The Positive Sciences of the Ancient Hindus c5.s6.4

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).