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lengths and thus they could determine the time of day directly from the tables of shadow-lengths versus the corresponding parts of the day elapsed as the practice is still in current among some sects of Buddhistic monks in Ceylon etc. 13 Jainas had also employed the use of shadowlengths for the determination of seasons.14 Such parallel gnomonic data, though with slight variations, have also been found in some Buddhistic texts like Sārdulakaraṇāvadāna.15 It is, however, worthy of note that the evolution of the science of gnomonics is well-traced through the study of Jaina astronomical system. Moreover, Jainas had advanced in measuring shadow-lengths to such an extant that Summer solstice was determined upto thirty muhurtas of one day.16
4. Kinematics of the Sun and the Moon
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As regards the kinematical studies of the Sun and the Moon, Jainas had determined the spiral paths of their motions whose equations are akin to that of the Archimedian spiral. Such a kinematical model of solar or lunar motion owes its provenance to the concept of a solar or lunar mandala (diurnal circle) which implied a notion of declination.17 The notion of declination has not been found in Vedanga Jyotisa. We have not yet come across any such findings in Puranic or Buddhistic texts.
5. Kinematics of Venus
In Vedanga Jyotisa, kinematical studies of the Sun and the Moon only were undertaken but in Jaina texts we find that the kinematical studies of Venus also form a peculiar feature of Jaina School of Astronomy. The average relative velocity of Venus in heliacal combustion in different parts of lunar zodiac was compared with some conventionally known relative as well as discrete velocities like those of a snake, horse, elephant
13 Lishk, S.S. and Sharma, S.D. (1976), "The Time of Day Measured through Shadow-Lengths in Surya Prajnapti', The Mathematics Education, Vol. 10, No.4, pp. 83-89.
14 Lishk, S.S. and Sharma, S.D. (1977), 'Seasons Determination through the Science of Sciatherics in Jaina School of Astronomy', Indian Journal of History of Science, Vol. 12, No.1, pp. 33-44.
15 Singhal, B.M., Sharma, S.D., and Lishk, S.S., Seasonal Sciatherics in Sardulakaranavadana (in the press).
16 Lishk, S.S. and Sharma, S.D. (1974), 'Post-Vedanga Pre-Siddhantic Indian Astronomy'. Paper presented at Summer School on History of Science, INSA, New Delhi. To appear in K.C.Shastri Memorial Volume, Jabalpur.'
17 Lishk, S.S. and Sharma, S.D., 'Notion of Declination Implied in the Concept of Mandala (Diurnal Circle) in Jaina School of Astronomy', Ganita, Lucknow University (to appear).
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