Pramāṇa · Search · About · API

The Positive Sciences of the Ancient Hindus c5.s6: Section 6. Measurement of Motion.—Units of Space and Time

The Positive Sciences of the Ancient Hindus c5.s6

Language
English

Contents

Section 6. Measurement of Motion.—Units of Space and Time

c5.s6.2

The solar day was taken as a natural measure or division of time. In the Nyâya-Vaiśeṣika school the day of twenty-four hours (solar) is stated to contain 30 × 30 × 30 × 18 × 2 × 2 units of time (*kṣaṇas*). The Nyâya unit of time therefore measures 2/45 of a second. The smallest measure of time mentioned by the astrono- mers is the Truṭi, which is 1/33750 of a second.

c5.s6.3

The natural measure of length was the cubit (Hasta), of which there were two fixed standards, the greater and the lesser cubit. The smallest measure of length mentioned in the Śilpa-śâstra (Technology) is the Paramânu, which is about 1/349525 of an inch. This is the same as the Trasareṇu of the Nyâya-Vaiśeṣika school, which stands for the thickness of the *minimum visibile* (the finest mote perceptible in the sunbeam as it comes slanting into a dark room through a chink).

c5.s6.4

Average velocity (स्थूलगति—Bhâskara) was measured in accordance with the formula v = s/t, but no unit of velocity appears to have been fixed upon. There was no idea of acceleration, and of course no measurement of force. Mahavîrâchâryya gives formulæ for computing the space travelled over in cases of Sankalitagati (velocity with regular increment at stated intervals), but this does not amount to acceleration, as the intervals are not indefinitely small. Where the velocity is uniform, the interval of time may be of any amount (स्थूलकाल), but where the velocity is variable (प्रतिक्षणं न समागतिः—Bhâskara), an indefinitely small quantity of time (सूक्ष्मकाल) must be taken; in other words, the positions of the particle in two successive *instants* must be considered, and the velocity must be supposed to be uniform during this interval (conceived as indefinitely small, सूक्ष्म). It was in this way that Bhâskara determined the instantaneous motion of a planet (तातकालिकी गति).

Component of Velocity

c5.s6.t1.1

The astronomers measured the motion of a heavenly body in different directions (longitude, right ascension, etc.), and calculated separately the components of motion (गतिकलाः) in these directions, and they adopted the device of transferring such component velocities from one body to another in the computation of relative motion (*e.g.* एवं सति चाचार्येण लाघवार्थं दृष्टटोत्सङ्गभ्विन्यो गतिकला अर्क प्रक्षिप्ताः—Bhâskara, Siddhânta-Śiromaṇi, Gaṇitâdhyâya, Ghaṭisphuṭî-prakaraṇa).

Linked texts (1)