John Sv;ett From the collection of the 7 n z _ m o Prelinger i a Uibrary San Francisco, California 2006 ELEMENTARY CLASS BOOK ASTRONOMY: IN WTTTCH MATHEMATICAL DEMONSTRATIONS ARE OMITTED. BY H. N. ROBINSON, LL. D. FORMERLY PEOFESSOR OF MATHEMATICS IN THE UNITED STATES NAYY ; AUTHOR OF A TREATISE ON ARITHMETIC, ALGEBRA, GEOMETRY, TRIGONOMETRY, SURVEYING, CALCULUS, 40. 40. NEW YORK: IVISON, PHINNEY & CO, 48 & 50 WALKER STREET. CHICAGO: S. C. GRTGGS & CO., 39 & 41 LAKE ST. CINCINNATI : MOORK, WIL6TACH, KKY8 A CO. ST. LOUIS I KKITH If WOODS, PHILADELPHIA. : BOWKR, BARNES k CO. BUFFALO: PUINNET A OO. 1860. R B I N S O N'S The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of MATHEMATICAL TEXT-BOOKS ever issued in this country t Robinson's Progressive Table Book, IL Robinson's Progressive Primary Arithmetic,- - in. Robinson's Progressive Intellectual Arithmetic, - - - IV. Robinson's Rudiments of Written Arithmetic, V. Robinson's Progressive Practical Arithmetic, VL Robinson's Key to Practical Arithmetic, VIL Robinson's Progressive Higher Arithmetic, VIIL Robinson's Key to Higher Arithmetic, IX. Robinson's New Elementary Algebra, X. Robinson's Key to Elementary Algebra, ----. XI. Robinson's University Algebra, ------, XIL Robinson's Key to University Algebra, * XIII. Robinson's New University Algebra, - s XIV. Robinson's Key to New University Algebra, XV. Robinson's New Geometry and Trigonometry, -* XVI. Robinson's Surveying and Navigation, - XVII. Robinson's Analyt. Geometry and Conic Sections, - XVIII. Robinson's Differen. and Int. Calculus, (in preparation,)- XIX. Robinson's Elementary Astronomy, - - - v XX. Robinson's University Astronomy, - - - - - <- XXI. Robinson's Mathematical Operations, .-_- XXII. Robinson's Key to Geometry and Trigonometry, Conia Sections and Analytical Geometry, Entered, according to Act of Congress, in the year 1857, by HOEATIO N. KOBINSON, LL.D., In the Clerk's Office of the District Court of the United States for the Northern District of New York. PREFACE EVERY one strives to adapt means to ends, and when the author pre- pared his large work on Astronomy, he had no other end in view than to teach Astronomy to such as may be competent to the task and fully pre- pared to learn it. His first aim was to produce a book of the right tone and character, without any regard to the number of persons who might be prepared to use it. That effort was entirely successful, but the book is not adapted to the great mass of pupils, because it requires of the learner considerable mathematical knowledge, and a corresponding discipline of mind, therefore but few persons, comparatively speaking, feel qualified to study that book. At the same time a book of like tone, character, and spirit, is demanded by teachers for the use of their more humble pupils, except that it must be on a lower mathematical plane, and this book is de- signed to supply that demand. In this work we have omitted mathematical investigations almost alto- gether. Yet we have endeavored to retain the spirit of the University edition, and much of the plain matter of fact in that book is the same in this. Some of the more abstruse parts of the science are omitted, and some of the more simple and elementary parts are more enlarged upon in this book, than in that. Because we have avoided mathematical investigations, and attempted to adapt our work to the common qualifications of pupils, it must not be in- ferred that we have therefore made an easy text book, one which requires iv PREFACE. no particular attention on the part of the reader to comprehend. Astron- omy is no study for children the subject admits of no careless reading, and however good the book, and however well qualified the teacher, the student must take vigorous hold of the study for himself, and, in a mea- sure, take his own way to meet with success. Although this professes to be but a primary and elementary work, it contains more than a mere statement of astronomical facts, it deduces hid- den truths from primary observations, and endeavors to draw out the logi- cal powers of the reader and make him feel the true spirit of the science. Science properly learned is never forgotten, but science committed to memory soon evaporates, and science cannot be obtained from books and teachers alone, in addition to the materials, the original perceptions and reasoning powers of the learner, must come in with decided earnestness and force, and these remarks are particularly applicable to the science of Astronomy. We make these remarks to impress on the mind of the teacher the ne- cessity of giving perfectly sound instruction, and not be contented with memoritor recitations, or the mere accumulation of facts. For instance, the sun is nearer to the earth in January than in July, but this fact alone is not science, scarcely knowledge and it would be only a dead weight to the mind to crowd it into the memory : but when it is ascertained how we know this fact, from what observation it was deduced, and what logical induction was applied, then it becomes another matter, then it is science, and thus learned, could never be lost. Some elementary works on Astronomy put great stress on pictorial illus- trations, but at best such illustrations are little better than caricatures, and some of them give incorrect impressions ; for instance, in attempting to show the relative motions of the sun and moon in space, by a figure, the moon's motion is generally represented as describing loops, when the true motion is progressively onward, and at all times concave towards the sun. PREFACE. r The difficulty of giving true representations on paper, in Astronomy, is so great that the teacher should be careful so to guide the perceptions of the learner, that they be more truthful and refined than the figure can possibly be, or the learner will draw distorted if not erroneous impressions from them. For instance, if we wished to make a correct representation of the sun, earth, and moon, and made the earth but one-eighth of an inch in diameter, the diameter of the moon's orbit must be 7j^ inches, the diame- ter of the moon the 32d part of an inch, the diameter of the earth's orbit 3000 inches, or 250 feet, and the diameter of the sun must cover 14 inches. These considerations show the utter impossibility of making correct as- tronomical representations on paper, for who would have the earth drawn out less than one-eighth of an inch in diameter, and even that small mag- nitude would require a sheet two hundred and fifty feet wide, on which none of the exterior planets could be drawn. For these reasons we do not place as much value on pictorial representations and astronomical maps as many do, and whenever we make use of such things, as we sometimes do, we take much care that the impressions drawn from them, are not as gross as the representations themselves. In conclusion, we would remind the reader that the subject of Astronomy is so vast and magnificent, that it is almost as impossible to do justice to it in composition as it is in geometrical diagrams. We have made no pre- tensions to delineate the high mental satisfaction that a knowledge of this science imparts ; we have only attempted to guide others in attaining that knowledge, and in this particular we do not claim to have made a perfect book, far from it, perfection is impossible, decidedly so, when applied to a book ; and if all books were perfect, there would be little need of schools and teachers. CONTENTS. SECTION I. CHAPTER I. PAGE. Introduction , 11 Definition of terms 1217 CHAPTER II. Preliminary observations 18 The north pole in the heavens the fixed point 19 Circumpolar stars 21 A definite index for the length of years 24 Wandering stars 25 CHAPTER HI. Fixed stars landmarks, ) on the 22d of August. The foregoing are called northern signs, because the sun must have north declination while the sun is in them. The following are designated as the southern signs of the Does the ecliptic intersect the equator ? At what angle ? "What point in the heavens is called the Vernal Equinoz ? What is the Zodiac ? What is meant by the signs of the Zodiac ? When does the sun enter the first sign of the Zodiac ? INTRODUCTION'. 17 zodiac, because the sun must have south declination while he is in them : The sun enters Libra (LTU) on the 23d of September; Scorpio (If) ) on the 22d of October ; Sagittarius (^() on the 22d of November ; Capricornus (/) on the 21st of December ; Aqua- rius (*) on the 20th of January ; and Pisces (^() on the 19th of February. Passing through this last sign the sun again enters (p) on the 20th of March, to perform the revolution over again, and thus it goes on year by year. The zodiac and signs of the zodiac being but the offspring of astrology and heathen mythology, they are entirely dis- carded by modern astronomers ; yet they still linger in country almanacs and in many school books, and it is with reluctance that we even mention them. They are of no use, even as points of reference, and they embrace no scientific principle whatever. Conjunction. When two celestial bodies have the same lon- gitude, they are said to be in conjunction. When two celestial bodies have the same right ascension, that is, come to the meridian at the same time, they are said to be in conjunction in right ascension. Opposition. When two celestial bodies have a difference of longitude of 180 degrees, they are said to be in opposition. Direct. Direct, in astronomy, is a motion to the eastward among the stars. Retrograde. Retrograde is a motion to the westward among the stars. Stationary means apparently so in respect to the stars. Other terms not here mentioned will be explained as we use them. Why are some of the signs called northern, and others southern signs ? Is the distinction of signs necessary ? What is meant by conjunction ? By opposition ? What by direct ? Retrograde ? 2 18 ELEMENTARY ASTRONOMY. CHAPTER II. PRELIMINARY OBSERVATIONS. To commence the study of astronomy, we must observe and call to mind the real appearance of the heavens. Take such a station, any clear night, as will command an extensive view of that apparent, concave hemisphere above us, which we call the sky, and fix well in the mind the directions of north, south, east, and west. At first, let us suppose the observer to be somewhere in the United States, or somewhere in the northern hemisphere, about 40 degrees from the equator. Soon he will perceive a variation in the position of the stars : those at the east of him will apparently rise ; those at the west will appear to sink lower, or fall below the horizon ; those at the south, and near his zenith, will apparently move westward ; and those at the north of him, which he may see about half way between the horizon and the zenith, will appear stationary. Let such observations be continued during all the hours of the night, and for several nights, and the observer cannot fail to be convinced that not only all the stars, but the sun, moon, and planets, appear to perform revolutions, in about twenty- four hours, round a fixed point; and that fixed point, as ap- pears to us (in the middle and northern part of the United States), is about midway between the northern horizon and the zenith. It should always be borne in mind that these motions are How can a person convince himself that some of the stars have an appa- rent motion from east to west, like the sun in the day time ? Do all the stars have such an apparent motion, as seen from this place ? What stars do not? PRELIMINARY OBSERVATIONS. 19 but apparent, the stars keeping the same positions with respect to each other, whether they are rising or falling, or north or south of the observer, and the general aspect of the heavens is the same now, as it was in the very earliest ages of astronomy, and will be the same in ages to come. All the heavenly bodies, whether sun, moon, planets, or stars, appear to have a diurnal motion round a fixed point, and all those stars which are 90 degrees from that point, appa- rently describe a great circle. Those stars which are nearer to the fixed point than 90 degrees, describe smaller circles; and the circles are smaller and smaller as the objects are nearer and nearer infixed point. There is one star so near this fixed point, that the small cir- cle, it describes, in about 24 hours, is not apparent from mere inspection. To detect the apparent motion of this star, we must resort to nice observations, aided by mathematical in- struments. This fixed point, that we have several times mentioned, is the North Pole of the heavens, and this one star that we have just mentioned, is commonly called the North Star, or the Pole Star. As the North Star appears stationary, to the common ob- server, it has always been taken as the infallible guide to direction; and every sailor of the ocean, and every wanderer of the African and Arabian deserts, has held familiar acquain- tance with it. If our observer now goes more to the southward, and makes the same observations on the apparent motions of the stars, he will find the same general results ; each individual star will describe the same circle ; but the pole, the fixed point, will be lower down, and nearer to the northern horizon ; and it will be Those stars that do not rise and set, what motion, real or apparent, do they have ? Is any star apparently stationery ? Is there a star just at the north pole ? What use has been made of the north star ? If a person should go south from this place, what apparent effect would that have on the north star, as viewed by him ? 20 ELEMENTARY ASTRONOMY. lower and lower in proportion to the distance the observer goes to the south. After the observer has gone sufficiently far, the fixed point, the pole, will no longer be up in the heavens, but down in the northern horizon ; and when the pole does appear in the horizon, the observer is at the equator, and from that line all the stars at or near the equator appear to rise up di- rectly from the east, and go down directly to the west ; and all other stars, situated out of the equator, describe their small circles parallel to this perpendicular equatorial circle. If the observer goes south of the equator, the north pole will sink below his horizon, and the south polar point will appear to rise up above his horizon, and it will rise more and more as he goes farther and farther south ; and if he could possibly get to the south pole on the earth, the south pole of the apparent revolving heavens would be right over his head, and the equa- tor of the heavens would bound his horizon. In a similar manner if an observer goes north, the north pole to him would appear to rise in the heavens; and should he con- tinue to go north, he would finally find the pole in his zenith, and all the stars would apparently make circles round the zenith, as a center, and parallel to the horizon ; and the horizon itself would be the celestial equator. When the north pole of the heavens appears at the zenith, the observer must then be at the north pole, on the earth, or at the latitude of 90 degrees. Any celestial body, which is north of the equator, is always visible from the north pole of the earth ; hence, the sun, which is north of the equator from the 20th of March to the 23d of September, must be constantly visible during that period, in a clear sky. Just as the sun comes north of the equator, its diurnal pro- gress, or rather, the progress of 24 hours, is around the horizon. When the sun's declination is 10 degrees north of the equator, What is the apparent diurnal motion of the stars, as seen from the equa- tor ? What from the south pole ? What part of the heavens bounds the horizon as seen from the south pole ? What from the north pole ? PRELIMINARY OBSERVATIONS. 21 the progress of the sun, in 24 hours, as seen from the north pole, is around the horizon at an altitude of about 10 degrees ; and so on for any other degree. From the north pole, all directions on the surface of the earth are south. North, strictly speaking, would be in a vertical direction, which would make the absolute south directly down towards the center of the earth. We have observed that the pole of the heavens rises as we go north, and sinks toward the horizon as we go south ; and when we observe that the pole has changed its position one degree, in relation to the horizon, we know that we must have changed place one degree on the surface of the earth. Now we know by observation, that if we go north about 69 English miles on the earth, the north pole will be one degree higher above the horizon. Therefore 69 miles corresponds to one degree, on the earth ; and hence, the whole circumference of the earth must be 69^ multiplied by 360 : for there are 360 degrees to every circle. This gives 24,930 miles for the cir- cumference of the earth, and 7,930 miles for its diameter, which is not far from the truth. Here, in the United States, or anywhere either in Europe, Asia, or America, north of the equator, say in latitude 40 de- grees, the north pole of the heavens must appear at an altitude of 40 degrees above the horizon ; and as all the stars and heavenly bodies apparently circulate round this point as a center, it follows that all those stars which are within 40 degrees of the pole, can never go below the horizon, but circulate round and round the pole. All those stars which never go below the horizon, are called circumpolar stars. At the north, and very near the north pole, the sun is a cir- compolar body while it is north of the equator, and it is a Describe the apparent diurnal motion of the sun from the north pole when its declination is 15 degrees north ? How far must we go north or south on the earth to change the apparent altitude of the pole one degree ? What does that show ? What is meant by circumpolar stars ? Would the term circumpolar apply if the observer were at the equator ? 22 ELEMENTARY ASTRONOMY. circumpolar body as seen from the south pole, while it is south of the equator ; this gives six months day and six months night, at the poles. North of latitude 66 degrees, and when the sun's decima- tion is more than 23 degrees north (as it is on and about the 20th of June in each year), then the sun comes at, or very near, the northern horizon, at midnight ; it is nearly east, at 6 o'clock in the morning; it is south, at noon, and about 46 de- grees in altitude ; and is nearly west at 6 in the afternoon. In all latitudes and from all places on the earth, the sun is observed to circulate round the nearest pole, as a center ; and when the sun is on the same side of the equator as the obser- ver, more than half of the sun's diurnal circle is above the ho- rizon, and the observer will have more than 12 hours sunlight. When the sun is on the equator, the horizon, of every lati- tude, cuts the sun's diurnal circle into two equal parts, and gives 12 hours day and 12 hours night, the world over. When the sun is on the opposite side of the equator from the observer, the smaller segment of the sun's diurnal circle is above the horizon, and, of course, gives shorter days than nights. We have, thus far, made but rude and very imperfect ob- servations on the apparent motion of the heavenly bodies, and have satisfied ourselves only of two facts : 1st. That all the stars, sun, moon, and planets, included, apparently circulate round the pole, and round the earth, in a day, or in about 24 hours. 2d. That the sun comes to the meridian, at different alti- tudes above the horizon, at different seasons of the year, giv- ing long days in June, and short days in December, in all northern latitudes. Describe the appearance of the sun, during 24 hours, as seen from latitude 66 degrees north, when the sun's declination is 23 degrees nortl. Describe the diurnal appearance of the sun, as seen from the north pole, when the sun is on the equator, when its declination is 13 degrees ncrth. What two facts are thus far established ? PRELIMINARY OBSERVATIONS. 23 Let us now pay attention to some other particulars. Let us look at tbe different groups of stars, and individual stars, so that we can recognize them night after night. By a little systematic observation, which we shall describe a little further on, or even without any particular system of observation, almost any one is able to recognize certain stars, or groups of stars, such as the Seven Stars, the Belt of Orion, Aldebaran, Sirius, and the like, and having likewise the use of a clock, he can observe when any particular star comes to any definite position. Let a person place himself at any particular point, to the north of any perpendicular line, as the edge of a wall or build- ing, and let him observe the stars as they pass behind the building, in their diurnal motions from the east to the west. For example, let us suppose that the observer is watching the star Aldebaran, and that, when the eye is placed in a particu- lar definite position, the star passes behind the building at exactly 8 o'clock. The next evening, the same star will come to the same point about 4 minutes before 8 o'clock ; and it will not come to the same point again, at 8 o'clock in the evening, until after the expiration of one year. But in any year, on the same day of the month, and at the same hour of the day, the same star will be at, or very near, the same position, as seen from the same point. For instance, if certain stars come on the meridian at a par- ticular time in the evening, on the first day of December, the same stars will not come on the meridian again, at the same time of the night, until the first day of the next December. On the first of January, certain stars come to the meridian at midnight ; and (speaking loosely) every first of January the same stars come to the meridian at the same time ; and there Does the same fixed star come to the meridian at the same hour every night ? Does it come to the meridian earlier or later ? If a star come to the meridian at 1 o'clock in the evening any particular night, when will it come to the meridian again at the same time in the evening ? 24 ELEMENTARY ASTRONOMY. will be no other day during the whole year, when the same stars will come to the meridian at midnight. Thus, the same day of every year is observed to have tho same position of the stars at the same hour of the night ; and this is the most definite index for the expiration of a year. The year is also indicated by the change of the sun's decli- nation, which the most careless observer cannot fail to notice. On the 21st of June, the sun declines about 23 degrees from the equator towards the north ; and, of course, to us in the northern hemisphere, its meridian altitude is so much greater, and the horizontal shadows it casts from the same fixed objects will be shorter ; and the same meridian altitude and short shadow will not occur again until the following June, or after the expiration of one year. Thus, we see, that the time of the stars coming on to the meridian, and the declination of the sun, have a close corres- pondence, in relation to time. In all our observations on the stars, we notice that their apparent relative situations are not changed by their diurnal motions. In whatever parts of their circles they are observed, or at whatever hour of the night they are seen, the same con- figuration is recognized, although the same group, in the dif- ferent parts of its course, will stand differently, in respect to the horizon. For instance, a configuration of stars resembling the letter A, when east of the meridian, will resemble the let- ter V, when west of the meridian. As the stars, in general, do not change their positions in respect to each other, they are called faed stars ; but there are a few important stars that do change, in respect to other stars ; and for that reason they become especial objects of attention, and form the most interesting portion of astronomy. In the earliest ages, those stars that changed their places, What is the most definite index of the expiration of a year ? What other index is there of the expiration of a year ? Do the stars change their configuration really or apparently while performing their diurnal circles ? Explain. PRELIMINARY OBSERVATIONS. 26 were called wandering stars; and they were subsequently found to be the planetary bodies of the solar system, like the earth on which we live ; or rather, the earth on which we live, after strict investigation, was found to be a planet belonging to that class of wandering stars ; and this striking fact gives to astron- omy much of its sublimity and importance. In a subsequent part of this work we hope to be able to explain to the general reader how science developed this and other facts, but at pre~ sent they must all be taken on authority. The fixed stars come to the meridian at intervals of 23h. 56m. 4.09s. of mean soler time, and if any star should be observed coming to the meridian at a greater interval of time, then that star could not be a fixed star, but a planet, or comet, whose motion was then eastward. But if the interval be less than 23h. 56m. 4.09s., the star is then wandering towards the west, and is said to be retrograding. The planets of our system, sometimes wander eastward sometimes westward and sometimes they appear stationary ; but the eastward motion prevails, and all the planets appear to make revolutions round the earth from west to east. The apparent irregularities of their motions, are perfectly natural results, arising from the motion of the earth round the sun; and these facts are brought in to show that the earth does revolve round the sun, and is, in fact, a planet. To study astronomy properly, it is not sufficient to read it off the pages of a book ; we must read it off of the face of the sky ; and before we can do that, we must be better acquainted with the face of the sky utan we are at present, and that will be the object of the following chapter. What stars became objects of special attention to the ancients ? Is tLe earth one of a class of stars ? Was this known in an early day ? 26 ELEMENTARY ASTRONOMY. CHAPTER III. THE FIXED STARS AS CELESTIAL LOCALITIES THE fixed stars are the only landmarks in astronomy, in respect to both time and space. They seem to have been thrown about in irregular and ill-defined groups and clusters, called constellations. The individuals of these groups and clusters differ greatly as to brightness, hue, and color ; but they all agree in one attribute a high degree of permanence, as to their relative positions in the group ; and the groups are as permanent in respect to each other. This has procured them the title of fixed stars; an expression which must be understood in a comparative, and not in an absolute, sense ; for, after long investigation, it is ascertained that some of them, if not all, are in motion ; although too slow to be percep- tible, except by very delicate observations, continued through a long series of years. The stars are also divided into different classes, according to their degree of brilliancy, called magnitudes. There are six magnitudes, visible to the naked eye ; and ten telescopic mag- nitudes in all, sixteen. The brightest are said to be of the first magnitude ; those less bright, of the second magnitude, etc.; the sixth magnitude is just visible to the naked eye. The stars are very unequally distributed among these classes; nor do all astronomers agree as to the number belonging t-> each ; for it is impossible to tell where one class ends and another begins ; nor is it important, for all this is but a matter of fancy, involving no principle. In the first magnitude there "What are constellations ? In what sense should we apply the term fixed stars ? What is meant by the magnitude of a star ? How many classes of magnitudes are there ? Can we define where one class of magnitudes begins or ends ? THE FIXED STARS. 27 is really but one star (Sirius) ; for this is manifestly brighter than any other ; but most astronomers put fifteen or twenty into this class. The second magnitude includes from fifty to sixty ; the third about two hundred, the numbers increasing very rapidly, as we descend in the scale of brightness. From some experiments on the intensity of light, it has been determined, that if we put the light of a star, of the average 1st magnitude, 100, we shall have: 1st magnitude =100 4th magnitude = 6 2d " = 25 5th " = 2 3d " = 12 6th " = 1 On this scale, Sir William Herschel placed the brightness of Sirius at 320. Ancient astronomy has come down to us much tarnished with superstition and heathen mythology. Every constellation bears the name of some pagan deity, and is associated with some absurd and ridiculous fable; yet, strange as it may appear, these masses of rubbish and ignorance these clouds and fogs, intercepting the true light of knowledge, are still not only retained, but cherished, in many modern works, and dig- nified with the name of astronomy.* * As a specimen of what was once called astronomy, and is even now studied for astronomy in some female boarding schools, we give the follow- ing extracts, taken from Keith on the globes. To say nothing of other branches of knowledge, we congratulate the learner that ancient fables no longer obscure astronomy. " COMA BERENICES is composed of the unformed stars, between the Lion's tail and Bootes. Berenice was the wife of Evergetes, a surname signifying benefactor : when he went on a dangerous expedition, she vowed to dedi- cate her hair to the goddess Venus, if he returned in safety. Sometime after the victorious return of Evergetes, the locks which were in the temple of Venus, disappeared ; and Conon, an astronomer, publicly reported that Jupiter had carried them away, and made them a constellation. " COR. CAROLI, or Charles's heart, in the neck of Chara, the southernmost of the two dogs held in a string by Bootes, was so" denominated by Sir Charles Scarborough, physician to king Charles II, in honor of King Charles I." How many stars are there in the first magnitude ? What is said of ar cieut superstition, and mythology ? 28 ELEMENTAKY ASTRONOMY. Merely as names, either to constellations or to individual stars, we shall make no objections ; and it would be useless, if we did ; for names long known, will be retained, however im- proper or objectionable ; hence, when we speak of Orion, the Little Dog, or the Great Bear, it must not be understood that we have any great respect for mythology. It is not our object now to give any very minute or scien- tific description of the starry heavens such as pointing out the variable, double, and multiple stars the Milky Way, and nebulce; these will receive special attention in somo future chapter : at present, our only aim is to point out the method of obtaining a knowledge of the mere appearance of the sky, to the common observer, which may be called the geography of the heavens. To give a person an idea of locality, on the earth, we refer to points and places supposed to be known. Thus, when we say that a certain town is 15 miles northwest of Boston, or that a ship is 100 miles east of the Cape of Good Hope, or that a certain mountain is 10 miles north of Calcutta, we have a pretty definite idea of the locality of the town, the ship, and the mountain, on the face of the earth, provided we have a clear idea of the face of the earth, and know the position of Boston, the Cape of Good Hope, and Calcutta. So it is with the geography of the heavens ; the apparent surface of the whole heavens must be in the mind, and then the localities of certain bright stars must be known, as land- marks, like Boston, the Cape of Good Hope, and Calcutta. We shall now make some effort to point out these landmarks. The North Star is the first, and most important to be recog- nized ; and it can always be known to an observer, in any northern latitude, from its stationary appearance and altitude ; which is never more than one and a half degrees from the lati- tude of the observer. Thus, a person in 10 north latitude, How does the author regard mythology? What is meant by the geography of the heavens? What star is the most important to be recog- nized ? How can it be kuowu ? THE FIXED STARS. 29 will find the north star very nearly in a northern direction, between 8 and 12 above the northern horizon. An observer in 25 north latitude, will find the north star nearly north in direction, and between 24 and 26 of altitude, and so on for any other northern latitude. It is by such observations on the north star, that latitude can be found. When the influence of refraction is allowed for, the latitude of a place is midway between the greatest and least altitudes of the north star. We have here attempted to make a faint representation of the region about the north pole to the distance of 40. The hours are hours of right ascension in the heavens. - The pole star is nearly (not exactly) in the center of this circle. Directly What star is always very nearly north? What is the latitude of any place in the northern hemisphere equal to? SO ELEMENTARY ASTRONOMY. opposite the cup or Great Bear, is the constellation Cassiopea. E is the position of the pole of the ecliptic, and a little south of E, in right ascension, about 18 hours, is the constellation called the Dragon or Draco. At the distance of about 32 de- grees from the pole, are seven bright stars, between the 1st and 2d magnitudes, forming a figure resembling a dipper, four of them forming the cup, and three the handle. They occupy a space between the right ascension of lOh. 45m. and 13h. 40m. The two stars forming the sides of the cup, opposite to the han- dle, are always in a line with the North Star, and are therefore called pointers : they always point to the North Star. The line joining the equinoxes, or the first meridian of right ascension, runs from the pole, between the other two stars forming the cup. The first star in the handle, nearest the cup, is called Alloth, the next Mizar, near which is a small star, of the 4th magnitude ; the last one is Benetnasch. The stars in the han- dle are said to be in the tail of the Great Bear. About four degrees from the pole star, is a star of the 3d magnitude, S Ursce Minoris. A line drawn through the pole (not pole star) and this star, will pass through, or very near, the poles of the ecliptic and the tropics. A small constellation, near the pole, is called Ursa Minor, or the Little Bear. An irregular semicircle of bright stars, between the dipper and the pole, is called the Serpent. If a line be drawn from Ursce Minoris, through the pole star, and continued about 45 degrees, it will strike a very beau- tiful star, of the 1st magnitude, called Capetta. Within five degrees of Capella are three stars, of about the 4th magnitude, forming a very exact isosceles triangle, the vertical angle about 28 degrees. A line drawn from Alioth, through the pole star, and continued about the same distance on the other side, passes through a cluster of stars called Cassiopea in her chair. The Why are two certain stars called pointers V What small constellation is near the north pole ? What stars are in the handle of the cup, or in the tail of the Great Bear ? THE FIXED STARS. 31 principal star in Cassiopea, with the pole star and Capella, form an isosceles triangle, Capella at the vertex. More attention has been paid to the constellations along the equator and ecliptic, than to others in remoter regions of the heavens, because the sun, moon, and planets, apparently traverse through them. There are nine bright stars near the ecliptic, which are used by seamen, in connection with the position of the moon, to find longitude from, and for this reason these stars are called lunar stars. Their proper names are Arietis, Aldebaran, Pollux, Reg- ulus, Spica, Antares, Aquilce, Fomalhaut, and Pegasi. Beginning with the first point of Aries as it now stands, no prominent stars are near it ; and, going along the ecliptic to the eastward, there is nothing to arrest special attention, until we come to the Pleiades, or Seven Stars, though only six are visible to the naked eye. This little cluster is so well known, and so remarkable, that it needs no description. Southeast of the Seven Stars, at the distance of about 18 degrees, is a remark- able cluster of stars, said to be in the Bull's Head ; the largest star in this cluster is of the 1st magnitude, of a red color, called Aldebaran. It is one of the nine stars selected as points from which to compute the moon's distance, for the assistance of navigators. This cluster resembles an A when east of the meridian, and a V when west of it. The Seven Stars, Aldebaran, and Capella, form a triangle very nearly isosceles Capella at the vertex. A line drawn from the Seven Stars, a little to the west of Alde- baran, will strike the most remarkable constellation in the heavens, Orion, (it is out of the zodiac however) ; some call it the Ell and Yard. The figure is mainly distinguished by three stars in one direction, within two degrees of each other ; and two other stars, forming, with one of the three first mentioned, another line at right angles with the first line. Why are certain stars called lunar stars ? Is there any star near the first point of Aries ? What is meant by the first point of Aries ? What bright star is about 18 southeast of the Seven Stars ? How would you find Orion on seeing the Seven Stars and Aldebaran ? 32 ELEMENTARY ASTRONOMY. The five stars thus in lines, are of the 1st or 2d magnitude. A line from the Seven Stars, passing near Aldebaran and through Orion, will pass very near to Sirius, the most brilliant star in the heavens. The ecliptic passes about midway between the Seven Stars and Aldebaran, in nearly an eastern direction. Nearly due east from the northernmost and brightest star in Orion, and at the distance of about 25 degrees, is the stai Procyon ; a bright, lone star. The northernmost star in Orion, with Sirius and Procyon, form an equilateral triangle. Directly north of Procyon, at the distances of 25 or 30 degrees, are two bright stars, Castor and Pollux. Castor is the most northern. Pollux is one of the nine lunar stars. Thus we might run over that portion of the heavens which is ever visible to us, and by this method every student of astro- nomy can render himself familiar with the aspect of the sky ; but it is not sufficiently definite and scientific to satisfy a ma- thematical mind. The only scientific method of defining the position of a place on the earth, is to mention its latitude and longitude; and this method fully defines any and every place, however unimpor- tant and unfrequented it may be : so in astronomy, the only scientific method of defining the position of a star, is to men- tion its latitude and longitude, or, more conveniently, its riyld ascension and declination. It is not sufficient to tell the navigator that a coast makes off in such a direction from a certain point, and that it is so far to a certain cape ; and, from one cape to another, it is about 40 miles south-west he would place very little reliance on any such directions. To secure his respect, and command hi& confidence, the latitude and longitude of every point, promon- tory, river, and harbor, along the coast, must be given ; and then he can shape his course to any point, or strike in upon it What three bright stars form an equilateral triangle ? Where is Castor and Pollux ? What is the scientific method of defining a place on the earth ? What of locating a star in the heavens ? THE FIXED STARS. 33 from the indefinite expanse of a pathless sea. So with an astronomer ; while he understands and appreciates the rough aud general descriptions, such as we have just given, he re- quires the certain description, comprised in right ascension and declination. . Accordingly, astronomers have given the right ascensions and declinations of every visible star in the heavens (and of very many that are invisible), and arranged them in tables, in the order of right ascension. There are far too many stars, for each to have a proper name ; and, for the sake of reference, Mr. John Bayer, of Augsburg, in Suabia, about the year 1603, proposed to denote the stars by the letters of the Greek and Roman alphabets ; by placing the first Greek letter a to the principal star in the constellation, /? to the second in magnitude, /to the third, and so on ; and if the Greek alphabet shall become exhausted, then begin with the Roman, a, b, c, etc. " Catalogues of particular stars, in sections of the heavens, have been published by different astronomers, each author numbering the individual stars embraced in his list, according to the places they respectively occupy in the catalogue." These references to particular catalogues are sometimes marked on celestial globes, thus : 79 H, meaning that the star is the 79th in HerschePs catalogue ; 37 M, signifies the 37th num- ber in the catalogue of Mayer, etc. Among our tables will be found a catalogue of a hundred of the prii cipal stars, inserted for the purpose of teaching a definite and sci ntific method of making a learner acquainted with the geograp ly of the heavens, which will be given in another chapter. What did John Bayer propose ? How are stars, in sectional catalogues, referm to? 34 ELEMENTARY ASTRONOMY. CHAPTER IV. TIME AND THE MEASURE OF TIME. TIME is but a measured portion of unlimited duration and it is measured off, directly or indirectly^ by astronomical events. The most obvious astronomical event is that of a natural day, from sunrise to sunset, or from sunrise to sunrise again, but as these intervals are variable in length, they are not proper standards for time. The interval embracing the four seasons of the year, is another astronomical period which serves to measure time on a large and indefinite scale. The interval from full moon to full moon again, is also an astronomical period, but after careful observation, it has been found to be a period of variable duration ; and, moreover, it is impossible for the unlearned to define the moment when such an interval begins or ends, therefore this period is use- less, as a measure of time and none but savages pretend to use it as such. For a standard of measure, we must find, if possible, some invariable period that can be distinctly defined. In the early ages of astronomy, the interval from noon, to noon again, was considered a constant interval, and taken for the measure of time, and for the common business of the world, this will be the standard for time, because it is the most obvious, natu- ral, and convenient. But after close investigation and careful observations, this interval was found to be slightly variable, and another interval, the passage of a fixed star from the meri- dian to the meridian again, was found to be a constant interval, therefore this interval is taken a* the standard measure of time. What is time ? What is an astronomical event ? Is from noon to noon, by the sun, an invariable interval of time? What astronomical events mark equal intervals of time ? TIME AND THE MEASURE OF TIME. 35 The interval from one passage of a star across the meridian, to the next, is a sidereal day, and measured by the common solar clock, the interval is 23h. 56m. 4.09s. No matter what star is observed, the interval is the same, and as this has been the universal experience of astronomers in all ages, it com- pletely establishes the fact, that all the fixed stars come to the meridian in exactly equal intervals of time ; and this gives us a standard measure for time, and the only standard measure, for all other motions are variable and unequal. Again, this interval must be the time that the earth employs in turning on its axis ; for if the star is fixed, it is a mark for the time, that the meridian is in exactly the same position in relation to absolute space. Soon after the fact was established that the fixed stars came to the meridian in equal times, and that interval less than 24 hours, astronomers conceived the idea of graduating a clock to that interval, and dividing it into 24 hours. Thus graduating a clock to the stars, and not to the sun, it is therefore called a sidereal, and not a solar, or common clock ; and as it was sug- gested by astronomers, and used only for the purposes of astronomy, it is also very appropriately called an astronomical clock ; but save its graduation, and the nicety of its construc- tion, it does not differ from a common clock. With a perfect astronomical clock, the same star will pass the meridian at exactly the same time, from one year's end to another. If the time is not the same, the clock does not run to sidereal time ; and the variation of time, or the difference between the time when the star passes the meridian, and the time which ought to be shown by the clock, will determine the rate of the clock. And with the rate of the clock, and its error, we can readily deduce the true time from the time shown by the face of the clock. We have several times mentioned the fact, that the same star returns to the same meridian again and What is a sidereal day ? What is an astronomical clock ? How does it differ from a common clock ? How can we determine whether the as- tronomical clock moves perfectly or not ? 36 ELEMENTARY ASTRONOMY. again, after every interval of 24 sidereal hours. So, two differ* ent stars come to the meridian at constant and invariable intervals of time from each other; and by such intervals wo decide how far, or how many degrees, one star is east or west of another. For instance, if a certain fixed star was observed to pass the meridian when the sidereal clock marked 8 hours, and another star was observed to pass at 9, just one sidereal hour after, then we know that the latter star is on a celestial meridian, just 15 degrees eastward of the meridian of the first mentioned star. With a perfect astronomical clock, or one which shows true sidereal time, we can find the right ascension of any heavenly body, by simply observing the time it passes the meridian. For right ascension is but another term for the sidereal time the 6ody passes the meridian. That meridian in the heavens which passes through the point where the ecliptic and equator intersect, at the first point of Aries, the point where the sun crosses the equator in the spring, is taken as the first meridian of right ascension, and from thence we reckon eastward, from hours to 24 hours, to the same meridian again. This being the case, the sidereal clock should show Oh. Om. Os. when the equinox is on the meridian ; and, if a star or a planet were observed to pass the meridian at 4h. 20m 30s., then the right ascension of that star or planet, at that time, was 4h. 20m. 30s. This, however, is on the supposition that the clock is perfect, and runs perfectly uniform, which is never the case ; unfor- tunately, there is no such thing as a perfect clock, and the difficulties thus arising, must be surmounted by artifice and multiplied observations. Just as the sun crosses the equator in the spring, its right How can we find the rate of the clock ? What difference is there be- tween true sidereal time and right ascension ? Define the first astronom- ical meridian ? What time should the clock show when the equinox is on the meridian ? TIME AND THE MEASURE OF TIME. 37 ascension is Oh., and from this, its right ascension increases about four minutes each day ; this shows that the sun has an apparent motion eastward, among the stars. The right ascensions of all the fixed stars increase at a very slow rate, in consequence of the precession of the equinoxes, that is, a slow motion of the first meridian to the westward, among the stars, of about 50"! per year ; this gives the stars the appear- ance of moving eastward and increasing their right ascensions. The entire increase since the first reliable observations on record, is about 30, or 2 hours. The great multitude of stars retain the same relative right ascensions, and the same relative declinations, for very long periods of time, that is, they retain the same positions with respect to each other. But occasionally, stars may be observed that change their right ascension from day to day, and these stars, in early times, were called wandering stars mentioned in the preceding chapter, they are the planets of our system, the earth itself being one of them. When it is discovered that a star does not pass the meridian at equal intervals of time, as shown by a good astronomical clock, we then decide that that star must have a motion of its own and of course must be a planet or a comet. The reason why astronomers commence the day at noon rather than at midnight, is because noon, the time that the sun passes the meridian, is a distinct and visible moment, which, with proper care and proper instruments, can be exactly defined by observation ; not so with midnight, or any other moment, du- ring the 24 hours. Suppose the right ascension of a star is 8h. 32m. 16s., what time should be shown by the astronomical clock, when that star passes the meridian ? How are planets and comets distinguished from the fixed stars? By what observations? Why do astronomers commence the day at noon ? 38 ELEMENTARY ASTRONOMY. CHAPTER V. LATITUDE DECLINATION ASTRONOMICAL INSTRUMENTS. IN the ast chapter we have given a general idea of finding the right ascensions of the heavenly bodies but to give a true view or map of the heavens, we must give the declinations also. To observe declination, we must have an instrument to measure angles, and with it, determine the latitude of the place from whence the observations are made. The true altitude of the celestial pole is the latitude of the place of observation, and primarily, the observation to find this alti- tude is the only method of finding the latitude, but after the positions of the heavenly bodies have been established, then there are many other methods of finding the latitude. As the north pole is but an imaginary point, no star being there, we cannot directly observe its altitude. But there is a bright star near the pole, called the Polar Star, which, like all other stars in the same region, apparently revolves round the pole, and comes to the meridian twice in 24 sidereal hours ; once above the pole, and once below it ; and it is evident that the altitude of the pole itself must be midway between the greatest and least altitudes of the same star, provided the appa* rent motion of the star round the pole is really in a circle; but before we examine this (act, we will show how altitudes can be taken by the mural circle. The mural, or wall circle, is a large metalic circle, firmly fastened to a wall, so that its plane shall coincide with the plane of the meridian. Define the latitude of a place. In the early stages of Astronomy, were there many ways of finding latitude ? When can we find many methods of finding latitude ? Is the celestial pole a visible point ? How then can we define it ? LATITUDE DECLINATION INSTRUMENTS. 39 A perpendicular line *hrough the center, ZJV, represents the zenith and nadir points ; and at right angles to this, through the center, is the horizontal line, Hh. A telescope, Tt, and an index bar, li, at right an- gles to the telescope, are firmly fixed together, and made to revolve on the center of the mural circle. The circle is graduated from the zenith and nadir points, each way, to the horizon, from to 90 degrees. When the telescope is directed to the horizon, the index points, /and i, will be at Z and ^Y, and, of course, show of altitude. When the telescope is turned perpendicular to Z, the index bar will be horizontal, and indicate 90 degrees of altitude. When the telescope is pointed toward any star, as in the figure, the index points, /and i, will show the position of the telescope, or its angle from the horizon, which is the altitude of the star. As the telescope, and index of this instrument, can revolve freely round the whole circle, we can measure altitudes with it equally well from the north or the south ; but as it turns only in the plane of the meridian, we can observe only meri- dian altitudes with it. This instrument has been called a transit circle, and, says Sir John Herschel, "The mural circle is, in fact, at the same time, a transit instrument ; and, if furnished with a proper sys- tem of vertical wires in the focus of its telescope, may be used as such." "When the telescope points to a star, how will the instrument show the altitude of the star ? Can the telescope move out of the meridian ? 40 ELEMENTARY ASTRONOMY. For a transit instrument, the focus of the eye-piece must be furnished with a system of wires, as here represented, "one horizontal and five equi-distant threads or wires, " which always appear in the field of view, when properly illuminated, by day by the light of the sky, by night by that of a lamp, introduced by a contrivance not necessary here to explain. The place of this system of wires may be altered by adjusting screws, giving it a lateral (hori- zontal) motion; and it is by this moans Meridian Wires, brought to such a position, that the middle one of the vertical wires shall intersect the line of collimation of the telescope, where it is arrested and permanently fastened. In this situation it is evident that the middle thread will be a visible representation of that portion of the celestial meridian to which the telescope is pointed; and when a star is seen to cross this wire in the telescope, it is in the act of culminating, or passing the celestial meridian. The instant of this event is noted by the clock or chronometer, which forms an indispen- sable accompaniment of the transit instrument. For greater precision, the moment of its crossing each of the vertical threads is noted, and a mean taken, which (since the threads are equi-distant) would give exactly the same result, were all the observations perfect, and will, of course, tend to subdivide and destroy their errors in an average of the whole." To measure altitudes in all directions, we must have another instrument, or a modification of this. Conceive this instrument to turn on a perpendicular axis parallel to ZN, in place of being fixed against a wall ; and conceive, also, that the perpendicular axis rests on the center of a horizontal circle, and on that circle carries a horizontal index, to measure azimuth angles. This instrument, so modified, is called an altitude ana How is the meridian made visible ? "What is the use of more than one verticil wire? What instrument must always accompany the transit instrument ? What is meant by azimuth angles ? LATITUDE DECLINATION INSTRUMENTS. 41 azimuth instrument, because it can measure altitudes and azi- muths at the same time. We have before said, that the altitude of the celestial pole must be midway between the greatest and least altitude of the polar star, provided that star apparently circulates round the pole in a circle. To decide that question, all we have to do is to measure the direction of the star, east and west of the meridian, and compare the amount with the difference between its great- est and least altitudes, and if the amount is the same, the appa- rent motion is unquestionably circular ; but observation shows that the horizontal diameter of the circle is greater than the perpendicular diameter. Hence, we cannot say that the midway altitude of the polar star is the measure of the latitude of the place. But if it is, the same kind of observation on other circumpolar stars, must give the same latitude. Such observations have been taken, and stars at the same distance from the pole gave the same lati- tude, and stars at different distances from the pole gave differ- ent latitudes ; and the greater the distance of any star from the pole, the greater the latitude deduced from it. A star 30 or 35 degrees from the pole, observed from about the latitude of 40 degrees, will give the latitude 12 or 15 minutes of a degree greater than the pole star. Astronomers investigated this subject thoroughly, and exam- ined the apparent paths of the stars round the pole, by means of the altitude and azimuth instrument, and they were found to be not exact circles; but departed more and more from a circle, as the star was a greater and greater distance from the pole. These curves were found to be somewhat like ovals the longer diameter passing horizontally through the pole the What is the latitude of a place measured by, or what does it correspond to ? Do the stars apparently circulate round the pole in perfect circles ? What kind of a figure does the motion of a star round the pole appear to describe ? What is the position of the longest diameter of these ovals ? What half of these ovals more nearly correspond to semicircles, the upper or lower V 4 42 ELEMENTARY ASTRONOMY. upper segments very nearly semicircles, and the lower segments flattened on their under sides. With such evidences before the mind, men were not long in deciding that these discrepancies were owing to ATMOSPHERICAL REFRACTION. It is shown, in every treatise on natural philosophy, that light, passing obliquely from a rarer medium into a denser, is bent towards a perpendicular to the new medium. Now, when rays of light pass, or are conceived to pass, from ar^ celestial objects, through the earth's atmosphere to an observer, the rays must be bent downward, unless they pass perpendicularly through the atmosphere; that is, come from the zenith. Let AE, CD, EF, ow that ? THE CAUSES OF THE CHANGE OF SEASONS. 89 The time of the greatest north declination is the 20th of June ; the sun's longitude is then 90, and is said to be at the summer solstice. The time of the greatest south declination is the 22d of December ; the sun's longitude, at that .time, is 270, and is eaid to be at the winter solstice. By inspecting the figure, we perceive, that when the earth is at the summer solstice, the north pole, P, and a considera- ble portion of the earth's surface around, is within the enlight- ened half of the earth ; and as the earth revolves on its axis JWS, this portion constantly remains enlightened, giving a con- stant day or a day of weeks and months duration, according as any particular point is nearer, or more remote from the pole : the pole itself is enlightened full six months in the year, and the circle of more than 24 hours constant sunlight, extends to 23 28' from the pole (not estimating the effects of refraction). On the other hand, the opposite, or south pole, S, is in a long season of darkness, from which it can be relieved only by the earth changing* position in its orbit. "Now, the temperature of any part of the earth's surface depends mainly, if not entirely, on its exposure to the sun's rays. Whenever the sun is above the horizon of any place, that place is receiving heat ; when below, parting with it, by the process called radiation ; and the whole quantities received and parted with in the year, must balance each other at every station, or the equilibrium of temperature would not be sup- ported. Whenever, then, the sun remains more than 12 hours above the horizon of anj- place, and less beneath, the general temperature of that place will be above the average ; when the reverse, below. As the earth, then, moves from A to B, the days growing longer, and the nights shorter, in the northern hemisphere, the temperature of every part of that hemisphere When does the sun attain its greatest northern declination? "When its greatest southern declination? Is there any night at the north pole while the sun's declination is north ? What is the extent of constant daylight from the pole when the sun's declination is 18 degrees north? 8 90 ELEMENTARY ASTRONOMY. increases, as we pass from spring to summer, while at the same time the reverse is going on in the southern hemisphere. As the earth passes from B to (7, the days and nights again ap- proach to equality the excess of temperature in the northern hemisphere, above the mean state, grows less, as well as its detect in the southern ; and at the autumnal equinox, C, the mean state, is once more attained. From thence to D, and, finally round again to A, all the same phenomena, it is obvious," must ngain occur, but reversed; it being now winter in the northern, and summer in the southern, hemisphere." The inquiry is sometimes made, why we do not have the warmest weather about the summer solstice, and the coldest weather about the winter solstice. This would be the case if the sun immediately ceased to give extra warmth, on arriving at the summer solstice ; but if it could radiate extra, heat to warm the earth three weeks before it came to the solstice, it would give the same extra heat three weeks after; and the northern portion of the earth must con- tinue to increase in temperature as long as the'sun continues to radiate more than its medium degree of heat over the sur- face, at any particular place. Conversely, the whole region of country continues to grow cold as long as the sun radiates less than its mean annual decree of heat over that rep-ion. The I medium degree of heat, for the whole year, and for all places, of course, takes place when the sun is on the equator ; the average temperature, at the time of the two equinoxes. The medium degree of heat, for our northern summer, considering only two seasons in the year, takes plage when the sun's decli- nation is about 12 degrees north ; and the medium degree of heat, for winter, takes place when the sun's declination is about 12 degrees south ; and if this be true, the heat of summer will begin to decrease about the 20th of August, and the cold of Why is not the 20th of June considered as mid-summer in the northern hemisphere, or, rather, why is July the mid-summer season, and not June ? At what time may we expect the seventy of winter to be past V THE CAUSES OF THE CHANGE OF SEASONS. 91 winter must essentially abate, on, or about, the 16th of Febru- ary, in all northern latitudes. The warmest part of the day, (other circumstances being equal,) is not at 12, but about 2 o'clock in the afternoon. The sun is then west of the meridian, and its rays will strike more perpendicularly on a plane whose downward slope is towards the west, than on one, whose downward slope is towards the east. This will account for the fact, that climates are more mild west of mountain ranges than on the eastern side of the same mountains, other circumstances being equal. The vicinity of large bodies of water, and the general elevation of the country above the level of the sea, have much to do with climate, but as these causes have no particular connection with astronomy, we omit them. "What time of day is warmest ? Why not at noon ? Which locality has the warmest climate, on the east or west side of the Alleghany mountains, in the same latitude and at the same elevation above the sea 1 92 ELEMENTARY ASTRONOMY. CHAPTER IV. EQUATION OF TIME. WE now come to one of the most important subjects in astronomy the equation of time. Without a good knowledge of this subject, there will be constant confusion in the minds of the pupils ; and such is the mature of the case, that it is difficult to understand even the facts, without investigating their causes. Sidereal time has no equation ; it is uniform, and, of itself, perfect and complete. The time, by a perfect clock, is theoretically perfect and Complete, and it is called mean solar time. The time, by the sun, is not uniform ; and, to make it agree with the perfect clock, requires a correction a quantity to make equality ; and this quantity is called the equation of If the sun were stationary in the heavens, like a star, it come to the meridian after exact and equal intervals ^f time ; and, in that case, there would be no equation of time. If the sun's motion, in right ascension, were uniform, then it would also come to the meridian after equal intervals of time, and there would still be no equation of time. But (speaking in relation to appearances) the sun is not stationary in the heavens, nor does it move uniformly ; therefore it can- not come to the meridian at equal intervals of time, and, of course, the solar days must be slightly unequal. * In astronomy, the term equation, is applied to all corrections, to con- vert a mean to its true quantity. Are all sidereal days alike in length? Are all solar days alike in length ? If solar days are unequal in length, what will it produce ? EQUATION OF TIME. 93 When the sun is on the meridian, it is then apparent noon for that day : it is the real solar noon, or, the half elapsed time between sunrise and sunset. A fixed star comes to the meridian at the expiration of every 23h. 56m. 04.09s. of mean solar time ; and if the sun were stationary in the heavens, it \vould come to the meridian after every expiration of just that same interval. But the sun in- creases its right ascension every day, by its apparent eastward motion ; and this increases the time of its coming to the meri- dian ; and the mean interval between its successive transits over the meridian is just 24 hours ; but the actual intervals are variable some less, and some more, than 24 hours. On and about the 1st of April, the time from one meridian of the sun to another, as measured by a perfect clock, is 23h. 69m. 52.4s. ; less than 24 hours by about 8 seconds. Here, then, the sun and clock must be constantly separating. On and about the 20th of December, the time from one meridian of the sun to another is 24h. Om. 24.2s., more than 24 seconds over 24 hours ; and the daily accumulation of a few seconds will soon amount to minutes and thus the sun and clock will become very sensibly separated and this is the equation of time. To detect the law which separates the sun and clock, and find the amount of separation for any particular day, we must consider 1st. The unequal apparent motion of the sun along the ecliptic. 2d. The variable inclination of this motion to the equator. If the sun's apparent motion along the ecliptic were uniform, still there would be an equation of time ; for that motion, in some parts of the orbit, is oblique to the equator, and, in other parts, parallel with it; and its eastward motion, in right ascen- sion, would be greatest when moving parallel with the equator. When is it apparent noon? When is it mean noon? The difference between these two noon's is always equal to what ? If the sun's apparent motion along the ecliptic were uniform, would there still be an equation of time, and why ? 94 ELEMENTARY ASTRONOMY. From the first cause, separately considered, the sun and clock would agree two days in a year the 1st of July and the 30th of December. From he second cause, separately considered, the sun and clock agree four days in a year the days when the sun crosses the equator, and the days he reaches the solsticial points. When the results of these two causes are combined, the sun and clock will agree four days in the year ; but it is on neither of those days marked out by the separate causes ; and the intervals between the several periods, and the amount of the equation, appear to want regularity and symmetry. The four days in the year on which the sun and clock agree, that is, show noon at the same instant, are April 15th, June 16th, September 1st, and December 24th. The elliptical form of the earth's orbit gives rise to the une- qual motion of the earth in its orbit, and thence to the appa- rent unequal motion of the sun in the ecliptic ; and this same unequal motion is what we have denominated the first cause of the equation of time. Indeed, this part of the equation of time is nothing more than the equation of the sun's center, changed into time, at the rate of four minutes to a degree. The greatest equation for the sun's longitude, is by obser- vation 1 55' 30"; and this, proportioned into time, gives 7m. 42s. for the maximum effect in the equation of time arising from the sun's unequal motion. When the sun departs from its perigee, its motion is greater than the mean rate, and, of course, comes to the meridian later than it otherwise would. In such cases, the sun is said to be slow and it is slow all the way from its perigee to its apogee ; and fast hi the other half of its orbit. On what days in the year would the sun and clock agree, if the sun's motion were uniform along the ecliptic? On what days in the year do the sun and clock agree ? What is the maximum effect for the sun's une- qual motion ? EQUATION OF TIME. 95 For a more particular explanation of the second cause, we must call attention to the figure in the margin. Let Y* @ LQJ represent the ecliptic, and r p C LQJ the equator. By the first correc- tion, the apparent mo- tion along the ecliptic is rendered uniform ; and the sun is then supposed to pass over equal spaces in equal intervals of time along the arc ^ S @. But equal spaces of arc, on the ecliptic, do not include the same meridians, as equal spa- ces on the equator. In short, the points on the ecliptic must be reduced to corresponding points on the equator. For instance, the number of degrees represented by ^ $on the ecliptic, is greater than to the same meridian along the equator. The difference between 'Y 1 S and p S f , turned into time, is the equation of time arising from the obliquity of the ecliptic cor- responding to the point S. At the points 'Y 1 , 69, and LQJ, and also at the southern tropic, the ecliptic and the equator correspond to the same meridian ; but all other equal distances, on the ecliptic and equator, are included by different meridians. It will be observed, by inspecting the figure, that what the sun loses in eastward motion, by oblique direction near the equa- tor, is made up, when near the tropics, by the diminished dis- tances between the meridians. For a more definite understanding of this matter, we give the folloAving table : When does the sun lose most in eastward motion on the ecliptic ? When does it gain most in eastward motion ? 96 ELEMENTARY ASTRONOMY. Table showing the separate results of the two causes for the equa- tion of time, corresponding to every fifth day of the second years after leap year ; but is nearly correct for any year. 1st cau*e. Bun slow of Clock. 2d cause. Sun slow of Clock. 1st cause fvn fast. 2d cause. Sun fast. m. s. m. s. m. 8. m. s. January 5 41 5 8 July 1 3 32 10 1 22 6 35 7 40 5 8 15 2 2 7 48 12 1 19 6 35 20 2 41 8 45 17 1 57 7 48 25 3 19 9 26 22 2 35 8 45 29 3 56 9 49 28 3 12 9 26 February 3 4 30 9 53 August 2 3 47 9 49 8 5 2 9 40 7 4 21 9 53 13 5 32 9 9 12 4 52 9 40 18 5 39 8 23 17 5 22 9 9 23 6 24 7 22 22 5 50 8 23 28 6 45 6 9 28 6 14 7 22 March 5 7 3 4 46 Sept. 2 6 36 6 9 10 7 18 3 15 7 6 56 4 46 15 7 29 1 39 12 7 12 3 15 20 7 37 sun fast. 17 7 24 1 39 25 7 42 1 39 23 7 34 sun fast. 30 7 42 3 15 28 7 40 1 39 April 4 7 40 4 46 October 3 7 42 3 15 9 7 34 6 9 8 7 40 4 46 14 7 24 7 22 13 7 34 6 9 19 7 12 8 23 18 7 24 7 22 24 6 56 9 9 23 7 12 8 23 30 6 36 9 40 28 6 56 9 9 May 5 6 14 9 53 Nov. 2 6 36 9 40 10 5 50 9 49 7 6 14 9 53 15 5 22 9 26 12 5 50 9 49 20 4 52 8 45 17 5 22 9 26 26 4 21 7 48 22 4 52 8 45 31 3 47 6 35 27 4 22 7 48 June 5 3 12 5 8 Dec. 2 3 47 6 35 10 2 35 3 32 7 3 12 5 8 16 1 57 1 48 12 2 35 3 32 21 1 19 sun slow 17 1 57 1 48 26 40 1 48 21 1 19 sun slow 26 40 1 48 By this table, the regular and symmetrical result of each cause is visible to the eye ; but the actual value of the equa- tion of time, for any particular day, is the combined results What is the first cause of the equation of time ? What is the second cause? EQUATION OF TIME. 97 of these two causes. Thus, to find the equation of time for the 5th day of March, we look in the table and find that The first cause gives sun slow - - 7m. 3s. The second " sun slow - 4 46 Their combined result (or algebraic sum) is 11 49 slow. That is, the sun being slow, it does not come to the meridian until llm. 49s. after the noon shown by a perfect clock ; but whenever the sun is on the meridian, it is then noon, apparent time ; and, to convert this into mean time, or to set the clock, we must add llm. 49s. By inspecting the table, we perceive that on the 1 4th of April the two results nearly counteract each other ; and conse- quently the sun and clock nearly agree, and indicate noon at the same instant. On the 2d of November the two results unite in making the sun fast; and the equation of time is thep the sum of 6 36 and 9 40, or 16m. 16s. ; the maximum result. The sun at this time being fast, shows that it comes to the meridian 16m. 16s. before 12 o'clock, true mean time; or, when the sun is on the meridian, the clock ought to show llh. 43m. 44s. ; and thus, generally, when the sun is fast, we must subtract the equation of time from apparent time, to obtain mean time; and add, when the sun is slow. As no clock can be relied upon, to run to true mean time, or to any exact definite rate, therefore clocks must be frequently rectified by the sun. We can observe the apparent time, and then, by the application of the equation of time, we determine the true mean time. A table for the equation of time, corresponding to each degree of the sun's longitude, is to be found in many astro- nomical works, and such a table would be perpetual, provided the longer axis of the solar orbit did not change its position in relation to the equinox. But as that change is very slow, a When is the sun said to be slow ? When fast ? Can any clock be relied upon to run to mean time ? How then is mean time discovered ? "W hy can we not have a perpetual table for the equation of time? 9 98 ELEMENTARY ASTRONOMY. table of that kind will serve for many years, with a trifling correction. We repeat, sidereal time is the interval of time elapsed since the equinoctial point in the heavens passed the meridian. The solar day is 3m. 56s. 55 of sidereal time, longer than a sidereal day. At the instant of mean noon, Greenwich time, on the 1st of March, 1857, the sidereal time was h. m. s. Estimated at - - - - 22 36 56.65 To this add - : - - 3 56.55 Sidereal time at noon, March 2d, 22 40 53.20 Thus we might compute the sidereal time at mean noon, Greenwich time, for any number of days, (omitting 24h. when we passed that sum.) At mean noon, the right ascension of the sun, plus or minus the equation of time, is always equal to the sidereal time. Twenty -four hours of mean solar time is equal to 24h. 3m. 56s. 55 of sidereal time. Therefore eight hours of solar time is equal to 8h. 1m. 18s. 82 of sidereal time ; and thus we may correct any hour of solar time to its corresponding value of sidereal time. On the 1st day of May, 1857, at mean noon, h. m. s. The sidereal time was - - - 2 37 26.46 Add, 81 18.82 Sidereal time at 8, mean time, - 10 38 45.28 Thus we might find the sidereal time corresponding to any other hour, on any other day, having the use of a Nautical Almanac. It is very important that the navigator, astronomer, and chcA regulator, should thoroughly understand the equation of time ; and persons thus occupied pay great attention to it ; but most people in common life are hardly aware of its existence. To whom is equation of time important ? APPARENT MOTIONS OF THE PLANETS. 99 CHAPTER V. THE APPARENT MOTIONS OF THE PLANETS. WE have often reminded the reader of the great regularity of the fixed stars, and of their uniform positions in relation to each other ; and by this very regularity and constancy of rela- tive positions, we denominate them fixed ; but there are certain other celestial bodies, that manifestly change their positions in space, and, among them, the sun and moon are most prom- inent. In previous chapters, we have examined some facts con- cerning the sun and moon, which we briefly recapitulate, as follows : 1. That the sun's distance from the earth is very great; but at present we cannot determine how great, for the want of one element its horizontal parallax. 2. Its magnitude is much greater than that of the earth. 3. The distance between the sun and earth is slightly varia- ble ; but it is regular in its variations, both in distance and in apparent angular motion. 4. The moon is comparatively very near the earth ; its distance is variable, and its mean distance and amount of variations are known. It is smaller than the earth, although, to the mere vision, it appears as large as the sun. The apparent motions of both sun and moon are always in one direction ; and the variations of their motions are never far above or below the mean. But there are several other bodies that are not fixed stars ; and although not as conspicuous as the sun and moon, have been known from time immemorial. What is repeated in chapter v. concerning the fixed stars ? What is mentioned again concerning the sun ? What in relation to the moon ? 100 ELEMENTARY ASTRONOMY. They appear to belong to one family ; but, before the true system of the world was discovered, it was impossible to give any rational theory concerning their motions, so irregular and erratic did they appear ; and this very irregularity of their apparent motions induced us to delay our investigations con- cerning them to the present chapter. In general terms, these bodies are called planets and there are several of recent discovery and some of very recent discovery ; but as these are not conspicuous, nor well known, all our investigations of principles will refer to the larger planets, Venus, Mars, Jupiter, and Saturn. We now com- mence giving some observed facts, as extracted from the Cam- bridge astronomy. " There are few who have not observed a beautiful star in the west, a little after sunset, and called, for this reason, the evening star. This star is Venus. If we observe it for several days, we find that it does not remain constantly at the same distance from the sun. It departs to a certain distance, which is about 45, or {th of the celestial hemisphere, after which it begins to return ; and as we can ordinarily discern it with the naked eye only when the sun is below the horizon, it is visible only for a certain time immediately after sunset. Subsequently it sets with the sun, and then we are entirely prevented from seeing it by the sun's light. But after a few days, we perceive in the morning, near the eastern horizon, a bright star which was not visible before. It is seen at first only a few minutes before sunrise, and is hence called the morning star. It departs from the sun from day to day, and precedes its rising more and more ; but after departing to about 45, it begins to return, and rises later each day ; at length it rises with the sun, and we cease to distinguish it. In a few days the evening star again appears in the west, very near the sun ; from which it departs in the same manner as before ; again returns; disap- What bodies are planets ? In what respects do their motions differ from the fixed stars ? Why has the author delayed mentioning these bodies until now ? What planet is called the morning and evening star ? APPARENT MOTIONS OF THE PLANETS. 101 pears for a short time ; and then, the morning star presents itself. These alternations, observed without interruption for more than 2000 years, evidently indicate that the evening and morn- ing- star are one and the same body. They indicate, also, that this star has a proper motion, in virtue of which it oscillates about the sun, sometimes preceding and sometimes following it. These are the phenomena exhibited to the naked eye ; but the admirable invention of the telescope enables us to carry our observations much farther." On observing Venus with a telescope, the irradiation is, in a great measure, taken away, and we perceive that it has phases, like the moon. At evening, when approaching the sun, it pre- sents a luminous crescent, the points of which are from the sun. The crescent diminishes as the planet draws nearer the sun ; but after it has passed the sun, and appears on the other side, the crescent is turned in the other direction ; the enlight- ened part always toward the sun, showing that it receives its light from that great luminary. The crescent now gradually increases to a semicircle, and finally, to a full circle, as the planet again approaches the sun ; but, as the crescent increases, the apparent diameter of the planet diminishes; and at every alternate approach of the planet to the sun, the phase of the planet is full, and the apparent diameter small; and at the other approaches to the sun, the crescent diminishes down to zero, and the apparent diameter increases to its maximum. When very near the sun, however, the planet is lost in the sunlight; but at some of these intervals, between disappearing in the evening and reappearing in the morning, it appears to run over the sun's disc as a round, black spot ; giving a fine opportunity to measure its greatest apparent diameter. When Venus appears full, its apparent diameter is not more than 10", and when a black spot on the sun, it is 59". 8, or very nearly 1'. How do we know that the morning and evening star must be the same body ? What is the appearance of the planet when viewed through a tel- escope ? How does it appear that Veuus receives its light from the sun 1 102 ELEMENTARY ASTRONOMY. Hence, its greatest distance must be, to its least distance, as 59". 8 to 10, or nearly as 6 to 1. The learner should impress this fact on his mind, that this planet is always in the same part of the heavens as the sun never departing more than 47 on each side of it called its greatest elongation. In consequence of being always in. the neighborhood of the sun, it can never come to the meridian near midnight. Indeed, it always comes to the meridian within three hours twenty minutes of the sun, and, of course, in day- light. But this does not prevent meridian observations being taken upon it, through a good telescope ;* and, as to this par- ticular planet, it is sometimes so bright as to be seen by the unassisted eye in the daytime. Even without instruments and meridian observations, the attentive observer can determine that the motion of Venus, in relation to the stars, is very irregular sometimes its motion is very rapid sometimes slow sometimes direct some- times stationary, and sometimes retrograde ;\ but the direct motion prevails, and, as an attendant to the sun, and in its own irregular manner, as just described, it appears to traverse round and round among the stars. But Venus is not the only planet that exhibits the appear- ances we have just described. There is one other, and only one Mercury; a very small planet, rarely visible to the naked * The stars continue visible through telescopes, during the day, as well as the night ; and that, in proportion to the power of the instrument, not only the largest and brightest of them, but even those of inferior luster, such as scarcely strike the eye, at night, as at all conspicuous, are readily found and followed, even at noonday, by those who possess the means of pointing a telescope accurately to the proper places unless the star is in that point of the heavens very near the sun. HEKSCHEL. t In astronomy, direct motion is eastward among the stars ; stationary is no apparent motion ; and retrograde is a westward motion. Is the distance of Venus from the earth very variable, and how great is the variation? How is that fact ascertained ? Describe the apparent motion of Venus among the stars. What is understood by stationary, in astronomy? What by direct and retrograde motions? What other planet exhibits like appearances to Venus 1 APPARENT MOTIONS OF THE PLANETS. 103 eye, and not known to the very ancient astronomers. "What- ever description we have given of Venus applies to Mercury, except in degree. Its variations of apparent diameter are nob so great, and it never departs so far from the sun ; and the interval of time, between its vibrations from one side to the other of the sun, is much less than that of Venus. These appearances clearly indicate that the sun must be the center t or near the center, of these motions, and not the earth; and tha Mercury must revolve in an orbit within that of Venus. So clear and so unavoidable were these inferences, that even the ancients (who were the most determined advocates for the immobility of the earth, and for considering it as the principal object in creation the center of all motion, etc.) were com- pelled to admit them; but with this admission, they contended, that the sun moved round the earth, carrying these planets as attendants. By taking observations on the other planets, the ancient astronomers found them variable in thei/ apparent diameters, and angular motions ; so much so, that ii was impossible to recon- cile appearances viiih the idea of a stationary point of observation; unless the appearances were taken for realities, and that was against all true notions of philosophy. The planet Mars is most remarkable for its variations ; and the great distinction between this planet and Venus, is, that it does not always accompany the sun ; but it sometimes, yea, at regular periods, is in the opposite pa?t of the heavens from the sun called Opposition at which, time it rises about sunset, and comes to the meridian about midnight. The greatest apparent diameter of Mars takes place when the planet is in opposition to the sun, and it is then 17".l ; and its least apparent diameter takes place when in the neigh bor- What do these appearances clearly indicate ? "What is the planet Mars most remarkable for ? What great distinction is there between some ap- pearances of Mars and Venus ? When a planet is in opposition to the sun, what time of the day does it pass the meridian ? What is shown by the great variation in the apparent diameter of Mars ? 104 ELEMENTARY ASTRONOMY. hood of the sun, and it is then but about 4"; showing that the sun, and not the earth, is the center of its motion. The general motion of all the planets, in respect to the stars, is direct; that is, eastward; but all the planets that attain op- position to the sun, while in opposition, and for some time before and after opposition, have a retrograde motion and thoso planets which show the greatest change in apparent diameter, show also, the greatest amount of retrograde motion and all the observed irregularities are systematic in their irregularities, showing that they are governed, at least, by constant and invariable laws. If the earth is really stationary, we cannot account for this retrograde motion of the planets, unless that motion is real ; and if real, why, and how can it change from direct to stationary, and from stationary to retro- grade, and the reverse? But if we conceive the earth in motion, and going the same ivay with the planet, and moving more rapidly than the planet, then the planet will appear to run back / that is, retrograde, And as this retrogradation takes place with every planet, when the earth and planet are both on the same side of the sun, and the planet in opposition to the sun ; and as these cir- cumstances take place in all positions from the sun, it is a suf- ficient explanation of these appearances ; and conversely, then, these appearances show the motion of the earth in an orbit round the sun. When a planet appears to be stationary, it must be really so, or be moving directly to or from the observer. And if it be moving to or from the observer, that circumstance will be indicated by the change in apparent diameter; and observa- tions confirm this, and show that no planet is really stationary, although it may appear to be so. If we suppose the earth to be but one of a family of bodies, called planets all circulating round the sun at different When do planets appear to retrograde ? When a planet appears to be stationary, is it really so ? What supposition is here made in respect earth ? APPARENT MOTIONS OF THE PLANETS. 105 times in the order of Mercury, Venus, Earth, Mars, (omitting the small telescopic planets), Jupiter, Saturn, Herschel, or Uranus, we can then give a rational and simple account for every appearance observed, and without discussing the ancient objections to the true theory of the solar system, we shall adopt it at once, and thereby save time and labor, and intro- duce the reader into simplicity and truth. This, the true solar system, as now known and acknowledged, is called the Copernican system, from its discoverer, Coperni- cus, a native of Prussia, who lived some time in the fifteenth century. But this theory, simple and rational as it now appears, and capable of solving every difficulty, was not immediately adop- ted ; for men had always regarded the earth as the chief object in God's creation ; and consequently man, the lord of creation, a most important being. But when the earth was urled from its imaginary, dignified position, to a more humble place, it was feared that the dignity and vain pride of man must fall with it ; and it is probable that this was the root of the oppo- sition to the theory. So violent was the opposition to this theory, and so odious would any one have been who had dared to adopt it, that it appears to have been abandoned for more than one hundred years, and was revived by Galileo about the year 1620, who, to avoid persecution, presented his views under the garb of a dialogue between three fictitious persons, and the points left undecided. But the caution of Galileo was not sufficient, or his dialogue was too convincing, for it woke up the Inquisition, and he was forced to sign a paper denouncing tha theory as heresy, on the pain of perpetual imprisonment. Thus, persecuting error, has always moved in advance of truth, and though powerful, it can never be finally successful. Who discovered the true solar system ? Give a brief outline of the Co- pernican system ? Why did men so violently oppose this system ? How long was this system lost, and how can we account for its being neglected and abandoned ? Who revived it ? What trouble did thig bring ou that Philosopher ? 10P ELEMENTARY ASTRONOMY. CHAPTER VI. THE COPERNICAN SYSTEM ILLUSTRATED. THE following figure is designed to be a partial representa- tion of the solar system. The center is the locality of the Sun, and the innermost circle represents the orbit of Mercury, the second circle the orbit of Venus, the third circle the orbit of the Earth, and the outermost circle represents the orbit of Mars. Whereabouts in the solar system is the sun located ? What orbit is nearest to the sua ? What orbit docs the tkird circle represent ? THE COPERNICAX SYSTEM ILLUSTRATED. 107 There is not space on the page to represent the orbit of tho planets, beyond or more remote from tjie sun than Mars, and, indeed, there is not space to represent these in due proportion, on a scale of sufficient magnitude. Far, far away beyond the orbits of the planets are the fixed stars so far, that the whole solar system is but a point in comparison. To help the imagination, we have represented stars about the borders of the figure. Let a, b, c, d, =(111.66)(7912) = 883454 miles. The sun's horizontal parallax is the angle at the vertex of a right angled triangle, and the base opposite, is the semi- diameter of the earth ; and if we call that distance unity, and compute the distance of one of the other sides by trigonometry, we shall find it equal to 23984 units, or semi-diameters of the What element must astronomers obtain before they can determine the magnitudes and distances of the planets? State the rule to find the diam- eter of the suu or a planet ? DIAMETERS AND MAGNITUDES OF THE PLANETS. 125 earth ; but to aid the memory, we may say that the distance is 24000 times the earth's semi-diameter. If we change the unit, from the semi-diameter of the earth, to an English mile, then the mean distance between the earth and sun must be (3956)(24000)=94.944000 miles. In round numbers we may say 95 millions of miles. By Kepler's third law, we know the relative distances of the planets from the sun, and now knowing the real distance, in miles, of one of them (the earth), we can determine the real distances of the others by multiplying each relative distance by 94.944000. Relative distances. True distances. 36.752.822 68.672.995 94.944000= 94.944.000 144.666.172 493.974.643 905.651.827 L 1814.417.800 ' By observations taken on the transit of Venus, in 1769, it, was concluded that the horizontal parallax of that planet was 30".4 ; and its semi-diameter, at the same time, was 29".2. Hence, 304 : 292 : : 7912 : to a fourth term; which gives 7599 miles for the diameter of Venus. . We cannot observe the horizontal parallax of Jupiter, Saturn, or any other very remote planet : if known at all, it becomes known by computation ; but the parallax of the sun being now known, and the relative distances of the earth and all the planets from the sun being known, the horizontal parallax of any planet can be computed as follows. Once more we remind the reader that the sun's horizontal parallax is the angle under which the earth appears, as seen from the sun seen from a What is the multiplier to the relative distances of the planets from the sun, to obtain the distances in miles? Do we observe the horizontal paral- lax of a remote planet, or compute it ? Mercury, - 0.3871 " Venus, - - 0.7233 Earth, - - 1.0000 Mars, 1.5237 Jupiter, - 5.2028 Saturn, - - 9.5388 Uranus, - 19.1824 , 126 ELEMENTARY ASTRONOMY. greater distance, the angle must be proportionally less. Seen from a distance equal to the mean distance of Jupiter from the o" r sun, the angle would be - - -- This, then, is the horizontal 5.2028 parallax of Jupiter, when Jupiter is at a distance from the earth equal to the mean distance of Jupiter from the sun. The appa- rent semi-diameter of Jupiter, when at the same distance, as determined by observation, is 18".35 ; therefore the diameter of Jupiter can be determined by the following proportion 7912 : D : : 8 ' 6 : 18.35, 5.2028 in which D represents the magnitude sought. Whence D: =7912*11 .1=87823 miles 8.6 In the same manner we can find the diameter of any other planet whose apparent diameter can be distinctly measured, and whose relative distance to the sun is known. The diameter may also be computed directly by plane trigonometry. We have just seen that the diameter of Jupiter is 11.1 times the diameter of the earth ; but this is the equatorial diameter of the planet. Its polar diameter is less, in the proportion of 167 to 177, as determined by the mean of many micrometrical measurements ; which proportion gives 82930 miles, for the polar diameter of Jupiter. These extremes give the mean diameter of Jupiter, to the mean diameter of the earth, as 10.8 to 1. But the magnitudes of similar bodies are to one another as the cubes of their like dimensions ; therefore the magnitude of Jupiter is to that of the earth, as (10.8) 3 to 1, and from thence we learn that Jupiter is 1260 times greater than the earth. In this manner are found the magnitudes, distances, velocity, &c. &c. of the planets, which appear in tables in various astro- nomical works. State the proportion to find the diameter of a planet when its horizontal parallax and apparent semi-diameter are both known. How much greater is the diameter of Jupiter than the earth ? How much greater then is the magnitude of Jupiter than that of the earth? DESCRIPTION OF THE SOLAR SYSTEM. 127 CHAPTER IX. A GENERAL DESCRIPTION OF THE SOLAR SYSTEM. THE solar system is so called because the K sun occupies the Central position, and apparently holds and governs the motion of all the planets which revolve around him. We shall commence our description with THE SUN. This body, as we have seen in the preceding pages, is of immense magnitude, much greater than all the planets taken together, comparatively stationary, the dispenser of light and heat, and apparently at least, the repository of that attractive force which holds the system together, and regulates the plan- etary motions. "Spots on the sun seem first to have been observed in the year 1611, since which time they have constantly attracted attention, and have been the subject of investigation among astronomers/' A spot first appears on the eastern limb of the sun, and by degrees comes forward to the middle, and passes off to the west. After being absent about the same length of time, the same spot appears in the same place as before, thus indicating a revo- lution of the sun on an axis, in 25 days 14 hours, the sy nodical revolution of the spots being 27 days 12*- hours. These spots change their appearance, "and become greater or less, to an observer on the earth, as they are turned to, or from him ; they also change in respect to real magnitude and number; one spot, seen by Dr. Herschel, was estimated to be Whereabouts in the solar system is the sun ? Does it revolve on an axis and if so, how did the fact become known ? AV hat is the time of revo- lution ? What is said of the size of some of these spots ? 128 ELEMENTARY ASTRONOMY. more than six times the size of our earth, being 50000 miles in diameter. Sometimes forty or fifty spots may be seen at the same time, and sometimes only one. They are often so large as to be seen with the naked eye; this was the case in 1816. " In two instances, these spots have been seen to burst into several parts, and the parts to fly in several directions, like a piece of ice thrown upon the ground. "Dr. Herschel, from many observations with his great tel- escope, concludes^ that the shining matter of the sun consists of a mass of phosphoric clouds, and that the spots on his sur- face are owing to disturbances in the equilibrium of this lumi- nous matter, by which openings are made through it. There are, however, objections to this theory, as indeed there are to all the others, and at present it can only be said, that no satis- factory explanation of the cause of these spots has been given." MERCURY. This planet is the nearest to the sun, and has been the sub- ject of considerable remark in the preceding pages. It is rarely visible, owing to its small size and proximity to the sun, and it never appears larger to the naked eye than a star of the fifth magnitude. Mercury is seen through a telescope sometimes in the form of a half moon, and sometimes a little more or less than half its disc is seen ; hence it is inferred, that it has the same phases as the moon, except that it never appears quite round, because its enlightened side is never turned directly towards us, unless when it is so near the sun as to become invisible, by reason of the splendor of the sun's rays. The enlightened side of this planet being always towards the sun, and its never appear- ing round, are evident proofs that it shines not by its own light; for, if it did, it would constantly appear round. The best observations of this planet are those made when it is seen on the sun's disc, called its transit ; for in its lower con- How large does Mercury appear ? What is its position when the best observations can be made on it ? DESCRIPTION OF THE SOLAR SYSTEM. 129 junction, he sometimes passes before the sun, like a little spot, eclipsing a small part of the sun's body. Mercury is too near the sun to admit of any observations on the spots on its surface ; but its period of rotation has been determined by the variations in its horns the same ragged corner comes round at regular intervals of time 24h. 5m. The best time to see Mercury, in the evening, is in the spring of the year, when the planet is at its greatest elongation east of the sun. It will then be visible to the naked eye about fifteen minutes, and will set about an hour and fifty minutes after the sun. When the planet is west of the sun, and at its greatest distance, it may be seen in the morning, most advantageously in August and September. The symbol for the greatest elon- gation of Mercury, as written in the common almanac, is Gr. Elon. VENUS. This planet is second in order from the sun, and in relation to its position and motion, it has been sufficiently described. The period of its rotation on its axis is 23h. 21m. The position of the axis is always the same, and is not at right angles to the plane of its orbit, which gives it a change of seasons. The tangent position of the sun's light across this planet shows a very rough surface ; indeed, high mountains. By the radiating and glimmering nature of the light of this planet, we infer that it must have a deep and dense atmosphere. These figures present a tele- scopic view of this planet ; the narrow crescent appears when the planet is near its inferior conjunction, the other when the planet is near its greatest elongation. The enlightened side is always towards the sun, which shows How was the revolution of Mercury, on an axis, determined ? Does Venus revolve on an axis, and in what tijne ? 130 ELEMENTARY ASTRONOMY. that it shines not by its own light, but by reflecting the light from the sun ; and indeed, observations show that this is true of all the planets. For the magnitude, motion, inclination of orbit, &c. of Venus, see tables. THE EARTH Is the next planet in ike system ; but it would be only for- mality to give any description of it in this connection. As a planet, it seems to be highly favored above its neighboring planets, by being furnished with an attendant, the moon ; and insignificant as this latter body is, compared to the whole solar system, it is the most important to the inhabitants of our earth. The two bodies, the earth and the moon, as seen from the sun, are very small : the former subtending an angle of about 17" in diameter, and the latter about 4", and their distance asunder never greater than between seven and eight minutes of a degree. We shall give a particular description of the moon, its orbit, motion, &c. Equinox. Longitude of Ascending Node, 430 8' 50") Inclination of the orbit, 1 46' 59' What observed facts suggested the existence of Uranus ? Was the dis- covery the lesult of such an hypothesis ? What other planet was dis- covered by similar facts, and a similar theory ? When and by whom was that planet discovered ? 142 ELEMENTARY ASTRONOMY. Eccentricity of the orbit, - - 0.008718 Mean daily sidereal motion, - 2l".5545 Mean time of revolution, 60126.65 days, or 165 yrs. nearly. Mean distance from the sun, 30.048, (the earth's distance being unity.) Future observations will undoubtedly modify and correct these results. We shall close this chapter with the following 'extract from HerschePs Astronomy, "which will convey to the minds of our readers a general impression of the relative magnitudes and distances of the parts of our system. Choose any well-leveled' field or bowling green. On it place a globe, two feet in diam- eter ; this will represent the sun ; Mercury will be represented by a grain of mustard seed, on the circumference of a circle 164 feet in diameter for its orbit; Venus a pea, on a circle 284 feet in diameter; the earth also a pea, on a circle 430 feet; Mars a rather large pin's head, on a circle of 654 feet ; Juno, Ceres, Vesta, and Pallas, grains of sand, in orbits of from 1000 to 1200 feet; Jupiter a moderate-sized orange, in a circle nearly half a mile across ; Saturn a small orange, on a circle of four-fifths of a mile; and Uranus a full-sized cherry, or small plum, upon the circumference of a circle more than a mile and a half in diameter. As to getting correct notions on this subject by drawing circles on paper, or still worse, from those very childish toys called orreries, it is out of the ques- tion. To imitate the motions of the planets in the above men- tioned orbits, Mercury must describe its own diameter in 41 seconds; Venus, in 4m. 14s. ; the earth, in 7 minutes ; Mars, in 4 m. 48s. ; Jupiter, in 2h. 56m.; Saturn, in 3h. 13m.; and Uranus, in 2h. 16m." From this description it will be seen that the true reason why the solar system cannot be accurately represented on paper, is this : That if we give the earth any sensible magni- tude, there will not be space enough on any paper to represent th6 sun, or to extend to the planets. What does Herschel say about representing the solar system on paper ? What term does he apply to orreries ? Why can we not make a propel map of the solar system ? SECTION III. CHAPTER I. THE MOON', ITS PERIODICAL REVOLUTIONS, AND APPEARANCES. NEXT to the sun, the moon is the most interesting and im- portant heavenly body, to the inhabitants of the earth, and we made that a reason for omitting an exposition of its motion, path, and other phenomena; until the student acquired a little astronomical discipline. In Section II, chapter I, we have explained parallax in general, and the moon's parallax in par- ticular, and found it to vary from 53' 50" to 61' 29", the- amount when the moon is at its mean distance from the earth, being 57' 3", corresponding to a distance of 60.26 semi-diameters from the earth. The position of the moon, in right ascension and declination, can be determined almost daily, at any observatory, when it passes the meridian ; and before observatories were established, the more rude observations of its approximate positions among the stars, from time to time, were sufficient to establish its periods with tolerable accuracy. Observations long continued, have established the fact that the average, or mean time, of the revolution of the moon from the longitude of any fixed star to the longitude of the same star again', is 27 days, 7 hours, 43 minutes, 1 1 seconds ; this is called its sidereal revolution. Its revolution in respect to the equinoxes is 7 seconds less, because the equinox itself runs back, or westward among the stars. This revolution is called the tropical revolution. What is the moon's mean parallax and mean distance ? By what kind of observations have the moon's periods been established? What is the mean revolution of the moon ? 144 ELEMENTARY ASTRONOMY. The mean daily motion of the moon from west to east is 13 10' 35". The mean daily motion of the sun, in the same direc- tion is 59' 08", hence the mean daily motion of the moon exceeds that of the sun by 12 11' 27", which will give a revo- lution in 29 days 12 hours 44 minutes and 3 seconds, which is called the synodic revolution. This is the average time from new moon to new moon again, and from full moon to full moon again. This interval is also called a lunation. Some lunations do not exceed 29 days and 7 hours, and others come near 29 days and 18 hours. The minimum lunations take place when the moon changes a day or two after the moon has passed its perigee, and the maxi- mum lunations take place when the moon changes a day or two after the moon has passed its apogee. If all lunations were alike in length of time, any one who can work problems in proportion, could compute the times of new and full moon. As it is, the computations are quite troublesome, as every dis- turbing cause of motion has to be separately considered and allowed for. To illustrate one of the principal causes of the inequality of lunations, we give the figure in the margin. Let E be the posi- tion of the earth, and CADB the moon's orbit, the moon moving in the direction from A to D and from D to B, and so on, round the ellipse. Let /S'be the direction of the sun ; then when the moon is near B, it is in conjunction with the sun. In 27d. 7h. 43m., or there- abouts, the moon will be round to the same point B again, but during that time the sun has apparently moved from S'to S , about 27, and the moon, to come again in range with the sun, What is the mean daily motion of the moon, in "longitude? What is the time from new moon to new moon again ? Why is this interval not always the same ? When is the interval the longest ? When the shortest T LUNAR MOTIONS. 145 must pass over about 27; but now, the moon being at its greatest distance from the earth, its motion is much slower than its mean motion, and therefore the time required to de- scribe this excess arc, will be greater than the mean time, and thus cause a long lunation. When the new moon takes place at B, the full moon will take place at A, and along in that part of the moon's orbit, the excess arc will be passed over by the moon in less than the average time, and thus cause the interval from full moon to full moon again, to be less than the average time, or a short lunation. By observing the moon's altitude when it comes on to the meridian, from time to time, it was early ascertained, that its pathway through the heavens among the stars, was not the same as that of the sun, but that the plane of its orbit was inclined to the plane of the ecliptic by an angle varying from 4 58' to 5 18', the mean inclination being 5 8'; the variation being caused by the disturbing action of the sun's attraction, that being different under different circumstances. The points where the moon's path crosses the ecliptic (the sun's path) are called the moon's nodes; the one where the moon passes from the south side of the ecliptic to the north side, is called the ascending node, and the one on the opposite side of the sphere where the moon crosses from the north side of the ecliptic to the south side, is called the descending node. The nodes are not stationary in the heavens they move backward on the ecliptic on an average of 19 19' 44" in a year, which will cause a com- plete revolution of the nodes in 18 years 228 days and 9 hours; (360 \ ) 19 19' 44 Y This period is nearer 19 than 18 years, and it is a period in which the path of the moon through the heavens is very nearly By what observation was the inclination of the moon's orbit to the eclip- tic determined ? What is that inclination ? What are these points called when the moon crosses the ecliptic ? Are these points stationary ? I* what time, and in what direction do they make a revolution? 13 146 ELEMENTARY ASTRONOMY. the same as it was 19 years before, and it is called the lunat cycle or golden number.* This period has a governing influence over solar and lunar eclipses, but we reserve that subject for the next chapter. When the sun is in, or near the moon's nodes, its attraction on the moon has no tendency to draw the moon out of the plane of its orbit, and at those times the natural inclination of the lunar orbit to the ecliptic is about 5 1 8'. When the sun is 90 from the moon's node, then the inclination of the lunar orbit to the ecliptic is often not more than 5, because the ten- dency of the sun's attraction is then to draw the moon towards the ecliptic, and this same tendency actually causes the moon to run into the ecliptic sooner than it otherwise would, thus producing a retrograde motion of the nodes themselves. The points in the heavens where the moon arrives at its apogee and perigee, are generally opposite to each other, but rarely exactly so, nor are these points stationary in the heavens but make a direct revolution in 3231.^^ days, nearly 9 years, but the true motion is very variable, some- times backward, sometimes forward, and sometimes stationary, but the forward or direct motion towards the east prevails, making a revolution in the time just noted. The lunar apogee is much influenced by the position of the sun ; it is dragged after the sun (so to speak), when the sun is a little in advance of it, and retarded in its motion, and even retrograde in its motion, when the sun is a little west of it. In short, the lunar orbit is not an ellipse, but resembles that figure more nearly than any other, and it is continually varying in its general eccentricity. * The Athenians, 433 before Christ, inscribed this number in letters of gold on the walls of the temple of Minerva. Hence it is denominated the GOLDEN NUMBER. What is the golden number ? What makes the period ? Why so called? What causes the retrocession of the nodes? Is the longer axis of the moon's orbit stationary in the heavens ? In -what direction and in what time do the apogee and perigee points revolve ? LUNAR MOTIONS. 147 The revolution of the apogee is called the anomalactic period. The fact that the same face of the moon is always towards the earth, shows that it turns on an axis in the same time it revolves round the earth, otherwise all sides oi it- would in time be presented to our view. The mean motion on its axis, and the mean motion or revo- lution round the earth, is exactly the same, but the motion on its axis is uniform, and the motion in its orbit is variable, and this gives the face of the moon an apparent vascillating motion, which is called the moon's libration. There is a lib-ration in longitude caused by the moon's unequal motion in longitude, and a libration in latitude caused by the varying inclination of its orbit with the ecliptic. " The moon, like the planets, is an opake body, and shines entirely by the light received from the sun, a portion of which is reflected to the earth. As the sun can only enlighten one- half of a spherical surface at once, it follows that according to the situation of an observer, with respect to the illuminated part of the moon, he will see more or less of the light reflected from her surface. At the conjunction, or time of new moon, the moon is between the earth and the sun, and consequently that side of the moon which is never seen from the earth, is enlightened by the sun; and that side which is, constantly turned towards the earth is wholly in darkness. Now, as the mean motion of the moon in her orbit exceeds the apparent motion of the sun by about 12 11' in a day, it follows that, about four days after the new moon, she will be seen in the evening a little to the east of the sun, after he has descended below the western part of the horizon. A spectator will see the convex part of the moon towards the west, and the -horns or cusps towards the east : or if the observer live in north latitude, as he looks at the moon the horns will appear to the left hand ; for if the line joining the cusps of the moon be What truth is revealed by the fact that the same face of th? moon is al- ways towards the earth? What is mean! by libration, and from what does it arise ? How do we know that the moon does not shine by its own light? 148 ELEMENTARY ASTRONOMY. bisected by a perpendicular passing through the enlightened part of the moon, that perpendicular will point directly to the sun. As the moon continues her motion eastward, a greater portion of her surface towards the earth becomes enlightened ; and when she is 90 degrees eastward of the sun, which will happen about 7} days from the time of new moon, she will come to the meridian about six o'clock in the evening, having the appearance of a bright semi-circle. Advancing still to tiie eastward, she becomes more enlightened towards the earth, and at the end of about 14 days, she will come to the meri- dian at midnight, being diametrically opposite to the sun ; and consequently she appears a complete circle, and it is said to be full moon. The earth is now between the sun and the moon, and that half of her surface, which is constantly turned towards the earth, is wholly illuminated by the direct rays of the sun , whilst that half of her surface, which is never seen from the earth, is involved in darkness. The moon continuing her pro- gress eastward, she becomes deficient on her western edge, and about 7-J days from the full moon she is again within 90 degrees of the sun, and appears a semi-circle with the convex side turned towards the sun: moving on still eastward, the deficiency on her western edge becomes greater, and she appears a cres- cent, with the convex side turned towards the east, and her cusps or horns turned towards the west: and about 14^- days from the full moon she has again overtaken the sun, this period being performed in 29 days 12 hours 44 minutes 3 seconds, at a mean rate, as has been mentioned before. Hence, from the new moon to the full moon, the phases are horned, half -moon, and gibbous; and as the convex or well-defined side of the moon is always turned towards the sun, the horns or irregular side will appear to the east, or towards the left hand of a spectator in north latitude. From the full moon to the change, the phases When the moon is full, what is its position in respect to the, sun ? When the moon is at the first quarter, what is its position in respect to the sun? When at the last quarter, what is its position, and about what time would it come to the meridian V LUNAR APPEARANCES. 149 are gibbous, half-moon, and horned; the convex or well-defined side of her face will appear to the east, and her horns or kregu- lar side towards the west, or to the right hand of a spectator. " As the full moons always happen when the moon is directly opposite to the sun, all the full moons, in our winter, happen when the moon is on the north side of the equinoctial. The moon, while she passes from Aries to Libra, will be visible at the north pole, and invisible during her progress from Libra to Aries ; consequently, at the north pole, there is a fortnight's moonlight and a fortnight's darkness by turns. The same phenomena will happen at the south pole during the sun's ab- sence in our summer." The surface of the moon is greatly diversified with inequali- What is said of the full moons in winter ? run high, or low ? Do the full moons of suramei 150 ELEMENTARY ASTRONOMY. ties, which, through a telescope, have all the appearances of hills, mountains, and valleys. Many attempts have been made, with considerable success, to delineate the face of the moon on paper, as it appears through a telescope, and the figure on the preceding page is a copy of one of them. Dr. Herschel informs us that, on the 19th of April, 1787, lie discovered three volcanoes in the dark pan of the moon, two of them apparently extinct, the third exhibited an actual eruption "of fire, or luminous matter. On the subsequent night it appeared to burn with greater violence, and might be computed to be about three miles in diameter. The eruption resembled a piece of burning charcoal, covered by a thin coat of white ashes; all the adjacent parts of the volcanic mountain were faintly illuminated by the eruption, and were gradually more obscure at a greater distance from the crater. That the surface of the moon is indented with mountains and caverns, is evident from the irregularity of that part of her surface which is turned from the sun : for, if there were no parts of the moon higher than the rest, the light and dark parts of her disc at the time of her quadratures, would be terminated by a perfectly Straight line ; and at all other times the termination would be an ellip- tical line, convex towards the enlighted part of the moon, in the first and fourth quarters, and concave in the second and third: but instead of these lines being regular, and well defined, when the moon is viewed through a telescope, they appear notched, and broken in innumerable places. It is rather singular that the edge of the moon, which is always turned towards the sun, is regular and well defined, and at the time of full moon no notches or indented parts are seen on her surface. In all situ- ations of the moon, the elevated parts are constantly found to cast a triangular shadow with its vertex turned from the sun ; and, on the contrary, the cavities are always dark on the side next the sun, and illuminated on the opposite side : these ap- pearances are exactly conformable to what we observe of hills How long are the winter full moons visible from the north pole ? What full moous are visible more than 24 hours, as seen from the north pole ? LUNAR ATMOSPHERE. 151 and valleys on the earth : and even in the dark part of the moon's disc, near the borders of the lucid surface, some minute specks have been seen, apparently enlightened by the sun's rays : these shining spots are supposed to be the summits of high mountains, which are illuminated by the sun, while the ad- jacent valleys nearer the enlightened part of the moon are entirely dark. Whether the moon has an atmosphere or not, is a question that has long been controverted by various astronomers ; some endeavor to prove that the moon has neither an atmosphere, seas, nor lakes ; while others contend that she has all these in common with our earth, though her atmosphere is not so dense as ours." Whenever our own atmosphere is clear and transparent, every appearance of hill, and valley all the varieties of light, and shade indeed, all the spots on the moon are equally well defined and distinct, and this could not be, were the moon sur- rounded with an atmosphere capable of holding vapors, and clouds, like the atmosphere of our earth. Therefore, most astronomers conclude that such an atmosphere does not there exist. On the other hand, we must not forget that volcanoes have been observed on the moon and we can have no distinct idea of combustion, without an atmosphere or a gas, to support it. An atmosphere might exist, having no affinity for vapors, one that would be transparent, and, in that case we could always see through it, as though it did not exist; and if the moon has an atmosphere, it must be one of that kind. But of all this, nothing is positively known. What is the appearance of the edge of themoori between the illuminated and unillurainated parts ? What does this appearance surely indicate ? Why have astronomers contended that the moon has no atmosphere ? Are you sure the moon has no atmosphere ? What kind of an atmosphere may it have ? 162 ELEMENTARY ASTRONOMY. CHAPTER II. ECLIPSES. THE path of the sun through the heavens is the same every year. It is the ecliptic, so called, because all eclipses of the sun, and moon, take place when the moon is in or near this line. If the moon's path round the sphere were the same as the sun's, that is, if the moon were all the while in the ecliptic, there would be an eclipse of the sun at every new moon, and an eclipse of the moon at every full moon. The moon's orbit or path, as we have seen in the preceding chapter, intersects the ecliptic or sun's path at an angle of 5 8'; the points of in- tersection are called the moon's nodes ; and when the sun is in that part of the ecliptic near the moon's nodes, the moon cannot pass its conjunction with the sun without falling in range be- tween some part of the ecliptic, and some part of the earth, and that produces an eclipse of the sun. The two nodes are opposite to each other, and when the sun is near one node, the full moon will take place when the moon is near the other node ; and the sun, earth, and moon will be near one right line the earth between the sun and moon and then the moon must fall into some portion of the earth's shadow, and this produces an eclipse of the moon. If the moon's nodes were always at the same points on the ecliptic, eclipses would take place in the same months every year, but the nodes moving backward about 19 19' each year, the eclipses, on an average, come about 19 days earlier each suc- ceeding year. Because the two nodes are opposite to each Why is the path of the sun among: the stars called the ecliptic ? If tho sun and moon passed round the earth in the same circle or path, how often would eclipses occur ? At what angle does the moon's path intersect, the ecliptic ? Where must the sun be on the ecliptic at the time eclipses ocur? If the moon's nodes were stationary, would eclipses then occur at tho ssuua seasons of the year continually ? ECLIPTIC LIMITS. 153 other, eclipses must happen about six months asunder. For instance, if an eclipse occurs in the month of March, in any year, there will certainly be one in September, or on some of the last days of August, at the new or full moon. If an eclipse occurs in June, there will certainly be another in December. If one occurs in May there will be another in November, and so on continually, the average being a few days less than six months, and from year to year, the average time being at in- tervals of about 346 days. Whenever the moon changes within 17 of either of the moon's nodes, there must be an eclipse of the sun. That is, the sun must then be within 17 of one of the nodes, because at the time of change, the longitude of both sun and moon is then the same. Whenever the moon fulls, when the sun is within 12 of either node, there must be an eclipse of the moon. Hence, the number of eclipses of the sun which take place in any long interval of time, (say 19 years) must be to the number of eclipses of the moon as 17 to 12. But, an eclipse of the sun is visible from only a very small portion of the earth at any one time, while an eclipse of the moon is visible from a whole hemisphere ; hence there are more visible eclipses of the moon than of the sun, as seen from any one place. The least number of eclipses that can take place in any one year is two, the greatest number seven, the average number is four. When but two eclipses occur in a year, they are both of the sun, and are central as seen from some portion of the earth near the plane of the ecliptic. That is, a central eclipse would be seen from some latitude near the sun's declination. For example : if in a certain year there were but two eclipses, both Why do eclipses occur at opposite months of the year? Give the limits within which the sun must be at the time of the lunar changes, to produce eclipses ? Give the ratio between the number of eclipses of the sim and moon that take place in any long interval ? State the least and greatest number of eclipses that can take place in any one year. 164 ELEMENTARY ASTRONOMY. would be of the sun, and suppose one of them should take place in June, the other would take place in December, and the one which took place in June would be cen- tral as seen from some latitude not far from 20 north, and the one in December would be central as seen from some latitude not far from 20 south. Eclipses of the sun which take place when the sun is 10 or more degrees from the node, are partial eclipses, visi- ble from places not far from the poles of the earth. To show more clearly that the sun and moon must come in con- junction near the moon's node, we give the figure in the margin. The right line through the cen- ter represents the equator, the curved line ^f' LOJ the ecliptic, and the other curved line repre- sents the moon's path crossing the ecliptic at ^ and !>. The sun and moon are represented in con- junction a little beyond the sign 69, but the two paths are here so far asunder, that the sun and moon cannot come in range with each other and produce an eclipse. It is obviously not so, on the paths near their intersections, that is, near the nodes. As here represented the as- cending node is in longtitude about 210, and the descending ECLIPSES. 155 node is in longitude about 30, and this was the position of the nodes in the year 1846, and the sun is at these points of the ecliptic in April and Octobej*, and therefore the eclipses in that year must have been and really were in those months. To make a general and rough computation of the times that eclipses will occur, all we have to do is to get the position of one of the moon's nodes, by observation or otherwise, and then trace it back at the rate of 19 19' for 365 days, or at the rate of 3'. 18 per day. On the 1st of January, 1850, the mean longitude of the moon's ascending node was 146 7', the opposite node was therefore in longitude 326. The sun attains the longitude of 326 on or about the 15th day of February in each year, and the longitude of 146 on or about the 19th of August. There- fore the new and full moons that took place within twelve days of these times, must and did produce eclipses. Diminishing 146 7' at the rate of 19 19' for each 365 days, brought the moon's ascending node to 68 47'. 8 on the 1st of January, 1854, and to 61 23' on the 21st of May, 1854. The sun attains this longitude on the 22d of May, and on the 26th of May the moon changed. There must then have been an eclipse. The sun and moon at that time were about 4 past the moon's ascending node, just sufficient to cast the moon's shadow into the northern hemisphere, making a central eclipse at noon, in latitude 45 33' north, in longitude 134 45' west. The following figure may assist some learners to form a dis- tinct and general idea of eclipses. How far does the node run back in 365 days ? How much in one day ? If I give you the longitude of the node, can you tell me at what times of the year eclipses will occur ? 156 ELEMENTARY ASTRONOMY. When an observer is in the moon's shadow, the dark bod> of the moon appears to him on the face of the sun. When an observer on the earth is in a certain space adjoining the shadow, as at e and f, a part of the sun is obscured by a part of the moon. When the moon is in the earth's shadow, it cannot shine because the direct rays of the sun are intercepted by the earth, and the moon is said to be in an eclipse. Never- theless when the moon is near the center of the earth's shadow, a sufficient amount of light is refracted through the earth's atmosphere to render the moon darkly visible. When the moon is eclipsed to the inhabitants of the earth, the sun must be eclipsed to an observer on the moon. An ob- server on the moon will see the sun partially eclipsed, when the moon falls into the partial shadow marked P P. Although this figure answers our purpose to a certain extent, it also illus- trates and verifies the remarks made about figures on page 142. The distance from the center of the earth to the moon's orbit, is 30 diameters of the earth, but in the figure it is not three diameters. The distance to the sun is 400 times the distance to the moon, but in the figure it is not five times that distance. When the earth is made of any apparent magnitude, there is not space enough on any paper for a true representation of any of these things. In reality, the moon's shadow comes to a point at about the distance of the earth from the moon, sometimes before it ex- tends to the earth, and then we have an annular, and not a total eclipse. When the moon is near her perigee, her shadow will extend beyond the earth ; when near her apogee, it will not extend to the earth. As we have before seen, the mean motion of the moon exceeds that of the sun by such an amount as to bring the two Can the moon be seen when in a total eclipse ? Is the figure on page 155 a true representation of the distances of the sun and moon 1 and if not, why was it nqt ma4e so ? Is the moon's shadow always of the same length ? and if nqt, what pauses its variation 1 ECLIPSES. 157 bodies in conjunction or opposition at the average interval of 29d. 12h. 44m. 3s., and the retrograde motion of the node is such as to bring the sun to the same node at intervals of 346d. 14h. 52m. 16s. Now let us suppose the sun, moon, and node are together at any point of time, and in a certain unknown interval of time, which we represent by P, they will be together again. In this time P, we will suppose the moon to have accomplished m lunations, and the sun to have returned to the same node n times. These suppositions give the following equations : (29d. 12A. 44m.)m=P. (1) And (346rf. 14A. 52m.)n=P. (2) Neglecting the seconds and reducing to minutes, we have 42524wi=P. (3) 499132ra=P. (4) Dividing (3) by (4), and reducing the numerator and de- nominator in the first member, gives us 10631m Or 124783 m As this fraction is irreducible, and as wand n must be whole numbers to answer the assumed conditions, therefore the smallest whole number for m is 124783, and for n 10631. That is, we see by equations (1) and (2), that to bring the sun, moon, and node a second time into conjunction, requires 124783 lunations, or 10631 returns of the sun to the node, which is 10088 years, and about 197 days. We say about, because we neglected seconds in the periods of revolution, and because the mean motions will change in some slight degree in a period of so long a duration. What number of lunations are required for the sun, moon, and node, to come in the .same position a second time ? Even then, will the coincidences be exact? 158 ELEMENTARY ASTRONOMY. This period, however, contemplates an exact return to the same positions of the sun, moon, and node, so that a line drawn from the center of the sun, through the center of the moon, will strike the earth at the same distance from the plane of the ecliptic ; but to produce an eclipse, it is not necessary that an exact return to former positions should be attained ; a greater or less approximation to former circumstances will produce a greater or less approximation to a former eclipse ; but exact coincidences, in all particulars, can never take place, however long the period. To determine the time when a return of eclipses may happen, (if we reckon from the most favorable positions), that is, com- mence with the supposition that the sun, moon, and node are together, it is sufficient to find the first approximate values of 4l , .. 10631 the fraction . 124783 If we find the successive approximate fractions, by the rule of continued fractions in arithmetic, we shall have the succes- sive periods of eclipses which will happen about the same node. The approximate fractions are T'T TV 3 3 T 4 4 y Jft rVVf These fractions show that at 1 1 lunations from the time an eclipse occurs, we may look for another; but if not at 11, it must be at 12, and it may be at both 1 1 and 12 lunations. At 5 and 6 lunations we shall find eclipses at the other node. To be more certain when an eclipse will occur, we take 35 lunations from a preceding eclipse, which is 1033 days and 14 hours nearly. There was a total eclipse of the moon, 1851, July 12th, 19 hours. Add to this 1033 days 14 hours, will bring up to May 12th, 1854, the time of another lunar eclipse. If an eclipse occurs within 10 of the node, it is certain that an eclipse will again happen at the lapse of 47 lunations. The period, however, which is most known and most remark - What do the numerators of the series of fractions indicate on page 158? What do the denominators indicate? Lunations between what events ? ECLIPSES. 159 able appears in the next fraction, which shows that 223 luna- tions have a very close approximate value to 19 revolutions of the sun to the node. 223 lunations equal - 6585.32 days. 19 returns of Q to node =6585.78 days. The difference is but a fraction of a day ; and if the sun and moon were at the node in the first instance, they would be only 20' from the node at the expiration of the period, and the dif- ference in the moon's latitude less than 2'; and, therefore, the eclipse at the close of this period must be nearly of the same magnitude as the eclipse at the beginning ; and hence, the expression "a return of the eclipse," as though the same eclipse could occur twice. This period was early discovered by the Chaldean astrono- mers, and hence, it is sometimes called the Chaldean period, and by it they were enabled to give general and indefinite predictions of eclipses that were to happen ; and by it any learner, however crude his mathematical knowledge, can desig- nate the day on which an eclipse will occur, from simply know- ing the date of some former eclipse. The period of 6585 days is 18 years (including four leap years) and 1 1 days over. Therefore, if we add 18 years and 11 days to the date of some former eclipse, we shall come within one day of the time of an eclipse arid it will be an eclipse of about the same mag- nitude as the one we reckon from. EX AMP LE S. In the year 1806 16 June, the sun was eclipsed. Add 18 11 1824 27 June, the sun was eclipsed. Add 18 10 How near do 19 revoluiions of the sun to the node correspond to 223 lu- nations ? What is meant by the Chaldean period ? What is its length and its use? An eclipse of the moon occurred July 1st, 1852 ; when may we look for another V 160 ELEMENTARY ASTRONOMY. 1842 8 July, the sun was eclipsed. Add 18 10 - (In this period are 5 leap years.) 1860 18 July, the sun will be eclipsed. Add 18 11 1878 29 July, the sun will be eclipsed. And thus we might go on over a great number of periods. The present year, 1854, May 26, a very remarkable eclipse of the sun will appear as visible in the north eastern part of the United States. From this we can predict the days for some future eclipses, as follows : 1854 26 May. Add 18 11 1 872 6 June, the sun will be eclipsed. Add 18 11 1890 17 June, the sun will be eclipsed. Thus we might go on, forward or backward, but to deter- mine on what portion of the earth any future eclipse will be visible, we must compute the time of day when the moon changes, and other circumstances, which in this work we do not pretend to take into account. These periods will not occur continually, because the returns are not exact, and the small variations which occur at each period, will gradually wear the eclipse away, and another eclipse will as gradually come on and take its place. In respect to these periods, those eclipses which take place about the moon's ascending node, commence near the north pole, and at each period come a little further south, and finally leave the earth at the south pole, after the lapse of 96 periods, or about 1729 years. Will an eclipse occur continually at periods of 18 years and 11 days ? How many periods are required to work one of these periods over the earth? ECLIPSES. 101 Those eclipses which take place about the moon's descending node, commence near the south pole and pass over the earth to the northward, in the same interval of time. Eclipses of the moon arj visible at all places where the moon is above the horizon, from the time the moon enters the earth's shadow until it leaves it; but ellipses of the sun are visible only to a limited distance from the center of the moon's shadow, and that limit does not exceed 60 on the earth. Eclipses of the sun, which occur in March, pass over the earth in a north- easterly direction; those which occur in September, pass over the earth in a southeasterly direction ; and those which occur in June and December, pass over in nearly an eastern direction. The moon eclipses other heavenly bodies as well as the sun. In its passage through the heavens the moon must occasionally pass between us and the planets, and between us and all those fixed stars that are situated within 6 of the ecliptic on either side. For in the period of 18 years, the moon must some time or other cover each portion of this space in the heavens. Such eclipses are called occupations, and if we include all the Btars from the first to the sixth magnitude, about 40 occultations take place each month, and on an average about two are visible from any one point each month. Unless it be an occasional eclipse of some of the larger planets by the moon, occultations are not visible to the naked eye, as the light of the moon obscures that of the stars, when the moon is near them, and therefore none but astronomers who have telescopes, can ob- serve these eclipses, and no others seem to be aware of their existence. A list of occultations can be found each year in the English Nautical Almanac. In what direction do solar eclipses pass over the earth ? Does the moon eclipse other bodies than the sun ? What are occultations, and about ho\v many occur each month ? 14 162 ELEMENTARY ASTRONOMY. CHAPTER III. THE TIDES. THE alternate rise and fall of the surface of the sea, as ob- served at all places directly connected with the waters of the ocean, is called tide ; and before its cause was definitely known, it was recognized as having some hidden and mysterious connec- tion with the moon, for it rose and fell twice in every lunar day. High water and low water had no connection with the hour of the day, but it always occurred in about such an interval of time after the moon had passed the meridian. When the sun and moon were in conjunction, or in opposition, the tides were observed to be higher than usual. When the moon was nearest the earth, in her perigee, other circumstances being equal, the tides were observed to be higher than when, under the same circumstances, the moon was in her apogee. The space of time from one tide to another, or from high water to high water (when undisturbed by wind), is 12 hours and about 24 minutes, thus making two tides in one lunar day ; showing high water on opposite sides of the earth at the same time. The declination of the moon, also, has a very sensible influ- ence on the tides. When the declination is high in the north, the tide in the northern hemisphere, which is next to the moon, is greater than the' opposite tide ; and when the declination of the moon is south, the tide opposite to the moon is greatest It is considered mysterious, by most persons,* that the moon Give a definition of tides. What connection was observed, in early times, between the moon and times of high water? When were tides higher than usual? What is the time from one high tide to another? THE TIDES. 163 by its attraction should be able to raise a tide on the opposite side of the earth. That the moon should attract the water on the side of the earth next to her, and thereby raise a tide, seems rational and natural, but that the same simple action also raises the oppo- site tide, is not as readily admitted; and, in the absence of clear illustration, it has often excited mental rebellion and not a few popular lecturers have attempted explanations from false and inadequate causes. But the true cause is the sun and moon's attraction ; and until this is clearly and decidedly understood not merely assented to, but fully comprehended it is impossible to understand the com- mon results of the theory of gravity, which are constantly exemplified in the solar system. We now give a rude, but striking, and we hope, a satisfactory expla- nation. Conceive the frame -work of the earth to be an inflexible solid, as it really is, composed of rock, and in- capable of changing its form under any degree of attraction ; conceive also that this solid protuberates out of the sea, at opposite points of the earth, at A and B, as represented in the figure, A being on the side of the earth next to the moon, m, and B opposite to it. Now, in connec- tion with this solid, conceive a great portion of the earth to be composed What is the true course of the tides ? Explain the true cause of the tide rising on the side of the earth opposite the moon ? 164 ELEMENTARY ASTRONOMY. of water, whose particles are inert, but readily move among themselves. The solid AB cannot expand under the moon's attraction, and if it move, the whole mass moves together, in virtue of the moon's attraction on its center of gravity. But the particles of water at a, being free to move, and being under a more powerful attraction than the center of the solid, rise toward A, producing a tide. The particles of water at I being less attracted toward m than the center of the solid, will not move toward m as fast as the solid, and being inert, they will be, as it were, left behind. The solid is drawn toward the moon more powerfully than the parti- cles of water at b, and the solid sinks in part into the water, but the observer at B, of course, conceives it the water rising upon the shore (which in effect it is), thereby producing a tide. Mathematicians have found, by analytical investigation, that the power of the moon's attraction to produce the tides, varies as the inverse cube of the distance to the moon. The sun's attraction on the earth is vastly greater than that of the moon ; but by reason of the great distance to the sun, that body attracts every part of the earth nearly alike, and, therefore, it has much less influence in raising a tide than the moon. From a long course of observations made at Brest, in France, it has been decided that the medium high tides, when the sun and moon act together in the syzigies, is 19. 317 feet; and when they act against each other (the moon in quadrature), the tides are only 9.151 feet. Hence the efficacy of the moon, in producing the tides, is to that of the sun, as the number 14.23 to 5.08.* * These numbers are found as follows : Let m represent the effective force of the moon, and s that of the sun. Then m-f-?=]9.3l7, and ms 9.151. Whence T?i=l4.23, and =5.08. Is the sun's attraction on the earth greater than that of the moon ? If so, why do we not have greater tides from the action of the sun than from the action of the mooii ? THE TIDES. 165 Among the islands in the Paciiic ocean, observations give the proportion of 5 to 2.2, for the relative influences of these two bodies; and, as this locality is more favorable to accuracy than that of Brest, it is he proportion generally taken. Having the relative influences of two bodies in raising the tides, we have the relative masses of those two bodies, pro- vided they were at the same distance. But the influence of the moon on the tides lias a variation corresponding with the inverse cube of the distance, and the distance to the sun is 397.2 times the mean distance to the moon. Hence, to have the influence of the moon on the tides, when that body is removed to the distance of the sun, we must divide its ob- served influence by the cube of 397.2. That is, the mass of the nioon, is to the mass of the sun, as the number - is to the number 2.2. If the mass of the earth is assumed to be unity, the mass of the sun, is found by its attraction, to be 354945; and now if we represent the mass of the moon by m, we shall have the following proportion : m : 354945 : : : 2.2. (397.2) 3 This proportion makes m, the mass of the moon, to be nearly T ' T . The more correct value is ^j, computed from other and more reliable data, which is to be found in our larger work. The time of high water at any given point is not commonly at the time the moon is on the meridian, but two or three hours after, owing to the inertia of the water ; and places, not far from each other, have high water at very different times on the same day, according to the distance and direction that the tide wave has to undulate from the main ocean. The interval between the meridian passage of the moon and the time of high water, is nearly constant at the same place. It is about fifteen minutes less at the syzigies than at the quad- Is the time of high water when the moon is on the meridian ? 166 ELEMENTARY ASTRONOMY. ratures ; but whatever the mean interval is at any place, it is called the establishment of the port. It is high water at Hudson, on the Hudson river, before it is high water at New York, on the same day; but the tide wave that makes high water one day at Hudson, made high water at New York the day before ; and the tide waves that make high water now, were, probably, raised in the ocean several days ago ; and the tides would not instantly cease on the annihilation of the sun and moon. The actual rise of the tide is very different in different places, being greatly influenced by local circumstances, such as the distance and direction to the main ocean, the shape and depth of the bay or river, o ny of the comets have wore than one tail ? COMETS. 171 of 1618, 100 degrees, so that its tail had not all risen when its head reached the middle of the heavens. The comet of 1680 was so great, that though its head set soon after the sun, its tail, 70 degrees long, continued visible all night. The comet of 1689 had a tail 68 degrees long. That of 1769 had a tail more than 90 degrees in length. That of 1.81 1 had a tail 23 degrees long. The recent comet of 1843 had a tail 60 degrees in length. " When we have determined the elements of a comet's orbit, we compare them with those of comets before observed, and see whether there is an agreement with respect to any of them. If there is a perfect identity as to the elements, we should have no hesitation in concluding that they belonged to different ap- pearances of the same comet. But this condition is not rigor- ously necessary ; for the elements of the orbit may, like those of other heavenly bodies, have undergone changes from the perturbations of the planets, or from their mutual attractions. Consequently, we have only to see whether the actual elements are nearly the same with those of any comet before observed, and then, by the doctrine of chances, we can judge what re- liance is to be placed upon this resemblance. "Dr. Halley remarked that the comets observed in 1531, 1607, 1682, had nearly the same elements ; and he hence con- cluded that they belonged to the same comet, which, in 151 years, made two revolutions, its period being about 76 years. It actually appeared in 1759, agreeably to the prediction of this great astronomer ; and again in 1 835, by the computation of several eminent astronomers. According to Kepler's third law, if we take for unity half the major axis of the earth's orbit, the mean distance of this comet must be equal to the cube root of the square of 76, that is, to 17.95. The major axis of its orbit must, therefore, be 35.9 ; and as its observed perihelion distance is found to be 0.58, it follows that its aphe- lion distance is equal to 35.32. It departs, therefore, from the sun tc thirty-five times the distance of the earth, and after- From what data do astronomers predict the return of comets ? 172 ELEMENTARY ASTRONOMY. ward approaches nearly twice as near the sun as the earth is, thus describing an ellipse extremely elongated. " The intervals of its return to its perihelion are not con* etantly the same. That between 1531 and 1607 was three months longer than that between 1607 and 1682; and this last was 18 months shorter than the one between 1682 and 1759. It appears, therefore, that the motions of comets are subject to perturbations, like those of the planets, and to a much more sensible degree. " Comets, in passing among and near the planets, are mate- rially drawn aside from their courses, and in some cases, have their orbits entirely changed. This is remarkably the case with Jupiter, which seems, by some strange fatality, to be constantly in their way, and to serve as a perpetual stumbling- block to them. In the case of the remarkable comet of 1770, which was found by Lexell to revolve in a moderate ellipse in the period of about five years, and whose return was predicted by him accordingly, the prediction was disappointed by the comet actually getting entangled among the satellites of Jupiter, and being completely thrown out of its orbit by the attraction of that planet, and forced into a much larger ellipse. By this extraordinary renconter, the motions of the satellites suffered not the least perceptible derangement a sufficient proof of the small- ness of the comet's mass." The comet of 1456, represented as having a tail of 60 in length, is now found to be Halley's comet, which has made several returns in 1531, 1607, 1682, 1759, and recently, in 1835. In 1607 the tail was said to have been over 30 degrees in length; but in 1835 the tail did not exceed 20 degrees. Does it lose substance, or does the matter composing the tail condense ? or, have we received only exaggerated and dis- torted accounts from the earlier times, such as fear, superstition, and awe, always put forth? We ask these questions, but can- not answer them. Does the same comet return at equal intervals? and if not, why? What circumstances show us that cornets have small masses ? COMETS. 173 " Professor Kendall, in his Uranography, speaking of the fears occasioned by comets, says : Another source of appre- hension, with regard to comets, arises from the possibility of their striking our earth. It is quite probable that even in the historical period, the earth has been enveloped in the tail of a comet. It is not likely that the effect would be sensible at the time. The actual shock of the head of a comet against the earth is extremely improbable. It is not likely to happen once in a million of years. 11 If such a shock should occur, the consequences might perhaps be very trivial. It is quite possible that many of the comets are not heavier than a single mountain on the surface of the earth. It is well known that the size of mountains on the earth is illustrated by comparing them to particles of dust on a common globe." The following cut represents a telescopic view of the comet of 1811: Is there a possibility that a comet may strike the earth ? If such a thing should occur, would it cause the destruction of the earth ? 174 ELEMENTARY ASTRONOMY. CHAPTER Y. ON THE PECULIARITIES OF THE FIXED STARS. FOR the facts as contained in the subject matter of this chapter, we must depend wholly on authority ; for that reason we give only a compilation, made in as brief a manner as the nature of the subject will admit. In the first part of this work it was soon discovered that the fixed stars were more remote than the sun or planets ; and now, having determined their distances, we may make further in- quiries as to the distances to the stars, which will give some index by which to judge of their magnitudes, nature, and peculiarities. " It would be idle to inquire whether the fixed stars have a sensible parallax, when observed from different parts of the earth. We have already had abundant evidence that their dis- tance is almost infinite. It is only by taking the longest base accessible to us, that we can hope to arrive at any satisfactory result. "Accordingly, we employ the major axis of the earth's orbit, which is nearly 200 millions of miles in extent. By observing a star from the two extremities of this orbit, at intervals of six months, and applying a correction for all the small inequalities, the effect of which we have calculated, we shall know whether the longitude and latitude are the same or not at these two epochs. " It is obvious, indeed, that the star must appear more ele- vated above the plane of the ecliptic when the earth is in the part of its orbit which is nearest to the star, and more de- pressed when the contrary takes place. The visual rays drawn What base is taken to measure the distance to the fixed stars? Do the fixed stars appear in the same direction from each extremity of this base? And if so, what does that prove? PECULIARITIES OF THE FIXED STARS. 175 from the earth to the star, in these two positions, differ from the straight line drawn from the star to the center of the earth's orbit ; and the angle which either of them forms with this straight line, is called the annual parallax. " As the earth does not pass suddenly from one point of its orbit to the opposite, but proceeds gradually, if we observe the positions of a star at the intermediate epochs, we ought, if the annual parallax is sensible, to see its effects developed in the same gradual manner. For example, if the star is placed at the pole of the ecliptic, the visual rays drawn from it to the earth, will form a conical surface, having its apex at the star, and for its base, the earth's orbit. This conical surface being produced beyond the star, will form another opposite to the first, and the intersection of this last with the celestial sphere, will constitute a small ellipse, in which the star will always appear diametrically opposite to the earth, and in the prolonga- tion of the visual rays drawn to the apex of the cones. " But notwithstanding all the pains that have been taken to multiply observations, and all the care that has been used to render them perfectly exact, we have been able to discover nothing which indicates, with certainty, even the existence of an annual parallax, to say nothing of its magnitude. Yet the precision of modern observations is such, that if this parallax were only 1", it is altogether probable that it would not have escaped the multiplied efforts of observers, and especially those of Dr. Bradley, who made many observations to discover it, and who, in this undertaking, fell unexpectedly upon the phe- nomena of aberration* and nutation. These admirable dis- coveries have themselves served to show, by the perfect agree- ment which is thus found to take place among observations, that it is hardly to be supposed that the annual parallax can amount to I". The numerous observations on the polar star, employed in measuring an arc of the meridian, through France, * Subjects which will come in tiie next chapter. What is meant by annual parallax ? Has such a parallax been observed? And if not, why? 176 ELEMENTARY ASTRONOMY. have been attended with a similar result, as to the amount of the annual parallax. From all this we may conclude, that as yet there are strong reasons for believing that the annual par- allax is less than 1", at least with respect to the stars hitherto observed. " Thus the semi-diameter of the earth's orbit, seen from the nearest star, would not appear to subtend an angle of 1"; and to an observer placed at this distance, our sun, with the whole planetary system, would occupy a space scarcely exceeding the thickness of a spider's thread. " It is evident that the stars undergo considerable changes, since these changes are sensible even at the distance at which we are placed. There are some which gradually lose their light, as the star g of Ursa Major. Others, as ft of Cetus, be- come more brilliant. Finally, there are some which have been observed to assume suddenly a new splendor, and then gradually fade away. Such was the new star which appeared in 1572, in the constellation Cassiopeia. It became all at once so brilliant that it surpassed the brightest stars, and even Venus and Jupi- ter, when nearest the earth. It could be seen at mid-day. Gradually this great brilliancy began to diminish, and the star disappeared in sixteen months from the time it was first seen, without having changed its place in the heavens. Its color, during this time, suffered great variations. At first it was of a dazzling white, like Venus ; then of a reddish yellow, like Mars and Aldebaran ; and lastly, of a leaden white, like Saturn. Another star which appeared suddenly in 1604, in the con- stellation Serpentarius, presented similar variations, and dis- appeared after several months. These phenomena seem to indicate vast flames, which burst forth suddenly in these great bodies. Who knows that our sun may not be subject to sim- ilar changes, by which great revolutions have perhaps taken place in the state of our globe, and are yet to take place. " Some stars, without entirely disappearing, exhibit varia- Do the fixed stars undergo any changes ? What is said of new stars, and in what constellations did they happen ? PECULIARITIES OF THE FIXED STARS. 177 tions not less remarkable. Their light increases and decreases alternately, in regular periods. They are called, for this reason, variable stars. Such is the star Algol, in the head of Medusa, which has a period of about three days ; ^ of Cepheus, which has one of five days ; /5 of Lyra, six ; v> of Antiuous, seven ; o of Cetus, 334 ; and many others. " Several attempts have been made to explain these period- ical variations. It is supposed that the stars which are subject to them, are, like to all the other stars, self-luminous bodies, or true suns, turning on their axes, and having their surfaces partly covered with dark spots, which may be supposed to present themselves to us at certain times only, in consequence of their rotation. Other astronomers have attempted to account for the facts under consideration by supposing these stars to have a form extremely oblate, by which a great difference would take place in the light emitted by them under different aspects. Lastly, it has been supposed that the effect in question is owing to large opake bodies, revolving about these stars, and occa- sionally intercepting a part of their light. Time, and the mul- tiplication of observations, may perhaps decide which of these hypotheses is the true one. One of the best methods of observing these phenomena is to compare the stars together, designating them by letters or numbers, and disposing of them in the order of their brilliancy. If we find, by observation, that this order changes, it is a proof that one of the stars thus compared, has likewise changed; and a few trials of this kind will enable us to ascertain which it is that has undergone a variation. In this manner, we can only compare each star with those which are in the neighbor- hood, and visible at the same time. But by afterward com- paring these with others, we can, by a series of intermediate terms, connect together the most distant extremes. This method, which is now practiced, is far preferable to that of the ancient astronomers, who classed the stars after a very vague What is understood by variable stars? How have astronomers at- tempted to acuut for these appearances? 178 ELEMENTARY ASTRONOMY. comparison, according to what they called the order of their magnitudes, but which was, in reality, nothing but that of their brightness, estimated in a very imperfect manner." DOUBLE AND MULTIPLE STARS. " There are stars which, when viewed by the naked eye, and even by the help of a telescope of moderate power, have the appearance of only a single star ; but, being seen through a good telescope, they are found to be double, and in some cases, a very marked difference is perceptible, both as to their bril- liancy and the color of their light. These Sir W. Herschel supposed to be so near each other, as to obey, reciprocally, the power of each other's attraction, revolving about their common center of gravity, in certain determinate periods. Castor. y Leonis. Rigel. Pole Star, n Monoc. $ Cancri. "The two stars, for example, which form the double star Castor, have varied in their angular situation more than 45 since they were observed by Dr. Bradley, in 1759, and appear to perform a retrograde revolution in 342 years, in a plane per- pendicular to the direction of the sun. Sir W. Herschel found them in intermediate angular positions, at intermediate times, but never could perceive any change in their distance. The retrograde revolution of y in Leo, another double star, is sup- posed to be in a plane considerably inclined to the line in which we view it, and to be completed in 1200 years. The stars 5 of Bootes, perform a direct revolution in 1681 years, in a plane oblique to the sun. The stars f of Serpens, perform a retro- grade revolution in about 375 years; and those of y in Yirgo in 708 years, without any change of their distance. In 1802, the large star of Hercules, eclipsed the smaller one, though What is understood by double stars? Do double stars revolve about ach ether ? Mwtieu the times of revolution sme !' tnem. PECULIARITIES OF THE FIXED STARS. 179 they were separate in 1782. Other stars ai;e supposed to be united in triple, quadruple, and still more complicated systems. " With respect to the determination of the real magnitude of the stars, and their respective distances, we have as yet made but little progress. Researches of this kind must be left to future astronomers. It appears, however, that the stars are not uniformly distributed over the heavens, but collected into groups, each containing many millions of stars. We can form some idea of them, from those small whitish spots called Nebulae, which appear in the heavens as rep- resented in the accompanying illustration. By means of the telescope, we distinguish in these collec- tions an almost infinite number of small stars, so near each other, that their rays are ordinarily blended by irradiation, and thus present to the eye only a faint uniform sheet of light. That large, white, luminous track, which tra- verses the heavens from one pole to the other, under the name of the Milky Way, is probably nothing but a nebula of this kind, which appears larger than the others, because it is nearer to us. With the aid of the telescope we discover in this zone of light such a prodigious number of stars that the imagination is bewildered in attempting to represent them. Yel, from the angular distances of these stars, it is certain that the space which separates those which seem nearest to each other, is at least a hundred thousand times as great as the radius of the What is meant by Nebulae ? What is said 412 2439 41 49 581 7 1 16 1 25 1 35 1 40 1 46 1 51 1 57 2 3 A 48 413 2844 45 55 1 4.1 14 1 25 1 35 1 471 531 592 52 112 28 h 51 514 3045 501 1 7 121 23 1 35 1 47 2 02 62 132 212 24'2 36 52 SM15 3.1 47 521 31 14 1 26 1 38 1 51 2 52 122 192 272 35,2 43 53 5 : 16 32 49 541 6 1 17 1 29 1 42 1 56 2 102 172 25 2 33 2 49i2 58 54 617 33 50 56 1 8 1 20 1 331 462 02 152 232 31 2 402 571 3 7 206 SEQUEL. EXAM PLES. 1. On the 10th day of January, 1858, the right ascensisn of the planet Jupiter will be 2/i. 16m. 525., and declination 12 32' north. The right ascension of the sun, at the same time, will bo \Qh. 28m. nearly. What time will the planet pass the meridian, and what lime will it rise and set, observed from latitude 42 north? h. m. s. From the R. A. of Jupiter, +24h. 26 16 52 Subt. the R. A. of sun, - - 19 28 Apparent time that Jupiter passes mer. 6 48 52 P. M. To 6h. add Ascensional diff. 45m. - 6 45 Jupiter rises, (apparent time, ) - 3 52 P. M. Jupiter sets, (next morning,) at 1 33 52 A. M. 2. What time (approximately) will Sirius rise, pass the mer* dian, and set, on 4th of March, observed from New York? h. m. FromR. A. Sirius +24h. (see Tab. II,) 30 39 nearly. Subt. R. A. of sun, (see p. 6, of Tables) 23 1 nearly. Sirius passes meridian, apparent time, 7 38 P. M. From 6h. take Ih. nearly, (semi-diur. arc,) 5 Sirius rises at 2 38 P. M. Sirius sets next morning at 38 A. M. Thus we might operate with any planet, or star. The moon requires more care ; we must have its right as- cension and declination, at times, as near that of rising and setting, as we can procure, and also, take parallax into account. TABLES. l EXTRACTS FROM THE NAUTICAL ALMANAC POR JANUARY, 1846. . THE SUN'S _ *U rt Apparent oi tne Radius THE MOON'S Vector 9 "5 Longitude. Latitude. of the Earth. Longitude. Latitude. Semi- diam. Hor. Paral. Q Noon. Noon. Noon. Noon. Noon. Noon. Noon. 1 O 1 II 280 46 15.3 n N.0.49 9.99266 o // 330 42 13.9 o / // N.4 54 8.5 16 21.6 / n 60 2.3 2 281 47 26.1 0.45 9.99266 445 7 12.0 4 24 8.7 16 8.3 59 13.5 282 48 36.5 0.37 9,99267 359 4 55.4 3 39 5.9 15 53.9 58 20.5 4 283 49 46.5 0.27 9.99267 12 35 34.7 2 43 1.9 15 39.8 57 28.7 O 284 50 56.1 0.1G J.!)9268 25 41 31.5 1 39 55.7 15 26.7 56 40.8 6 285 52 5.3 N.0.03 9.99268 38 26 25.0 N.O 33 28.3 15 15.2 55 58.7 m 286 53 13.9 S. 0.11 9.99270 50 54 23.2 S.O 33 36 15 5.6 55 23.3 8 287 54 22.0 0.25 9.99271 63 9 30.1 1 36 46.8 14 57.6 54 54.1 y 288 55 29.7 0.38 9.99272 75 15 21.8 2 35 8.6 14 51.5 54 31.6 10 289 56 36.8 0.49 9.99274 87 14 56.3 3 25 55.4 14 46.9 54 14.6 11 290 5V 43.4 0.58 9.99277 99 10 31.3 4 7 13.7 14 43.8 54 3.3 12 291 58 49-5 0.65 9.99279 111 3 50.8 4 37 30.7 14 42.1 53 57.0 13 292 59 55.3 0.70 9.99282 122 56 17.6 4 55 38.9 14 41.7 53 55.7 14 294 1 0.5 0.71 9.99285 134 49 7.9 5 564 14 42.8 53 59.8 i: 295 2 5.4 0.69 9.9928t 146 43 48.4 4 53 7.6 14 45.5 54 9.7 16 296 3 9.9 0.64 9.99292 158 42 11.3 4 32 23.1 14 50.0 54 26.0 17 297 4 14.0 0.57 9.99295 170 46 44.8 3 59 17.1 14 56.3154 49.0 18 298 5 17.8 0.47 9.99299 183 38.7 3 14 47.1)15 4.6 55 19.7 19 299 6 21.21 0.35 9.99304 195 27 41.8 2 20 14.215 15.2 55 58.4 2( 300 7 24.21 0.23 9.99308 208 12 10.4 1 17 27.8 15 27.756 44.4 21 301 8 26.7J S.0.09 9.99313 221 18 27 5 S.O 8 53.1 15 42.0 57 37.0 j I 22 302 9 28.9 N.0.04 9.99318 234 50 26.7 N.I 2 20.515 57.3 58 32.9 2: 303 10 30.4 0.15 9.99323 248 50 42.5 2 12 11.716 12.5 59 28.8 2- 304 11 31.31 0.25 '1.99328 263 19 30.4 3 15 50.9 16 26.2 60 iy.o i 25 305 12 31.5 0.33 9.99334 278 13 48.8 4 8 2.8 16 36.8 60 57.9 26 306 13 30.9 0.38 9.9:)339 293 26 49.2 4 43 49.4 16 42.9 61 20.2 27 307 14 29.3 0.40 9.99345 308 48 22.8 4 59 32.416 43.5 61 22.6 98 308 15 26.8 0.40 9.99351 :;24 6 34.0 4 53 45.4 16 38.7 61 4.9 29 309 16 23.3 0.37 9.99357 339 9 55.3 4 27 32.S 16 28.960 29.1 30 310 17 18.5 0.30 1.9936: 353 49 32.0 3 44 %.<< 16 15.6 59 40.2 31 311 18 12.6 0.21 9.99369 8 13.1 2 47 5e.l 16 0.2 58 487 32 312 19 5.3J N.0.10 9.99.7J 5 21 40 34.3 N.I 43 50.( 515 44.2 57 45.1 TABLES. TABLE I. MEAN ASTRONOMICAL REFRACTIONS. Barometer 30 in. Thermomefer, Fah. 50. Ap. Alt. Rcfr. Ap. Alt. Refr. Ap. Alt. Reft. Alt. Refr. 0' 33' 51" 4-' 0' 11' 52" 12* 0' 4' 2>U" 42 W 1 4.6' 5 32 53 10 11 30 10 4 24.4 43 1 2.4 V 31 58 20 11 10 20 4 20.8 44 1 0.3 Jl5 31 5 30 10 50 30 4 17.3 45 58.1 fji) 30 13 40 10 32 40 4 13.9 46 56.1 25 29 24 50 10 15 50 4 10.7 47 54.2 30 28 37 5 9 58 13 4 7.5 43 52.3 35 27 51 10 9 42 10 4 4.4 49 50.5 40 27 6 20 Q 27 20 4 14 50 48.8 45 26 24 30 9 11 80 3 5K4 51 47.1 50 25 43 40 8 58 40 3 55.5 52 45.4 55 25 3 50 8 45 50 3 52.6 53 43.8 1 24 25 6 8 32 14 3 49.9 54 42.2 5 23 48 10 8 20 10 3 47.1 55 40.8 10 23 13 20 8 9 20 3 44.4 56 39.3 15 22 40 30 7 58 30 3 41.8 57 37.8 20 22 8 40 7 47 40 3 39.2 i)8 36.4 25 21 '37 50 7 37 50 3 36.7 59 35.0 30 21 7 7 7 27 15 3 34.3 60 33.6 35 20 28 10 7 17 15 30 3 27.3 B] 32.3 40 20 10 2!) 7 8 16 3 20.6 62 31.0 45 19 43 30 6 59 16 30 3 14.4 63 29.7 50 19 17 40 6 51 17 3 8.5 64 28.4 55 18 52 50 6 43 17 30 3 2.9 65 27.2 2 18 29 8 6 35 18 2 57.6 66 25.9 5 18 5 10 6 28 19 2 47.7 67 24.7 10 17 43 20 6 21 20 2 38.7 68 23.5 15 17 21 30 6 14 21 2 30.5 69 22.4 20 17 40 6 7 22 2 23.2 70 21.2 25 16 40 50 6 23 2 16.5 71 19.9 30 16 21 9 5 54 24 2 10.1 72 18.8 35 16 2 10 5 47 25 2 4.2 73 17.7 40 15 43 20 5 41 26 58.8 74 16.6 45 15 25 30 5 36 27 53.8 75 15.5 50 15 8 40 5 HO 28 49.1 76 14.4 55 14 51 50 5 25 29 44.7 77 13.4 3 14 35 10 5 2U 30 40.5 78 12.3 5 14 19 10 5 15 31 36.6 79 11.2 10 14 4 20 5 10 32 33J) 80 10.2 15 13 50 30 5 5 33 29.5 PI 9.2 20 13 35 40 5 34 26.1 F2 8.2 25 13 21 50 4 56 35 23.0 b3 71 30 13 7 11 4 51 36 20.0 t-4 6.1 35 12 53 10 4 47 37 13.1 F5 , r ;.l 40 19 41 20 4 43 38 14.4 b6 4.1 45 12 28 30 4 39 39 1 11.8 87 3.1 50 12 16 40 4 35 40 1 9.3 88 2.0 55 12 3 50 4 31 41 1 6.9 89 1-0 TABLE C. CORRECTION OF MEAN REFRACTION. Hight of the Thermometer. - 24 28 o 320 360 40 44 52" 56 60^ 640 68 72 Jt>o 800 Lit.' H / a , ' ' 0.10: u.Oi) 0.2:) 0.30 0.40 0.50 i.OO 1.10 1.20 1.30 1.40 1.50 2.00 2.20 2.40 3.00 3.20 3.40 4.00 430 5.00 5.30 6.00 6.30 7.00 Q i. 12 .05 .59 .53 .48 .43 .38 .33 .29 .25 .21 .18 .11 .06 .01 57 53 49 45 41 38 35 33 31 27 1.55 1.49 1.44 1.39 1.34 1.29 1.25 1.21 1.17 1.14 1.11 1.08 1.05 1.00 55 51 47 44 41 38 35 32 30 28 26 23 ^28 .24 .20 .16 .12 .09 1.06 1.03 l.OC 57 55 53 48 44 41 38 36 33 31 28 26 24 22 21 19 1.11 1.08 1.04 1.01 58 55 53 50 48 46 44 42 39 37 34 32 29 28 26 24 22 20 19 17 16 15 51 48 46 44 42 40 38 36 34 32 31 30 29 26 24 22 21 20 18 17 16 14 13 12 12 10 31 29 28 26 25 24 23 22 21 20 18 17 17 16 14 13 13 12 11 10 9 9 8 7 7 6 10 9 9 8 8 8 7 7 6 6 6 6 5 5 5 4 4 4 4 3 3 3 2 2 2 2 29 27 26 25 24 23 21 20 19 18 18 17 16 15 14 13 12 11 10 9 9. 8 7 7 6 5 48 45 44 41 39 37 36 34 32 31 30 28 27 25 23 21 20 18 17 16 14 13 12 11 10 9 1.07 1.04 1.01 58 55 52 50 48 45 43 41 39 37 35 32 30 28 26 24 22 20 19 17 15 14 13 1.25 1.21 1.17 1.13 1.10 1.06 1.03 1.00 57 54 52 50 48 44 41 38 35 33 31 28 26 24 22 20 19 16 .43 .38 .33 .28 .24 .20 .17 .13 .09 .06 .04 .01 58 54 50 46 43 40 37 34 31 29 26 24 23 20 2.01 .54 .49 .43 1.38 .34 1.30 1.26 1.21 1.18 1.15 1.11 1.08 1.03 58 54 50 47 44 40 36 34 31 29 27 24 2.19 2.12 2.05 1.59 1.53 1.48 1.43 1.38 1.33 1.29 1.25 1.21 1.18 1.11 1.06 1.01 57 53 50 45 40 38 35 33 31 27 9 24 20 16 13 9 5 2 5 8 11 14 18 21 24 10 22 20 18 17 15 14 12 11 8 8 5 5 1 1 4 4 7 7 10 9 13 12 16 15 19 18 22 20 12 18 15 13 10 7 4 1 4 6 9 11 13 16 18 13 17 14 12 i 7 4 1 3 6 8 10 12 15 17 14 16 13 11 8 6 4 1 3 5 7 c 11 14 16 15 15 12 10 8 6 3 1 3 5 1 11 13 15 16 14 12 c 5 3 1 3 5 6 8 10 12 14 17 IS 1 ( ' 5 3 1 3 4 6 8 j 11 13 1 4 18 12 11 8 1 5 3 1 2 4 6 j ( 10 12 19 11 8 1 4 3 1 2 4 5 ' 8 10 11 20 11 i 6 4 2 1 2 4 t 6 8 9 11 21 10 i 5 4 2 1 2 3 i 6 ' 9 10 j*A 22 1C 5 4 2 1 2 3 r 6 ' 8 10 *** 23 c i 5 4 2 1 2 3 i 6 ' 8 9 24 ( 5 3 2 1 2 3 t t 1 8 9 25 i 5 3 2 1 2 3 i 1 7 8 s 4 3 2 1 2 3 i i 1 7 t 27 5 4 3 2 1 2 3 i r ( 7 : 28 J 4 3 2 1 2 'i c t 6 1 30 - 4 3 2 I 2 3 1 5 6 7 28.2 28.5C > 28.8o 291 29.75 30. Oa 30.35 30.64 30.93 Higlit of the Barometer. 18 TABLES. TABLE II. MEAN PLACES FOR 100 PRINCIPAL FIXED STARS, FOR JAN. 1, 1846. Star's Name. u CO % Right Ascen, Annual Yar Declination. Ann. Van t ANDROMED^E 1 2.3 3 3 2.3 2.3 3 1 3 3 o s 26.257 5 18.691 17 34.168 31 48.294 35 51.339 1 3 52.226 1 16 19.692 1 31 58.291 1 58 30.193 2 35 19.633 2 54 14.072 3 13 21.403 3 38 20.382 3 50 50.760 4 27 5.404 5 5 19.317 5 7 8.383 5 16 33.662 5 24 8.428 5 25 56.406 5 28 24.062 5 34 4 531 5 46 50.189 6 13 38.621 6 20 32.145 6 26 30.287 6 38 21.883 6 52 34.440 7 10 55.298 7 24 46.065 7 31 14.2.37 7 35 53.153 8 59.232 8 38 37 154 8 48 38.088 9 12 58.192 9 20 1.170 9 22 31.453 9 37 6.098 10.062 + 3.0720 3.0784 3.3054* 3.3418 + 2.9995 17.1346* 3.0015 2.2339 + 3.3475 3.1085 3.1266 4.2324 + 3.5473 2.7898 3.4274 4.4082 + 2.8787 3.7827 3.0609 2.6425 + 3 0404 2.1691 3.2433 3.6257 + 1.3279 30.7946 2.6459* 2.3558 + 3.5918 3.8561 3.1445* 3.6829* + 2.5596 3.1966 4.1261* 1.6100 + 2.9499 4.0504* 3.4258 + 3.2211 (leg. niin. sec. N.28 14 25.40 N.14 19 37.80 S.78 7 24.40 N.55 41 31.08 S.18 49 59.01 +2 8 0.'055 20.050 19.997 19.862 4-19.810 19.279 18.952 18.461 +17.432 15.621 14.532 13.329 +11.620 10.711 7.097 4.737 + 4.583 3.776 3.123 2.968 + 2.754 2.262 + 1.149 1.196 1.796 2.337 4.484* 4.562 6.110 7.253 8.758* 8.152 10.10-1 12.800 13.464 14961 15.366 1 6.108* 16.283 -17.377 y PEGASI (Algenib),.. . . & Hydri, $ Ceti, a URS. MiN. (Polaris),. 6 1 Ceti N.88 29 17.88 S. 8 58 45 93 S.58 1 14.34 N.22 43 53.86 N. 2 35 1.17 N. 3 28 55.70 N.49 18 28.20 N.23 37 27.73 S. 1357 1.50 N.16 11 41.39 N.45 50 6.56 S. 8 23 3.33 N.28 28 17.49 S. 25 4.86 S. 17 56 12.77 S. 1 18 17.53 S.34 9 36.95 N. 7 22 22.32 N.22 35 13.16 S.52 36 49.17 N.87 15 31.20 S. 16 30 32.83 S. 28 45 59.38 N.22 15 37.47 N.32 13 12.93 N. 5 36 54 95 N.28 23 34.06 S.23 51 50.94 N. 6 58 48.51 N.48 38 32.35 S.58 37 49.78 S. 7 59 39.05 N.52 22 31.09 N.24 28 49.46 N.12 43 2.96 t Eridani (Achernar),. a. ARIETIS y Ceti, o 3 Tauri, 3 2.3 1 1 1 2 2 3.4 2.3 2 1 3 1 6 1 2.3 3.4 3 1 .2 2 3.4 4 3.4 2 2 3 3 1 J Eridani, ee TAURI, (Aldebarari) ,. . a. AuRlUJE, (Capella),.. . ORIONIS, (Rigel), 10 TAURI, fj. Gcminorum, Argus, (Canopus),. . . 51 (Hev.) Cephei a CAMS MAJ., (Sirius), i Canis Majoris J Gerntnoruni a 2 GEMINOR. (Castor),... a CAN. MIN., (Procyon), $ GEMINOR, (Pollux),.. t Hydrae, / Urs Majoris, v. HYDROS LEONIS, (Regulus),. . . TABLE II. Star's Name. g Right Ascen, Annual Var. Declination. Ann. Var. 2 t) 3 3.4 2 5 1 2 2^3 1 2 [ 3 1 1 1 3 3 3 2 .3 2 2 .3 4 2 3 1 3 2 4 3.4 6 2 2 2 3. 3 1 3 3 3. 3 3'. 3 39 6.223 54 10.737 1 5 54.583 1 11 38.718 1 41 12.066 1 45 42.219 2 9 26.893 12 18 4.916 12 26 18.465 12 48 49 007 13 17 5.233 13 41 27.894 13 47 21.140 13 53 0.800 14 8 38.366 14 29 11.925 14 38 15.706 14 42 22.132 14 51 13.199 15 8 43.595 15 28 10.083 15 36 41 077 4- 2.3051 3.8001 3.1928 3.0010 + 3.0654* 3.1874 3.3409 3.2710 + 3.1342 2.8403 3.1512 2.3525* + 2.8606 4.1508 2.7336* 4.0165* + 2.6229 -+- 3.3102 0.2692 + 3.2226 + 2.5279 + 2.9391 2.3520 + 3.4742 + 3.1382 3.6638 0.7960 + 6.2587 6.5328* + 2.7320 106.8627 1.3513 4- 2.7727 1.3900 + 3.5861 19.2683 -|- 2.0118 2.2124 2.75G6 + 3.0086 + 2.8511 2.9254 2.944H 3.3315 deg. min. sec. S. 58 52 34.26 N.62 34 51.81 N.21 21 59.86 S.13 56 46.85 N.15 25 58.12 N 54 33 3.18 S.78 27 26.15 S. 62 14 39.74 S. 22 32 39.93 N.39 9 4.18 S. 10 21 20.80 N.50 5 1.45 N.19 10 21.03 S.59 37 33.93 N.19 59 12.07 S. 60 11 37.00 N.27 43 35.23 S. 15 23 53.52 N.74 47 5.58 S. 8 48 38.53 N.27 14 11.07 N 6 54 49 88 18.33 19.24 19.50 19.61 1999 20.02 20.04 19.99 19.92 19.60 18.94 18.12 17.89 17.67 18.9-1* 15.12* 15.46 15.23 14.71 13.63 12.33 11.74 10.80 10.29 9.55 8.48 8.32 7.48 5.03 4.54 3.14 2.88 2.81 0.61 + 0.40 + 1.91 + 2.77 3.86 5.05 + 6.67 + 8.39 8.74 8.55 10.74 A URS^E MAJORIS .... J 1 LKONIS 2.36120 2.3788; > 2.42190 2.52630 2.5895 2.66514 2.76910 2.77125 5.202776 9 538786 19182390 29.59 DAYS. 9.587818 87.969258 9.859306 224.700787 G.O.'OOO!)! 365.256383 0.1828I0 1 686979646 0.373100 1324.289 0.376384 1327.973 0384 '04 1375. nearly 0.402487 1469.76 0.413211! I5l2.nearly 0.425710 1594.721 " 0442334 1683.064 0.442725 1685.162 0.716212 4332.584821 097947610759.219817 1.28285330686.8208 1.4771216012814 1.944324 2351610 2 562598' 2.836942! 3.121991J 3.123190 3.138303 3.167300 3.179547 3.202700 3.226086 3.226610 3.636738 4.031718 4.486953 4.779076 Mercury . Venus . . . The Earth Mars .... Vesta ... Iris 1 . Hebe 1 Flora [ * AstreaJ . Juno. . . Ceres .... Pallas . . . Jupiter.. . Saturn.. . Uranus . . Neptune . TABLE III. ELEMENTS OF ORBITS FOR THE EPOCH OF 1850, JANUARY 1, MEAN NOON A.1 GREENWICH. Planets. Inclinati'n of orbits to ecliptic. Variation in 100 years. Long, of the ascending nodes. Variation in 100 years. Longitude of Perihelion. Variation in 100 years. Mean longi- tude at epoch. Mercury Venus. . Earth... Mars . . . Vesta... O ' " 7 18 3 23 26 1 51 6 7 8 29 13 2 53 +18.2 4.6 0.2 12. O ' " 46 34 40 75 17 40 48 20 24 103 20 47 170 53 +51 +42 +26 75 9 47 129 22 53 100 22 10 333 17 57 254 4 34 54 18 32 + 93 + 78 103 +110 157 O ' 327 17 9 243 58 4 100 47 1 182 9 30 113 28 12 165 17 38 10 37 17 80 47 56 147 25 41 1 3 10 Pallas 34 37 44 172 42 38 121 30 13 327 31 24 Jupiter.. Saturn. . Uranus. . 1 18 42 2 29 29 46 27 22. 15. 3. 98 55 19 112 22 54 73 12 +57 +51 +24 11 56 90 7 168 14 47 + 95 +116 + 87 160 21 50 13 58 13 28 20 22 * We give the logarithms in the tables, that the data may be at hand to exercise tlie student on Kepler's third law. TABLE III. TABULAR VIEW OF THE SOLAR SYSTEM. Names. Mass. Density. Gravity. Siderial. Rotation, ' -f and Heat. Mercury . . WI**Tff 3.244 1.22 h. m. *. 24 5 28 6.680 Venus Iffl'zTT 0.994 0.96 23 21 7 1.911 Earth Mars ..... WAW 1.000 0973 1.00 050 24 24 39 21 1.000 431 Jupiter . . 0.232 2.70 9 55 50 .037 Saturn .... *iff-F 0.132 1.25 10 29 17 .011 Uranus . . . TTilff 1 0.246 0.256 1.06 28.19 Unknown. 25d. I2h. Om .003 Moon 0.665 0.18 27 7 43 TABLE III. Planets. Eccentricities of orbits. Variation in 100 years. Motion_jn mean long, in 1 year of 365 days. Mean Daily n Motion in longitude. Mercury . . . Venus 0.20551494 0.00686074 -|- .000003868 .000062711 O ' " 53 43 3.6 224 47 29.7 O ' " 4 5 326 1 36 78 Earth Mars 001678357 0.09330700 .000041630 4- .0000901 76 14 19.5 191 17 9.1 59 8.3 31 26.7 Vesta 08856000 4- OOH004009 16 179 25556000 13 33 7 Ceres 07673780 000005830 12 494 Pallas 24199800 12 48 7 Jupiter Saturn Uranus 0.04816-210 0.05615050 0.04661080 + .000159350 .000312402 .000025072 30 20 31.9 12 13 36.1 4 17 45.1 4 59.3 2 0.6 42.4 TABLE III. LUNAR PERIODS. Mean sidereal revolution, 27.321661418 Mean synodical revolution, 29.530588715 Mean revolution of nodes (retrograde), 6793.391080 Mean revolution of perigee (direct), 3232.575343 Mean inclination of orbit, . 5 8' 48" Mean distance, in measure, of the equatorial radius of the earth, 29.98217 Meau distance, in measure, of the mean radius, 30.20000 TABLES. SATELLITES OP JUPITER. Bat. Mean Distance. Sidereal Revolu- tion. Inclination of Orbit to that of Jupiter. Mass ; that of Jupiter being 1000000000. 1 2 3 4 604853 9.62347 15.35024 26.99835 d. h. m. 1 18 28 3 13 14 7 3 43 16 16 32 O ' " 3 5 30 Variable. Variable. 2 58 48 17328 23235 88497 42659 SATELLITES OF SATURN. Sat. Mean Distance. Sidereal Revolu- tion. Eccentricities and Inclinations. d. b. m. The orbits of the six inte- 1 33.51 22 38 rior satellites are nearly cir- 2 4.300 1 8 53 cular, and very nearly in the 3 5.284 1 21 18 plane of the ring. That, of 4 6.819 2 17 45 the seventh is considerably 5 9.524 4 12 25 inclined to the rest, and ap- 6 7 22.081 64.359 15 22 41 79 55 proaches nearer to coincidence with the ecliptic. SATELLITES OF URANUS. Sat. Mean Distance. Sidereal Period. Inclination to Ecliptic. 1? 2 3? 4 52 6? 13.120 17.022 19.845 22.752 45.507 91.008 d. h. m. . 5 21 25 8 16 56 5 10 23 4 13 11 8 59 38 1 48 107 16 40 Their orbits are inclined about 78 58' to the ecliptic, and their motion is retrograde. The periods of the 2d and 4th require a trifling correction. The orbits appear to be nearly circles. 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