Letters on Astronomy Part 7

Recollect that the path in which the earth moves round the sun is called the ecliptic. We are not to conceive of this, or of any other celestial circle, as having any real, palpable existence, any more than the path of a bird through the sky. You will perhaps think it quite superfluous for me to remind you of this; but, from the habit of seeing the orbits of the heavenly bodies represented in diagrams and orreries, by palpable lines and circles, we are apt inadvertently to acquire the notion, that the orbits of the planets, and other representations of the artificial sphere, have a real, palpable existence in Nature; whereas, they denote the places where mere geometrical or imaginary lines run.

You might have expected to see an orrery, exhibiting a view of the sun and planets, with their various motions, particularly described in my Letter on astronomical instruments and apparatus. I must acknowledge, that I entertain a very low opinion of the utility of even the best orreries, and I cannot recommend them as auxiliaries in the study of astronomy. The numerous appendages usually connected with them, some to support them in a proper position, and some to communicate to them the requisite motions, enter into the ideas which the learner forms respecting the machinery of the heavens; and it costs much labor afterwards to divest the mind of such erroneous impressions. Astronomy can be exhibited much more clearly and beautifully to the mental eye than to the visual organ. It is much easier to conceive of the sun existing in boundless s.p.a.ce, and of the earth as moving around him at a great distance, the mind having nothing in view but simply these two bodies, than it is, in an orrery, to contemplate the motion of a ball representing the earth, carried by a complicated apparatus of wheels around another ball, supported by a cylinder or wire, to represent the sun. I would advise you, whenever it is practicable, to think how things are in Nature, rather than how they are represented by art. The machinery of the heavens is much simpler than that of an orrery.

In endeavoring to obtain a clear idea of the revolution of the earth around the sun, imagine to yourself a plane (a geometrical plane, having merely length and breadth, but no thickness) pa.s.sing through the centres of the sun and the earth, and extended far beyond the earth till it reaches the firmament of stars. Although, indeed, no such dome actually exists as that under which we figure to ourselves the vault of the sky, yet, as the fixed stars appear to be set in such a dome, we may imagine that the circles of the sphere, when indefinitely enlarged, finally reach such an imaginary vault. All that is essential is, that we should imagine this to exist far beyond the bounds of the solar system, the various bodies that compose the latter being situated close around the sun, at the centre.

Along the line where this great circle meets the starry vault, are situated a series of constellations,--Aries, Taurus, Gemini, &c.,--which occupy successively this portion of the heavens. When bodies are at such a distance from each other as the sun and the earth, I have said that a spectator on either would project the other body upon the concave sphere of the heavens, always seeing it on the opposite side of a great circle one hundred and eighty degrees from himself. The place of a body, when viewed from any point, is denoted by the position it occupies among the stars. Thus, in the diagram, Fig. 25, page 114, when the earth arrives at E, it is said to be in Aries, because, if viewed from the sun, it would be projected on that part of the heavens; and, for the same reason, to a spectator at E, the sun would be in Libra. When the earth s.h.i.+fts its position from Aries to Taurus, as we are unconscious of our own motion, the sun it is that appears to move from Libra to Scorpio, in the opposite part of the heavens. Hence, as we go forward, in the order of the signs, on one side of the ecliptic, the sun seems to be moving forward at the same rate on the opposite side of the same great circle; and therefore, although we are unconscious of our own motion, we can read it, from day to day, in the motions of the sun. If we could see the stars at the same time with the sun, we could actually observe, from day to day, the sun's progress through them, as we observe the progress of the moon at night; only the sun's rate of motion would be nearly fourteen times slower than that of the moon. Although we do not see the stars when the sun is present, we can observe that it makes daily progress eastward, as is apparent from the constellations of the zodiac occupying, successively, the western sky immediately after sunset, proving that either all the stars have a common motion westward, independent of their diurnal motion, or that the sun has a motion past them from west to east. We shall see, hereafter, abundant evidence to prove, that this change in the relative position of the sun and stars, is owing to a change in the apparent place of the sun, and not to any change in the stars.

[Ill.u.s.tration Fig. 25.]

To form a clear idea of the two motions of the earth, imagine yourself standing on a circular platform which turns slowly round its centre.

While you are carried slowly round the entire of the circuit of the heavens, along with the platform, you may turn round upon your heel the same way three hundred and sixty-five times. The former is a.n.a.logous to our annual motion with the earth around the sun; the latter, to our diurnal revolution in common with the earth around its own axis.

Although the apparent revolution of the sun is in a direction opposite to the real motion of the earth, as regards absolute s.p.a.ce, yet both are nevertheless from west to east, since these terms do not refer to any directions in absolute s.p.a.ce, but to the order in which certain constellations (the constellations of the Zodiac) succeed one another.

The earth itself, on opposite sides of its...o...b..t, does in fact move towards directly opposite points of s.p.a.ce; but it is all the while pursuing its course in the order of the signs. In the same manner, although the earth turns on its axis from west to east, yet any place on the surface of the earth is moving in a direction in s.p.a.ce exactly opposite to its direction twelve hours before. If the sun left a visible trace on the face of the sky, the ecliptic would of course be distinctly marked on the celestial sphere, as it is on an artificial globe; and were the equator delineated in a similar manner, we should then see, at a glance, the relative position of these two circles,--the points where they intersect one another, const.i.tuting the equinoxes; the points where they are at the greatest distance asunder, that is, the solstices; and various other particulars, which, for want of such visible traces, we are now obliged to search for by indirect and circuitous methods. It will aid you, to have constantly before your mental vision an imaginary delineation of these two important circles on the face of the sky.

The equator makes an angle with the ecliptic of twenty-three degrees and twenty-eight minutes. This is called the obliquity of the ecliptic. As the sun and earth are both always in the ecliptic, and as the motion of the earth in one part of it makes the sun appear to move in the opposite part, at the same rate, the sun apparently descends, in Winter, twenty-three degrees and twenty-eight minutes to the south of the equator, and ascends, in Summer, the same number of degrees north of it.

We must keep in mind, that the celestial equator and celestial ecliptic are here understood, and we may imagine them to be two great circles delineated on the face of the sky. On comparing observations made at different periods, for more than two thousand years, it is found, that the obliquity of the ecliptic is not constant, but that it undergoes a slight diminution, from age to age, amounting to fifty-two seconds in a century, or about half a second annually. We might apprehend that, by successive approaches to each other, the equator and ecliptic would finally coincide; but astronomers have discovered, by a most profound investigation, based on the principles of universal gravitation, that this irregularity is confined within certain narrow limits; and that the obliquity, after diminis.h.i.+ng for some thousands of years, will then increase for a similar period, and will thus vibrate forever about a mean value.

As the earth traverses every part of her orbit in the course of a year, she will be once at each solstice, and once at each equinox. The best way of obtaining a correct idea of her two motions is, to conceive of her as standing still for a single day, at some point in her orbit, until she has turned once on her axis, then moving about a degree, and halting again, until another diurnal revolution is completed. Let us suppose the earth at the Autumnal equinox, the sun, of course, being at the Vernal equinox,--for we must always think of these two bodies as diametrically opposite to each other. Suppose the earth to stand still in its...o...b..t for twenty-four hours. The revolution of the earth on its axis, from west to east, will make the sun appear to describe a great circle of the heavens from east to west, coinciding with the equator. At the end of this period, suppose the sun to move northward one degree, and to remain there for twenty-four hours; in which time, the revolution of the earth, will make the sun appear to describe another circle, from east to west, parallel to the equator, but one degree north of it. Thus, we may conceive of the sun as moving one degree north, every day, for about three months, when it will reach the point of the ecliptic furthest from the equator, which point is called the _tropic_, from a Greek word, signifying _to turn_; because, after the sun has pa.s.sed this point, his motion in his...o...b..t carries him continually towards the equator, and therefore he seems to turn about. The same point is also called the _solstice_, from a Latin word, signifying to _stand still_; since, when the sun has reached its greatest northern or southern limit, while its declination is at the point where it ceases to increase, but begins to decrease, there the sun seems for a short time stationary, with regard to the equator, appearing for several days to describe the same parallel of lat.i.tude.

When the sun is at the northern tropic, which happens about the twenty-first of June, his elevation above the southern horizon at noon is the greatest in the year; and when he is at the southern tropic, about the twenty-first of December, his elevation at noon is the least in the year. The difference between these two meridian alt.i.tudes will give the whole distance from one tropic to the other, and consequently, twice the distance from each tropic to the equator. By this means, we find how far the tropic is from the equator, and that gives us the angle which the equator and ecliptic make with each other; for the greatest distance between any two great circles on the sphere is always equal to the angle which they make with each other. Thus, the ancient astronomers were able to determine the obliquity of the ecliptic with a great degree of accuracy. It was easy to find the situation of the zenith, because the direction of a plumb-line shows us where that is; and it was easy to find the distances from the zenith where the sun was at the greatest and least distances; respectively. The difference of these two arcs is the angular distance from one tropic to the other; and half this arc is the distance of either tropic from the equator, and of course, equal to the obliquity of the ecliptic. All this will be very easily understood from the annexed diagram, Fig. 26. Let Z be the zenith of a spectator situated at C; Z _n_ the least, and Z _s_ the greatest distance of the sun from the zenith. From Z _s_ subtract Z _n_, and then _s n_, the difference, divided by two, will give the obliquity of the ecliptic.

[Ill.u.s.tration Fig. 26.]

The motion of the earth in its...o...b..t is nearly seventy times as great as its greatest motion around its axis. In its revolution around the sun, the earth moves no less than one million six hundred and forty thousand miles per day, sixty-eight thousand miles per hour, eleven hundred miles per minute, and nearly nineteen miles every second; a velocity nearly sixty times as great as the greatest velocity of a cannon ball. Places on the earth turn with very different degrees of velocity in different lat.i.tudes. Those near the equator are carried round on the circ.u.mference of a large circle; those towards the poles, on the circ.u.mference of a small circle; while one standing on the pole itself would not turn at all. Those who live on the equator are carried about one thousand miles an hour. In our lat.i.tude, (forty-one degrees and eighteen minutes,) the diurnal velocity is about seven hundred and fifty miles per hour. It would seem, at first view, quite incredible, that we should be whirled round at so rapid a rate, and yet be entirely insensible of any motion; and much more, that we could be going so swiftly through s.p.a.ce, in our circuit around the sun, while all things, when unaffected by local causes, appear to be in such a state of quiescence. Yet we have the most unquestionable evidence of the fact; nor is it difficult to account for it, in consistency with the general state of repose among bodies on the earth, when we reflect that their relative motions, with respect to each other, are not in the least disturbed by any motions which they may have in common. When we are on board a steam-boat, we move about in the same manner when the boat is in rapid motion, as when it is lying still; and such would be the case, if it moved steadily a hundred times faster than it does. Were the earth, however, suddenly to stop its diurnal revolution, all movable bodies on its surface would be thrown off in tangents to the surface with velocities proportional to that of their diurnal motion; and were the earth suddenly to halt in its...o...b..t, we should be hurled forward into s.p.a.ce with inconceivable rapidity.

I will next endeavor to explain to you the phenomena of the _Seasons_.

These depend on two causes; first, the inclination of the earth's axis to the plane of its...o...b..t; and, secondly, to the circ.u.mstance, that the axis always remains parallel to itself. Imagine to yourself a candle placed in the centre of a ring, to represent the sun in the centre of the earth's...o...b..t, and an apple with a knittingneedle running through it in the direction of the stem. Run a knife around the central part of the apple, to mark the situation of the equator. The circ.u.mference of the ring represents the earth's...o...b..t in the plane of the ecliptic. Place the apple so that the equator shall coincide with the wire; then the axis will lie directly across the plane of the ecliptic; that is, at right angles to it. Let the apple be carried quite round the ring, constantly preserving the axis parallel to itself, and the equator all the while coinciding with the wire that represents the orbit. Now, since the sun enlightens half the globe at once, so the candle, which here represents the sun, will s.h.i.+ne on the half of the apple that is turned towards it; and the circle which divides the enlightened from the unenlightened side of the apple, called the _terminator_, will pa.s.s through both the poles. If the apple be turned slowly round on its axis, the terminator will successively pa.s.s over all places on the earth, giving the appearance of sunrise to places at which it arrives, and of sunset to places from which it departs. If, therefore, the equator had coincided with the ecliptic, as would have been the case, had the earth's axis been perpendicular to the plane of its...o...b..t, the diurnal motion of the sun would always have been in the equator, and the days and nights would have been equal all over the globe. To the inhabitants of the equatorial parts of the earth, the sun would always have appeared to move in the prime vertical, rising directly in the east, pa.s.sing through the zenith at noon, and setting in the west. In the polar regions, the sun would always have appeared to revolve in the horizon; while, at any place between the equator and the pole, the course of the sun would have been oblique to the horizon, but always oblique in the same degree. There would have been nothing of those agreeable vicissitudes of the seasons which we now enjoy; but some regions of the earth would have been crowned with perpetual spring, others would have been scorched with the unremitting fervor of a vertical sun, while extensive regions towards either pole would have been consigned to everlasting frost and sterility.

To understand, then, clearly, the causes of the change of seasons, use the same apparatus as before; but, instead of placing the axis of the earth at right angles to the plane of its...o...b..t, turn it out of a perpendicular position a little, (twenty-three degrees and twenty-eight minutes,) then the equator will be turned just the same number of degrees out of a coincidence with the ecliptic. Let the apple be carried around the ring, always holding the axis inclined at the same angle to the plane of the ring, and always parallel to itself. You will find that there will be two points in the circuit where the plane of the equator, that you had marked around the centre of the apple, will pa.s.s through the centre of the sun; these will be the points where the celestial equator and the ecliptic cut one another, or the equinoxes. When the earth is at either of these points, the sun s.h.i.+nes on both poles alike; and, if we conceive of the earth, while in this situation, as turning once round on its axis, the apparent diurnal motion of the sun will be the same as it would be, were the earth's axis perpendicular to the plane of the equator. For that day, the sun would revolve in the equator, and the days and nights would be equal all over the globe. If the apple were carried round in the manner supposed, then, at the distance of ninety degrees from the equinoxes, the same pole would be turned from the sun on one side, just as much as it was turned towards him on the other. In the former case, the sun's light would fall short of the pole twenty-three and one half degrees, and in the other case, it would reach beyond it the same number of degrees. I would recommend to you to obtain as clear an idea as you can of the cause of the change of seasons, by thinking over the foregoing ill.u.s.tration. You may then clear up any remaining difficulties, by studying the diagram, Fig. 27, on page 122.

[Ill.u.s.tration Fig. 27.]

Let A B C D represent the earth's place in different parts of its...o...b..t, having the sun in the centre. Let A, C, be the positions of the earth at the equinoxes, and B, D, its positions at the tropics,--the axis _n s_ being always parallel to itself. It is difficult to represent things of this kind correctly, all on the same plane; but you will readily see, that the figure of the earth, here, answers to the apple in the former ill.u.s.tration; that the hemisphere towards _n_ is above, and that towards _s_ is below, the plane of the paper. When the earth is at A and C, the Vernal and Autumnal equinoxes, the sun, you will perceive, s.h.i.+nes on both the poles _n_ and _s_; and, if you conceive of the globe, while in this position, as turned round on its axis, as it is in the diurnal revolution, you will readily understand, that the sun would describe the celestial equator. This may not at first appear so obvious, by inspecting the figure; but if you consider the point _n_ as raised above the plane of the paper, and the point _s_ as depressed below it, you will readily see how the plane of the equator would pa.s.s through the centre of the sun. Again, at B, when the earth is at the southern tropic, the sun s.h.i.+nes twenty-three and a half degrees beyond the north pole, _n_, and falls the same distance short of the south pole, _s_. The case is exactly reversed when the earth is at the northern tropic, and the sun at the southern. While the earth is at one of the tropics, at B, for example, let us conceive of it as turning on its axis, and we shall readily see, that all that part of the earth which lies within the north polar circle will enjoy continual day, while that within the south polar circle will have continual night; and that all other places will have their days longer as they are nearer to the enlightened pole, and shorter as they are nearer to the unenlightened pole. This figure likewise shows the successive positions of the earth, at different periods of the year, with respect to the signs, and what months correspond to particular signs. Thus, the earth enters Libra, and the sun Aries, on the twenty-first of March, and on the twenty-first of June, the earth is just entering Capricorn, and the sun, Cancer. You will call to mind what is meant by this phraseology,--that by saying the earth enters Libra, we mean that a spectator placed on the sun would see the earth in that part of the celestial ecliptic, which is occupied by the sign Libra; and that a spectator on the earth sees the sun at the same time projected on the opposite part of the heavens, occupied by the sign Cancer.

Had the axis of the earth been perpendicular to the plane of the ecliptic, then the sun would always have appeared to move in the equator, the days would every where have been equal to the nights, and there could have been no change of seasons. On the other hand, had the inclination of the ecliptic to the equator been much greater than it is, the vicissitudes of the seasons would have been proportionally greater, than at present. Suppose, for instance, the equator had been at right angles to the ecliptic, in which case, the poles of the earth would have been situated in the ecliptic itself; then, in different parts of the earth, the appearances would have been as follows: To a spectator on the _equator_, (where all the circles of diurnal revolution are perpendicular to the horizon,) the sun, as he left the vernal equinox, would every day perform his diurnal revolution in a smaller and smaller circle, until he reached the north pole, when he would halt for a moment, and then wheel about and return to the equator, in a reverse order. The progress of the sun through the southern signs, to the south pole, would be similar to that already described. Such would be the appearances to an inhabitant of the equatorial regions. To a spectator living in an _oblique_ sphere, in our own lat.i.tude, for example, the sun, while north of the equator, would advance continually northward, making his diurnal circuit in parallels further and further distant from the equator, until he reached the circle of perpetual apparition; after which, he would climb, by a spiral course, to the north star, and then as rapidly return to the equator. By a similar progress southward, the sun would at length pa.s.s the circle of perpetual occultation, and for some time (which would be longer or shorter, according to the lat.i.tude of the place of observation) there would be continual night. To a spectator on the _pole_ of the earth and under the pole of the heaven, during the long day of six months, the sun would wind its way to a point directly over head, pouring down upon the earth beneath not merely the heat of the torrid zone, but the heat of a torrid noon, acc.u.mulating without intermission.

The great vicissitudes of heat and cold, which would attend these several movements of the sun, would be wholly incompatible with the existence of either the animal or the vegetable kingdom, and all terrestrial Nature would be doomed to perpetual sterility and desolation. The happy provision which the Creator has made against such extreme vicissitudes, by confining the changes of the seasons within such narrow bounds, conspires with many other express arrangements in the economy of Nature, to secure the safety and comfort of the human race.

Perhaps you have never reflected upon all the reasons, why the several changes of position, with respect to the horizon, which the sun undergoes in the course of the year, occasion such a difference in the amount of heat received from him. Two causes contribute to increase the heat of Summer and the cold of Winter. The higher the sun ascends above the horizon, the more directly his rays fall upon the earth; and their heating power is rapidly augmented, as they approach a perpendicular direction. When the sun is nearly over head, his rays strike us with far greater force than when they meet us obliquely; and the earth absorbs a far greater number of those rays of heat which strike it perpendicularly, than of those which meet it in a slanting direction.

When the sun is near the horizon, his rays merely glance along the ground, and many of them, before they reach it, are absorbed and dispersed in pa.s.sing through the atmosphere. Those who have felt only the oblique solar rays, as they fall upon objects in the high lat.i.tudes, have a very inadequate idea of the power of a vertical, noonday sun, as felt in the region of the equator.

The increased length of the day in Summer is another cause of the heat of this season of the year. This cause more sensibly affects places far removed from the equator, because at such places the days are longer and the nights shorter than in the torrid zone. By the operation of this cause, the solar heat acc.u.mulates there so much, during the longest days of Summer, that the temperature rises to a higher degree than is often known in the torrid climates.

But the temperature of a place is influenced very much by several other causes, as well as by the force and duration of the sun's heat. First, the _elevation_ of a country above the level of the sea has a great influence upon its climate. Elevated districts of country, even in the torrid zone, often enjoy the most agreeable climate in the world. The cold of the upper regions of the atmosphere modifies and tempers the solar heat, so as to give a most delightful softness, while the uniformity of temperature excludes those sudden and excessive changes which are often experienced in less favored climes. In ascending certain high mountains situated within the torrid zone, the traveller pa.s.ses, in a short time, through every variety of climate, from the most oppressive and sultry heat, to the soft and balmy air of Spring, which again is succeeded by the cooler breezes of Autumn, and then by the severest frosts of Winter. A corresponding difference is seen in the products of the vegetable kingdom. While Winter reigns on the summit of the mountain, its central regions may be encircled with the verdure of Spring, and its base with the flowers and fruits of Summer. Secondly, the proximity of the _ocean_ also has a great effect to equalize the temperature of a place. As the ocean changes its temperature during the year much less than the land, it becomes a source of warmth to contiguous countries in Winter, and a fountain of cool breezes in Summer. Thirdly, the relative _humidity_ or _dryness_ of the atmosphere of a place is of great importance, in regard to its effects on the animal system. A dry air of ninety degrees is not so insupportable as a humid air of eighty degrees; and it may be a.s.serted as a general principle, that a hot and humid atmosphere is unhealthy, although a hot air, when dry, may be very salubrious. In a warm atmosphere which is dry, the evaporation of moisture from the surface of the body is rapid, and its cooling influence affords a most striking relief to an intense heat without; but when the surrounding atmosphere is already filled with moisture, no such evaporation takes place from the surface of the skin, and no such refres.h.i.+ng effects are experienced from this cause. Moisture collects on the skin; a sultry, oppressive sensation is felt; and chills and fevers are usually in the train.

LETTER XII.

LAWS OF MOTION.

"What though in solemn silence, all Move round this dark, terrestrial ball!

In reason's ear they all rejoice, And utter forth a glorious voice; For ever singing, as they s.h.i.+ne, 'The hand that made us is divine.'"--_Addison._

HOWEVER incredible it may seem, no fact is more certain, than that the earth is constantly on the wing, flying around the sun with a velocity so prodigious, that, for every breath we draw, we advance on our way forty or fifty miles. If, when pa.s.sing across the waters in a steam-boat, we can wake, after a night's repose, and find ourselves conducted on our voyage a hundred miles, we exult in the triumphs of art, which could have moved so ponderous a body as a steam-s.h.i.+p over such a s.p.a.ce in so short a time, and so quietly, too, as not to disturb our slumbers; but, with a motion vastly more quiet and uniform, we have, in the same interval, been carried along with the earth in its...o...b..t more than half a million of miles. In the case of the steam-s.h.i.+p, however perfect the machinery may be, we still, in our waking hours at least, are made sensible of the action of the forces by which the motion is maintained,--as the roaring of the fire, the beating of the piston, and the das.h.i.+ng of the paddle-wheels; but in the more perfect machinery which carries the earth forward on her grander voyage, no sound is heard, nor the least intimation afforded of the stupendous forces by which this motion is achieved. To the pious observer of Nature it might seem sufficient, without any inquiry into second causes, to ascribe the motions of the spheres to the direct agency of the Supreme Being. If, however, we can succeed in finding the secret springs and cords, by which the motions of the heavenly bodies are immediately produced and controlled, it will detract nothing from our just admiration of the Great First Cause of all things. We may therefore now enter upon the inquiry into the nature or laws of the forces by which the earth is made to revolve on her axis and in her orbit; and having learned what it is, that causes and maintains the motions of the earth, you will then acquire, at the same time, a knowledge of all the celestial machinery.

The subject will involve an explanation of the laws of motion, and of the principles of universal gravitation.

It was once supposed, that we could never reason respecting the laws that govern the heavenly bodies from what we observe in bodies around us, but that motion is one thing on the earth and quite another thing in the skies; and hence, that it is impossible for us, by any inquiries into the laws of terrestrial Nature, to ascertain how things take place among the heavenly bodies. Galileo and Newton, however, proceeded on the contrary supposition, that Nature is uniform in all her works; that the same Almighty arm rules over all; and that He works by the same fixed laws through all parts of His boundless realm. The certainty with which all the predictions of astronomers, made on these suppositions, are fulfilled, attests the soundness of the hypothesis. Accordingly, those laws, which all experience, endlessly multiplied and varied, proves to be the laws of terrestrial motion, are held to be the laws that govern also the motions of the most distant planets and stars, and to prevail throughout the universe of matter. Let us, then, briefly review these great laws of motion, which are three in number. The FIRST LAW is as follows: _every body perseveres in a state of rest, or of uniform motion in a straight line, unless compelled by some force to change its state_.

By _force_ is meant any thing which produces motion.

The foregoing law has been fully established by experiment, and is conformable to all experience. It embraces several particulars. First, a body, when at rest, remains so, unless some force puts it in motion; and hence it is inferred, when a body is found in motion, that some force must have been applied to it sufficient to have caused its motion. Thus, the fact, that the earth is in motion around the sun and around its own axis, is to be accounted for by a.s.signing to each of these motions a force adequate, both in quant.i.ty and direction, to produce these motions, respectively.

Secondly, when a body is once in motion, it will continue to move for ever, unless something stops it. When a ball is struck on the surface of the earth, the friction of the earth and the resistance of the air soon stop its motion; when struck on smooth ice, it will go much further before it comes to a state of rest, because the ice opposes much less resistance than the ground; and, were there no impediment to its motion, it would, when once set in motion, continue to move without end. The heavenly bodies are actually in this condition: they continue to move, not because any new forces are applied to them; but, having been once set in motion, they continue in motion because there is nothing to stop them. This property in bodies to persevere in the state they are actually in,--if at rest, to remain at rest, or, if in motion, to continue in motion,--is called _inertia_. The inertia of a body (which is measured by the force required to overcome it) is proportioned to the quant.i.ty of matter it contains. A steam-boat manifests its inertia, on first starting it, by the enormous expenditure of force required to bring it to a given rate of motion; and it again manifests its inertia, when in rapid motion, by the great difficulty of stopping it. The heavenly bodies, having been once put in motion, and meeting with nothing to stop them, move on by their own inertia. A top affords a beautiful ill.u.s.tration of inertia, continuing, as it does, to spin after the moving force is withdrawn.

Thirdly, the motion to which a body naturally tends is _uniform_; that is, the body moves just as far the second minute as it did the first, and as far the third as the second; and pa.s.ses over equal s.p.a.ces in equal times. I do not a.s.sert that the motion of all moving bodies is _in fact_ uniform, but that such is their _tendency_. If it is otherwise than uniform, there is some cause operating to disturb the uniformity to which it is naturally p.r.o.ne.

Fourthly, a body in motion will move in a _straight line_, unless diverted out of that line by some external force; and the body will resume its straight-forward motion, whenever the force that turns it aside is withdrawn. Every body that is revolving in an orbit, like the moon around the earth, or the earth around the sun, _tends_ to move in a straight line which is a tangent[7] to its...o...b..t. Thus, if A B C, Fig.

28, represents the orbit of the moon around the earth, were it not for the constant action of some force that draws her towards the earth, she would move off in a straight line. If the force that carries her towards the earth were suspended at A, she would immediately desert the circular motion, and proceed in the direction A D. In the same manner, a boy whirls a stone around his head in a sling, and then letting go one of the strings, and releasing the force that binds it to the circle, it flies off in a straight line which is a tangent to that part of the circle where it was released. This tendency which a body revolving in an orbit exhibits, to recede from the centre and to fly off in a tangent, is called the _centrifugal force_. We see it manifested when a pail of water is whirled. The water rises on the sides of the vessel, leaving a hollow in the central parts. We see an example of the effects of centrifugal action, when a horse turns swiftly round a corner, and the rider is thrown outwards; also, when a wheel pa.s.ses rapidly through a small collection of water, and portions of the water are thrown off from the top of the wheel in straight lines which are tangents to the wheel.

[Ill.u.s.tration Fig. 28.]

The centrifugal force is increased as the velocity is increased. Thus, the parts of a millstone most remote from the centre sometimes acquire a centrifugal force so much greater than the central parts, which move much slower, that the stone is divided, and the exterior portions are projected with great violence. In like manner, as the equatorial parts of the earth, in the diurnal revolution, revolve much faster than the parts towards the poles, so the centrifugal force is felt most at the equator, and becomes strikingly manifest by the diminished weight of bodies, since it acts in opposition to the force of gravity.

Although the foregoing law of motion, when first presented to the mind, appears to convey no new truth, but only to enunciate in a formal manner what we knew before; yet a just understanding of this law, in all its bearings, leads us to a clear comprehension of no small share of all the phenomena of motion. The second and third laws may be explained in fewer terms.

The SECOND LAW of motion is as follows: _motion is proportioned to the force impressed, and in the direction of that force_.

The meaning of this law is, that every force that is applied to a body produces its full effect, proportioned to its intensity, either in causing or in preventing motion. Let there be ever so many blows applied at once to a ball, each will produce its own effect in its own direction, and the ball will move off, not indeed in the zigzag, complex lines corresponding to the directions of the several forces, but in a single line expressing the united effect of all. If you place a ball at the corner of a table, and give it an impulse, at the same instant, with the thumb and finger of each hand, one impelling it in the direction of one side of the table, and the other in the direction of the other side, the ball will move diagonally across the table. If the blows be exactly proportioned each to the length of the side of the table on which it is directed, the ball will run exactly from corner to corner, and in the same time that it would have pa.s.sed over each side by the blow given in the direction of that side. This principle is expressed by saying, that a body impelled by two forces, acting respectively in the directions of the two sides of a parallelogram, and proportioned in intensity to the lengths of the sides, will describe the diagonal of the parallelogram in the same time in which it would have described the sides by the forces acting separately.

The converse of this proposition is also true, namely, that any single motion may be considered as the _resultant_ of two others,--the motion itself being represented by the diagonal, while the two _components_ are represented by the sides, of a parallelogram. This reduction of a motion to the individual motions that produce it, is called the _resolution of motion_, or the _resolution of forces_. Nor can a given motion be resolved into _two_ components, merely. These, again, may be resolved into others, varying indefinitely, in direction and intensity, from all which the given motion may be considered as having resulted. This composition and resolution of motion or forces is often of great use, in inquiries into the motions of the heavenly bodies. The composition often enables us to subst.i.tute a single force for a great number of others, whose individual operations would be too complicated to be followed. By this means, the investigation is greatly simplified. On the other hand, it is frequently very convenient to resolve a given motion into two or more others, some of which may be thrown out of the account, as not influencing the particular point which we are inquiring about, while others are far more easily understood and managed than the single force would have been. It is characteristic of great minds, to simplify these inquiries. They gain an insight into complicated and difficult subjects, not so much by any extraordinary faculty of seeing in the dark, as by the power of removing from the object all incidental causes of obscurity, until it s.h.i.+nes in its own clear and simple light.

If every force, when applied to a body, produces its full and legitimate effect, how many other forces soever may act upon it, impelling it different ways, then it must follow, that the smallest force ought to move the largest body; and such is in fact the case. A snap of a finger upon a seventy-four under full sail, if applied in the direction of its motion, would actually increase its speed, although the effect might be too small to be visible. Still it is something, and may be truly expressed by a fraction. Thus, suppose a globe, weighing a million of pounds, were suspended from the ceiling by a string, and we should apply to it the snap of a finger,--it is granted that the motion would be quite insensible. Let us then divide the body into a million equal parts, each weighing one pound; then the same impulse, applied to each one separately, would produce a sensible effect, moving it, say one inch. It will be found, on trial, that the same impulse given to a ma.s.s of two pounds will move it half an inch; and hence it is inferred, that, if applied to a ma.s.s weighing a million of pounds, it would move it the millionth part of an inch.

It is one of the curious results of the second law of motion, that an unlimited number of motions may exist together in the same body. Thus, at the same moment, we may be walking around a post in the cabin of a steam-boat, accompanying the boat in its pa.s.sage around an island, revolving with the earth on its axis, flying through s.p.a.ce in our annual circuit around the sun, and possibly wheeling, along with the sun and his whole retinue of planets, around some centre in common with the starry worlds.

The THIRD LAW of motion is this: _action and reaction are equal, and in contrary directions_.

Whenever I give a blow, the body struck exerts an equal force on the striking body. If I strike the water with an oar, the water communicates an equal impulse to the oar, which, being communicated to the boat, drives it forward in the opposite direction. If a magnet attracts a piece of iron, the iron attracts the magnet just as much, in the opposite direction; and, in short, every portion of matter in the universe attracts and is attracted by every other, equally, in an opposite direction. This brings us to the doctrine of universal gravitation, which is the very key that unlocks all the secrets of the skies. This will form the subject of my next Letter.

FOOTNOTE:

[7] A tangent is a straight line touching a circle, as A D, in Fig. 28

LETTER XIII.