Pramāṇa · Search · About · API

The Positive Sciences of the Ancient Hindus c5.s3: Section 3. Cause of Motion, or Force

The Positive Sciences of the Ancient Hindus c5.s3

Language
English

Contents

Section 3. Cause of Motion, or Force

c5.s3.2

Force is of the following kinds:—
1. Continued pressure (नोदन).
2. Impact (अभिघात).
3. Persistent tendency (संस्कार), of which there are two kinds: (*a*) Vega (वेग, impressed motion, momentum), the persistent tendency to motion in a moving body, and (*b*) the tendency to restitution of shape in an elastic body (स्थितिस्थापकसंस्कार).

c5.s3.3

*N.B.*—The psychical *sanskâra* (भावना) is here omitted.

c5.s3.4

4. Transmitted force, as in pulling by a string, pushing by a rod, etc.
5. Gravity.
6. Fluidity.
7. Volition.
8. Adṛiṣṭa, comprising various unknown agencies.

c5.s3.5

In every case of motion produced by contact, Vega is a contributory cause, as the body originating the motion must possess Vega (impressed motion, momentum).

The Concept of Vega (वेगाख्यसंस्कार)

c5.s3.t1.1

A motion (*karma*) being conceived as a change of place in a particle is held to be incapable of producing another motion; but the pressure, impact, or other force which produces the first motion produces through that motion a *sanskâra* or persistent tendency to motion (Vega), which is the cause of continued motion in a straight line, *i.e.* in the direction of the first motion (नियतदिक्रिया प्रबन्धहेतुः यद्दिगाभिमुख्येन क्रियावेगो जन्यते तद्दिशभिमुख्येनैव क्रियासन्तानस्य हेतुरिति—श्रीधर, न्याय-कन्दली, संस्कार-निरूपणम्).

c5.s3.t1.2

The Vaiśeṣikas accept one *sanskâra* (impressed motion, momentum) lasting till the cessation of the motion. Udyotakara and other writers of the Nyâya school suppose a series of *sanskâras*, each generating the one that succeeds it. (संस्कारेण उत्तरोत्तरकर्म्मसन्तानो जायते अनन्योत्तरसंयोगेन कर्म्मणि नष्टे संस्कारेण कर्म्मान्तरजननात् एक एव संस्कारः कर्म्मसन्तानजनकः नतु कर्म्मसन्तानवत् संस्कारसन्तानोऽपि अभ्युपगन्तुमुचितः—शङ्करमिश्र।) It will be seen that the Nyâya view is adequate to explain acceleration, which it logically implies. The force of *sanskâra* (शक्ति) diminishes by doing work (कार्य्यकरणात्) against a counteracting force, and when the *sanskâra* is in this way entirely destroyed, the moving body comes to rest (संस्कारो यावत्पतनमनुवर्त्तते। यथा यथा चास्य कार्य्यकरणात् शक्तिः क्षीयते तथा तथा कार्य्यमन्दतरतमादि-भेदभिन्नमुपजायते—श्रीधर—न्याय-कन्दली-कर्म्मग्रन्थ). Vega, it will be seen, corresponds to inertia in some respects, and to momentum (impressed motion) in others. This is the nearest approach to Newton's First Law of Motion in the Vaiśeṣika theory of motion.

c5.s3.t1.3

Vega (impressed motion), or this tendency to move on in a straight line, is counteracted by contact with tangible objects (स्पर्शवद्द्रव्यसंयोग), *e.g.* by impact or friction, including friction with the still atmosphere (स्तिमितवायु), as in the case of the arrow.

c5.s3.t1.4

Vega (momentum) produces work in opposition to the resisting force, and thereby becomes weaker and weaker (मन्दतर मन्दतम) until it comes to an end (तत्र वेगो मूर्त्तिमत्सु पञ्चसु द्रव्येषु निमित्तविशेषापेक्षात् कर्म्मणो जायते, नियत-दिक्-क्रिया-प्रबन्धहेतुः स्पर्शवद्द्रव्यसंयोग-विशेषविरोधी Praśastapâda, संस्कार-निरूपणम्—मन्दस्तु वेगः स्पर्शवद्द्रव्यसंयोगमात्रेण विनश्यति यथा अतिदूरगतस्य इषोः स्तिमितवायु-प्रतिबद्धस्य—श्रीधर, संस्कारनिरूपणम्).

c5.s3.t1.5

*Causes of Pressure* (नोदन) *and of Impact* (अभिघात).

c5.s3.t1.6

Pressure is produced by contact acting in conjunction with Vega (impressed motion), elasticity, gravity, fluidity or volition, *e.g.* the Vega of the wind produces pressure (नोदन) on the grass, that of a current of water on the reed, that of the bow-string on the arrow. Gravity with contact produces pressure, as when the earth sinks under a heavy load.

c5.s3.t1.7

Impact is produced by contact with a body possessing Vega (impressed motion) where the contact is instantly followed by disjunction (or rebounding). If the contact continues, the result is pressure (नोदन). (तत्र नोदन गुरुत्व-द्रवत्व-वेग-प्रयत्नान् समस्त-व्यस्तान् अपेक्षामानः यः संयोग-विशेषः नोदनं अविभाग-हेतुः एकस्य कर्म्मणः कारणं तस्मात् चतुर्षु अपि महाभूतेषु कर्म्म भवति . . . . . . वेगापेक्षो यः संयोग-विशेषः विभागहेतुः एकस्य कर्म्मणः कारणं स अभिघात तस्मादपि चतुर्षु-महाभूतेषु कर्म्म भवति—प्रशस्तपाद-भाष्य।)

c5.s3.t1.8

It is expressly noted that the four elements, earth, water, air, and fire, are all subject to the forces of pressure and impact. Pressure and impact may be of different degrees (तीव्रमन्दादिभेद). So also Vega (impressed motion, momentum).

c5.s3.t1.9

*Illustrations of Combination of Forces.*

c5.s3.t1.10

(1) Pressure acting concurrently with impressed motion or Vega, as when the moving hand possessing Vega throws the quoit or a projectile. (पाणिमुक्तेषु गमनविधिः) (ततः संस्कारनोदनाभ्यां तावत् कर्माणि भवन्ति यावत् हस्ततोमर-विभाग इति—प्रशस्तपादभाष्य।)

c5.s3.t1.11

Similarly, in the case of the bow-string impelling the arrow, or the potter’s wheel impelled by the rod, the first motion is due to pressure (नोदन), and results in a *sanskâra* (persistent tendency to motion, impressed motion or momentum), but the subsequent motions are produced by the pressure acting concurrently with the *sanskâra* (impressed motion). (तस्मात् संस्कारात् नोदन-सहायात् तावत् कर्माणि भवन्ति यावत् इषुज्या-विभागः—प्रशस्त-पाद, कर्माग्रन्थ—प्रथमं चक्रावयविनि दण्डसंयोगात् कर्म्म उत्पद्यते उत्तरोत्तराणि कर्माणि अभिघातात् कर्मजात् संस्कारात् च भवन्ति दण्डविगमे तु चक्रं तदवयवेषु च संस्कारादेव केवलात्। श्रीधर, न्याय-कन्दलो, कर्माग्रन्थ।)

c5.s3.t1.12

(2) Impact (अभिघात) with impressed motion (संस्कार), as when the mortar thrown by the hand rebounds after striking the pestle (संस्कारापेक्षात् अभिघातात् मुसले उत्पतन-कर्म—प्रशस्तपाद भाष्य).

c5.s3.t1.13

(3) Pressure (नोदन) acting concurrently with impact (अभिघात), as when the mud sinks when we strike against the ground with the feet. Here, if the feet be not in contact with the mud, but only with the surrounding ground, there is transmitted force (संयुक्तसंयोग).

c5.s3.t1.14

(पदादिभिर्नुद्यमानायामभिहन्यमानायां वा पंकाख्यायां पृथिव्यां यत् संयो-गोन्नोदनाभिघातयोरन्यतरापेक्षो उभयापेक्षो वा स संयुक्तसंयोगः। तस्मादपि पृथिव्यादिषु कर्म्म भवति।—Praśastapâda.)

c5.s3.t1.15

(4) Gravity concurrently with *sanskâra* or persistent tendency, as in the case of a falling body in the second and following instants. Also the case of a stone thrown against the mud, where gravity (the weight of the stone) combines with the Vega of the stone to produce motion in the mud (Praśastapâda). (आद्यं कर्म्म गुरुत्वात् भवति। तेन कर्म्मणा संस्कारः क्रियते तदनन्तरं उत्तरकर्म्माणि गुरुत्वसंस्काराभ्यां जायते द्वयोरपि प्रत्येकं अन्यत्र सामर्थ्यावधारणात्—श्रीधर, न्याय-कन्दली, कर्म्मग्रन्थे साप्रत्यय-कर्म्मणिरूपणम्।) This case will be further noticed below.

c5.s3.t1.16

Udyotakara, the commentator on the Nyâya-Bhâṣya, states that a heavier body falls to the ground with greater Vega (and velocity) than one that is lighter. Udyotakara also holds, and Śrîdhara agrees with him, that the gravity (गुरुत्व) of a body (अवयवी) as a whole composed of particles (अवयवाः) is not the same as the sum of the gravities of the particles. There is a difference in amount which is, however, so small as to be imperceptible. The concept of mass in the New Mechanics of Lorenz may lend some countenance to this curious metaphysical speculation. (Śrîdhara, गुणग्रन्थ, गुरुत्वनिरूपणम्।)

c5.s3.t1.17

(5) Volition acting concurrently with gravity, as in lifting up the hand. This is accompanied by transmission when an object, *e.g.* the quoit, is lifted by the hand.

c5.s3.t1.18

Sanskâra (impressed motion, momentum), with or without pressure (नोदन) or impact (अभिघात), may be transmitted (दृढ़संयुक्तस्य अवयवस्य उत्तरोत्तरकर्म्माणि संस्कारात् नोदनाच्च अपरेषां संस्कारात् संयुक्तसंयोगाच्च।—Śrîdhara).

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.

Motion of a Particle in the Case of a Composition of Forces

c5.s3.t3.1

Any number of motions or Vegas may be impressed on a particle, but so long as these are in a uniform direction (नियतदिग्विदिष्ट) the resultant motion or Vega is in a straight line, and may be conceived as one (द्वितीयकल्पना-वैय्यर्थम्, Praśastapâda, कर्मग्रन्थ). It is only when we come to Gamana (curvilinear motion) and its causes that the question of composition assumes a real significance. In all such cases, each separate particle has only one Vega (impressed motion) in a definite direction (नियतदिगाभिमुख्य) at any given instant, but the composition of the successive motions and Vegas in the same particle produces the curvilinear motion (गमन), *e.g.* the rotation of each constituent particle of the potter's wheel. The motion of the body (अवयवी, *e.g.* the wheel) results from the combined motions of the particles (अवयवाः). If pressure or impact produces motion in an opposite direction to the Vega already impressed on the body, the original direction would be changed, as is seen in the case of rebounding (उत्पतन) after impact (अभिघात). The mortar rebounding after striking the pestle is a typical instance of such change of direction in Vega or motion. The impressed force, *e.g.* impact (अभिघात), produces a changed motion in a different direction. One view is that the original Vega (momentum) is destroyed before a new motion and a new Vega are produced by the impact. Others hold that the impact does not destroy the original Vega (momentum), but conjointly with it produces the changed motion and, through such motion, a changed Vega in a new direction. (उलूखलमुसलयोरभिघाताख्यः संयोगो-मुसलगमवेगमपेक्षमाणः मुसले उत्पतनकर्म करोति यद्यपि प्राक्तनसंस्कारो विनष्टः तथापि मुसलोलूखलयोः संयोगः पटुकर्मोत्पादकः तस्य संस्कारारम्भ-साचिव्यसमर्थो भवति अथवा प्राक्तन एव पटु संस्कारः अभिघातान् अविनश्यन् अवस्थित इति *et seq.*, Prasastapâda, कर्मग्रन्थ ।)

Typical Cases of Curvilinear Motion (Gamana)

c5.s3.t4.1

*Vortical Motion.*—This is due to the contact of two bodies moving in opposite directions with a like or equal Vega, *e.g.* two currents of air or water meeting from opposite directions. The change of direction is seen in the fact that water which flows downwards, or air which moves obliquely, may receive an upward motion as the result of such collision. (अथ किमिदं संमूर्च्छनं नाम। समानजयोः (तुल्यवेगयोः) वाय्वोर्विरुद्ध-दिक्क्रिययोः सन्निपातः Praśastapâda, वायुनिरूपणं). The scholiast Udayana adds: वाय्वोरितिप्रकृतत्वेन स्पर्शवत्तोरिति तु विवक्षितम्। अपां यथा द्रव्यान्तर-संमूर्च्छनाद् ऊर्द्धगमनं परस्पराभिहतनदीपयः — उदयन, द्रव्यकिरणावली. Śrîdhara notes: तिर्य्यग्गतिस्वभाव-द्रव्योदूर्द्धगतित्वात् परस्पराभिहत-जलतरङ्गोदूर्द्धगमनवत् असमानवेगयो संमूर्च्छनं न भवति एकेन अपरस्य विनयात् — Śrîdhara.)

Vibratory Motion (कम्पन, स्पन्दन)

c5.s3.t5.1

This will be analysed in the chapter on Acoustics.

Rotatary Motion (भ्रमण)

c5.s3.t6.1

Each particle of the rotating body, *e.g.* the potter's wheel (चक्र), has, at any given instant, a motion in a definite direction. The rotatory motion of the body results from the separate motions of the particles and their persistent tendencies (संस्काराः), joined with the fact of the rigid conjunction of the particles. When the rod strikes one part of the wheel, the motion in the part struck is in the first instant produced by impact (अभिघात); while the other parts move through the transmission of force due to the rigid cohesion of parts. The subsequent motions in the part struck are due to continued pressure (नोदन) and the persistent tendency (संस्कार) set up by the first motion; while the subsequent motions in the other parts are explained by their own persistent tendencies and the transmission due to rigid cohesion. When the rod is disjoined from the wheel the rotatory motion continues, being due merely to the persistent tendencies in the constituent parts and the resultant persistent tendency in the whole.

c5.s3.t6.2

Other varieties of curvilinear motion in bodies are to be similarly explained (*i.e.* by the composition of Vegas) (तथा चक्रादिषु अवयवानाम् पार्श्वतः प्रतिनियतदिग्देशसंयोगविभा-गोत्पत्तौ यदवयविनः संस्कारादनियतदिग्देशसंयोगविभागनिमित्तं कर्म्म तत्-भ्रमणामिति । श्चमादयो गमनविशेषाः—Praśastapâda,—कर्म्मग्रन्थ । एवं वेगात् दण्डसंयोगचक्रावयवे आद्यं कर्म्म दण्डसंयोगात् । अवयवान्तरेषु च संयुक्तसंयोगात् दण्डसंयुक्तस्य अवयवस्य उत्तरोत्तरकर्म्माणि संस्कारात् नोदनात् च । अपरेषां संस्कारात् संयुक्तसंयोगात् च दण्डविगमेतु चक्रे तदवयवेषु च संस्कारादेव केवलात् श्वमादयो गमनविशेषाः—Śrīdhara).

Linked texts (1)