pass within the original polygon of support, and the weight will act to return the body to its original state of rest. Hence it is that we find chairs, lamps, candlesticks, and many other familiar utensils constructed with broad bases, to render them more stable.

The leaning tower of Pisa is so much inclined that it appears about to fall; yet it stands, because the vertical through the centre of gravity passes within the base of the tower. Fig. 28 represents a tower at Bologna, which is even more inclined than that at Pisa. This tower was built in the year 1112, and received its inclination from unequal settling of the ground on which it was built. It does not fall, because the vertical through the centre of gravity, G, passes within its base.

In the cases considered, the position of the centre of gravity remains the same for the same body. With men and animals the position of the centre of gravity changes with every change of attitude, which requires a proper adjustment of the feet, to maintain a position of stability.

When a man carries a burden, as shown in Fig. 29, he leans forward, that the direction of his own weight with that of his burden

may pass between his feet. When a man carries a weight in one hand, as shown in Fig. 30, he throws his body toward the opposite side for the same reason.

In the art of rope-dancing, the great difficulty consists in keeping the centre of gravity exactly over the rope. To attain this result the more easily, a rope-dancer carries a long pole, called a balancing pole, and when he feels himself inclining towards one side, he advances his pole towards the other side, so as to bring the common centre of gravity over the rope, thus preserving his equilibrium The rope-dancer is in a continual state of unstable equilibrium.

The Balance.

44. A BALANCE is a machine for weighing bodies.

Balances are of continual use in commerce and the arts, in the laboratory, and in physical researches; they are consequently extremely various in their forms and modes of construction. We shall only describe that form which is in most common use in the shops.

It consists of a metallic bar, AB (Fig. 31), called the Beam, which is simply a lever of the first order. At its middle point is a knife-edged axis, n, called the Fulcrum. The fulcrum projects from the sides of the beam, and rests on two supports at the top of a firm and inflexible standard. The knife-edged axis, and the supports on which it rests, are both of hardened steel, and nicely polished, in order to make the friction as small as possible. At the extremities of the beam are suspended two plates or basins, called Scale Pans, in one of which is placed the body to be weighed, and in the other the weights of iron or brass to counterpoise it. Finally, a needle projecting from the beam, and playing in front of a graduated scale, a, serves to show when the beam is exactly horizontal.

Explain the principle of rope-dancing. (44.) What is a balance? Explain the details of the common Balance. The Beam. The Fulcrum. The Scale Pans. The Scale.

To weigh a body, we place it in one of the scale pans, and then put weights into the other pan until the beam

becomes horizontal. The weights put in the second pan indicate the weight of the body.

Requisites for a good Balance.

45. A good balance ought to satisfy the following conditions:

1. The lever arms, An and Bn, should be exactly equal.

We have seen in discussing the lever, that its arms must be equal, in order that there may be an equilibrium between the power and resistance, when these are equal. If the arms are not equal, the weights placed in one scale pan will not indicate the exact weight of the body placed in the other.

2. The balance should be sensitive; that is, it should turn on a very small difference of weights in the two scale pans.

This requires the fulcrum and its supports to be very hard and smooth, so as to produce little friction. By making the needle long, a slight variation from the horizontal will be more readily perceived.

3. The centre of gravity of the beam and scale pans should be slightly below the edge of the fulcrum.

If it were in the edge of the fulcrum, the beam would not come to a horizontal position when the scales were equally loaded, but would remain in any position where it might chance to be placed. If it were above the edge of the fulcrum, the beam would remain horizontal if placed so, but if slightly deflected, it would tend to overturn by the action of the weight of the beam.

The nearer the centre of gravity comes to the edge of the fulcrum, the more accurate it will be; but at the same time, it would turn more slowly, and might finally come to turn too slowly to be of use for weighing.

It is to be observed that when the scale pans are heavily loaded, an increased weight is thrown on the fulcrum, which

(45.) Explain the requisites of a good balance. 1. Lever arms. Illustrate. 2. Sensitiveness. Illustrate. 8. Position of centre of gravity. Illustrate.

causes an increase of friction, and consequently a diminution of sensitiveness.

Methods of Testing a Balance.

46. To see whether the arms are of equal length, let a body be placed in one scale pan, and counterbalanced by weights put in the other; then change places with the body and the weights. If the beam remains horizontal after this change, the arms are of equal length, otherwise the balance is false.

To test the sensitiveness, load the balance and bring the beam to a horizontal position, then deflect it slightly by a small force and see whether it returns slowly to its former position. It ought to come to a state of rest by a succession of oscillations.

Method of weighing correctly with a false Balance.

47. To weigh a body with a false balance, place it in one scale pan and counterbalance it by any heavy matter, as shot or sand, placed in the other pan. Then take out the body and replace it by weights which will exactly restore the equilibrium of the balance. The weights will be exactly equal to the weight of the body. The reason for this method is apparent.

48.

Laws of falling bodies.

When bodies starting from a state of rest fall freely in vacuum, that is, without experiencing any resistance, they conform to the following laws:

1. All bodies fall equally fast.

(46.) How is a balance to be tested? (47.) How may a body be weighed cor rectly by a false balance? (48.) What is the first law of falling bodies?