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orbit described are not in that ratio. The the gravitating power singly have caused it planets being at different distances from the to descend from B to y; and these two sun, perform their periodical revolutions in forces being duly proportioned, the planet different times: but it has been found that obeying them both will move in the circle the cubes of their mean distances are con- BYTV. But if, whilst the projectile force stantly as the squares of their periodical would carry the planet from B to b, the times; viz. of the times of their performing sun's attraction should bring it down from B their periodical revolutions. These two last to 1, the gravitating power would then be propositions were discovered by Kepler, by too strong for the projectile force, and would observations on the planets; but Sir Isaac cause the planet to describe the curve BC. Newton demonstrated, that it must have When the planet comes to C, the gravitating been so on the principle of gravitation, which power (which always increases as the square formed the basis of his theory. This law of of the distance from the sun, S, diminishes) universal attraction, or gravitation, disco. will be yet stronger for the projectile force, vered by Newton, completely confirms the and by conspiring in some degree therewith, system of Copernicus, and accounts for all will accelerate the planet's motion all the the phenomena which were inexplicable way from C to K, causing it to describe the on any other theory. The sun, as the arcs BC, CD, DE, EF, &c. all in equal largest body in our system, forms the centre times. Having its motion thus accelerated, of attraction, round which all the planets it thereby acquires so much centrifugal force, move; but it must not be considered as the or tendency to fly off at K, in the line K k, only body endued with attractive power, as overcomes the sun's attraction; and the for all the planets also have the property of centrifugal force being too great to allow the attraction, and act upon each other as well planet to be brought nearer to the sun, or as upon the sun. The actual point therefore even to move round him in the circle klm about which they move will be the common n, &c. it goes off, and ascends in the curve centre of gravity of all the bodies which are KLMN, &c. its motion decreasing as graincluded in our system; that is, the sun, dually from K to B as it increased from B with the primary and secondary planets. to K, because the sun's attraction now acts But because the bulk of the sun greatly ex against the planet's projectile motion just as ceeds that of all the planets put together, much as it acted with it before. When the this point is in the body of the sun. The at planet has got round to B, its projectile traction of the planets on each other also force is as much diminished from its mean somewhat disturbs their motions, and causes state as it was augmented at K; and so the some irregularities. It is this mutual attrac- sun's attraction being more than sufficient to tion between them and the sun that pre. keep the planet from going off at B, it devents them from flying off from their orbits scribes the same orbit over again by virtue by the centrifugal force which is generated of the same forces or powers. A double by their revolving in a curve, while the cen- projectile force will always balance a quatrifugal force keeps them from falling into . druple power of gravity. Let the planet at the sun by the force of gravity, as they B have twice as great an impulse from would do if it were not for this motion im- thence towards X as it had before; that is, pressed upon them. Thus these two powers in the same length of time that it was probalance each other, and preserve order and jected from B to b, as in the last example; regularity in the system. It is well known, let it now be projected from B to c, and it that if, when a body is projected in a straight will require four times as much gravity to line it be acted upon by another force, retain it in its orbit; that is, it must fall as drawing it towards a centre, it will be made far as from B to 4 in the time that the
pron to describe a curve, which will be either a jectile force would carry it from B to C, circle or an ellipsis, according to the pro- otherwise it would not describe the curve portion between the projectile and centri- BD, as is evident from the figure. But in petal force. If a planet at B(fig. 3, Plate II.) as much time as the planet moves from B to gravitates or is attracted towards the sun, C, in the higher part of its orbit, it moves S, so as to fall from B to y, in the time that from I to K or from K to L in the lower the projectile force would have carried it part thereof; because from the joint action from B to X, it will describe 'the curve BY of these two forces, it must always describe by the combined action of these two forces equal areas in equal times throughout its anin the same time that the projectile force dual course. These areas are represented singly would have carried it from B to X, or by the triangles BSC, CSD, DSE, ESF,
&c. whose contents are equal to one another rent semi-diameter, the altitude of the sun's from the properties of the ellipsis. We have centre was known. But the methods now now given a general idea of the solar system; adopted are much more accurate. In a we shall next describe the bodies that com known latitude, a large astronomical qua
drant, of six, eight, or ten feet radius, is Of the sun. The sun, as the most conspicuous fixed truly upon the meridian; the limb of this and most important of all the heavenly bodies, quadrant is divided into minutes and smalwould naturally claim the first place in the ler subdivisions by means of a vernier, and attention of astronomers. Accordingly its it is furnished with a telescope, having cross motions were first studied, and they have hairs, &c. turning properly upon the centre. had considerable influence on all the other By this instrument the altitude of the sun's branches of the science. That the sun has centre is very carefully measured, and the a motion of its own, independent of the appa- proper deductions made. The orbit in rent diurnal motion common to all the hea- which the sun appears to move is called the venly bodies, and in a direction contrary to ecliptic. It does not coincide with the that motion, is easily ascertained, by ob- equator, but cuts it, forming with it an angle, serving with care the changes which take which in the year 1769 was determined by place in the starry hemisphere during a com Dr. Maskelyne at 23° 28' 10", or 939.46944. plete year. If we note the time at which This angle is called the obliquity of the ecany particular star rises, we shall find that it liptic. rises somewhat sooner every successive day, It is known that the apparent motion of the till at last we lose it altogether in the west. sun in its orbit is not uniform. Observations, But if we note it after the interval of a year, made with precision, have ascertained, that we shall find it rising precisely at the same the sun moves fastest in a point of his orbit hour as at first. Those stars which are situated near the winter solstice, and slowest situated nearly in the track of the sun, and in the opposite point of his orbit near the which set soon after him, in a few evenings summer solstice. When in the first point, lose themselves altogether in his rays, and the sun moves in 24 hours 10.01943; in the afterwards make their appearance in the second point, he moves only 09.95319. The east before sunrise. The sun then moves daily motion of the sun is constantly vary. towards them in a direction contrary to his ing in every place of its orbit between these diurnal motion. It was by observations of two points. The medium of the two is this kind that the ancients ascertained his 09.98632, or 59' 11", which is the daily moorbit. But at present this is done with tion of the sun about the beginning of Ocgreater precision, by observing every day tober and April. It has been ascertained, the height of the sun when it reaches the that the variation in the angular velocity of meridian, and the interval of time which the sun is very nearly proportional to the elapses between his passing the meridian mean angular distance of it from the point and that of the stars. The first of these ob- of its orbit where its velocity is greatest. servations gives us the sun's daily motion It is natural to think, that the distance of northward or southward, in the direction of the sun from the earth varies as well as its the meridian ; and the second gives us his angular velocity. This is demonstrated by motion eastward in the direction of the pa- measuring the apparent diameter of the rallels; and by combining the two together sun. Its diameter increases and diminishes we obtain his orbit. The height of the sun in the same manner and at the same time from the horizon, when it passes the meri with its angular velocity, but in a ratio dian, on the arch of the meridian between twice as small. In the beginning of Jathe sun and the horizon, is called the sun's nuary his apparent diameter is about 39" altitude. The ancients ascertained the sun's 39", and at the beginning of July it is about altitude in the following manner :--They 31' 34", or more exactly, according to De erected an upright pillar at the south end of la Place, 32 35" =1955" in the first case, a meridian line, and when the shadow of it and 31' 18"=1878" in the second. Optiexactly coincided with that line, they accu cians have demonstrated, that the distance racely measured the shadow's length, and of any body is always reciprocally as its apthen, knowing the height of the pillar, they rent diameter. The sun must follow the found by an easy operation in plane trigo same law; therefore its distance from the nometry the altitude of the sun's upper earth increases in the same proportion that limb, whence, after allowing for the appa. its apparent diameter diminishes. In that
point of the orbit in which the sun is nearest constant emanation of heat and light, as an the earth, his apparent diameter is greatest, immense globe of fire. When viewed and his motion swiftest; but when he is in through a telescope several dark spots are the opposite point, both his diameter and visible on its surface, which are of various the rapidity of his motion are the smallest sizes and durations. From the motion of possible.
these spots the sun has been found to move To determine the distance of the sun round its axis, and its axis is found to be in. from the earth, has always been an interest- clined to the ecliptic. Various opinions have ing problem to astronomers, and they have been formed respecting these spots; they tried every method which astronomy or have been considered as opaque islands in geometry possesses in order to resolve it. the liquid igneous matter, and by some as The amplest and most natural is that which pits or cavities in the body of the sun. In mathematicians employ to measure distant 1788, Mr. King published a Dissertation on terrestrial objects. From the two extre the Sun, in which he advanced that the mities of a base whose length is known, the real body of the sun is less than its appaangles which the visual rays from the object, rent diameter ; that we never discern the whose distance is to be measured, make real body of the sup itself, except when we with the base, are measured by means of a behold its spots; that the sun is inhabited quadrant; their sum subtracted from 180° as well as our earth, and is not necessarily gives the angle which these rays form at the subject to burning heat, and that there is in object where they intersect. This angle is reality no violent elementary heat existing called the parallax, and when it is once in the rays of the sun themselves essentially, known it is easy, by means of trigonometry, but that they produce heat only when they to ascertain the distance of the object. Let come into contact with the planetary bodies. A B, in fig. 4, be the given baso, and C the Several years after this Mr. Herschel pubobject whose distance we wish to ascertain. lished his theory of the nature of the sun, The angles CAB and C B A, formed by the which is briefly as follows: he considers the rays CA and C B with the base, may be sun as a most magnificient habitable globe, ascertained by observation; and their sumn surrounded by a double set of clouds. Those subtracted from 180° leaves the angle ACB, which are nearest its opaque body are less which is the parallax of the object C. It bright, and more closely connected together gives us the apparent size of the base A B than those of the upper stratum, which as seen from C. When this method is ap- form the luminous apparent globe we bes plied to the sun, it is necessary to have the hold. This luminous external matter is of largest possible base. Let us suppose two a phosphotic nature, having several acciden. observers on the same meridian, observing tal openings in it, throngh which we see at the same instant the meridian altitude of the sun's body, or the more opaque clouds the centre of the sun, and his distance from beneath. These openings form the spots the same pole. The difference of the two that we see. distances observed will be the angle under Mercury. This planet being the nearest which the line which separates the observers to the sun, and the least in magnitude, is will be seen from the centre of the sun.
very seldom visible,
It never appears The position of the observers gives this line
few degrees from the sun's ia parts of the earth's radius. Hence, it is disc, and is generally lost in the splendor easy to determine, by observation, the an of the solar beams. On this account astrogle at which the semidiameter of the earth nomers have had few opportunities of makwould be seen from the centre of the sun. ing accurate observations upon it; no spots This angle is the the sun's parallax. But it have been observed upon it, consequently is too small to be determined with precision the time of its rotation on its axis is not by that method. We can only conclude known. Being an inferior planet it confrom it, that the sun's distance from the seqnently must shew phases like the moon; earth is at least equal to 10,000 diameters and it never appear's quite full to us. It is of the earth. Other methods have been seen sometimes passing over the sun's disc, discovered for finding the parallax with which is called its transit. much greater precision. It amounts very Venus is the brightest and largest to apnearly to 8.8 : hence it follows that the pearance of all the planets, and is distindistance of the sun from the earth amounts guished from the rest by her superiority of to at least 23.405 semidiameters of the earth. lustre. It is generally called the Morning
The sun was long considered, from its or Evening Star, according as it precedes or
follows the apparent course of the sun. would be necessary. Twilight is owing to Some have thought that they could discover the refraction of the rays of light by our spots upon its disc; but Herschel has not atmosphere through which they pass, and been able to see them ; consequently the which, by bending them, occasion some to time of rotation round its axis is not decid- arrive at a part of the earth that could not edly known. Venus also appears with receive any direct rays from the sun. It is phases, and transits sometimes take place; the annual motion of the earth round the which are of very great importance in sun which occasions the diversity of seasons. astronomy.
To understand this, we must observe what The Earth which we inhabit is as has been has been already mentioned, that the axis of proved, a globular body; it is not, however, the earth is inclined to the plane of its orbit a perfect sphere, but a spheroid, having its 234°, and it keeps always parallel to itself; equatorial diameter longer than the polar that is, it is always directed to the same diameter or axis. It is consequently flattest star. Let fig. 5, Plate II. represent the at the poles, and more protuberant at the earth in different parts of its elliptic orbit, equator. The diameter at the equator is In the spring the circle which separates the 7893 English miles; that at the pole is 7928 light from the dark side of the globe called miles. The surface of the earth is much the terminator, passes through the poles n,8, diversified with mountains and vallies, land as appears in the position A. The earth and water. The highest mountains in it then, in its diurnal rotation about its axis, are the Andes in South America, some of has every part of its surface as long in light which are about four miles in perpendicular as in shade; therefore the days are equal to altitude. About two-thirds of the globe is the nights all over the world ; the sun being covered with water. In consequence of the at that time vertical to the equatorial parts earth's being a globe, people standing upon of the earth. As the earth proceeds in its opposite sides of it must have their feet to- orbit and comes into the position B, the sun wards to each other. When in this situation becomes vertical to those parts of the earth they are called antipodes to each other. under the tropic, and the inhabitants of the Hence it appears that there is no real up or northern hemisphere will enjoy summer on down; for what is up to one country is accoumt of the solar rays falling more perdown to another. It must seem strange to pendicularly upon them; they will also bave those who are ignorant of the shape of the their days longer than their nights, in prothe earth, to suppose that if we could bore portion as they are more distant from the a hole downwards, deep enough, we should equator; and those within the polar circle, come to the other side of the world, where as will be perceived by the figure, will have we should find a surface and sky like our constant day-light. At the same time the own; yet if we reflect a moment we shall inhabitants of the southern hemisphere have perceive that this is perfectly true. As we winter, their days being shorter than their are preserved in our situations by the power nights, in proportion as they are farther from of attraction which draws us towards the the equator; and the inhabitants of the polar centre of the earth, we call that direction regions will have constant night. The earth down which tends to the centre, and the then continues its course to the position C, contrary. We mentioned before that the when the terminator again passes through earth has two motions, the one a diurnal the poles, and the days and nights are equal. motion round its own axis, the other an After this the earth advances to the position annual motion round the sun. It is the for- D, at which time the inhabitants of the mer which causes light and darkness, day and northern hemisphere have winter, and their night; for when one side of the earth is turned days are shorter than their nights. The towards the sun it receives his rays and is positions B and D are the solstitial points, illuminated, causing day; on the contrary, and A and C the equinoctial points; they when one side of the earth is turned from are not equidistant from each other, because the sun, we are in darkness, and then we the sun is not in the centre but in the focus have night. We see, therefore, by how of the ellipsis. In summer, when the earth much more simple means this change is is at B, the sun is farther from it than in the effected, than they imagined who supposed winter when the earth is at D; and in fact, that the earth was fixed, and that the im- the diameter of the sun appears longer in mense globe of the sun was whirled round winter than in summer. The difference of the earth with the amazing velocity that heat is not owing to the sun's being neares
to us, or more remote, but to the degree of The moon has scarcely any difference of obliquity with which its rays strike any part seasons ; her axis being almost perpendiof the earth.
cular to the ecliptic. What is very singuThe Moon is, next to the sun, the mostlar, one half of her has no darkness at all; remarkable of the celestial objects. Its form the earth constantly affording it a strong is spherical like that of the earth round, light in the sun's absence; while the other which it revolves, and by which it is carried half has a fortnight's darkness and a fortround the sun. Its orbit is also elliptical, night's light by turns. Our earth, as we having the earth in one of the foci of the have already observed, is undoubtedly a ellipsis. The moon always keeps the same moon to the moon ; waxing and waning side towards the earth, shewing only at one regularly, but affording her 13 times as time a little more of one side, and at another much light as she does us. When she time a little more of the other side. When changes to us, the earth appears full to her; the moon is viewed through a good teles- and when she is in her first quarter to us, cope, its surface appears covered with the earth is in its third quarter to her; and ridges, mountains, pits, and cavities of great vice versa. But from one half of the moon variety. Some parts of its surface also the earth is never seen at all: from the reflect less light than the rest. It has been middle of the other half, it is always seen conjectured that the part which reflects the over head ; turning round almost 30 times least light is water, and the brightest part as quick as the moon does. From the cirland. The heights of the lunar mountains cle which limits our view of the moon, only were formerly supposed to be much greater one half of the earth's side next her is seen ; than those of our earth ; but Dr. Herschel the other half being hid below the horizon has demonstrated that very few are more of all places on that circle. To her, the than half a mile high, and the highest little earth seems to be the biggest body in more than a mile. Several volcanos, or the universe. As the earth turns round burning mountains, have been discovered in its axis, the several continents, seas, and it. It has been doubted whether the moon islands, appear to the moon's inhabitants has an atmosphere like ours, but the latest like so many spots of different forms and observations appear to prove that it has. brightness, inoving over its surface; but The moon is seen by means of the light much fainter at sometimes than others, as which comes to it from the sun being re our clouds cover them or leave them. By flected from it. Its changes or phases de- these spots the Lunarians can determine the pend upon its situation relatively to the time of the earth's diurnal motion, just as earth and the sun. When the moon is in we do the motion of the sun : and perhaps opposition to the sun, the enlightened side they measure their time by the motion of is turned towards the earth, and it ap. the earth's spots; for they cannot have pears full ; when the moon is in conjunc- a truer dial. The moon's axis is so nearly tion with the sun, its dark side is turned perpendicular to the ecliptic, that the sun towards us, and it is invisible. As it never removes sensibly from her equator ; proceeds in its orbit, a small part of the and the obliquity of her orbit, which is next enlightened side is seen, and then we have to nothing as seen from the sun, cannot a new moon; and we continue to see more cause the sun to decline sensibly from her and more of the enlightened side, as the equator. Yet her inhabitants are not desmoon approaches to the state of opposition, titute of means for ascertaining the length or full moon. The waning, or decreasing of their year, though their method and ours of the moon takes place in the same man must differ. For we can know the length ner, but in a contrary order. The earth of our year by the return of our equinoxes ; must perform the same office to the moon but the Lunarians, having always equal day that the moon does to us; and it will ap- and night, must have recourse to another pear to the inhabitants of the moon (if there method; and we may suppose, they meabe any), like a very magnificent moon, sure their year by observing when either being to them about 13 times as big as of the poles of our earth begins to be enthe moon to us, and it will also have the lightened, and the other to disappear, which same changes or phases. The moon's mo is always at our equinoxes; they being contion is subject to many irregularities, on veniently situated for observing great tracts account of the inclination of its orbit to of land about our earth's poles, which are the plane of the ecliptic, and the attraction entirely unknown to us. Hence we may of the sun and the other planets.
conclude, that the year is of the same ah.