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 one of the forms which is in common use in the shops.

It consists of a metallic bar, AB (Fig. 55), 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.

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.

93. Requisites for a good Balance. 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 per

ceived.

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

94. Methods of testing a Balance. - To see whether the arms are of equal length, let a body be placed in one scalepan, 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.

95. To weigh correctly with a false Balance. - 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.

96. The Steel-Yard. The common steel-yard used in weighing is a lever of the first class, which differs from the balance in having unequal arms. Fig. 56 represents a form in common use.

The pivot C is the fulcrum; the weight W is suspended from the hook A, and the power P is movable on the long arm of the lever, which is graduated to indicate pounds and ounces. It is evident that a pound weight at D will balance as many pounds at

W as the distance A C is contained times in DC. The same counterpoise P may be used for a greater weight by turning the

Three Laws relating to Intensity of Force, Velocity, and

The Balance.

Description.

Requisites for a good Balance.

Methods of Testing.

Weighing with a false Balance.

The Steel-Yard.

Scales for Great Weights.

97. The Wheel and Axle consists of a wheel, or drum,

A, mounted upon an axle, B. The power is applied at one extremity of a cord wrapped around the wheel, and the resistance at one extremity of a second cord wrapped around the axle in a contrary direction. The whole is supported on a suitable frame, by means of pivots projecting from the ends of the axle.

Ꭱ

P

Fig. 57.

[B

The wheel and axle acts as a perpetual lever of the first kind, the fulcrum being at the common centre, and the radii of the wheel and axle being respectively the arms of the lever.

In Fig. 58, F is the fulcrum, A F is the power arm, and FB the weight arm of the lever. Hence, according to the law of the lever, P × AF = W × F B.

It is evident that during one revolution of the wheel and axle the power moves through a space equal to the circumference of the wheel, and the weight through a space equal to the circumference of the axle. Hence, according to the second general law of machines, the power multiplied by the circumference of the wheel is equal to the weight multiplied by the circumference of the axle.

B

A

W

Fig. 58.

P

Since the radii of circles are proportional to their circumferences, the law of the wheel and axle may be stated in two ways, viz.:

The power multiplied by the radius of the wheel equals the