Read Ebook: Letters on Astronomy in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers by Olmsted Denison

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thus to give the disk an oval form. This effect is particularly remarkable when the sun, at his rising or setting, is observed from the top of a mountain, or at an elevation near the seashore; for in such situations, the rays of light make a greater angle than ordinary with a perpendicular to the refracting medium, and the amount of refraction is proportionally greater. In some cases of this kind, the shortening of the vertical diameter of the sun has been observed to amount to six minutes, or about one fifth of the whole.

The apparent enlargement of the sun and moon, when near the horizon, arises from an optical illusion. These bodies, in fact, are not seen under so great an angle when in the horizon as when on the meridian, for they are nearer to us in the latter case than in the former. The distance of the sun, indeed, is so great, that it makes very little difference in his apparent diameter whether he is viewed in the horizon or on the meridian; but with the moon, the case is otherwise; its angular diameter, when measured with instruments, is perceptibly larger when at its culmination, or highest elevation above the horizon. Why, then, do the sun and moon appear so much larger when near the horizon? It is owing to a habit of the mind, by which we judge of the magnitudes of distant objects, not merely by the angle they subtend at the eye, but also by our impressions respecting their distance, allowing, under a given angle, a greater magnitude as we imagine the distance of a body to be greater. Now, on account of the numerous objects usually in sight between us and the sun, when he is near the horizon, he appears much further removed from us than when on the meridian; and we unconsciously assign to him a proportionally greater magnitude. If we view the sun, in the two positions, through a smoked glass, no such difference of size is observed; for here no objects are seen but the sun himself.

Were it not for the power the atmosphere has of dispersing the solar light, and scattering it in various directions, no objects would be visible to us out of direct sunshine; every shadow of a passing cloud would involve us in midnight darkness; the stars would be visible all day; and every apartment into which the sun had not direct admission would be involved in the obscurity of night. This scattering action of the atmosphere on the solar light is greatly increased by the irregularity of temperature caused by the sun, which throws the atmosphere into a constant state of undulation; and by thus bringing together masses of air of different temperatures, produces partial reflections and refractions at their common boundaries, by which means much light is turned aside from a direct course, and diverted to the purposes of general illumination. In the upper regions of the atmosphere, as on the tops of very high mountains, where the air is too much rarefied to reflect much light, the sky assumes a black appearance, and stars become visible in the day time.

Although the atmosphere is usually so transparent, that it is invisible to us, yet we as truly move and live in a fluid as fishes that swim in the sea. Considered in comparison with the whole earth, the atmosphere is to be regarded as a thin layer investing the surface, like a film of water covering the surface of an orange. Its actual height, however, is over a hundred miles, though we cannot assign its precise boundaries. Being perfectly elastic, the lower portions, bearing as they do, the weight of all the mass above them, are greatly compressed, while the upper portions having little to oppose the natural tendency of air to expand, diffuse themselves widely. The consequence is, that the atmosphere undergoes a rapid diminution of density, as we ascend from the earth, and soon becomes exceedingly rare. At so moderate a height as seven miles, it is four times rarer than at the surface, and continues to grow rare in the same proportion, namely, being four times less for every seven miles of ascent. It is only, therefore, within a few miles of the earth, that the atmosphere is sufficiently dense to sustain clouds and vapors, which seldom rise so high as eight miles, and are usually much nearer to the earth than this. So rare does the air become on the top of Mount Chimborazo, in South America, that it is incompetent to support most of the birds that fly near the level of the sea. The condor, a bird which has remarkably long wings, and a light body, is the only bird seen towering above this lofty summit. The transparency of the atmosphere,--a quality so essential to fine views of the starry heavens,--is much increased by containing a large proportion of water, provided it is perfectly dissolved, or in a state of invisible vapor. A country at once hot and humid, like some portions of the torrid zone, presents a much brighter and more beautiful view of the moon and stars, than is seen in cold climates. Before a copious rain, especially in hot weather, when the atmosphere is unusually humid, we sometimes observe the sky to be remarkably resplendent, even in our own latitude. Accordingly, this unusual clearness of the sky, when the stars shine with unwonted brilliancy, is regarded as a sign of approaching rain; and when, after the rain is apparently over, the air is remarkably transparent, and distant objects on the earth are seen with uncommon distinctness, while the sky exhibits an unusually deep azure, we may conclude that the serenity is only temporary, and that the rain will probably soon return.

FOOTNOTE:

Sir J. Herschel.

THE SUN.

THE subjects which have occupied the preceding Letters are by no means the most interesting parts of our science. They constitute, indeed, little more than an introduction to our main subject, but comprise such matters as are very necessary to be clearly understood, before one is prepared to enter with profit and delight upon the more sublime and interesting field which now opens before us.

We will begin our survey of the heavenly bodies with the SUN, which first claims our homage, as the natural monarch of the skies. The moon will next occupy our attention; then the other bodies which compose the solar system, namely, the planets and comets; and, finally, we shall leave behind this little province in the great empire of Nature, and wing a bolder flight to the fixed stars.

Ninety-five millions of miles is indeed a vast distance. No human mind is adequate to comprehend it fully; but the nearest approaches we can make towards it are gained by successive efforts of the mind to conceive of great distances, beginning with such as are clearly within our grasp. Let us, then, first take so small a distance as that of the breadth of the Atlantic ocean, and follow, in mind, a ship, as she leaves the port of New York, and, after twenty days' steady sail, reaches Liverpool. Having formed the best idea we are able of this distance, we may then reflect, that it would take a ship, moving constantly at the rate of ten miles per hour, more than a thousand years to reach the sun.

The diameter of the sun is towards a million of miles; or, more exactly, it is eight hundred and eighty-five thousand miles. One hundred and twelve bodies as large as the earth, lying side by side, would be required to reach across the solar disk; and our ship, sailing at the same rate as before, would be ten years in passing over the same space. Immense as is the sun, we can readily understand why it appears no larger than it does, when we reflect, that its distance is still more vast. Even large objects on the earth, when seen on a distant eminence, or over a wide expanse of water, dwindle almost to a point. Could we approach nearer and nearer to the sun, it would constantly expand its volume, until finally it would fill the whole vault of heaven. We could, however, approach but little nearer to the sun without being consumed by the intensity of his heat. Whenever we come nearer to any fire, the heat rapidly increases, being four times as great at half the distance, and one hundred times as great at one tenth the distance. This fact is expressed by saying, that the heat increases as the square of the distance decreases. Our globe is situated at such a distance from the sun, as exactly suits the animal and vegetable kingdoms. Were it either much nearer or much more remote, they could not exist, constituted as they are. The intensity of the solar light also follows the same law. Consequently, were we nearer to the sun than we are, its blaze would be insufferable; or, were we much further off, the light would be too dim to serve all the purposes of vision.

The sun is one million four hundred thousand times as large as the earth; but its matter is not more than about one fourth as dense as that of the earth, being only a little heavier than water, while the average density of the earth is more than five times that of water. Still, on account of the immense magnitude of the sun, its entire quantity of matter is three hundred and fifty thousand times as great as that of the earth. Now, the force of gravity in a body is greater, in proportion as its quantity of matter is greater. Consequently, we might suppose, that the weight of a body would be increased in the same proportion; or, that a body, which weighs only one pound at the surface of the earth, would weigh three hundred and fifty thousand pounds at the sun. But we must consider, that the attraction exerted by any body is the same as though all the matter were concentrated in the centre. Thus, the attraction exerted by the earth and by the sun is the same as though the entire matter of each body were in its centre. Hence, on account of the vast dimensions of the sun, its surface is one hundred and twelve times further from its centre than the surface of the earth is from its centre; and, since the force of gravity diminishes as the square of the distance increases, that of the sun, exerted on bodies at its surface, is the square of one hundred and twelve, or twelve thousand five hundred and forty-four times less than that of the earth. If, therefore, we increase the weight of a body three hundred and fifty-four thousand times, in consequence of the greater amount of matter in the sun, and diminish it twelve thousand five hundred and forty-four times, in consequence of the force acting at a greater distance from the body, we shall find that the body would weigh about twenty-eight times more on the sun than on the earth. Hence, a man weighing three hundred pounds would, if conveyed to the surface of the sun, weigh eight thousand four hundred pounds, or nearly three tons and three quarters. A limb of our bodies, weighing forty pounds, would require to lift it a force of one thousand one hundred and twenty pounds, which would be beyond the ordinary power of the muscles. At the surface of the earth, a body falls from rest by the force of gravity, in one second, sixteen and one twelfth feet; but at the surface of the sun, a body would, in the same time, fall through four hundred and forty-eight and seven tenths feet.

La Lande, an eminent French astronomer of the last century, held that the sun is a solid, opaque body, having its exterior diversified with high mountains and deep valleys, and covered all over with a burning sea of liquid matter. The spots he supposed to be produced by the flux and reflux of this fiery sea, retreating occasionally from the mountains, and exposing to view a portion of the dark body of the sun. But it is inconsistent with the nature of fluids, that a liquid, like the sea supposed, should depart so far from its equilibrium and remain so long fixed, as to lay bare the immense spaces occupied by some of the solar spots.

Dr. Herschel's views respecting the nature and constitution of the sun, embracing an explanation of the solar spots, have, of late years, been very generally received by the astronomical world. This great astronomer, after attentively viewing the surface of the sun, for a long time, with his large telescopes, came to the following conclusions respecting the nature of this luminary. He supposes the sun to be a planetary body like our earth, diversified with mountains and valleys, to which, on account of the magnitude of the sun, he assigns a prodigious extent, some of the mountains being six hundred miles high, and the valleys proportionally deep. He employs in his explanation no volcanic fires, but supposes two separate regions of dense clouds floating in the solar atmosphere, at different distances from the sun. The exterior stratum of clouds he considers as the depository of the sun's light and heat, while the inferior stratum serves as an awning or screen to the body of the sun itself, which thus becomes fitted to be the residence of animals. The proofs offered in support of this hypothesis are chiefly the following: first, that the appearances, as presented to the telescope, are such as accord better with the idea that the fluctuations arise from the motions of clouds, than that they are owing to the agitations of a liquid, which could not depart far enough from its general level to enable us to see its waves at so great a distance, where a line forty miles in length would subtend an angle at the eye of only the tenth part of a second; secondly, that, since clouds are easily dispersed to any extent, the great dimensions which the solar spots occasionally exhibit are more consistent with this than with any other hypothesis; and, finally, that a lower stratum of clouds, similar to those of our atmosphere, was frequently seen by the Doctor, far below the luminous clouds which are the fountains of light and heat.

Such are the views of one who had, it must be acknowledged, great powers of observation, and means of observation in higher perfection than have ever been enjoyed by any other individual; but, with all deference to such authority, I am compelled to think that the hypothesis is encumbered with very serious objections. Clouds analogous to those of our atmosphere cannot exist in hot air; they are tenants only of cold regions. How can they be supposed to exist in the immediate vicinity of a fire so intense, that they are even dissipated by it at the distance of ninety-five millions of miles? Much less can they be supposed to be the depositories of such devouring fire, when any thing in the form of clouds, floating in our atmosphere, is at once scattered and dissolved by the accession of only a few degrees of heat. Nothing, moreover, can be imagined more unfavorable for radiating heat to such a distance, than the light, inconstant matter of which clouds are composed, floating loosely in the solar atmosphere. There is a logical difficulty in the case: it is ascribing to things properties which they are not known to possess; nay, more, which they are known not to possess. From variations of light and shade in objects seen at moderate distances on the earth, we are often deceived in regard to their appearances; and we must distrust the power of an astronomer to decide upon the nature of matter seen at the distance of ninety-five millions of miles.

I think, therefore, we must confess our ignorance of the nature and constitution of the sun; nor can we, as astronomers, obtain much more satisfactory knowledge respecting it than the common apprehension, namely, that it is an immense globe of fire. We have not yet learned what causes are in operation to maintain its undecaying fires; but our confidence in the Divine wisdom and goodness leads us to believe, that those causes are such as will preserve those fires from extinction, and at a nearly uniform degree of intensity. Any material change in this respect would jeopardize the safety of the animal and vegetable kingdoms, which could not exist without the enlivening influence of the solar heat, nor, indeed, were that heat any more or less intense than it is at present.

ANNUAL REVOLUTION.--SEASONS

WE have seen that the apparent revolution of the heavenly bodies, from east to west, every twenty-four hours, is owing to a real revolution of the earth on its own axis, in the opposite direction. This motion is very easily understood, resembling, as it does, the spinning of a top. We must, however, conceive of the top as turning without any visible support, and not as resting in the usual manner on a plane. The annual motion of the earth around the sun, which gives rise to an apparent motion of the sun around the earth once a year, and occasions the change of seasons, is somewhat more difficult to understand; and it may cost you some reflection, before you will settle all the points respecting the changes of the seasons clearly in your mind. We sometimes see these two motions exemplified in a top. When, as the string is pulled, the top is thrown forwards on the floor, we may see it move forward at the same time that it spins on its axis. Let a candle be placed on a table, to represent the sun, and let these two motions be imagined to be given to a top around it, and we shall have a case somewhat resembling the actual motions of the earth around the sun.

When bodies are at such a distance from each other as the earth and the sun, 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.

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 space, 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 passing 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 shifts 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.

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 analogous 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 space, yet both are nevertheless from west to east, since these terms do not refer to any directions in absolute space, but to the order in which certain constellations succeed one another. The earth itself, on opposite sides of its orbit, does in fact move towards directly opposite points of space; 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 space 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, constituting 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 diminishing for some thousands of years, will then increase for a similar period, and will thus vibrate forever about a mean value.

The motion of the earth in its orbit 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 latitudes. Those near the equator are carried round on the circumference of a large circle; those towards the poles, on the circumference 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 latitude, 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 space, 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 orbit, we should be hurled forward into space with inconceivable rapidity.

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 orbit, turn it out of a perpendicular position a little, 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 pass 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 shines 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 illustration. You may then clear up any remaining difficulties, by studying the diagram, Fig. 27, on page 122.

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 passing through the atmosphere. Those who have felt only the oblique solar rays, as they fall upon objects in the high latitudes, have a very inadequate idea of the power of a vertical, noonday sun, as felt in the region of the equator.

LAWS OF MOTION.

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 passing 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-ship over such a space 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 orbit more than half a million of miles. In the case of the steam-ship, 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 dashing 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.

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 assigning to each of these motions a force adequate, both in quantity and direction, to produce these motions, respectively.

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 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 passed 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.

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 mass of two pounds will move it half an inch; and hence it is inferred, that, if applied to a mass 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 passage around an island, revolving with the earth on its axis, flying through space 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.

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:

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

TERRESTRIAL GRAVITY.

We owe chiefly to the great Galileo the first investigation of the laws of terrestrial gravity, as exemplified in falling bodies; and I will avail myself of this opportunity to make you better acquainted with one of the most interesting of men and greatest of philosophers.

Galileo was born at Pisa, in Italy, in the year 1564. He was the son of a Florentine nobleman, and was destined by his father for the medical profession, and to this his earlier studies were devoted. But a fondness and a genius for mechanical inventions had developed itself, at a very early age, in the construction of his toys, and a love of drawing; and as he grew older, a passion for mathematics, and for experimental research, predominated over his zeal for the study of medicine, and he fortunately abandoned that for the more congenial pursuits of natural philosophy and astronomy. In the twenty-fifth year of his age, he was appointed, by the Grand Duke of Tuscany, professor of mathematics in the University of Pisa. At that period, there prevailed in all the schools a most extraordinary reverence for the writings of Aristotle, the preceptor of Alexander the Great,--a philosopher who flourished in Greece, about three hundred years before the Christian era. Aristotle, by his great genius and learning, gained a wonderful ascendency over the minds of men, and became the oracle of the whole reading world for twenty centuries. It was held, on the one hand, that all truths worth knowing were contained in the writings of Aristotle; and, on the other, that an assertion which contradicted any thing in Aristotle could not be true. But Galileo had a greatness of mind which soared above the prejudices of the age in which he lived, and dared to interrogate Nature by the two great and only successful methods of discovering her secrets,--experiment and observation. Galileo was indeed the first philosopher that ever fully employed experiments as the means of learning the laws of Nature, by imitating on a small what she performs on a great scale, and thus detecting her modes of operation. Archimedes, the great Sicilian philosopher, had in ancient times introduced mathematical or geometrical reasoning into natural philosophy; but it was reserved for Galileo to unite the advantages of both mathematical and experimental reasonings in the study of Nature,--both sure and the only sure guides to truth, in this department of knowledge, at least. Experiment and observation furnish materials upon which geometry builds her reasonings, and from which she derives many truths that either lie for ever hidden from the eye of observation, or which it would require ages to unfold.

It is a remarkable fact, that two such characters as Bacon and Galileo should appear on the stage at the same time, who, without any communication with each other, or perhaps without any personal knowledge of each other's existence, should have each developed the true method of investigating the laws of Nature. Galileo practised what Bacon only taught; and some, therefore, with much reason, consider Galileo as a greater philosopher than Bacon. "Bacon," says Hume, "pointed out, at a great distance, the road to philosophy; Galileo both pointed it out to others, and made, himself, considerable advances in it. The Englishman was ignorant of geometry; the Florentine revived that science, excelled in it, and was the first who applied it, together with experiment, to natural philosophy. The former rejected, with the most positive disdain, the system of Copernicus; the latter fortified it with new proofs, derived both from reason and the senses."

When we reflect that geometry is a science built upon self-evident truths, and that all its conclusions are the result of pure demonstration, and can admit of no controversy; when we further reflect, that experimental evidence rests on the testimony of the senses, and we infer a thing to be true because we actually see it to be so; it shows us the extreme bigotry, the darkness visible, that beclouded the human intellect, when it not only refused to admit conclusions first established by pure geometrical reasoning, and afterwards confirmed by experiments exhibited in the light of day, but instituted the most cruel persecutions against the great philosopher who first proclaimed these truths. Galileo was hated and persecuted by two distinct bodies of men, both possessing great influence in their respective spheres,--the one consisting of the learned doctors of philosophy, who did nothing more, from age to age, than reiterate the doctrines of Aristotle, and were consequently alarmed at the promulgation of principles subversive of those doctrines; the other consisting of the Romish priesthood, comprising the terrible Inquisition, who denounced the truths taught by Galileo, as inconsistent with certain declarations of the Holy Scriptures. We shall see, as we advance, what a fearful warfare he had to wage against these combined powers of darkness.

Were a body to fall from a great distance,--suppose a thousand times that of the radius of the earth,--the force of gravity being one million times less than that at the surface of the earth, the motion of the body would be exceedingly slow, carrying it over only the sixth part of an inch in a day. It would be a long time, therefore, in making any sensible approaches towards the earth; but at length, as it drew near to the earth it would acquire a very great velocity, and would finally rush towards it with prodigious violence. Falling so far, and being continually accelerated on the way, we might suppose that it would at length attain a velocity infinitely great; but it can be demonstrated, that, if a body were to fall from an infinite distance, attracted to the earth only by gravity, it could never acquire a velocity greater than about seven miles per second. This, however, is a speed inconceivably great, being about eighteen times the greatest velocity that can be given to a cannon-ball, and more than twenty-five thousand miles per hour.

But the phenomena of falling bodies must have long been observed, and their laws had been fully investigated by Galileo and others, before the cause of their falling was understood, or any such principle as gravity, inherent in the earth and in all bodies, was applied to them. The developement of this great principle was the work of Sir Isaac Newton; and I will give you, in my next Letter, some particulars respecting the life and discoveries of this wonderful man.

SIR ISAAC NEWTON.--UNIVERSAL GRAVITATION.--FIGURE OF THE EARTH'S ORBIT.--PRECESSION OF THE EQUINOXES.

SIR ISAAC NEWTON was born in Lincolnshire, England, in 1642, just one year after the death of Galileo. His father died before he was born, and he was a helpless infant, of a diminutive size, and so feeble a frame, that his attendants hardly expected his life for a single hour. The family dwelling was of humble architecture, situated in a retired but beautiful valley, and was surrounded by a small farm, which afforded but a scanty living to the widowed mother and her precious charge. The cut on page 144, Fig 30, represents the modest mansion, and the emblems of rustic life that first met the eyes of this pride of the British nation, and ornament of human nature. It will probably be found, that genius has oftener emanated from the cottage than from the palace.

This law asserts, first, that attraction reigns throughout the material world, affecting alike the smallest particle of matter and the greatest body; secondly, that it acts upon every mass of matter, precisely in proportion to its quantity; and, thirdly, that its intensity is diminished as the square of the distance is increased.

Observation has fully confirmed the prevalence of this law throughout the solar system; and recent discoveries among the fixed stars, to be more fully detailed hereafter, indicate that the same law prevails there. The law of universal gravitation is therefore held to be the grand principle which governs all the celestial motions. Not only is it consistent with all the observed motions of the heavenly bodies, even the most irregular of those motions, but, when followed out into all its consequences, it would be competent to assert that such irregularities must take place, even if they had never been observed.

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