CHAPTER III.

MOTION AND FORCE.

14. Rest and motion.-To understand what we have to say about inertia, weight, universal gravitation, and the motion of liquids and gases, it is first of all necessary to give some very elementary notions about motion and force.

A body is said to be at rest, when it remains in the same place; to be in motion when it passes from one place to another. Both rest and motion are either absolute or relative.

Absolute rest would be the entire absence of motion. No such condition, however, is known in the universe; for the earth and the other planets rotate both about the sun and about their own axes ; and therefore, all the parts composing them share this double motion. Even the sun itself has a motion of rotation which exIcludes the idea of absolute rest.

Relative or apparent rest is the condition of a body which appears fixed in reference to surrounding objects, but which really shares with them a double motion. For instance, a passenger in a railway carriage may be in a state of relative rest with respect to the train in which he travels, but he is in a state of relative motion with respect to the objects (fields, houses, etc.) past which the train rushes. These houses again enjoy merely a state of relative rest, for the earth itself which bears them is in a state of incessant relative motion with respect to the celestial bodies of our solar system.

The absolute motion of this passenger would be that measured in regard to a fixed point in space, which cannot be realised, for we know no such point. In short, absolute motion and rest are unknown to us; in nature, relative motion and rest are alone presented to our observation.

15. Different kinds of motion. Motion is either rectilinear or curvilinear rectilinear when the moving body travels along a straight line, as when a body falls to the ground; curvilinear when it goes along a curved line, as in the case of a horse turning in a mill.

Each kind of motion is either uniform or varied.

-18]

Inertia.

13

16. Uniform motion.-Motion is said to be uniform when the moving body passes over equal spaces in equal intervals of time; such, for instance, as the motion of a water-wheel when it makes exactly the same number of turns in a minute. Such, again, is the motion of the hands of a watch. A regiment of soldiers marching in step affords an example of uniform motion.

The velocity of motion is the space traversed in a given time, a second or an hour, for example. A train which moves thirty miles in each successive hour is said to have a velocity of thirty miles an hour.

17. Varied motion.-Varied motion is that in which unequal spaces are traversed in equal times. If the spaces traversed in the same time go on increasing, the motion is said to be accelerated; such is the motion of a train starting from a station; if the spaces decrease, as is the case when the trains come into a station, the motion is retarded.

If the distances, traversed in equal times, always increase by the same amount, the motion is said to be uniformly accelerated; if, on the other hand, they constantly decrease by the same amount, the motion is uniformly retarded. We shall soon see examples of these kinds of motion in the case of falling bodies.

18. Inertia. Inertia is a purely negative property of matter; it is the incapability of matter to change its own state of motion or

rest.

Daily observation shows that a body never spontaneously passes from a state of rest into one of motion. Bodies in falling to the ground seem to set themselves in motion. This is, however, not in consequence of any inherent property; but, as we shall afterwards see, because they are acted upon by the force of gravity.

Not merely do bodies at rest persist in a state of rest, but bodies in motion continue to move. This principle may seem less obvious than the former, because we are accustomed to see many bodies gradually move more slowly, and ultimately stop, as is the case with a billiard ball for example. But this is not due to any inherent preference for a state of rest on the part of the billiard ball, but because its motion is impeded by the friction of the cloth on which it rolls, and by the resistance of the air. The smaller these resistances, the more prolonged is its motion; as is observed, for instance, if a ball be set rolling on a smooth sheet of ice. If all impeding causes were removed, a body once in motion would continue to move for ever.

19. Effects due to inertia. Innumerable phenomena may be explained by the inertia of matter. For instance, before leaping

a ditch we run towards it, in order that the motion of our bodies at the time of leaping may add itself to the muscular effort then made.

On descending carelessly from a carriage in motion, the upper part of the body retains its motion, whilst the feet are prevented from doing so by friction against the ground; the consequence is we fall towards the moving carriage.

If a man in running strikes his foot against an obstacle he is apt to fall down in front, because the rest of his body tends to retain the motion it has acquired. When a horse at full gallop suddenly stops, if the rider does not hold fast with his knees, he is thrown over the horse's head in virtue of his inertia.

The terrible accidents on our railways are chiefly due to inertia. When the motion of the engine is suddenly arrested the carriages strive to continue the motion they had acquired, and in doing so are shattered against each other.

The action of projectiles is another case. When a bullet traverses a wall, or cuts a tree in two, it is owing to its tendency to retain the velocity which the explosion of the powder had imparted to it. In the action of hammers and of pile driving we have analogous cases.

20. Forces, powers, resistances.-Bodies being of themselves inert, and having no tendency to change either their state of rest or that of motion, any cause capable of making them pass from a state of rest to one of motion, or conversely from a state of motion to one of rest, is called a force.

The attractions and repulsions exerted between the molecules are forces; the muscular action which men and animals bring into play is a force, as is also the elasticity of gases and vapours which we shall subsequently discuss.

The forces which tend to produce motion are called powers; those which tend to destroy motion are called resistances. Thus, when a man drags a burden along the ground his muscular force is a power, while the friction of the burden against the ground is a resistance.

Forces of the kind called powers are always tending to accelerate motion, and are called accelerating forces. Resistances on the contrary, always tending to retard it, are called retarding forces.

21. Distinctive characters of forces.-Three things are to be

-22]

Measurement of Forces.

15

distinguished in each force; the point of application, the direction, and the intensity.

The point of application of a force is the point at which it exerts its action. Having attached a cord to a carriage, as shown in fig. 6, the point of application is the point A, at which the cord is actually attached.

The direction of a force is the right line along which it urges or tends to urge the point of application. In fig. 6 the cord AB represents the direction of the force.

The intensity of a force is its energy, its magnitude, or value, in reference to a certain standard. In fig. 6, which represents a boy

drawing a small carriage, a certain exertion of force is required on the part of the boy; if the carriage were loaded twice or thrice as much, the force required must be twice or thrice as great.

22. Measurement of forces. Dynamometer.-The force which a motor developes in pushing or drawing a body, is measured by the number of pounds necessary to produce the same pressure or the same pull; so that a force is said to be a force of 40 or 50 pounds, when it can be replaced by the action of a weight of 40 or 50 pounds.

The weight which thus represents the intensity of a force is determined by means of the dynamometer. There are several forms of this instrument, one of the simplest being that represented in fig. 7. It consists of a V-shaped plate of tempered steel, AB. At one end of the limb B is fixed an iron arc, n, which passes freely through an aperture at the end of the limb A. To this latter is fixed an arc, m, fitting in the same manner in the limb B. The arc m is provided at the end with a crook, and n with a ring, and on

the latter n there is a graduation obtained in the following

manner :

The apparatus being fixed to a resisting support, weights of 1, 2,

n

B

Fig. 7.

Fig. 8.

3, 4, or more pounds are successively suspended to the crook. The limb B, supported by the arc n, remains fixed, while the limb A, being moved by the weight attached to the arc m, is lowered to an extent dependent on the weight. The load is gradually increased until it has reached the utmost limit possible without breaking, care being taken at each load to mark a line on the arc n at the point at which the limb A stops.

In order to apply it to the measurement of forces, to estimate, for instance, the effort necessary to drag a load (fig. 8), the crook of the arc m is fixed to the load, then holding in the hand the ring of the arc n it is pulled until the load is moved. The flexure of the limb A marks on the arc n the value in pounds of the effort of traction.

The apparatus described is also used as a balance to determine the weight of bodies, and is known as the steelyard.

Forces once measured in weight, they may be represented as to their intensity by means of the line which indicates their direction. For this purpose a length is measured off on this line, starting from the point of application, which contains the unit of length as many times as the intensity of the force contains pounds. Thus, if in fig. 6 the effort of traction is 15 pounds, a length, AB, would be measured from A equal to 15 times the unit of length, which may be an inch for distance. Thus the work of