Letters on Astronomy Part 6

Beside the change of place which these heavenly bodies undergo, in consequence of parallax, there is another, of an opposite kind, arising from the effect of the atmosphere, called _refraction_. Refraction elevates the apparent place of a body, while parallax depresses it. It affects alike the most distant as well as nearer bodies.

In order to understand the nature of refraction, we must consider, that an object always appears in the direction in which the _last_ ray of light comes to the eye. If the light which comes from a star were bent into fifty directions before it reached the eye, the star would nevertheless appear in the line described by the ray nearest the eye.

The operation of this principle is seen when an oar, or any stick, is thrust into water. As the rays of light by which the oar is seen have their direction changed as they pa.s.s out of water into air, the apparent direction in which the body is seen is changed in the same degree, giving it a bent appearance,--the part below the water having apparently a different direction from the part above. Thus, in Fig. 22, page 96, if S _a x_ be the oar, S _a b_ will be the bent appearance, as affected by refraction. The transparent substance through which any ray of light pa.s.ses is called a _medium_. It is a general fact in optics, that, when light pa.s.ses out of a rarer into a denser medium, as out of air into water, or out of s.p.a.ce into air, it is turned _towards_ a perpendicular to the surface of the medium; and when it pa.s.ses out of a denser into a rarer medium, as out of water into air, it is turned _from_ the perpendicular. In the above case, the light, pa.s.sing out of s.p.a.ce into air, is turned towards the radius of the earth, this being perpendicular to the surface of the atmosphere; and it is turned more and more towards that radius the nearer it approaches to the earth, because the density of the air rapidly increases near the earth.

[Ill.u.s.tration Fig. 22.]

Let us now conceive of the atmosphere as made up of a great number of parallel strata, as A A, B B, C C, and D D, increasing rapidly in density (as is known to be the fact) in approaching near to the surface of the earth. Let S be a star, from which a ray of light, S _a_, enters the atmosphere at _a_, where, being much turned towards the radius of the convex surface, it would change its direction into the line _a b_, and again into _b c_, and _c_ O, reaching the eye at O. Now, since an object always appears in the direction in which the light finally strikes the eye, the star would be seen in the direction O _c_, and, consequently, the star would apparently change its place, by refraction, from S to S', being elevated out of its true position.

Moreover, since, on account of the continual increase of density in descending through the atmosphere, the light would be continually turned out of its course more and more, it would therefore move, not in the polygon represented in the figure, but in a corresponding curve line, whose curvature is rapidly increased near the surface of the earth.

When a body is in the zenith, since a ray of light from it enters the atmosphere at right angles to the refracting medium, it suffers no refraction. Consequently, the position of the heavenly bodies, when in the zenith, is not changed by refraction, while, near the horizon, where a ray of light strikes the medium very obliquely, and traverses the atmosphere through its densest part, the refraction is greatest. The whole amount of refraction, when a body is in the horizon, is thirty-four minutes; while, at only an elevation of one degree, the refraction is but twenty-four minutes; and at forty-five degrees, it is scarcely a single minute. Hence it is always important to make our observations on the heavenly bodies when they are at as great an elevation as possible above the horizon, being then less affected by refraction than at lower alt.i.tudes.

Since the whole amount of refraction near the horizon exceeds thirty-three minutes, and the diameters of the sun and moon are severally less than this, these luminaries are in view both before they have actually risen and after they have set.

The rapid increase of refraction near the horizon is strikingly evinced by the _oval_ figure which the sun a.s.sumes when near the horizon, and which is seen to the greatest advantage when light clouds enable us to view the solar disk. Were all parts of the sun equally raised by refraction, there would be no change of figure; but, since the lower side is more refracted than the upper, the effect is to shorten the vertical diameter, and 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 seash.o.r.e; 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 a.s.sign to him a proportionally greater magnitude. If we view the sun, in the two positions, through a smoked gla.s.s, no such difference of size is observed; for here no objects are seen but the sun himself.

_Twilight_ is another phenomenon depending on the agency of the earth's atmosphere. It is that illumination of the sky which takes place just before sunrise and which continues after sunset. It is owing partly to refraction, and partly to reflection, but mostly to the latter. While the sun is within eighteen degrees of the horizon, before it rises or after it sets, some portion of its light is conveyed to us, by means of numerous reflections from the atmosphere. At the equator, where the circles of daily motion are perpendicular to the horizon, the sun descends through eighteen degrees in an hour and twelve minutes. The light of day, therefore, declines rapidly, and as rapidly advances after daybreak in the morning. At the pole, a constant twilight is enjoyed while the sun is within eighteen degrees of the horizon, occupying nearly two thirds of the half year when the direct light of the sun is withdrawn, so that the progress from continual day to constant night is exceedingly gradual. To an inhabitant of an oblique sphere, the twilight is longer in proportion as the place is nearer the elevated pole.

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 suns.h.i.+ne; every shadow of a pa.s.sing 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 ma.s.ses 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.[6] 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 a.s.sumes 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 a.s.sign its precise boundaries.

Being perfectly elastic, the lower portions, bearing as they do, the weight of all the ma.s.s 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 lat.i.tude.

Accordingly, this unusual clearness of the sky, when the stars s.h.i.+ne 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:

[6] Sir J. Herschel.

LETTER X.

THE SUN.

"Great source of day! best image here below Of thy Creator, ever pouring wide, From world to world, the vital ocean round, On Nature write, with every beam, His praise."--_Thomson._

THE subjects which have occupied the preceding Letters are by no means the most interesting parts of our science. They const.i.tute, 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.

The _distance_ of the sun from the earth is about ninety-five millions of miles. It may perhaps seem incredible to you, that astronomers should be able to determine this fact with any degree of certainty. Some, indeed, not so well informed as yourself, have looked upon the marvellous things that are told respecting the distances, magnitudes, and velocities, of the heavenly bodies, as attempts of astronomers to impose on the credulity of the world at large; but the certainty and exactness with which the predictions of astronomers are fulfilled, as an eclipse, for example, ought to inspire full confidence in their statements. I can a.s.sure you, my dear friend, that the evidence on which these statements are founded is perfectly satisfactory to those whose attainments in the sciences qualify them to understand them; and, so far are astronomers from wis.h.i.+ng to impose on the unlearned, by announcing such wonderful discoveries as they have made among the heavenly bodies, no cla.s.s of men have ever shown a stricter regard and zeal than they for the exact truth, wherever it is attainable.

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 s.h.i.+p, 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 s.h.i.+p, 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 s.h.i.+p, sailing at the same rate as before, would be ten years in pa.s.sing over the same s.p.a.ce.

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, const.i.tuted 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 quant.i.ty 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 quant.i.ty of matter is greater. Consequently, we might suppose, that the weight of a body (weight being nothing else than the measure of the force of gravity) 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 (so far as this cause operates) 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.

The sun turns on his own axis once in a little more than twenty-five days. This fact is known by observing certain dark places seen by the telescope on the sun's disk, called _solar spots_. These are very variable in size and number. Sometimes, the sun's disk, when viewed with a telescope, is quite free from spots, while at other times we may see a dozen or more distinct cl.u.s.ters, each containing a great number of spots, some large and some very minute. Occasionally, a single spot is so large as to be visible to the naked eye, especially when the sun is near the horizon, and the glare of his light is taken off. One measured by Dr. Herschel was no less than fifty thousand miles in diameter. A solar spot usually consists of two parts, the _nucleus_ and the _umbra_.

The nucleus is black, of a very irregular shape, and is subject to great and sudden changes, both in form and size. Spots have sometimes seemed to burst asunder, and to project fragments in different directions. The umbra is a wide margin, of lighter shade, and is often of greater extent than the nucleus. The spots are usually confined to a zone extending across the central regions of the sun, not exceeding sixty degrees in breadth. Fig. 23 exhibits the appearance of the solar spots. As these spots have all a common motion from day to day, across the sun's disk; as they go off at one limb, and, after a certain interval, sometimes come on again on the opposite limb, it is inferred that this apparent motion is imparted to them by an actual revolution of the sun on his own axis. We know that the spots must be in contact, or very nearly so, at least, with the body of the sun, and cannot be bodies revolving around it, which are projected on the solar disk when they are between us and the sun; for, in that case, they would not be so long in view as out of view, as will be evident from inspecting the following diagram. Let S, Fig. 24, page 106, represent the sun, and _b_ a body revolving round it in the orbit _a b c_; and let E represent the earth, where, of course, the spectator is situated. The body would be seen projected on the sun only while pa.s.sing from _b_ to _c_, while, throughout the remainder of its...o...b..t, it would be out of view, whereas no such inequality exists in respect to the two periods.

[Ill.u.s.tration Fig. 23.]

[Ill.u.s.tration Fig. 24.]

If you ask, what is the _cause_ of the solar spots, I can only tell you what different astronomers have supposed respecting them. They attracted the notice of Galileo soon after the invention of the telescope, and he formed an hypothesis respecting their nature. Supposing the sun to consist of a solid body embosomed in a sea of liquid fire, he believed that the spots are composed of black cinders, formed in the interior of the sun by volcanic action, which rise and float on the surface of the fiery sea. The chief objections to this hypothesis are, first, the _vast extent_ of some of the spots, covering, as they do, two thousand millions of square miles, or more,--a s.p.a.ce which it is incredible should be filled by lava in so short a time as that in which the spots are sometimes formed; and, secondly, the _sudden disappearance_ which the spots sometimes undergo, a fact which can hardly be accounted for by supposing, as Galileo did, that such a vast acc.u.mulation of matter all at once sunk beneath the fiery flood. Moreover, we have many reasons for believing that the spots are _depressions_ below the general surface.

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 s.p.a.ces occupied by some of the solar spots.

Dr. Herschel's views respecting the nature and const.i.tution 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 a.s.signs 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 enc.u.mbered with very serious objections. Clouds a.n.a.logous to those of our atmosphere (and the Doctor expressly a.s.serts that his lower stratum of clouds are a.n.a.logous to ours, and reasons respecting the upper stratum according to the same a.n.a.logy) 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 const.i.tution 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.

If we inquire whether the surface of the sun is in a state of actual combustion, like burning fuel, or merely in a state of intense ignition, like a stone heated to redness in a furnace, we shall find it most reasonable to conclude that it is in a state of ignition. If the body of the sun were composed of combustible matter and were actually on fire, the material of the sun would be continually wasting away, while the products of combustion would fill all the vast surrounding regions, and obscure the solar light. But solid bodies may attain a very intense state of ignition, and glow with the most fervent heat, while none of their material is consumed, and no clouds or fumes rise to obscure their brightness, or to impede their further emission of heat. An ignited surface, moreover, is far better adapted than flame to the radiation of heat. Flame, when made to act in contact with the surfaces of solid bodies, heats them rapidly and powerfully; but it sends forth, or _radiates_, very little heat, compared with solid matter in a high state of ignition. These various considerations render it highly probable to my mind, that the body of the sun is not in a state of actual combustion, but merely in a state of high ignition.

The solar beam consists of a mixture of several different sorts of rays.

First, there are the _calorific_ rays, which afford heat, and are entirely distinct from those which afford light, and may be separated from them. Secondly, there are the _colorific_ rays, which give light, consisting of rays of seven distinct colors, namely, violet, indigo, blue, green, yellow, orange, red. These, when separated, as they may be by a gla.s.s prism, compose the _prismatic spectrum_. They appear also in the rainbow. When united again, in due proportions, they const.i.tute white light, as seen in the light of the sun. Thirdly, there are found in the solar beam a cla.s.s of rays which afford neither heat nor light, but which produce chemical changes in certain bodies exposed to their influence, and hence are called _chemical_ rays. Fourthly, there is still another cla.s.s, called _magnetizing_ rays, because they are capable of imparting magnetic properties to steel. These different sorts of rays are sent forth from the sun, to the remotest regions of the planetary worlds, invigorating all things by their life-giving influence, and dispelling the darkness that naturally fills all s.p.a.ce.

But it was not alone to give heat and light, that the sun was placed in the firmament. By his power of attraction, also, he serves as the great regulator of the planetary motions, bending them continually from the straight line in which they tend to move, and compelling them to circulate around him, each at nearly a uniform distance, and all in perfect harmony. I will hereafter explain to you the manner in which the gravity of the sun thus acts, to control the planetary motions. For the present, let us content ourselves with reflecting upon the wonderful force which the sun must put forth, in order to bend out of their courses, into circular orbits, such a number of planets, some of which are more than a thousand times as large as the earth. Were a s.h.i.+p of war under full sail, and it should be required to turn her aside from her course by a rope attached to her bow, we can easily imagine that it would take a great force to do it, especially were it required that the force should remain stationary and the s.h.i.+p be so constantly diverted from her course, as to be made to go round the force as round a centre.

Somewhat similar to this is the action which the sun exerts on each of the planets by some invisible influence, called gravitation. The bodies which he thus turns out of their course, and bends into a circular orbit around himself, are, however, many millions of times as ponderous as the s.h.i.+p, and are moving many thousand times as swiftly.

LETTER XI.

ANNUAL REVOLUTION.--SEASONS

"These, as they change, Almighty Father, these Are but the varied G.o.d. The rolling year Is full of Thee."--_Thomson._

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 (sometimes in a circle) 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.