of them, in the brief manner here required, under the branches of 1. Mechanics; 2. Astronomy; 3. Optics; 4. Ceraunics, including Calorics, Electricity, Magnetism, and Galvanism; and 5. Chemistry.

CHAPTER I.

MECHANICS.

MECHANICS, is the science which treats of forces acting upon matter, and which investigates the laws of equilibrium and motion, both of solids, and of fluids. The name is derived from the Greek unxan, a machine; as the construction of machines probably first led to the study of this science. The term matter, has been already defined, and the principal properties of matter explained, in the introduction to this department. A force, is an agent, tending either to produce or to resist motion. When the forces acting upon a body counteract each other, or do not produce any motion, the body is said to be in equilibrium. When a body moves through equal spaces in equal times, its motion is said to be uniform; but in all other cases it is variable. In the former case, the forces cease to act, or else counteract each other: but all cases of variable motion are owing to the action of continuous or incessant forces.

The best sub-division of Mechanics, is probably into the four heads of Statics, Dynamics, Hydrics, and Pneumatics. Statics, treats of the conditions of equilibrium, and of uniform motion, particularly in regard to solids; though many of its principles are also applicable to fluids. Dynamics, treats of the laws of variable motion; with the same restriction concerning its application. Hydrics, including both Hydrostatics and Hydrodynamics, treats of those laws of equilibrium and motion which are peculiar to liquids; and Pneumatics, treats of the corresponding laws, in so far as they are peculiar to aeriform fluids, or gases. The term Hydraulics, more properly applies to those constructions for the conveyance of water, the study of which belongs to Civil Engineering; and Acoustics, or the doctrine of sound, may properly be included under the head of Pneumatics. The science of Mechanics, finds its applications not only in the construction of Machinery, but also in the succeeding branches of the present department; to some of which, the study of it is an indispensable preliminary.

According to Vitruvius, the ancients were from time immemorial acquainted with several of the mechanical powers, so called; as the inclined plane, capstan, and pulley; to which, no doubt, should be added the wedge, and the lever, as the simplest of them all. The screw was also known to, if not invented by, Archimedes; to whom the theory of the mechanical powers is justly attributed. The most ancient writings extant, on this science, are those of Aristotle; who understood the principle of momenta, but not that of the lever. This latter principle was first discovered by Archimedes; who deduced from it the principle of the centre of gravity, as explained in his

work entitled Isoporrika, concerning equiponderants. He also discovered the important law of the equilibrium of fluids; and applied it to the finding of specific gravities, in the celebrated problem of Hiero's crown. The invention of pumps for raising water, is due to Ctesibius, and Hero, of Alexandria, 150 to 120 B. C.: and the first correct ideas on the motion of water in canals, belong to Frontinus of Rome, who flourished A. D. 100. The initial theory of Acoustics, or at least of musical sounds, belongs to Pythagoras; and was suggested, it is said, by the concordant notes of several hammers, whose weights he found to have a certain ratio.

The discovery of the parallelogram of forces, was made by Stevens, or Stevinus of Holland, about A. D. 1600; to which Varignon afterwards added the ratio of the sines of the angles. Galileo discovered the laws of falling bodies, and invented the pendulum; thus founding the branch of Dynamics. Torricelli's discovery of the pressure of the air, and his invention of the barometer, were in like manner the basis of Pneumatics, as already mentioned. Pascal first noticed the principle of the transmission of pressure, afterwards applied by Bramah to the hydrostatic press; and Mariotte discovered the law of pressure in gases when confined. Huyghens invented the cycloidal pendulum, and explained its peculiar properties; and contemporaneously with Wallis and Wren, he demonstrated the laws of collision of bodies. Newton, in his Principia, or Principles of Natural Philosophy, investigated the resistance of the air, and first revealed the great law of Universal gravitation. Euler, by a happy analysis, generalized the theorems of Mechanics, and reduced the whole to a system of analytical formulas. James Bernouilli studied the centre of percussion; D'Alembert discovered the principle of efficient and residual forces; Coulomb investigated the laws of friction; and Prony, those of running water: but many other discoveries, in this branch of science, it is beyond our limits to notice.

We proceed to explain some of the leading principles of mechanics, under the four heads of Statics, Dynamics, Hydrics, and Pneumatics.

§ 1. The science of Statics, relates to the conditions of equilibrium and of uniform motion, applied particularly to solid bodies. A force is measured, by the velocity which it communicates to a given mass and the momentum, or quantity of motion, is equal to the product of the mass into the velocity. The mass, is represented by the weight; and is equal to the product of the bulk by the density; which latter is the weight of the unit of mass. The velocity of a body, is the space over which it moves in a unit of time; as so many feet per second. The resultant, of two or more forces, is a single force, which might take the place of them all, and produce the same effect. The forces which together are equivalent to the resultant, are called components. A force equal and opposite to the resultant, may be called a quiescent force; as it produces equilibrium.

If two forces act in the same straight line, their resultant is equal to their sum, or difference, according as they act in the same, or in opposite directions. If two component forces are oblique to each other, but lie in the same plane, they will meet, and may be repre

sented by the two contiguous sides of a parallelogram; having the directions of the forces for those of the sides, and the momentum of the forces proportional to the lengths of the sides; in which case the diagonal will represent the resultant, both in momentum and direction. The moment, or leverage, of a force, is the product of its momentum by the perpendicular distance from it to a fixed point called the origin of moments: and it measures the tendency of the force to turn the body around the origin, considered as a fixed axis. In any system of forces, the moment of the resultant is equal to the sum of the moments of all the components. This important fact is called the principle of moments. The centre of gravity, of any body, or system, is a point through which will pass the resultant of all the component forces of gravity, acting on the different particles, or parts of the system. It may be found by the principle of moments; and if this point be supported, the whole body is supported thereby.

The rope machine, or funicle, consisting of forces acting on three or more cords, or ropes, connected together at one point, is sometimes regarded as a mechanical power. There are, however, usually reckoned six mechanical powers, or simple machines for rendering forces more available; viz. the lever, wheel and axle, pulley, inclined plane, screw, and wedge. The lever, is essentially an inflexible rod or bar, supported by a fulcrum, either a prop or a pivot, and acted upon by two or more forces tending to turn it, or to resist its turning. In the case of the balance, or steelyard, the forces, when in equilibrium, are inversely as their distances from the fulcrum. In the wheel and axle, capstan, or windlass, the forces are inversely as the radii on which they act. In the simple fixed pulley, the power is equal to the resistance, but acts in a different direction; whereas, in the simple moveable pulley, the weight supported by the pivot, is double the force at either end of the rope.

In the inclined plane, the force parallel to the slope, is to the weight of the body which it sustains, as the height to the slope. In the screw, acted upon by a lever, the power is to the resistance, as the distance between the spiral threads, is to the circumference described by the power. In the common wedge, the forces are as the length of the sides against which they act. Such are the ratios required to produce equilibrium; but, having regard to friction, the forces must be considerably augmented when they are designed to produce motion. The principle of virtual velocities, is, that whatever is gained in the pressure exerted, or mass moved, is compensated for by the greater space which the power must move over: so that what is gained in weight is lost in velocity. Friction, always acts as a retarding force, proportional to the pressure which produces it.

§ 2. Dynamics, treats of variable motion, produced by continuous forces, applied particularly to solid bodies. An impulsive force, is one which acts momentarily; or is imparted momentarily, from one body to another. The body receiving it, moves consequently in a right line, and with a uniform motion, unless affected by the resistance of the air, or by gravity, or other forces; and when it strikes another

X. DEPARTMENT:

ACROPHYSICS.

In the department of Acrophysics, we include those branches of science which relate to the dynamical laws of matter, or the agencies by which the inanimate material world is regulated. The name is derived from the Greek, axpos, high, and puois, nature; properly signifying the higher study of nature; that is, as regards material objects. The term Physics, has been variously applied; sometimes limited to the mathematical, and at others extended to the chemical laws of matter; sometimes including both Natural Philosophy and Natural History, but more frequently confined to the former. Hence the desirableness of a generic term, which, being strictly defined, may designate exclusively the class of sciences constituting the present department. The term Natural Philosophy, might suffice for this purpose, were it not liable to ambiguity: but it sometimes excludes Astronomy; and is generally considered as exclusive of Chemistry; although we have high authority for regarding this latter branch as part of the same group of sciences.

In the department of Acrophysics, we therefore place not only Mechanics, Optics, Electricity, and Calorics, which are usually comprehended under Natural Philosophy; but also the branches of Astronomy and Chemistry; as chiefly relating to the general laws, though partly to the special productions of nature. Most of these sciences depend more or less on the pure mathematics for their elucidation; and hence were formerly, and are still occasionally designated as Mixed Mathematics. But the data, or facts, to which the calculations are applied, we obtain chiefly from observation and experiment: hence these branches have also been comprehended under the name of Experimental Philosophy; though this term is most frequently applied to the studies of Optics, Electrics, and Calorics. The uses to which this department of science may be applied, are numerous and important; not only in dispelling superstition, and elevating the mind, by explaining the wonderful phenomena and operations of nature; but in aiding the physical arts, by a knowledge of the facts which they require, for their successful practice, and farther improvement.

By the general term, matter, is meant any substance which is capable of affecting our senses. Matter exists in three states; solid, liquid, and gaseous. In the first, the particles cohere together, so as not to be freely separated; in the second, they cohere slightly, but separate freely; and in the third, or aeriform state, they not only separate freely, but tend to recede from each other, as far as the space which they occupy, or pressure which they experience, will allow. Liquids and gases are both termed fluids; the former in

increasing solely with the depth, and without regard to the shape. When a close vessel is filled with a liquid, a pressure applied to any one part, is distributed and felt on every part alike.

When a body floats on a liquid, it displaces a bulk of liquid of equal weight with itself; and is thus supported by the upward pressure of the liquid tending to regain its level. A floating body can be in equilibrium, only when the centre of gravity is in the same vertical line with that of the liquid displaced. If the body is totally immersed, it is still pressed upwards; and if thus suspended by a thread, it will weigh less in the liquid than in the air, by the weight of an equal bulk of the liquid; which weight may thus be found. The specific gravity of any body, denotes the number of times that it is heavier than water, taking equal bulks of each. Thus as platinum is 21 times as heavy as water, the number 21.000 expresses its specific gravity; and cork is so much lighter than water that its specific gravity is expressed by the decimal 0.240. In the case of gases, air, instead of water, is taken as the standard of comparison.

Water, and all other liquids, have some viscidity, or cohesiveness; as shown by their collecting in drops, before, or while falling. A similar cohesion between them and the containing tubes or vessels, causes the phenomenon of capillary attraction; shown also in sponges, and other porous bodies; by which the water along the edges is raised above its general level. When water is confined in a bent tube, or an enclosure of any shape whatever, it tends to rise to the same level, or horizontal plane, in every part of its exposed surface. If there be any aperture or orifice by which it can flow out, its velocity will depend somewhat upon the shape of the aperture, but principally on its depth below the surface of the liquid: it being nearly the same velocity which a heavy body would acquire in falling freely through the same depth. Allowance must be made here for friction, and the resistance of the air.

§ 4. Under the division of Pneumatics, are included all the peculiar mechanical laws of elastic or compressible fluids, whether gases or vapours. Gases, retain their aeriform state at all ordinary temperatures and pressures; but vapors, are substances ordinarily liquid, which have taken the gaseous form, owing to heat or diminished pressure. The air, or atmosphere, is a permanently gaseous fluid, elastic and compressible, surrounding the earth on every side, and extending at least to a height of 45 miles above its surface. The lower parts of it are compressed by the weight of the upper parts, so that for each three miles that we ascend, its density is reduced by about one-half; or, the height increasing in arithmetical, the density diminishes in geometrical progression. Its total weight is about 15 pounds for every square inch of the earth's surface, at or near the level of the sea. This pressure would counterpoise a column of water 34 feet high, as shown in the sucking pump; or a column of mercury 30 inches high, as shown in the barometer.

In the sucking pump, as the piston rises and removes the air from within, the pressure of the air on the external water forces it into, and up the pump, till it is in equilibrium. Then, when the piston descends, the fixed valve, below, closes, and prevents the descent of