SECTION III. RESISTANCES TO MOTION.

113. Friction is the resistance which one body experiences in moving upon another when the two bodies are pressed together. This resistance arises from inequalities in the surfaces, the projections of the one sinking into the depressions of the other. To overcome the resistance thus produced, a force must be applied sufficient to break off, or bend down, the projecting points, or else to lift the moving body over the inequalities.

Friction is distinguished as sliding and rolling. The former arises when one body is drawn upon another; the latter, when one body is rolled upon another. Everything else being equal, the former is greater than the latter.

114. Measurement of Friction. The comparative amount of sliding friction for many different surfaces has been determined by the ap

Fig. 77.

paratus shown in Fig. 77.

Blocks of different materials and of different size and shape, sometimes loaded with weights, were made to move over surfaces of different kinds, by means of weights placed in the

pan, P. By these experiments the following facts have been ascertained:

1. Friction is nearly proportional to pressure.

2. Friction is not affected by extent of surface, except within extreme limits.

The same force is required to draw a brick across a board, whether it rests on its broad face or on its edge.

3. Friction is greater between soft bodies than hard ones.

4. Friction is greater between surfaces of the same materials than between those of different kinds.

The friction of iron upon iron is greater than that of iron upon copper or brass.

For this reason the axles of railway cars being made of steel, the boxes in which they revolve are made of brass or some other metal. For the same reason, the axles in the wheel-work of the best watches are made to revolve in holes bored in the harder precious Such watches are said to be "jewelled."

stones.

5. Friction is diminished by polishing or lubricating the surfaces.

Polishing removes projecting points that would catch against each other and increase friction. The application of lubricants like oils, tallow, black-lead, etc., diminishes friction by filling up minute cavities and smoothing the surfaces.

6. Friction is greatest at the beginning of motion.

When surfaces remain long in contact, especially under pressure, the projections of one sink deeper into the depressions of the other, and render it more difficult to separate them.

115. Advantages of Friction. Although friction occasions a loss of power in the working of machines, it has some advantages.

Common nails and screws would be useless were it not that friction holds them in place. A wedge could not be driven if friction did not hold it and prevent it from rebounding after a blow. A locomotive depends upon friction for its power to draw a heavy train of cars.

Sometimes when great loads are to be moved the friction of the driving wheels upon the rails is not sufficient to prevent slipping, and therefore boxes are provided from which sand may be sifted upon the rails when required, thus increasing the friction and enabling the engine to draw its load.

116. Stiffness of Cords. - When a cord is wound upon a wheel or axle, a certain amount of force is required to bend it. The resistance which the cord thus offers to bending is classed as a hurtful resistance. This resistance should be obviated, as far as possible, by selecting bands and cords which are as flexible as is consistent with due strength.

處

117. Atmospheric Resistance. The atmosphere exerts a powerful resistance to the motion of bodies moving through it. It has been found, both by theory and experiment, that this resistance is proportional to the greatest cross section of the body, made by a plane perpendicular to the direction of the motion, and also to the square of the body's velocity. To obviate this resistance as far as possible, the pieces which have a rapid motion should have as small a cross section as is consistent with due strength.

Summary.

The Inclined Plane.

Resolution of the Force of Gravity in a body resting on an
Inclined Plane.

Law of the Inclined Plane.

Illustration by Movable Inclined Plane.

Common Roads and Railroads.

The Wedge. Reasons why the Force exerted by the Wedge cannot be accurately estimated.

Practical Applications of the Wedge.

The Screw.

Combined Lever and Screw.

Law of the Screw.

The Endless Screw.

Resistances to Motion.

Friction. Sliding and Rolling Friction.

Measurement of Friction.

Six Facts relating to Friction.
Advantages of Friction.

Stiffness of Cords.

Atmospheric Resistance.

CHAPTER IV.

THE MECHANICS OF LIQUIDS.

Part I.- HYDROSTATICS.

SECTION I. GENERAL PRINCIPLES.

The

118. Hydrostatics and Hydrodynamics. Mechanics of Liquids is divided into two branches : HYDROSTATICS, which treats of the laws of equilibrium of liquids, and HYDRODYNAMICS, which treats of the laws of motion of liquids.

119. Properties of Liquids. The following properties are common to all liquids:

1. The molecules of liquids are extremely movable, yielding to the slightest force.

There is very little cohesion between the molecules of liquids, whence their readiness to slide among one another. It is to this principle that they owe their fluidity.

2. Liquids are only slightly compressible.

Liquids are so slightly compressible, that for a long time they were regarded as absolutely incompressible. In 1823, OERSTED demonstrated, by an apparatus which he contrived, that liquids are slightly compressible. He showed that for a pressure of one atmosphere, that is, of 15 pounds on each square inch of surface, water is compressed the 10th of its original volume. Slight as is the compressibility of water, it is nevertheless ten times as compressible as mercury.

3. Liquids are porous, elastic, and impenetrable, like other bodies.

That liquids are porous, has already been shown. That they are elastic, is shown by their recovering their volume after the compressing force is removed. It is also shown by the fact that they transmit sound. Their impenetrability is shown by plunging a solid body into a vessel filled with liquid. If there is no imbibition, a volume of water will flow over the vessel just equal to that of the solid introduced. Upon these three properties of liquids depends their property of transmitting pressures in all directions.

I20.

Pascal.

Fig. 78.

Transmission of Pressures. Principle of Let a bottle be filled with water and corked, as represented in Fig. 78. If the cork be pressed inwards, the pressure will be transmitted to the molecules in contact with it; these molecules will in their turn press upon the neighboring ones, and so on until the pressure is finally transmitted to every point of the interior surface of the bottle.

It is shown by experiment that the pressure thus transmitted is equal to that applied to the cork; that is, the pressure upon each square inch of the interior surface of a vessel is equal to that upon a square inch of the cork. The pressure is everywhere perpendicular to the surface, as shown by the arrow-heads.

This principle is called the Principle of Pascal, because it was first demonstrated by BLAISE PASCAL in the seventeenth century. Upon it depends the whole theory of Hydrostatics.

Fig. 79.

The same principle may be shown by another experiment. A cylinder (Fig. 79) provided with a piston is fitted into a hollow sphere. Perpendicular to the sides of the globe are small tubular open

ings. Fill the cylinder and globe with water, and press the piston against the water, and it will come from all the orifices equally, and not merely from that which is opposite the piston.