PART I.

Mechanics.

Definitions. In commencing the study of Mechanics it is necessary that the following terms, which are of constant occurrence, should be thoroughly understood. Matter. A general term for any kind of substance. Body.-A portion of matter.

Atom.1-A body of the smallest conceivable size, so small that we cannot imagine it to be divided into smaller parts.

Point. The position of an atom, without regard to its size or shape.

Rest and Motion.-A body constantly occupying the same position, is said to be at rest; a body successively occupying different positions, is said to be in motion. To illustrate this, let us place a stone on the ground. If left to itself it will constantly remain in the same place; that is, it will continue at rest. If, however, it be not allowed to remain by itself, but some power, such as a push, be brought to bear upon it, it will not continue in the same position, but will move. Motion, therefore, is change of position.

Force. The power employed, as in the preceding example, to move a body, is called force.3

Hence, whenever we see a body in motion, we may conclude that some force has been used to give it that motion.

1 Gr., atomos, not to be cut. 3 L., fortis, strong.

2 L., moveo, motus, to move,

If a force be applied to a body previously at rest, it will cause it to move in a straight line, there being no reason why it should incline to one side more than to another. Wherefore, if we see a body moving otherwise than in a straight line, we know that some other than the original force is brought to bear upon it, causing it to deflect from a straight line.

As a body comes to rest sooner when moving along a rough than when moving along a smooth surface, it is evident that its motion is impeded by the resistance it meets with. The less the resistance, the longer will the motion continue; and it may be inferred that if all resistance were removed, the motion would continue for

ever.

No terrestrial body, however, will continue to move thus perpetually, but will, after a certain interval of time, return to its previous state of rest, by reason of opposing forces.

Force, therefore, may be defined as a cause tending to impart motion to a body previously at rest, to change the direction of that motion, or to make it cease.

Divisions of Mechanics.-All considerations included under the head of Mechanics have relation either to motion or to force, or to the two combined; the subject, therefore, naturally divides itself into two parts, namely:

I. KINEMATICS, treating of motion; and II. DYNAMICS, treating of force.

SECTION I.

KINEMATICS.

CHAPTER I.

NATURE OF MOTION.

Definition. Kinematics is the purely geometrical consideration of motion, apart from the moving body or the force by which the motion has been produced.

In the investigation of motion, means are requisite for ascertaining and describing its character. To this end certain units of measurement, are adopted, showing the relation of motion-(1) to the space moved over, (2) to the mass of the moving body, (3) to the time during which the motion continues.

1. Units of Space are of three kinds, having reference to-(a) length, (b) surface, and (c) volume.

(a) Units of Length.-The English standard unit of length is the yard, which is defined to be "that distance between the centres of the two points in the gold studs of the straight brass bar in the House of Commons, at a temperature of 62° F." Any fractional part of this yard may also be taken as a unit, such as a foot, an inch, or a line. To measure length, we have, then, simply to find how many such units are contained in the space to be measured.

(b) Units of Surface. The standard unit of surface is a square whose side is equal to a unit of length. The number of times this unit of surface, or any of its subdivisions or multiples, as the square foot, square pole, etc., is contained in a given surface, will represent the extent of that surface.

1 L., unus, one. Something to call one.

(c) Units of Volume.-The standard unit of volume is a cube whose side is equal to a unit of surface. The number of times this unit of volume, or any of its subdivisions or multiples, as the cubic foot, load, etc., is contained in a given body, will represent the volume of the body.

2. Units of Mass.-The standard unit of mass is the grain, which is defined to be 1228 of a cubic inch of distilled water at 62° F., 7000 of these grains making a pound avoirdupoise. To determine the mass of any body, we must find how many units of mass it contains. This is done by weighing it.

3. Units of time.-The standard unit of time is the mean duration of a revolution of the earth upon its axis. This is divided into twenty-four parts, called hours, which are again divided into 60ths, called minutes, and these again into 60ths, called seconds. The second is usually employed in Mechanics as the unit of time.

By means of the above units of measurement, we are able to compare the value of one motion with that of another. Thus, if a railway train, A, has a motion of ten miles an hour, and another train, B, has a motion of twenty miles an hour, we know that the motion of B is to that of A as 2 is to 1; or in other words, that B moves twice as fast as A.

CHAPTER II.

MOTION OF A POINT.

Path.-When a point is in motion, the line described by its successive positions is called its path, which may be either straight, curved, or composed of straight and curved lines.

The direction of the motion of a moving point at each instant, is the straight line in which it moves, or the tangent to its position, if its path be a curve.

Velocity. The rate of motion of a point is called its velocity.

Velocity may be represented by lines. Thus, if a line of any length be taken to represent one foot, a velocity of three feet per second will be represented by a line three times as long as the assumed unit. Velocities are of several kinds.

Uniform1 Velocity.-When a body continues to move over equal units of length in equal units of time, its velocity is said to be uniform; and is measured by the number of units of length passed over in a single unit of time. Thus, if a body move at a uniform rate of sixty miles an hour, its velocity may be also expressed as one mile per minute, or eighty-eight feet per second.

Accelerated Velocity. When a body moves over a greater number of units of length in each succeeding unit of time, the motion is said to be accelerated. Again, if the body move over a lesser number of units of length in each succeeding unit of time, its velocity is also said to be accelerated; but it is called negative accelerated velocity, or retardation, to distinguish it from the former, which is known as positive accelerated velocity.

Accelerated velocity may be either uniform or varied. It is uniform when the increments in successive units of time are equal; and varied when they are unequal.

Varied accelerated velocity "is measured by the increment of velocity which would have been generated in a unit of time, had the acceleration remained throughout that unit the same as at its commencement. The average acceleration during any time is the whole velocity gained during that time divided by the time." -Thomson.

Accelerated velocity may be represented as fol

lows:

Let A be a point at which the body is at rest, and B

1 L., unus, one; forma, kind.

2 L., accelero, to hasten.