other unit of weight, taken at the equator. The pound is generally assumed as the unit of mass. The terms weight and mass may be regarded as synonymous, provided we understand that the weight is taken at the equator.

Density.

12. The DENSITY of a body is the quantity of matter contained in a unit of volume of the body, or it is the mass of a unit of volume.

At the same place the densities of two bodies are proportional to the weights of equal volumes. The mass of any body is therefore equal to its volume multiplied by its density, or denoting the volume by V, and the density by D, we have

13. The MOMENTUM of a moving body, or its QUANTITY of MOTION, is the product obtained by multiplying the mass moved, by the velocity with which it is moved; that is, we multiply the number of units in the mass moved by the number of units in the velocity with which it is moved and the product is the number of units in the momentum. This will be explained more in detail hereafter.

Properties of Bodies.

14. All bodies are endowed with certain attributes, or properties, the most important of which are, magnitude and form; impenetrability; mobility; inertia; divisibility, and porosity; compressibility, dilatibility and elasticity; attraction, repulsion, and polarity.

Magnitude and Form.

15. Magnitude is that property of a body by virtue of which it occupies a definite portion of space; every body

possesses the three attributes of extension, length, breadth, and height. The form of a body is its figure or shape.

Impenetrability.

16. Impenetrability is that property by virtue of which no two bodies can occupy the same space at the same time. The particles of one body may be thrust aside by those of another, as when a nail is driven into wood; but where one body is, no other body can be.

Mobility.

17. Mobility is that property by virtue of which a body may be made to occupy different positions at different instants of time. Since a body cannot occupy two positions at the same instant, a certain interval must elapse whilst the body is passing from one position to another. Hence motion requires time, the idea of time being very closely connected with that of motion.

Inertia.

18. Inertia is that property by virtue of which a body tends to continue in the state of rest or motion in which it may be placed, until acted upon by some force. A body at rest cannot set itself in motion, nor can a body in motion increase or diminish its rate, or change the direction of its motion. Hence, if a body is at rest, it will remain at rest, or if it is in motion, it will continue to move uniformly in a straight line, until acted upon by some force. This principle is called the law of inertia. It follows immediately from this law, that if a force act upon a body in motion, it will impart the same velocity, and in the same general direction as though the body were at rest. It also follows that if a body, free to move, be acted upon simultaneously by two or more forces in the same, or in different directions, it will move in the general direction of each force, as though the other did not exist.

When a force acts upon a body at rest to produce motion, or upon a body in motion to change that motion, a resistance is developed equal and directly opposed to the effective force

exerted. This resistance, due to inertia, is called the force of inertia. The effect of this resistance is called re-action, and the principle just explained may be expressed by saying that action and re-action are equal and directly opposed. This principle is called the law of action and re-action.

These two laws are deduced from observation and experiment, and upon them depends the mathematical theory of mechanics.

Divisibility and Porosity.

19. Divisibility is that property by virtue of which a body may be separated into parts. All bodies may be divided, and by successive divisions the fragments may be rendered very small. It is probable that all bodies are composed of ultimate atoms which are indivisible and indestructible; if so, they must be exceedingly minute. There are microscopic beings so small that millions of them do not equal in bulk a single grain of sand, and yet these animalcules possess organs, blood, and the like. How inconceivably minute, then, must be the atoms of which these various parts are composed.

Porosity is that property by virtue of which the particles of a body are more or less separated. The intermediate spaces are called pores. When the pores are small, the body is said to be dense; when they are large, it is said to be rare. Gold is a dense body, air or steam a rare one.

Compressibility, Dilatability, and Elasticity.

20. Compressibility, or contractility, is that property by virtue of which the particles of a body are susceptible of being brought nearer together, and dilatability is that property by virtue of which they may be separated to a greater distance. All bodies contract and expand when their temperatures are changed. Atmospheric air is an example of a body which readily contracts and expands.

Elasticity is that property by virtue of which a body tends to resume its original form after compression, or extension. Steel and India rubber are instances of elastic bodies. No bodies are perfectly elastic, nor are any perfectly inelastic. The force which a body exerts in endeavoring to resume its

form after distortion, is called the force of restitution. If we denote the force of distortion by d, the force of restitution by r, and their ratio by e, we shall have

Those

in which e is called the modulus of elasticity. bodies are most elastic which give the greatest value for e. Glass is highly elastic, clay is very inelastic.

Attraction, Repulsion, and Polarity.

21. Attraction is that property by virtue of which one particle has a tendency to pull others towards it. Repulsion is that property by virtue of which one particle tends to push others from it. The dissimilar poles of two magnets attract each other, whilst similar poles repel each other. It is supposed that forces of attraction and repulsion are continually exerted between the neighboring particles of bodies, and that the positions of these particles are continually changing, as these forces vary.

Polarity is that property by virtue of which the attractive and repellent forces between the particles exert an arranging power, so as to give definite forms to masses. The phenomena of crystalization already referred to, depend upon this property. It is to polarity that many of the most interesting phenomena of physics are to be attributed.

Equilibrium.

22. A system of forces is said to be in equilibrium when they mutually counteract each other's effects. If a system of forces in equilibrium be applied to a body, they will not change its state with respect to rest or motion; if the body be at rest it will remain so, or if it be in motion, it will continue to move uniformly, so far as these forces are concerned. The idea of an equilibrium of forces does not imply either rest or motion, but simply a continuance in the previous state, with respect to rest or motion. Hence two kinds of equilibrium are recognized; the equilibrium of rest, called

statical equilibrium, and the equilibrium of motion, called dynamical equilibrium. If we observe that a body remains at rest, we infer that all the forces acting upon it are in equilibrium; if we observe that a body moves uniformly, we in like manner infer that all the forces acting upon it are in equilibrium.

Definition of Mechanics.

23. MECHANICS is that science which treats of the laws of equilibrium and motion. That branch of it which treats of the laws of equilibrium is called statics; that branch which treats of the laws of motion is called dynamics. When the bodies considered are liquids, of which water is a type, these two branches are called hydrostatics and hydrodynamics. When the bodies considered are gases, of which air is a type, these branches are called ærostatics and arodynamics.

Measure of Forces.

24. We know nothing of the absolute nature of forces, and can only judge of them by their effects. We may, however, compare these effects, and in so doing, we virtually compare the forces themselves. Forces may act to produce pressure, or to produce motion. In the former case, they are called forces of pressure; in the latter case, moving forces. There are two corresponding methods of measuring forces, first, by the pressure they can exert, secondly, by the quantities of motion which they can communicate.

A force of pressure may be expressed in pounds; thus, a pressure of one pound is a force which, if directed vertically upwards, would just sustain a weight of one pound; a pressure of two pounds is a force which would sustain a weight of two pounds, and so on.

A moving force may be a single impulse, or it may be made up of a succession of impulses.

The unit of an impulsive force, is an impulse which can cause a unit of mass to move over a unit of space in a unit of time. A force which can cause two units of mass to move over a unit of space in a unit of time, or which can cause a