The Universal System of Astronomy

Sisābhau-8

The Construction of the Sight-Holes

For the purpose of allowing light to enter the different divisions, holes should be fashioned in the instrument. In this manner, the external lines are directed toward the interior. 65

A hole should be made exactly at the head in the center of the interior to serve as a support. Through this, the gnomon śaṅku: a vertical pillar or rod used to cast a shadow for measurement is to be passed. From this central hole to the outer edge, the length of the gnomon determines the divisions of the instrument as established in the scientific treatises. 66

Calculating Time and Shadow Lengths

The external gnomon should be measured in finger-breadths aṅgula: a traditional unit of measurement approximately the width of a thumb. Using the method previously described, a wise practitioner should determine the sine of the altitude unnata-jyā: the sine of the Sun's height above the horizon for the desired time of day ghaṭī: a unit of 24 minutes. 67

The solar sine of the zenith distance nata-jyā: the sine of the angle between the Sun and the point directly overhead is divided by the sine of the altitude. This result provides the shadow length in fingers for the desired time. From the hole to the markings, the measure in fingers is laid out on a level surface. 68

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When the instrument is suspended by a chain, the gnomon is positioned so that its shadow falls upon the level surface. From the tip of the shadow to the designated mark, one should calculate the elapsed time in units of time nāḍikā: synonymous with ghaṭī, a 24-minute period. The remaining sections of the wall or instrument face are used to calculate the intervals between these time divisions through proportion. 69

The Mathematical Rationale

The Proof:
In this construction, the staff represents the vertical line and the ground represents the horizontal base. At the moment of sunrise, the shadow’s proportions are determined within the celestial sphere. From the sine of the altitude and the gnomon's height, the shadow length in fingers is derived according to the stated rule. 70

The Wheel Instrument (Cakra-Yantra)

Now, following the same logic, the construction of a circular instrument is described. A fine wheel-shaped instrument cakra-yantra should be crafted from metal or other suitable materials. Its radius should be equal to twelve fingers original: vyāsārka-bhāgena; "arka" is a numerical code for 12, referring to the 12 suns of the zodiac. 71

At the center, a pin or gnomon equal to twelve fingers should be fixed, or it may be slightly smaller if needed for the specific scale. The circumference is then divided into segments. 72

A wise person should draw individual lines from the base of the gnomon to each of these markings on the perimeter. On the surface of these divisions, the markings should be inscribed clearly so they may be read sequentially even by those who are not highly learned original: strī-paṇḍitārha, literally "suitable for women and scholars," implying the instrument is so user-friendly that even those without specialized training can use it. 73

The sine of the zenith distance divided by the sine of the altitude, when adjusted for the specific hour, yields the shadow's measure in fingers. By subtracting the gnomon's height, the individual units for each unit of time are established. 74