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, 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. Mustrate. 2. Sensitiveness. Illustrate. 8. Position of centre of gravity. Illustrate.

causes an increase of friction, and consequently a diminu tion 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 correctly by a false balance? (48.) What is the first law of falling bodies?

When resisted by the air, bodies whose bulk is very large in pro-portion to their weight, fall more slowly than those whose bulk is small; thus, a soap-bubble falls more slowly than a bullet.

2. The velocities acquired during the fall are proportional to the times occupied in falling.

A body acquires a velocity of 32 feet in one second; it will therefore acquire a velocity of 643 feet in two seconds, a velocity of 96 feet in three seconds, and so on.

3. The spaces passed over are proportional to the squares of the times occupied in falling.

A body falls from rest through 16 feet in one second; it will therefore fall 4 x 16, or 643, in two seconds, 9x162, or 1443 feet, in three seconds, 16x161, or 257 feet in four seconds, and so on.

The first law is verified by the following experiment. A glass tube, six feet long (Fig. 32), is closed at one end, and at the other it has a stop-cock, by which it can be closed or opened at pleasure. A small leaden ball and a feather are introduced within the tube. So long as the tube is full of air, if it be suddenly inverted, it will be observed that the ball reaches the bottom sooner than the feather. If now the air be exhausted by means of an air

Fig. 32.

Effect of atmospheric resistance. What is the second law? Illustrate. Third law? Illustrate. How is the first law verified?