pipe and the pressure 5 lbs. to the sq. in., what will be the sure in the adjoining part of the wider pipe?

pres

Ans. 5. 14 lbs. per sq. in.

The pressure given is gauge pressure, or the excess above that of the atmosphere. The total or absolute pressure is 5+ 14.7 19.7 lbs. per sq. in.

6. The nozzle of a fire hose has an opening 2 in. in diameter, while the pipe just back of it is 3 in. in diameter. Find the pressure just back of the nozzle when it can throw a jet 60 ft. vertically upward. Ans. 20.9 lbs. per sq. in.

PROPERTIES OF MATTER

AND ITS

INTERNAL FORCES

STRUCTURE.

229. Density.-On comparing a block of wood or aluminum with an equal weight of lead or gold, it is clear that substances differ greatly in the quantity of matter concentrated in a given volume. The mass of any substance contained in unit volume is known as its density.

Densities of some Substances in Grams per Cubic Centimeter.

230. Molecular Forces.-When a lead bullet is divided by a clean cut, if the two halves are pressed together they will cling with considerable force. This is an imperfect exhibition because of poor contact of the force which originally held the two parts together. This force is known as cohesion, or when the attraction is between different substances it is known as adhesion. drop of water is held together by cohesion, but it clings to a glass rod by adhesion.

A

231. Molecular Theory. All matter is conceived as made up of separate molecules which are the smallest portions of the substance that can exist in a free state, as in gas or vapor. It is believed that the molecules of any particular substance are all alike, and, in substances not at the absolute zero of temperature, are in more or less active motion or vibration, the energy of vibration.

depending on the temperature. In solids the vibrating molecules are held by their mutual attractions in such a way that they cannot move far away from their mean relative positions. In liquids the phenomena of diffusion show that molecules move about in the mass, and are not held in fixed positions relative to each other, though the force of cohesion may be very great. In gases or vapors there is the greatest freedom of motion of the molecules, and their average distance apart is much greater than in liquids or solids, while there is scarcely any cohesion.

It is supposed that any two molecules of matter attract each other, according to the Newtonian law of gravitation, with a force varying inversely as the square of the distance between them for all considerable distances, but when very near each other the force of attraction varies with the distance according to some unknown law, giving rise to the phenomena of cohesion and adhesion, until the molecules come into what is called contact, when a force of repulsion opposes nearer approach.

The experiments of Quincke indicate that molecules must be less than 5X10-6 cms. apart in order that the cohesive force may be perceptible.

The idea that matter is molecular in its structure is supported by a great variety of evidences found especially in the phenomena of heat, gases, and radiation, as well as by chemical evidence.

232. Molecular Equilibrium.-The molecules of a substance may be regarded as in a state of equilibrium under three forces: external pressure, cohesive force, and an internal pressure due to the rebounding of adjoining molecules against each other as they vibrate to and fro. This latter force may be considered to balance the other two.

We may form a conception of these forces by the following model. Imagine a row of small rubber balls drawn together by springs stretched between them. Let two outer springs also press them together, and let the balls be thought of as rapidly vibrating to and fro, rebounding

against each other, and so keeping a greater distance apart than if they were at rest.

The force of the outer springs represents the external pressure and that of the springs joining the balls together the cohesive force, and these are balanced by the repulsion due to the impacts of the balls against each other.

In solids and liquids the pressure due to cohesion is that which chiefly balances the internal repulsion, the external pressure being usually quite insignificant in comparison.

But in gases the case is different. In consequence of the great average distance between the molecules the cohesion is so insignificant that the external pressure alone may be said to balance the internal pressure due to the motions of the molecules. This theory of gaseous pressure is more fully discussed in $271 et seq.

233. Structure. When the properties of any one portion of a mass are exactly like those of any other portion, the mass is said to be homogeneous. Whether a substance is called homogeneous or not depends on the point of view. One part of a brick wall is just like another part, and so it may be said to be homogeneous; but if we compare minute parts we find in some spots brick and others mortar and so there is a limit to its homogeneity. So water is regarded as homogeneous unless we are dealing with portions so small that the molecular structure is significant.

If the various physical properties of a substance are the same in all directions throughout its mass, it is said to be isotropic. Water, glass, and mercury are isotropic. Most crystalline substances are not isotropic, and may be called anisotropic.

234. Crystals.-In solids which pass slowly into the solid state, either directly from vapor or as the result of the slow cooling of a fused mass or of separation from a solution, there are often formed masses called crystals which have regular and distinctive forms and are bounded by plane faces.

The crystallization begins at certain isolated points and the minute crystals gradually grow in size, until they may meet and form a solid agglomeration.

The study of the fundamental crystal forms has led mineralogists to divide them into six classes or systems.

Some idea of the cause of the formation of crystals may be obtained by considering the forms which may be built up of shot when placed together so that each shall touch as many others as possible. Suppose such a pyramid as that represented in figure 129, where one layer is incomplete; if we think of it as a growing crystal in which the balls represent the molecules and suppose it immersed in a medium in which there are free molecules surrounding it, there will clearly be a tendency for these to fill out the incomplete surface, for a molecule. will touch more neighbors when placed along the incomplete edge than anywhere else, and so may be powerfully attracted into that position. bounded by plane surfaces would result.

FIG. 129.

conceived to be more In consequence a figure

The piling of balls would give the crystal forms characteristic of the first or regular system, but to explain the variety of crystal groups it is necessary to suppose that the molecules themselves have properties different in one direction from what they have in another, and that when built up into crystal forms they are all similarly oriented or directed.

ELASTICITY AND VISCOSITY.

235. Stress and Strain.-When a portion of matter is acted on by forces tending to change its size or shape it is said to be under stress, and the accompanying distortion or change in volume is called the strain.

A stress tending to stretch any portion of matter is called a tension, while a stress tending to shorten it is called a pressure. Stress is measured by force per unit surface, as in pounds per square inch, or in grams or dynes per square centimeter.

236. Strain Ellipsoid.-When a body is strained, a small spherical portion of it is in general distorted into an ellipsoid, and the axes of the ellipsoid are the three principal directions of strain at that point.

When the strain is the same everywhere throughout a body,