kind is the force of gravity, which by constantly acting upon descending bodies, continually accelerates their velocities.

An impulse is that force which acts instantaneously upon a body, according to our perception, and then leaves the body, without repeating the act. Such is the stroke of a hammer; or of one body impinging upon another.

For the sake of perspecuity, the science of dynamics arranges the different movements of bodies under the following heads :

Uniform, rectilinear motion.

Collision, both direct and oblique.

Motions arising from the actions of central forces.

Motions arising from the joint actions of a central, and an impulsive force; that is, of a pressure and an impulse.

Projectiles.

Descent of bodies along inclined planes.
Vibrations of pendulums.

Curve of swiftest descent.

Rotation of bodies about fixed axes.

Centres of oscillation, of percussion, of gyration.

Movements of machines.

There are three rules applicable to all these kinds of motion, which are commonly denominated Newton's laws of motion.

First. Every body will remain in a state of rest, or of uniform motion in a straight line, unless it be compelled to change that state, by forces impressed.

Second. The change of motion is always

proportionate to the moving force impressed, and is always made in the direction of the right line in which that force is impressed.

Third. Action and reaction are always equal and contrary to each other. Or, the mutual actions of two bodies upon each other, are always equal, and directed contrary ways.

The following theorem is one of the most important in dynamics, and of the most extensive use in mechanics, the practical application of the former.

If a body be acted upon by two moving forces at the same time, so that each of those forces would, by itself, cause it to describe the side of a parallelogram, uniformly in a given time; the body, in consequence of their joint actions, will describe the diagonal of that parallelogram, uniformly in the same time.

The line of swiftest descent is a curve called the cycloid, in which a body will descend from a superior to an inferior place, not in the same perpendicular, in less time, than along a straight line.

When a body is suspended by a flexible string, or by a pin which, passing through a hole in it, is fixed to a steady support; or whenever a body hangs down from any point, so as to be capable of swinging about that point, it is called a pendulum, or pendulus body; and as pendulums are of most extensive use in mechanics, their properties have been investigated with great attention, both theoretically and experimentally.

That point from which the length of the pendulum to the point of suspension must be

reckoned, is called the centre of oscillation, or of percussion.

The centre of gyration is that point in a body, or system of bodies, in which, if all their matter were condensed, the same angular velocity would be generated in a given time, that would be generated in the whole body, or system, by the same force similarly applied.

The centre of spontaneous gyration is a point about which a body begins to revolve at the instant when it is struck by a force acting out of its centre of gravity.

QUESTIONS

What

What is a solid? How are solids generally divided? What are the regular solids? What are the irregular solids ? What is the science, termed statics, and what objects does it comprehend or regard? is volume? What is density? What is mass? What accelerated and retarded motion? What is the science is named dynamics? What is equable motion? What is velocity? What is a force? What is momentum ? What is a pressure? What is an impulse? How does the science of dynamics arrange the various movements of bodies? What are Newton's three laws of motion? What is the theorem concerning a body acted upon by two moving forces at the same time, in certain different directions? What is the line of swiftest descent? What is a pendulum? What is the centre of oscillation or percussion? What is the centre of gyration? What is the centre of spontaneous gyration?

CHAP. XXXV.

MECHANICS.

By the science of dynamics two important ends are answered. The human being is enabled to comprehend and to explain some of the grandest phenomena of nature; and he is furnished with machines, which enable him to perform operations, and to produce effects, far beyond his unaided corporeal powers..

Sir Isaac Newton first conceived the sublime idea of a general connection between the most distant bodies of the universe. He imagined that the celestial bodies were actuated and connected by a general and mutual gravitation, or tendency towards one another, and towards a common centre. Desirous of proving the conception of his vast and vigorous mind, he began by endeavouring to investigate the laws of such forces, or gravitating powers; and proceeding from truth to truth, he at last formed an ample demonstrative theory. His next step was to examine how far astronomical observations were conformable to that theory; and he was gratified to find a coincidence so exact, as to confirm the justness of his supposition. Mathematical improvements, more accurate observations, and farther discoveries that have been made since his time, have brought the science so near to perfection, that it is now possible to calculate and to foretel the nicest astronomical phenomena; whence have been derived incalculable ad

vantages, especially in navigation. But the application of the science of dynamics to mechanics, is, perhaps, of yet greater and more extensive utility: for this gives man a command over some of the most powerful agents in the natural world; wind, water, steam, heat, and many others.

The term mechanics is given to that branch of practical mathematics which considers motion, and moving powers, their nature, laws, and effects. This science is divided, by Newton, into practical and rational mechanics; the former of which relates to the mechanical and the latter to the theory of motion.

powers,

SIMPLE MACHINES, OR MECHANICAL POWERS.

The simple machines, or mechanical powers, are usually accounted to be the six following: the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw.

A lever is an inflexible bar, or rod, moving freely round a point, called its fulcrum, or centre of motion. Levers have generally been considered as being of three kinds. The first kind of lever has the fulcrum between the power which acts, and the weight which is to be raised. To this kind of lever belong the steelyard, scissors, pincers, and other useful implements. The second kind of lever has the weight between the power and the fulcrum. To this kind of lever belong cutting knives fastened to handles at each end, and the oars of a boat, where the water is regarded as the fulcrum. In the third kind of