Length of the Day in Jaina Astronomy

Abstract

According to post-Vedānga pre-Siddhāntic Jaina canonical texts, 18 muhūrtas (1 muhūrta = 48 minutes) and 12 muhūrtas are respectively the greatest and the smallest lengths of daylight. The length of any day (daylight) of the year can be computed therefrom through a simple linear zigzag function. However, the ratio 3: 2 between the greatest and the smallest length of daylight holds good for a latitude 35° north very near to that of Babylon. This ratio is also propounded in Jyotisa Vedāngam. It is exposed here that the ratio 3: 2 holds equally good for Gandhāra, a renowned seat of ancient Indian culture. Gandhāra might have been used for purposes like those of a standard station for purposes of time-reckoning in ancient India. However, by applying a correction for the variable rate of flow of water through the orifice of a water-clock, it has been exposed that the actual ratio of maximum and minimum lengths of daylight measured in time-units is different from the ratio of the amounts of water to be poured into the water-clock on the respective days. It is revealed that the ratio 3:2 of the amounts of water to be poured into the water-clock on the longest and shortest days (daylights) is equivalent to the ratio √3: √2 of the actual time-lengths of the longest and the shortest days respectively. It refers to a latitude 19° 6 north, very near to that of Ujjainī, another renowned seat of ancient Indian culture.