The Universal System of Astronomy

Stability and the Gnomon Shadow

The sighting instrument original: "damsa-yantra," likely a variant of "drish-yantra" or "darsha-yantra," meaning an observation instrument should be held or fixed such that it does not wobble. The shadow of the gnomon śaṅku: a vertical rod used to cast a shadow must fall upon its own designated plate. From the distance between the root of the gnomon and the end of the shadow, the knowledge of the time-units nāḍikā: a unit of 24 minutes is obtained. 75

The Circular Instrument and Directions

Next, consider the instrument fashioned in the form of a half-circle likely referring to a Dhanur-yantra or "Bow instrument". On its circumference, the markings for the Sun’s shadow are made. Facing the instrument, the front-to-back axis represents the East-West direction pūrvāpara: the line from East to West, while the side-to-side axis represents the North-South direction uttara-dakṣiṇa: the meridian line. 76

The solar amplitude original: "agra," the distance of the Sun from the East-West line at sunrise/sunset in degrees should be calculated for one's own direction. From the tip of the base bhuja: the side of a right-angled triangle, often representing the sine of an angle in these contexts, the rising and setting points are determined on the circumference. After establishing the path of the Sun, the hour angle nata-nāḍī: the time-distance from the meridian and the base must be calculated. 77

Calibration and the Equinoctial Shadow

The measure of the desired gnomon is calculated here. The equinoctial shadow palaprabhā: the length of the shadow cast by a 12-finger gnomon at noon on the day of the equinox is used with a standard gnomon of twelve fingers original: "arka," a code word for 12, referring to the 12 names of the Sun. The resulting values are added or subtracted according to the direction of the Sun's declination to find the position of the shadow’s tip. 78

This calculation involving the radius and the sine jyā: a mathematical function similar to the modern sine should be held using a marking rod original: "śalākā". At the top, a thread original: "sūtra" marked with degrees is attached. This instrument is said to provide the desired gnomon and the base. 79

Alignment and the Plumb-Line

From the point where the plumb-line lamba: a weighted string used to ensure verticality is attached to the instrument, a distance equal to the versed sine śara: literally "arrow," mathematically the distance between the arc and its chord is measured. In this manner, a mark is made on the instrument at the position of the specified base. 80

Once marked, the lines for the rising and setting points are drawn, following the numerical values of the base. These lines should touch the sine markings and extend toward the North-South markings; these are known as the "mother lines" or principal meridian lines of the instrument. 81

Measuring the Time of Day

The instrument should be marked with the units of time elapsed since sunrise unnata-nāḍikā: the "elevated" time units. A wise practitioner should place the instrument on a level surface, correctly aligned with the cardinal directions, during the morning or afternoon parts of the day. 82

Depending on whether it is before or after noon, the pointer-rod original: "śalākā" should be adjusted using the sines and versed sines. The rod is turned to face the solar disk sūryabimba: the visible circle of the Sun so that its shadow falls exactly along the plumb-line of the horizon. 83

Where the shadow meets the midday line, one finds the time elapsed since sunrise or the time remaining until sunset. If the shadow falls between markings, a proportion original: "anupāta" must be calculated to find the exact time. 84

Measuring Distances on Earth and Sky

Now, regarding a desired pole original: "yaṣṭi" placed on the ground or a riverbank: when an object is visible in the sky, its measurement is determined by...