Pramāṇa · Search · About · API

The Positive Sciences of the Ancient Hindus c5.s3.t2: Composition of Gravity with Vega (Momentum)

The Positive Sciences of the Ancient Hindus c5.s3.t2

Language
English

Composition of Gravity with Vega (Momentum)

c5.s3.t2.1

When a body is let go and falls to the ground, the force acting on it is gravity (गुरुत्व), which the astronomers ascribe to the attraction of the earth. Motion is produced in the first instance by gravity alone, and this leads to a *sanskâra* (impressed motion) in the same direction. But the force of gravity continues to operate, so that, in the moments following the first, the motion is due to gravity as well as *sanskâra*. The resultant motion is one, but both the causes must be conceived as contributing to the resultant. The reason for supposing this combined action is that both gravity and *sanskâra* (impressed motion or momentum) are seen elsewhere to produce motion separately.

c5.s3.t2.2

In the case of the falling body, therefore, there is the composition of the two, gravity and Vega, acting in the same direction (उभयसमावेशः) from the second instant onwards. It is as if two motions coalesced and resulted in one.

c5.s3.t2.3

Here a good foundation is laid for the explanation of the accelerated motion of falling bodies, but Galileo's discovery was not anticipated, as Galileo's observations and measurements of motion were wanting. (आद्यं कर्म गुरुत्वात् भवति तेन कर्म्मणा संस्कारः क्रियते तदनन्तरं उत्तरकर्म्माणि गुरुत्व-संस्काराभ्याम् जायन्ते द्वयोरपि प्रत्येकं अन्यत्र सामर्थ्यावधारणात्—श्रीधर, कर्म्मग्रंथ—तत् आद्यं गुरुत्वात् द्वितीयादीनि तु गुरुत्वसंस्काराभ्याम्. —प्रशस्तपाद, कर्म्मग्रन्थ ।)

c5.s3.t2.4

But in the case of the flying arrow or other projectile, the impulsive force which produces Vega counteracts the force of gravity; in the end, this Vega is lost through friction with air, and then gravity (गुरुत्व) brings the arrow to the ground. The meaning of this "counteraction" is not clear. Is it intended that the action of gravity is suspended as long as the Vega continues? We have seen that, in the case of a body let fall, Praśastapâda expressly states that gravity (गुरुत्व) and *sanskâra* (Vega, momentum) both act in the second and following instants. Praśastapâda seems to have thought that some *sanskâras* (*e.g.* the Vega of an arrow or other projectile) suspend the action of gravity (गुरुत्वं संयोगप्रयत्नसंस्कारविरोधि, Praśastapâda, गुणग्रन्थ। वेगेन प्रतिबन्धात् अपतनं बहिःक्षिप्तस्य शरशलाकादेः निवृत्ते नोदने कर्माणि उत्तरोत्तराणि इषुसंस्कारादेवापतनादिति Praśastapâda, कर्मग्रन्थ). Other *sanskâras* (*e.g.* in the case of a falling body) coalesce with gravity to produce a single resultant motion. The later commentators (from Śrîdhara downwards) certainly interpret the Vaiśeṣika Sûtras in this sense.

Linked texts (1)