5. A body in motion must at every instant of time tend to some point. If it always tend to the same point, its direction is in a straight line, but if this point be perpetually changing, the motion will be curvilinear.

6. If a body is acted upon only by one force, in one direction, as in driving a ball along smooth ice, or by several successive forces in the same direction, as the motion given to a vessel on water by a man continually pulling it towards him, then the motion will be in the same direction.

7. If a body be acted upon by two or more forces in different directions at the same time, as it cannot move in all, it will move in a direction somewhere between them. The theorems relating to this are said to relate to the composition and resolution of forces.

Example. When a ship is driven by wind due west, and by the tide due north, it will go neither to the west nor to the north, but if the forces be equal, it will be driven exactly north-west.

8. Accelerated motion is that in which the velocity is continually increasing.

Example. A body falling to the earth from some high building, as the cupola of St. Paul's Church, affords an instance of accelerated motion, which is caused by the constant action of gravity.

9. Motion is said to be retarded when its velocity is continually decreasing.

Example. If a cannon ball were fired perpendicularly upwards, its motion would be retarded every instant, till at length its direction being changed, it would fall again with an accelerated motion; and it would take precisely the same space of time in its fall as in the ascent.

10. The velocities of falling bodies, and also the spaces passed over by them increase as the odd numbers 1, 3, 5, 7, 9, &c. that is, a body would fall 16 feet in the first second; in the next it would fall three times 16, or 48 feet; in the third second it would fall five times 16, or 80 feet; in the fourth seven times 16, or 112, and so on.

11. The whole spaces passed over by a falling body, from the beginning of motion, will be as the squares of

the times, that is, as it falls 16 feet in the first second, it will fall through four times 16, or 64 feet in two seconds; nine times 16, or 144 feet in three seconds; and in four seconds it will fall through 16 times 16, or 256, and so on; because 4, 9, 16, 25, &c. are the squares of 2, 3, 4, 5, &c.

12. The force with which a body moves, or which it would exert upon another body opposed to it, is in proportion to the velocity multiplied by its weight: this force is called the momentum.

Example. If two cricket balls of equal weight be so struck that the velocity of one be double that of the other, then the force of the swiftest will be double that of the slowest.

QUESTIONS FOR EXAMINATION.

1. What is meant by the term motion?
2. How many kinds of motion are there?
3. What are the causes of motion?

4. How is the velocity of motion estimated?
Give the example.

5. To what does a body in motion tend?

6. When is motion said to be in the same direction?

7. What will be the direction of a body in motion that is acted upon by two or more forces in different directions?

Give the example.

8. What is meant by accelerated motion?

9. When is motion said to be retarded?

Give the example.

10. What is the law with regard to the velocities of falling bodies, and also with regard to the spaces passed over by them? 11. What is the law with respect to the whole spaces passed over?

12. What is meant by the momentum of a body?

LESSON THE THIRD.

CENTRE OF GRAVITY.

1. The centre of gravity of a body is that point in which the whole force of its gravity or weight is united, and whatever supports that point, supports the body, therefore the whole weight of the body may be considered as centered in that point.

Example. If I balance my pen or a cane on my finger, I know that the centre of gravity rests upon the finger.

2. The common centre of gravity of two or more bodies is the point upon which they would rest in any position.

Example. If I have two brass or marble balls connected together with a wire, and I am able to balance them by placing the wire in a certain position on my finger, I know the common centre of gravity of the two balls rests on the finger.

3. An imaginary line drawn from the centre of gravity of any body towards the centre of the earth is called the line of direction, because it is the line that the centre of gravity would describe, if the body were suffered to fall.

4. If the line of direction fall within the base upon which the body stands, the body cannot fall, but if it fall without the base, the body will tumble.

Examples. The inclining body ABCD, fig. 1, whose centre of gravity is E, stands firmly, because the line of direction ED falls within the base: but if another body be placed upon it, the centre of gravity will be raised to L, and then the line of direction LD will fall out of the base, and the centre of gravity not being supported, the whole body will fall. In a coach or boat likely to be overset, the passengers should slip to the bottom, which lowers the centre of gravity, and diminishes the danger.

Hence buildings, as the tower A B, fig. 3, may lean many feet out of the perpendicular, and yet stand firm, provided a plumb-line, Cc, suspended from C, the centre of gravity, fall within the base.

5, If a plane, CD, see fig. 2, p. 218, be inclined, on which a heavy body A, is placed, the body will slide down the plane, while the line of direction falls within the base, but if, as in B, the line of direction fall out of the base, the body will roll.

6. The broader the base of a body the firmer will it stand: thus the human body will stand

Fig. 1.

H

L

K

D DF

C

D

Fig. 2.

most steadily when the line of direction C falls in the middle point between the feet.

Example.-Rope dancers perform their feats by knowing how exactly to keep the common centre of gravity of themselves, and their pole, just within the base.

QUESTIONS FOR EXAMINATION.

1. What is meant by the centre of gravity?

Give the example.

2. What is the common centre of gravity of two or more bodies? 3. What is meant by the line of direction?

4. In what case will a body stand, and when will it fall? Give the examples.

5. In what case will a body slide, and when will it roll down a plane?

6. What makes a body stand very firmly?

LESSON THE FOURTH.

MECHANICAL POWERS.

1. The mechanical powers are simple engines that enable men to raise heavy weights, and overcome resistances, which they could not do with their natural strength.

2. Every machine is composed of one or more of the mechanical powers, of which there are six, viz. the lever, the wheel and axis, the pulley, the inclined plane, the wedge, and the screw.

3. A lever is an inflexible bar of wood, iron, &c. chiefly used to raise large weights, and it is supported by a prop or fulcrum, on which all the other parts turn, as the centre of motion. There are three kinds of levers, distinguished from one another by the different ways of using them.

5. A poker stirring the fire is a lever of the first kind, for the bar of the grate is the fulcrum, the coals the weight to be moved, and the hand the power. Steelyards, scissars, pincers, snuffers, &c. are levers of the first kind.

6. Every door that turns on hinges is a lever of the second kind, the hinges are the fulcrum, or centre of motion, the door is the weight to be moved, and the hand in opening it is the power. An oar in the act of moving a boat is a lever of this kind, so is the rudder of a ship; also nut-crackers, and knives used in cutting chaff, &c.

7. A ladder to be raised by the strength of a man's arms is a lever of the third kind: the end fixed against the wall is the fulcrum, the top of the ladder may be regarded as the weight, and the power is the strength applied. The human arm in raising a weight is a lever of this kind.

8. A hammer drawing a nail is a lever of the first kind, but with a different application. The longer the handle of the hammer, compared with the shank or iron part applied to the nail, the easier the nail is drawn.

9. In all the mechanical powers it is a maxim that the