The Universal System of Astronomy

Calculated from the zenith distance = ...the Sun? divided, the result diminished by the remainder and added to the pillar of the gnomon. From the string, the distance of the pin in the North-South direction is determined. 8

Multiplying that distance by the sine of altitude and dividing by the measure of the pin, the result is the corrected value. The solar amplitude original: agrā; the angular distance of the Sun from the East or West point on the horizon is then subtracted or added depending on whether the direction is North or South. 9

Multiply the solar amplitude by the hypotenuse of the equinoctial shadow original: palakarṇa; a constant used in local latitude calculations and divide by the radius to find the sine of declination original: krāntijyakā. Subtract the square of that from the square of the radius; the square root of the remainder is the "great sine." Multiply the sine of declination by its own shadow; 10

Divide by twelve and then by the radius. Sine of altitude × 12 × Radius / ... × 42 = This result, divided by the cosine of declination, gives the sine of the ascensional difference original: carasiñjinī; used to calculate the length of the day. From the radius and the sine of the altitude, the day-sine and the Sun's position are determined through division. 11

This gives the "desired time" original: iṣṭakāla; the time elapsed since sunrise. When subtracted from the midday time, the result is the time from the previous or following period. The arc of this value, multiplied by six Multiplied by 6, then divided by 1 ... / 3 and divided, gives the hours and minutes elapsed since sunrise or until midday. 12

Multiply the sine of declination by the radius and divide by the sine of the maximum declination original: jina-tattva-jyā; specifically 24 degrees in Indian astronomy. The resulting arc gives the Sun’s position. In the first quadrant, it is the actual value; in the second, subtract it from the sign; in the third, add it to the sign; and in the fourth, subtract it from the full circle. Thus, the True Sun original: sphuṭo bhāskaraḥ; the mathematically corrected position of the Sun is revealed. 13

Through these mathematical degrees, the seasons—beginning with Aries and the spring—are established. However, scholars note that the manifestations of these seasons vary by country and region, as the world is diverse. 14

The appearance of fresh mango sprouts, the gathering of dark clouds, and the extreme clarity of water reflecting the moon—all these are the visible markers of the passing seasons. 15

Thus, for the benefit of the "Middle Land" original: Madhyadeśa; the heartland of North India, poets and astronomers have described the beauty of the seasons, starting with Spring, following the ancient wisdom of Bhāskara. 16

In the Land of Kashmir, specifically regarding... these signs appear differently. Because of the constant abundance of snow there, the signs of mango blossoms and arriving summer heat occur only rarely or at different intervals. 17

When the shadow falls upon the Kīlaka the central pin or gnomon of the instrument of the machine, and the planet's reflection is seen within the instrument, one must determine the North or South direction carefully. 18

One should then observe the planet's reflection between the two points... 2