor are marked 45 Azimuthal circles on the walls - each equal to a degree of Altitude. At a first glimpse towards the top portion of the walls gives a feeling that these markings are equidistant - in fact, they are not - they are marked in Tangents of degrees - as we come closer to the junction between the wall and the floor one can easily see the length between these markings increase. This length between each degree marking increase further as one moves from the junction between the wall and the floor - towards the gnomon. When the shadow falls on the floor - the Altitude is between 45 degrees (at the Junction) to 90 degrees at the gnomon. To achive finer accuracy than a degree - one could use tape measure and read the length of the fractional part of a degree that the shadow marks out and compare with the total length on a degree marking - mind, there is no longer a linear relationship between the two - tangents of angles are involved - the best accuracies could be achieved by simply measuring the complete length of the shadow and the length of a complete sector and using inverse Tan of Gnomon length / shadow length. This was the method used by the most enthusiastics students present there (for instance, by Sneh of Nutan Marathi School and Samridhi of Lady Irwin school - the most meticulous observers amongst the students present on that day). However, reasonable accuracies were being obtained even by those who used a linear calibration for markings within a degree of the scale.

Now, for the results of the March 29 2004 measurements for the Sun.

Evening Measurements

The details about the observers in each of these groups are here.

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