retard its progress, their resultant is equal to the difference

of the forces.)

Equilibrium of Forces.

26. When several forces acting upon a body exactly balance each other, they are said to be in equilibrium.

Fig. 12.

The simplest case of equilibrium is that of two equal forces acting against each other, as in the case where two men of equal strength pull at the two ends of a rope, as shown in Fig. 12.

In the same manner, if two buckets of equal weight are suspended in a well from the ends of a rope passing over a pulley, they will be in equilibrium.

When a body rests upon a table, there is an equilibrium between the weight of the body which urges it downwards, and the resistance of the table which prevents it from falling. If the weight becomes greater than the resistance, the table breaks and the body falls.

Centrifugal and Centripetal Forces.

27. The CENTRIFUGAL FORCE is the resistance which a body offers to a force which tends to deflect it from its

course.

In consequence of its inertia, a body always tends to move in a straight line, and if we see it move in a curved line it is because some force is acting to turn it from its path. This deflecting force is called the Centripetal Force, and

(26.) When are forces in equilibrium? Illustrate by examples. (27.) What is the Centrifugal Force? Centripetal Force?

because action and reaction are always equal, the centripetal and centrifugal forces are always opposed and equal to each other. If a ball is whirled about the hand, being retained by a string, it has a continual tendency to fly off, which tendency is resisted by the strength of the string; the tendency to fly off is due to the centrifugal force, and the force which resists this tendency is the centripetal force.

The curved path in which a body moves may be regarded as made up of short straight lines, and if at any instant the centripetal

force were destroyed, the body would continue to move along that line on which it was situated; that is, its new path would be tangent to its old one.

The existence of the centrifugal force may be shown experiment

ally by the apparatus represented in Fig. 13. It consists of a bar, AB, having its ends bent up so as to hold a wire which is stretched between them. On this wire two ivory balls are strung so as to slide along it, and the whole bar is made to turn about an axis at right angles to it by means of a crank and two bevelled wheels. When the bar is made to revolve about the axis, the balls, acted upon by the centrifugal force, are thrown against the ends of the bar with an energy which becomes greater as the motion of revolution becomes more rapid.

Some Effects of the Centrifugal Force.

28. When a train of cars turns round a curve in the road, the centrifugal force tends to throw the train off the track, a tendency which is resisted by raising the outer rail. and by making the wheels conical.

It is in consequence of the centrifugal force, that the mud adhering to the tire of a carriage-wheel is thrown off in all directions.

In the circus, where horses are made to travel rapidly around in a curved path, the centrifugal force tends to overturn them outwards, which tendency is partly overcome by making the outside of the track higher than the inside, and partly by both horse and rider inclining inwards, so as to make the resultant of their weight and the centrifugal force perpendicular to the path.

When a sponge filled with water and held by a string is whirled rapidly around, the centrifugal force throws off the water and leaves the sponge dry. This principle has been used for drying clothes in the laundry.

A very remarkable effect of the centrifugal force is the flattening of our earth at the poles. The earth turns on its axis every twenty-four hours, which rotation gives rise to a centrifugal force at every point of its surface. At the

Explain the experiment. (28) Give examples of the action of the centrifugal force. Cars on a curve. Mud from wheel. Circus. Sponge. Effect on the form of the earth.

equator the centrifugal force is greatest, because the velocity is there the greatest, and from the equator it grows feebler towards each pole, where it is zero. The centrifugal force at every point is perpendicular to the axis, and may be resolved into two components, one directed outwards from the centre, and the other perpendicular to this. The former component lessens the weight of bodies, and the latter acts to heap the particles up towards the equator. It has been found that the earth is a spheroid, flattened at the poles. The polar diameter is about twenty-six miles shorter than the equatorial diameter. Observations upon the heavenly bodies show that other planets are in like manner flattened at their poles.)

The manner in which the centrifugal force acts to flatten a sphere, is shown experimentally by an apparatus, represented in Fig. 14. This apparatus consists of a vertical rod to which a motion of rotation may be imparted, as shown in Fig. 13. At the lower part of this rod four strips of brass are firmly fastened and bent into circles, as shown by the dotted lines; their upper ends are fastened to a ring which is free to slide up and down the rod. When the axis is made to revolve rapidly, the centrifugal force causes the ring to slide down the rod, the hoops become more curved, as shown in the figure, and the whole assumes the appearance of a flattened sphere.

Machines.

Fig. 14.

29. A MACHINE is any contrivance that transmits the action of a force. A force which is used to move a machine is a motor.

Effect on the weight. Explain the experiment. (29.) What is a Machine? What is a Motor?

When we cut an apple with a knife, the hand is the motor and the knife is a machine.

A horse drawing a cart is a motor, and the cart which serves to utilize the force of the horse is a machine.

Water turning a water-wheel, wind turning a wind-mill, and steam driving a locomotive, are all motors.

Machines do not increase the energy of the motors, but by modifying their action they enable us to do work which we could not otherwise perform. For example, by the aid of a lever, about to be described, a man may raise a weight which he could not otherwise

overcome.

The Lever.

30. A LEVER is an inflexible bar free to turn about a fixed point, called the Fulcrum, and acted upon by two forces which tend to turn it in opposite directions. The force which acts as a motor, is called the Power, the other one is called the Resistance.

Levers are of three classes, according to the position of the fulcrum with respect to the power and resistance.

Lever of the first class.-In this class the fulcrum is between the power and the resistance. Such a lever is represented in Fig. 15. The hand is the power, the weight P is the resistance, and the fixed point C is the fulcrum.

Examples. What is the advantage of Machines? Example. (30.) What is a Lever? How many classes? Give examples of each class.