SECTION III.

THE CENTRE OF GRAVITY OF BODIES AND OF ANIMALS.

375. IF you balance any body on your finger, as a Gunter's scale, for example, it will rest in a horizontal position when the figure 12 is over your finger. That point, therefore, on which the scale is exactly balanced, is called the centre of gravity.

376. Again, if you place a body upright as a pillar, it will remain perpendicular, provided the line of direction falls exactly in the centre of its base.

Thus, the inclining body ABCD, whose centre of gravity is E, stands firmly on it base CDIK, because the line of direction EF falls within the base. But suppose ABCD were the first stone of a column, and that we had not placed it perfectly on the base, and were then to lay another block of stone upon it, as ABGH, the centre of gravity would be raised to L, and then as the line of direction LD falls without the base at D, the centre of gravity is not supported, and the whole weight must fall just as the Gunter's scale would slide off your finger if you attempted to balance it at the figures 13 or 11.

377. Upon the principle here laid down, the safety coaches now in use have been built. The base of these coaches is made as broad as possible, the line of direction is brought as near their middle as possible.

378. In this too consists the great difficulty of posture-masters and rope-dancers.

The dancer on the rope balances himself by a long pole loaded with lead, and keeps his eye steadily upon some one point exactly parallel to the rope, by which he can see whether his centre of gravity is either on one side or the other of his slippery foundation, and if any irregularity takes place he rectifies it by his balancing pole.

379. If a plane be inclined on which a heavy body is placed, the body will slide down the plane, while the line of direction falls

within the base; but it will roll down when this line is beyond the base.

Thus the body E will only slide down

the plane CD, but the body B rolls down the plane CD; because the line of direction BR is beyond the base.

Hanging Towers of Pisa and Bologna.

380. In old buildings where the whole fabric is closely bound together, it may occur that a part may overhang the base, and yet that part not fall; but if the centre of gravity of the whole building were brought without the base, ruin would instantly equis

The famous campanill or hanging tower of Pisa, is erected in a square, close to the great church of the same name. It is composed wholly of white marble, and was built for the purpose of containing the bells. Its height is about two hundred feet, and its inclination nearly fifteen feet from the perpendicular, but the plummet C falls within the base, and therefore it stands. The cause of this very extraordinary inclination is supposed to be a want of care in laying the foundation. The two towers of Bologna, in Italy, close beside one another, hang several feet beyond the perpendicular, and seem to beholders as if ready to fall; but as the whole building firmly adheres together, and as the centre of gravity is still above the base, they are perfectly secure. They must have been long in this state, as they are mentioned in the poems of Dante who died in

In ascending a stair or a steep hill we bend our body forwards; in descending we lean backwards, as it were, to preserve our centre of gravity. In carrying a burden we lean forwards. All that is applicable to man, is applicable to quadrupeds, birds, and fishes. The mule on the Andes will drop on his haunches and slide down a rock; birds to preserve their centre of gravity flying are obliged to stretch out their necks and make great use of their tails; fishes of their fins, &c. In short, the economy of nature is as marvellous in this matter as in the exact system of the world.

CHAPTER XVII.

MECHANICS.

382. THE mechanical powers are simple engines, with which to raise weights, to move heavy bodies, and to overcome resistances, that are above our natural strengh.

The importance of these mechanical powers to society is incalculable, and a knowledge of them indispensable.

Every machine is composed of one or more of these powers; and sometimes of several of them combined.

Three things are to be considered in treating of mechanical engines, 1. The weight to be raised. 2. The power by which it is to be raised. 3. The instrument or engine by which this is to be effected.

The mechanical powers are six: 1st, the lever; 2d, the pulley; 3d, the wheel and axis; 4th, the inclined plane; 5th, the wedge; and 6th, the screw; which may, perhaps, be reduced to two; for the pulley and wheel are only assemblages of levers, and the wedge and screw are inclined planes.

Of the Lever.

383. The lever, the simplest of all machines, is only a straight bar of iron, or wood, supported on, and moveable round, a prop, called the fulcrum.

In the lever, there are three circumstances to which we must principally attend.

1. The fulcrum or prop by which the lever is supported, or on which it turns as an axis, or centre of motion. 2. The power to raise and support the weight: and, 3. The resistance or weight to be raised or sustained. The point of suspension is that point where the weight really is, or from which it hangs freely.

The power and the weight are supposed to act at right angles to the lever, except otherwise expressed.

There are three sorts of levers, according to the different situations of the fulcrum, or prop, and the power, with re spect to each other.

1. When the prop is placed between the power and the weight.

A lever of this kind is principally used for loosening stones; or to raise weights to small heights, to get ropes under them, or other means of raising them to still greater heights: it is the most common species of lever.

Example. If a stone (W), weighing 500 pounds, is to be raised one foot by a man acting at (P), who can only lift 100 pounds, he cannot raise it, unless he contrive to make his arm move five feet

while the stone moves only one foot; because 100 × 5500 x 1; therefore to effect this the arm of the lever (P F) must be five times as long as the arm between F and the weight, in order that the power and weight may balance each other.

This increase of motion in the arm is effected by the lever; because the motion of one end is in the same proportion to the motion of the other, as the distance of the two ends are from the fulcrum.

If a lever, six yards in length, call it, if you please, an eighteen feet plank, be laid on a fulcrum (P), at one yard from one end and the aforesaid stone be fixed to that end of the plank or lever, the hand which pulls at the long, or five yards' end (P) of the lever, moves over five times the space that the other end does, consequently, though pulling but 100 pounds, it will balance 500 pounds at the short end of the lever.,

2. When the prop is at one end of the lever, the power at the other, and the weight between them. The advantage gained by the lever, as in the first, is as great as the distance of the power (P) from the

prop (F), exceeds the distance of the weight (w) from it.

This lever shews the reason why two men carrying a burthen between them, as a cask upon a pole, may bear unequal shares of the weight according to their strength; for the nearer either of them is to the burthen, the greater share he will bear of it: their shares of its weight will, in fact, be to either of them in the inverse proportion of his distance from it.

If the pole be eight feet long, and a cask be slung directly at its half length, at one end of the pole each of the men will bear 56lbs. weight, supposing the cask to weigh one cwt.; but if it be placed five times nearer the one man than the other, the former will bear five times as much weight as the latter.

This is likewise applicable to the case of two horses of unequal strength so yoked, that each horse may draw a part in proportion to his strength. This is done by so dividing the beam they pull, that the point of attraction may be as much nearer to the stronger horse than to the weaker, as the strength of the former exceeds that of the latter.

To this kind of lever may be reduced oars, rudders of ships, cutting knives which are fixed at one end, &c.

3. When the prop is at one end, the weight at the other, and the power applied between them. In this lever we suppose

the power and weight to change places, the power (P) is between the weight

W

(w), and prop (F). And here, that there may be a balance between the power and the weight, the intensity of the power must exceed the intensity of the weight as much as the distance of the weight from the prop exceeds the distance of the power.

A ladder, raised by the strength of a man's arms, repre