light of the sun; and this would form what is called an eclipse of the moon. But it is evident that in no other situation than this could the earth's shadow affect the moon, as in no other situation is it directed immediately towards that body.

Therefore eclipses of the sun can only happen at new moon, and eclipses of the moon only at full moon; but if the moon's orbit were in the same piane with the ecliptic, the sun would be eclipsed at every new moon, and the moon at every full. The angle which they form with each other prevents this, and makes the moon, in the majority of cases, pass either higher or lower in the heavens than the sun at new moon, or the earth's shadow at full; but when the revolution of the moon's orbit brings the node or point, where that orbit crosses the ecliptic is very near the place of the new moon or full moon, an eclipse takes place to a greater or less extent, according as the new or full moon is nearer to, or further from the node.

SECTION VII.

COMETS.

These bodies, of one of which a kind of representation is given in the first copper-plate engraving, derive their name from the tail or train of pale light which follows them in a direction opposite to the sun. The comets have a sort of nucleus more radiant than the tail, but they have no defined disc like the planets, and they move in every direction, and though they appear but seldom, and continue not long, they appear in all parts of the heavens. Reasoning from analogy, and also from the return of certain comets having been predicted, and the prediction verified, we are led to conclude, that those bodies revolve in ellipses with the sun in the one focus, as well as the planets; but from the length of time that even the returning ones are absent, the eccentricities of their orbits must be very great, and there are many instances in which their stay is so short that we are unable so to observe them as to determine their curvature, even during the visible part of their revolution; and hence we are unable to anticipate their re-appearance with anything like accuracy. Thus we are unable by reference to them to determine any thing very useful respecting time or situation as connected with the earth, and thus the study of them for practical purposes is more curious than useful, although their singular form, the great rapidity of their motions, and the immense distance to which they must recede into the viewless abyss of space, cannot fail to impress us with the grandeur of the system, and the Almighty power of its Maker and Pre

server.

Ir is not a little singular, that the whole of the varied motions of those mighty masses that compose the solar system, should, in all their variations, be explainable by the simple fact of an apple falling to the ground; and, it is reported, that it was this very fact which led Newton to the last step of that beautiful chain of reasoning by which the identity of the celestial motions with one another, and with that of a heavy body falling to the earth, is completely established. The philosopher had left Cambridge in order to avoid the contagion of the plague, and retired into the country, there to pursue his investigations, and, in his orchard, the fall of the apple. became his instructor in the most abstruse problem of the sublimest of sciences. This should teach us to beware how we slight every-day subjects and events, for the sake of those which are rare and curious; because, He, whose nod is nature's law, can both accomplish his purposes and reveal the knowledge of them by, what seem to us, the most humble and simple of

means.

D

Were it not that we see them every day, and refrain from the examination of them because they are so common, we might be apt to wonder why the smoke of the fire ascends up the chimney, while the cinders and ashes fall under the grate; why a ball, a book, or any other substance rests on the side of our hand which is farthest from the earth, and produces there the sensation which we call weight or pressure, but does not rest, or weigh, or press, upon the side which is nearest to the earth; or why the apple does not fall upwards to the sky, or sideways against the wall, instead of downwards to the ground; seeing that there appears to us to be nothing more to produce action or motion in the one direction than in any of the others.

Though we could not arrive either at this fact itself or at any explanation of the cause to which it is owing, by any process of reasoning, yet experience teaches us the universality of its occurrence; and in all the natural substances not endowed with life, with which we are acquainted, all the ascents and descents-the risings and the fallings, that we observe, are just so many instances of the same fact. We call it weight, or heaviness, and we give the same name to that quality of the body which, as we suppose, produces it. Nay, even in common language and common business, we take it for granted, that equal quantities of matter have equal weights, and upon this, we found many of our exchanges of commodities. Lead sinks to the bottom of water, because it is weightier than its own bulk of water, and cork swims upon the surface, because it is lighter. Cork, again, falls down through air, because it is heavier than its bulk of air, while smoke, so long as it retains its heat, rises up through air, because it is lighter. Indeed, all the substances with which we are acquainted obey this law, and would range themselves, the weightiest lowest, and so on the others, were they not restrained by some other force which overcomes this weight. Thus, this pen with which I am writing has but little weight, but still if I open my fingers away from it, it will fall on the table; if that were away, on the floor; if that were away, on the ground; or, if a pit were dug there, however deep, the pen would, if it met with no obstacle, fall to the bottom. Generalizing our observations, we come to this conclusion as a general law of

nature:

That all bodies near the earth's surface fall toward the earth or press upon that on which they are laid, with forces that are proportioned to the quantities of matter in them; and that this falling and pressure are constant, always acting, and always producing this effect, unless prevented by some other body or power.

This is called the law of terrestrial gravitation.

A body can be kept from falling only by some supporter, such as being laid on a table, or hung by a string-and this will remain while the supporter lasts; or in the air by the action of some force-and this will remain only till the action produced by that force has been overcome by gravitation. There are only three such forces with which we are acquainted: Animal

force, as when I throw a stone with my hand; the force of elasticity, as when I shoot an arrow from a cross-bow; and chemical force, as when I shoot a bullet from a musket by the explosion of gunpowder. The only difference of these forces, as regards their counteraction of gravity, is the difference of their intensity.

If a body be thrown by any of these forces in a direction slanting upwards, it continues to rise for a greater or a less distance, according to the intensity of the force; but its path becomes gradually less and less elevated, till, after a time, it begins to slant the other way, and at last falls to the ground. The reason of this is, that the force of gravity continues always the same, while the force with which the body is projected, having ceased to act at the moment of projection, gradually diminishes. So long as the force of projection exceeds the force of gravity, the body continues to ascend when the two forces are exactly equal, the body is at the top of its path ; and when the force of gravity becomes the greater, the body descends. There is one inference here, which, though it be an anticipation, the reader will find some pleasure in drawing: suppose, when the body is at the highest point of its path, that is, when the force of projection which drives it forward, is exactly equal to the force of gravitation which draws it toward the earth, one could get after it and continue to urge it forward, with precisely the same force, what would be the result? It could not fall lower ; it could not rise higher: what then?

We must not, in this case, be misled by the effect that is produced by the resistance of the air. We feel that resistance in winds, and we see it driving light bodies before it; but when any body is driven against the air with any degree of rapidity, the resistance is obviously just the same as if the air were driven, or blown as wind, against it, with the same degree of rapidity. Hence the same force will throw a leaden bullet higher and farther than a paper pellet, although the quantity of matter, and consequent gravitation of the pellet be not the twentieth part of those of the bullet.

If a body be projected directly upwards, it ascends with a velocity constantly decreasing, till the force of projection has diminished to the same ás that of gravity, and then it descends with a velocity constantly increasing until it strike the ground with a force equal to that by which it was projected. From experiments of this kind, as well as from mathematical calculations, we are enabled to deduce the particular law of terrestrial gravitation, namely:

That bodies gravitate toward the earth directly as their quantities of matter, and inversely as the squares of their distances; that is to say, at the same distance from the earth's centre a body containing twice the quantity of matter will be exactly twice as heavy; and that the same body will, at double the distance, be one-fourth of the weight, at three times the distance one-ninth of the weight, and so on,-the distance in this case

being estimated not from the surface of the earth but from its centre: so that any substance which, at the surface of the earth, acted upon a power not affected by gravitation, to the extent of four pounds, would, at the height of about four thousand miles in the air, act upon the same to the extent of only one pound.

At the earth's surface, a body falls through 16.083 feet, or in round numbers 16 feet, in the first second of time. Thus it will fall through 64 in the next, through 144 in the third, and so on. Comparing the distance of the moon, the quantity of matter in that luminary, and the velocity or rate at which it moves in its orbit, with this, we find that the forces by which the moon is sustained in its orbit, deducting the resistance of the atmosphere or air, are precisely the same with those which would cause a projectile thrown from the earth to revolve constantly round that body. This was the method which Newton took to verify the fact of the law of gravitation being that which sustains the moon, and, by analogy, the earth and all the planets in their orbits. The distance of the moon from the earth's centre is about sixty times the half diameter of the earth; and, therefore, gravitation toward the earth should be about 60 x 60, or 3600 times less than it is at the earth's surface. Now, as the circumferences of circles are as their diameters, and those of ellipses as their mean diameters, the circumference of the moon's orbit will be about sixty times that of the earth, or about 7,926,336,000 feet. But the revolution in this orbit is performed in 27d. 7h. 43m., or in 39,343 minutes; and dividing the number of feet by this, we find that the mean motion in a minute is about 201,467 feet, and the versed sine of this arch (which very nearly coincides with the moon's deflection) from a straight line, is about 16.087 feet, which differs very little from 16.083, the quantity that would be produced by gravitation toward the earth. This coincidence is so near that we are warranted in concluding,

That the force with which the moon is deflected, or drawn from a straight line, and made to revolve round the earth, is the same as that by which all bodies near the earth tend to fall to its surface; or, in other words, that gravitation toward the earth is only a particular modification of that force by which the planets are deflected from the rectilineal path and made to revolve, the primaries round the sun, and the secondaries round their primaries.

Before, however, we proceed to a more particular application of this doctrine, it may be proper to enumerate those simple laws of motion which are suggested by common sense, and have been proved by reasoning and experience.

1. Every body, which is not endowed with life and the power of locomotion (qualities which cannot be attributed to the earth, the moon, and the other bodies that compose the solar system) must remain at rest for