An introduction to astronomy ...

Introduction

ASTRONOMY

JJKSIGNED AS A

READER AND TEXT-BOOK

SCHOOLS AND FAMILIES.

Rev. JOHN T)AA^IS, A.M

PHILADELPHIA: J. B. LIPPINCOTT & CO.

Entered, according to Act of Congress, in the year 1867, by

JOHN DAYIS,

in the Clerk's OflBce of the District Court of the United States for the Western

District of Pennsylvania.

CAXTON PRESS OF ;RMAN & CO., PHILADELPHIA

Preface

This work is designed to fill a vacuum in schools and families. With the advancement of science there should be a corresponding advancement in the facilities for acquiring a knowledge of it. To economize time and expense in this department is of as much importance to the student as frugality and industry are to the success of the manufacturer or the merchant. Impressed with the importance of these facts, and having a desire to aid in the general diffusion of useful knowledge by giving them some practical form, this work has been prepared. It has a double purpose. As a reader, it contains a great variety of topics ; and, being almost entirely divested of scientific terms and phrases, its language is level to the comprehension of the youthful mind. As a text-book, it treats first of the sun and those heavenly bodies with which we are all, by observation, most familiar, and advances, consecutively, in the investigation of other worlds and systems which the telescope has revealed to our view. Thus to enhance the interest and value of this work to the student and casual reader, nearly all of the topics that it contains are fully illustrated by engravings, prepared expressly for that purpose. And to promote this object still further, and impart knowledge in the most impressive manner by a sensible demonstration of the arrangement, relations, and various motions of the component parts

4 PREFACE.

of the planetary system, the Planetelles, Heliotellus, and Lunatellus, have been invented by the author and put into public use. Each of these instruments is invaluable in acquiring a knowledge of astronomy and geography. With these facilities for illustration which address themselves to the mind through the eye, and the plainness and simplicity which characterize the entire work, the author would respectfully present it to a generous public, trusting that it may be the means of disseminating a general knowledge of that ennobling science on which it treats.

Contents

PAaE

Planetelles 11

Heliotellus 13

luxatellus 15

Section I. — History of Astronomy 17 II.— The Planetary or Solar System 19

TIL— The Sun 23

IV. — Sun's Atmosphere 21

v.— Solar Spots 25

VL— Motions of the Sun 2G

VII.— Mercury 29

VIII.— Venus 33

IX. — Transits, Conjunctions, and Motions of Mercury

and Venus 34

X. — The Earth, — its Annual Motion 36

XL— Daily Motion of the Earth 38

XII.— The Moon 40

XIII. — Phases of the Moon 41

XIV. — Solar and Lunar Eclipses 42

XV. — Lunar Eclipses 45

XVI. — Lunar Influences 45

XVII. — Lunar Atmosphere 48

XVIIL— Lunar Surface 50

XIX.— Mars 54

XX.— The Asteroids 55

XXI. — Jupiter 58

XXII. — Jupiter's Moons 60

XXIIL— Saturn and his Rings 62

XXIV.— Saturn and his Moons 66

XXV. — Uranus, Herschel, or Georgium Sidus 68

1* 5

6 CONTENTS.

PAGE

Section XXYL— Satellites of Uranus 69

XXVIL— Neptune 70

XXVIIL— Satellites of Neptune 71

XXIX.— Light and Heat on Neptune 72

XXX.— The Earth— one of a Class 74

XXXL— Planets inhabited 75

XXXII. — General Configuration of the Heavenly Bodies 77

XXXIIL— Specific Form of the Earth 79

XXXI v.— The Planets— Oblate Spheroids 81

XXXV. — Position of the Solar System in Relation to the

Starry Heavens 82

XXXVI.- -Motions of the Planets around the Sun 85-

XXX VII.— Centrifugal and Centripetal Forces 87

XXXVII L— Motion of the Planets on their Axes 90

XXXIX.— Weight of Objects on the Sun and Planets 91

XL. — Earth's Atmosphere 93

XLL— Eefraction 96

XLIL— Twilight 99

XLIIL— Aurora Borealis 101

XLIV.— Shooting Stars 105

XLV. — Meteorites, Aerolites, and Fireballs 108

XLVL— Zodiacal Light 112

XLVIL— Light 115

XLVIIL— Colors of Light 119

XLIX.—Eefracting Telescope 123

L. — Reflecting Telescope 125

LL— Comets— Their Early History 127

LIL— Encke's Comet 129

LIII.—Biela's Comet 132

LIV.— Halley's Comet 135

LV.— The Comet of 1744 137

LVL— The Comet of 1843 140

LVII. — General Form and Appearance of Comets 142

LVIIL— Gravity of Comets 144

CONTENTS. 7

PAGE

Section LIX. — Earity of Comets 145

LX.— Nature of Comets 148

LXI.— Comets shine by Keflected Light.. 149

LXII. — Anomalous Aspect of Comets 152

LXIIL— Tails of Comets— How formed 154

LXIY. — Superstitious Notions concerning Comets 157

LXV.— Distance to Fixed Stars 159

LXVL— Classification of Fixed Stars 161

LXVIL— Stars have no Sensible Discs 164

LXVIII.— Eeal Magnitude of Stars 165

LXIX. — Method of computing Distances to Fixed Stars

by Trigonometry 167

LXX. — Telescopic Method of computing Distances of

Heavenly Bodies 168

LXXI. — The Stars are Self-Luminous Bodies 171

LXXIL— Color of Fixed Stars 174

LXXIII. — New Temporary Stars 175

LXXIV. — New Permanent and Periodical Stars 177

LXX v.— Eelations of Multiple Stars 179

LXXVL— Stars Optically United 179

LXXVIL-Stars Physically United 181

LXXYIIL— Clusters of Stars 183

LXXIX.-Nebulffi 186

LXXX.— The Milky Way 189

LXXXL— Magellan Clouds 190

LXXXIL— Nebula Proper 191

LXXXIIL— Annular Nebulffi 193

LXXXIV.— Stellar Nebula?, and Nebulous Stars 195

LXXXV.— Planetary Nebulffi 197

LXXXVL— Globular Nebulse or Clusters 199

LXXXVn.— Spiral Nebula 201

LXXXVni.— Structure and Harmony of the Universe 203

Defixitioxs of Astroxomicae Ter:^is and Phrases 333

P LANETELLE S.

The Planetelles, which is represented by Fig. 1 on the opposite page, was invented by the author of this Avork, and has been in the course of construction for more than twenty years. Its first conception originated in the conviction that if the solar system, constituted as it is of many parts, and all of these parts having various motions, could be represented by an artificial system like itself, exhibiting the same phenomena in the same order, aid of incalculable value would be furnished in the acquisition of knoAvledge. With the view of rendering this idea practical, the construction of a machine for that purpose was commenced, and pursued, till the otie which is here represented was completed. This instrument represents the motion of the sun on his axis, the relative annual motions of the eight primary planets, also their relative diurnal motions, and the various motions of the moon and of all the satellites around their primaries in difierent periods. It shows the relations existing between the sun and all the primary planets, and their satellites and each other, and is designed to illustrate, also, the phenomena resulting therefrom. It presents to the eye eighty difierent motions of these bodies, and illustrates the succession of day and night on each of the primary planets, the inclination of their axes to the planes of their orbits, the change of their seasons, the amount of change in the sun's declination in relation to each, and his rising and setting on each, the difierent lengths of their days and nights, the difierence in the length of their seasons, their conjunctions, and the phases of Mercury and Venus, the retrogression of the moon's nodes, and the length of lunar days and nights, the solar and lunar eclipses, and the changes, phases, fulling, and eclipses, of all the satellites.

All these phenomena, besides a vast amount of other useful knowledge, may be explained by the use of this instrument and the artificial zodiac that is connected with it, so that even the youthful and uneducated mind cannot fail to understand the astronomy of the solar system, if disposed to give the subject any attention. No mechanical device that has ever been brought before the public presents such an ocular demonstration of the planetary system in motion, and expresses its phenomena Avitli such precision and accuracy, as the Planetelles ; and as it is portable, occupies but little space, and is not liable to get out of order, is in every way adapted to the private study and the student's class-room, — places which it fills, as an illustrator of science, with greater fidelity, in manv respects, than the living instructor. 10

Fig. 1.— Planetelles.

HELIOTELLUS.

The Heliotelltjs, which is represented by Fig. 2 on the opposite page, is constructed on the same principle on which the Planetelles is, and is designed in part for the same purpose. It contains five globular bodies, which, by their arrangement, relations, and motions, exhibit the arrangement, relations, and motions of the sun, Mercury, Venus, Earth, and the moon, as so many parts of the solar system. This instrument represents the motion of the sun on his axis, the relative yearly motions of Mercury, Venus, and the earth, ako their relative daily motions, and the motions of the moon around the earth, around the sun, and on her axis. It shows the inclination of the axes of Venus and the earth to the planes of their orbits, and is designed to illustrate the respective widths of their difierent zones, the succession and duration of their different seasons, the different lengths of their days and nights, the amount of change of the sun's declination in relation to each, and his rising and setting on each, the superior and inferior conjunctions and phases of Mercury and Venus, also the solar and lunar eclipses, the length of lunar days and nights, the retrogression of the moon's nodes, and the changes, phases, and fulling of the moon .

By the use of the Heliotellus and the artificial zodiac connected therewith, these phenomena, the tides also, and other elements of useful knowledge, can be explained with such clearness and simplicity that even a child, with little attention, cannot fail to comprehend them. This instrument, for the purpose of illustrating a portion of the planetary system and the phenomena resulting therefrom, is invaluable ; and, as it can be carried in the hand, and occupies but little space, economizes the time and expense of the pupil, and diminishes the labor of the teacher, is especially adapted to the use of families, and every grade of schools in which the elements or more advanced branches of Astronomy or Geographv are taught, ]2

Fig. 2 — Heliotellus, 2

LUNATELLDS.

The LtjnatelLiUS, which is represented by the cut on the opposite page, illustrates the astronomical phenomena of the sun, earth, and moon in their natural order, with the geography of the earth in its proper relation to them. The sun is made to turn on his axis, the earth revolves at her proper inclination on her axis and around the sun, producing not only the change of seasons and the vicissitudes of day and night, but also their natural increase and decrease in length. The moon revolves around the sun, on her axis, and around the earth, producing the alternation of her days and nights, her changes, phases, and fulling, and also, by her retrograding at every revolution, the interesting phenomena of solar and lunar eclipses. And as the natural divisions of the surface of the earth and the political divisions of every country are marked on the body that is employed to represent the earth, the geographical and astronomical relations of every locality, at any particular period during the year, are clearly exhibited to the eye.

The daily use of the Lunatellus by both teacher and pupil has clearly demonstrated that, in addition to its advantages in the study of astronomical phenomena, it is almost indispensable in acquiring an accurate knowledge of Descriptive and Physical Geography, as the bodies that represent the earth and the moon occupy their relative places and positions in relation to the sun and each other, and can have given to them at pleasure their relative motions in their relative periods.

LTinatelliis.

Introduction To Astronomy

SECTION I.

Pbtorg of gistronomi).

1. Astronomy is the most ancient of all the sciences. The first astronomers were shepherds, and some of their observations date back more than twenty-four hundred years before Christ. Job, who was a native of Chaldea during its early history, speaks of Orion and the Pleiades, — certain groups of stars which still retain their former names. Homer and Hesiod also had a knowledge of at least some of the divisions of the starry heavens, Avhich had been made; and Aratus enumerated nearly all of the ancient constellations.^

2. It is highly probable that the Chaldeans and Egyptians were the first to draw boundary lines of the richest stellar districts and designate them by certain names. The Greeks and Romans did the same ; and to these nations are we indebted for at least some of the divisions of the heavens which we find noted in our astronomical maps.

3. To Avhat extent the Chaldeans and Egyptians carried their divisions, or where the Greeks and Romans took the subject up, is uncertain ; yet it is evident from their records that not only they, but the Chinese also, had a knowledge of many of the prominent constella-

^ Constellations — are groups of stars.

Questions. — 1. "What is the most ancient science? AVho were the first astronomers? 2. Wlio first divided the starry heavens into constellations? Who next? 3. What other nation had a knowledge of them ?

2* 17

18 HISTORY OF ASTRONOMY.

tions in both hemispheres/ as well as those that constitute the zodiac.^

4. Thales, one of the seven wise men of Greece, who lived six hundred years before the Christian era, was the first regular teacher of astronomy. Pythagoras, also of Greece, shortly afterwards taught this science in a celebrated school at Crotona, and was the first to discover the true theory of planetary motion ; but did not succeed in having his views adopted, owing to the ancient prejudices and incredulity of those who regarded themselves as being pre-eminent in science and discovery.

5. Hipparchus — about three hundred years before the Christian era — distinguished himself as a teacher of astronomy in the most celebrated school in Egypt; and Ptolemy, of the same nation, one hundred and seventy years afterwards, acquired still greater celebrity. He devised a theory from what was merely apparent in the heavens, regarding the earth as stationary and the centre of the universe, by which he endeavored to account for nearly all the changes and phenomena which we discover in the solar system.

6. His opinions were entertained and adopted by the various schools as being most consonant with what presented itself at different times in the heavens to ^he senses, and, in consequence of its resemblance to the truth, continued to be taught in the academies and schools, till Copernicus, of Prussia, revived, in fifteen hundred and thirty, the Pythagorean or true theory of planetary motion, viz. : — that the sun is the central orb of the system, and that all the planets revolve around

^ Hemisphere — is half a sphere.

^Zodiac — is twelve constellations which form a belt of stars, 16° wide, clear round the heavens.

Questions. — 4. Who were the first teachers of astronomy ? Who discovered the true theory of planetary motion? 5. What distinguished astronomers succeeded Thales and Pythagoras? Whose astronomical theory was taught in the schools from the second till the sixteenth century ? 6. Whose theory was revived by Copernicur,, in fifteen hundred and thirty ?

THE SOLAR SYSTEM. 19

him. He discussed the true theory of the celestial motions, distinguishing between what was real and what was only apparent, and thereby rescued tliis science from the doubt and uncertainty which had always surrounded it.

7. Tycho l^rahe, of Denmark, also lent invaluable aid to discovery, in the use of those instruments which were then employed in astronomical observation; and Kepler, a German astronomer, discovered the three great laws of planetary motion. So also did Galileo, with the aid of the telescope, make new discoveries which were higlily interesting; and Sir Isaac Newton saw and made known the application of that grea|/ principle in tlie law of gravitation, whereby all worlds and heavenly systems are governed and controlled."

8. And to more fully develop and more firmly establish the facts already obtained, many studious observers are still engaged, in the Old World and the New, in exploring and investigating the motions and movements of those celestial bodies wdiich are silently satisfying the will of their Creator in the economy of nature.

Section II

1. This system of worlds and heavenly bodies is the one to which our earth belongs, and is now known to contain eight primary planets,^ eighty-five asteroids^ or smaller planets, twenty-one satellites,^ moons, or second-

^ Planet — a wanderer, 2 Asteroid — a small planet.

^ Satellites, moons, or secondary planets, are those that revolve around the primary planets.

Questions. — 7. What celebrated astronomer succeeded Copernicus? Who applied the principle of gravitation to the heavenly bodies ? 8. Are astronomers now engaged in the study of this science ?

Sec. II. — 1. How many primary planets are there? How many asteroids? How many satellites, moons, or secondary planets? Are there manv comets?

THE SOLAR SYSTEM.

Fig. 3.— Solar System,

ary planets, a great number of comets, and the sun also, which is the controlling centre of them all.

2. The primary^ planets are of different magnitudes, and revolve around the sun in different periods and at different distances from him. They are all known by

* Primary planet — a large planet.

Questions. — 2. Are the primary planets alike in magnitude? Are tliey at different distances from the sun ? Do they all revolve around him in the same length of time ? Are they known by certain names? What were they named after? What are the names of the two nearest the sun ?

THE SOLAR SYSTEM.. 21

certain names, which are derived from the names of heathen gods or objects of idolatrous worship. Mercury, which is the planet nearest the sun, was named after the god of dishonesty and injustice; aud Venus, the second planet from the sun, was named after the goddess of love and beauty.

3. Mars, the fourth planet from the sun, received his name from the god that was supposed to rule over war and battle; and Jupiter, the fifth planet in point of distance from the sun, received his name from the name of the imaginary being that was supposed to be god over all. Saturn, the sixth planet from the sun, obtained his name from the imaginary being who was supposed to preside over time and chronology; and Uranus, the seventh planet from the sun, obtained his name from the god of astronomy. Neptune, the outermost planet from the sun, was named after the imaginary deity that was supposed to preside over the seas.

4. The asteroids are small planets that revolve around the sun as their centre of motion. They travel around him in orbits^ which lie between those of Mars aud Jupiter. Nearly all of them are invisible to the naked eye; and had it not been for the aid of the telescope they would have remained undiscovered.

5. The length of their annual periods is nearly the same, each being about the length of four and one-half of our years. Their average distance from the sun is about two hundred and sixty-one millions of miles. Like the primary planets, they are all known by certain names, which were given to them generally by their discoverers, and will be noticed hereafter.

6. The secondary planets are small bodies that revolve

^ Orbit — the path of a planet round the sun.

Questions. — 3. What are the names of all further away from the sun than the earth? 4. "What do the asteroids revolve around? Between the orbits of what two planets do they revolve ? Are they visible without the aid of the telescope ? 5. What is the average length of their years? What is their average distance from the

22 THE SOLAR SYSTEM.

around some of the primary planets as they travel around the sun. Our moon is one of them, and the only one that revolves around the earth. Jupiter, the fifth planet from the sun, has four of them, which revolve around him in different periods. The one nearest to him moves fastest, and has the shortest period. The second moves slower than the first, and has a longer period. In like manner is it with the third and fourth.

7. Saturn, the sixth planet from the sun, has eight moons or satellites that revolve around him. They are at cliiferent distances from him, travel with different velocities, and have different periods. They follow the order of all heavenly bodies in their movements that have a centre of motion, diminishing in their velocities and increasing in their periods as their distances increase from their primaries.

8. Herschel, or Uranus, the seventh planet from the sun, has six moons, which are at different distances from him and revolve around him with various velocities and in different periods. Neptune, the outermost planet, has two moons, which are similar to those of the other planets which we have noticed, in their distances, movements, and length of their periods.

9. The comets are rare bodies which revolve around the sun, and are seldom seen except when they'^are near to him. Several hundred of them have been discovered with the aid of the telescope, and the motions and elements of the orbits of many of them have been pretty accurately computed. Thongh some of them are very large, they have very little matter in them, as has been fully demonstrated by the slight attraction which they have for other bodies that are sometimes comparatively near to them.

10. All of these heavenly bodies to which we have

Questions. — 6. What do the secondary planets revolve around ? Is the moon a secondary planet ? How many has Jupiter ? 7. How many has Saturn? 8. Hoav many has Herschel, or Uranus? How many has Neptune? 9. Are comets rare or dense bodies? Are they large or small? Around what body do they revolve?

THE SUN. 23

in this section referred are objects of special interest, and we will notice them in their order of distance from the sun, making him the subject of our first remarks.

SECTION III. -Telescopic View of tlie Sim

1. The sun, which is the central orb of our system, being the most prominent of all the heavenly bodies,

Qhestioxs.— 1. What distance is it to the sun? What is his diameter? How much larger is the sun than all the bodies that revolve around him ? How much heavier ?

24 sun's atmosphere.

claims now our immediate attention.^ He is ninety-five millions of miles distant from us, and nearly nine hundred thousand in diameter, and his axis is inclined about 7° to the plane of the ecliptic. His volume is six hundred times greater than that of all the bodies that revolve around him, and in mass or weight he is about seven hundred greater.

2. He is fourteen hundred thousand times larger than the earth, and his density is nearly one-fourth that of the earth, and a little greater than that of water. He revolves on his axis-^ in about twenty-five and one-half days, and is the great source of light and heat, which enlightens and gives warmth to all of the pLanets and bodies that revolve around him.

SECTION IV. Mini's gitmospbrn

1. The sun is nearly globular in form, and appears to be invested with three envelopes or atmospheres, differing in their nature and densities. The one next to his body seems to be in a measure transparent, sustaining cloudy matter in its upper regions, sinjilar to the clouds which are suspended in our own atmosphere. This opinion is entertained from the different shades of light and darkness which are associated with the spots which frequently appear on his disk.^

2. The second envelope, or atmosphere, is supposed to

^ Axis — an imaginary line passing through the centre of a body from one pole to the other.

"^ Disk — the face of the sun.

Questions. — 2. How much larger is he than the earth ? Is he as dense as the earth ? Is he as dense as water ? Does he revolve on his axis ? In what time ?

Sec. IV. — 1. How many atmospheres are supposed to surround the sun ? What is the nature of the inner one ?

* For purposes of convenience, round numbers are generally employed in this work to express the magnitudes, distances, and velocities of the henvenlv bodies.

SOLAR SPOTS. 20

be the great reservoir of solar light and heat, and the place where they are generated. From experiments which have been made recently, it has been discovered that the light which is reflected or emitted from a solid or liquid substance heated to a certain temperature differs from what is emitted from a gaseous or ethereal substance.

3. The sunlight is of the latter kind; which would indicate that his solid body is not its source. This light and heat may be produced by the agency of electrical currents without combustion, as it is not always essential to their production.

4. The existence of a third or outer envelope, consisting of very attenuated matter, is insisted on by some astronomers, from tlie peculiarities attending the sun when he is totally eclipsed. Thin cloudy matter was observed at and beyond his margin, and columns of rose-colored light ascended sometimes from it to the height of forty or fifty thousand miles, and would then move off in a horizontal direction.

5. These phenomena are indicative of the existence of a gaseous substance, capable of sustaining visible matter, and more remote from the solid solar globe than his photosphere.^

SECTION V. ^olar §jjots

1 . The spots which frequently aj^pear on the sun are supposed to be openings in his luminous atmosphere —

^ Photosphere — the spherical gaseous matter around the sun's body, in which his light is produced.

QuESTioxs. — 2. Where is the sunlight supposed to he generated ? Does the light that is emitted from a gaseous or ethereal substance differ from what is emitted from a solid or liquid substance ? 3, What kind of light is sunlight ? What agency may produce his light and heat? 4. What is the nature of the sun's outer atmosphere ? 5. What evidence is there of its existence and nature ?

26 MOTIONS OF THE SUN.

produced probably by whirlwinds beneath, or other disturbing causes originating in their own vicinity. They are seldom seen within three degrees of the sun's equator, and never at his poles.

2. The atmosphere of the earth, at certain elevations, is in a far greater state of agitation in zones that are on either side of the equator than elsewhere; and may it not be so in similar regions on the sun? His whole surface appears, when viewed by the telescope, to be in a state of constant agitation, the agitation being always greatest where the spots break out, and their funnelshaped forms, with other attending circumstances, show that they are not scoriae nor any solid substance.

3. Some of them at times are forty or fifty thousand miles in diameter; and sometimes so many of them have been on the sun's disk as to diminish his light and heat at least one per cent. These spots are not only variable, but periodical, increasing in number for five and one-half years, and decreasing for the same period, corresponding exactly in point of time with a certain variation observed in the intensity of terrestrial magnetism. See Fig. 4.

SECTION VI. Potions of t^e 3mx

1. The sun has three motions, — one around the centre of gravity of the planetary system, the second on his own axis, and the third around the centre of this stellar

Questions. — 1. What are the spots on the sun supposed to be ? What may cause them ? Are they observed near his equator, or his poles ? 2. Where is the earth's atmosphere, at certain elevations, agitated most ? How does the sun's surface appear when viewed with the telescope? What evidence is there that these spots are not composed of solid substance ? 3. What is the diameter of some of these spots ? Are they ever so numerous as to diminish the sun's light and heat ? Do these spots change in size ? Are they periodical ? What is the length of their periods ? With what do they correspond that belongs to the earth ?

Sec. VI. — 1. How many motions has the sun ?

MOTIONS OF THE SUN.

Pig. 5.

28 MOTIONS OF THE SUN.

universe, supposed to be at or near the star Alcyone in the Pleiades.

2. By Fig. 5 we will illustrate the first of these motions. If all of the planets with their satellites were attached to a rod at their relative distances from the sun, and the sun himself attached to the other end, and the rod placed on a fulcrum at the point where the sun would balance or hold in equilibrium all the other bodies, that point would be the centre of gravity of the whole system.

3. By revolving this rod, all of these bodies would revolve around this centre; and, the sun being hundreds of times heavier than the aggregate of all the rest, he would be always nearest to it, even so near that it would generally be between his surface and his centre. This centre of gravity constantly changes a little in position, in consequence of the changes which the planets make in their orbits in performing their annual revolutions.

4. Besides the motion of the sun around the centre of gravity of our system, he has a motion from west to east on his axis. This fact is known by observing the spots on his disk. They always pass over his surface in one general direction, exhibiting at the same time all those changes of form which would result from the revolution of a globular body on its axis. The time they occupy in passing from one side of his disk to the other indicates that it requires nearly twenty-five and a half days for him to make one rotation.