Astronomy/a_text_book_of_elementary_astronomy_1946.md

ELEMENTARY ASTRONOMY

Beet  5682 £2-00

John de Selden Sewerford Settringham Carluke

Jan 1947.

A coat of arms with two lions on either side, a shield in the center with a cross, a fleur-de-lis, and other symbols. Below the shield, "Aether Mysterium" and "MCMXCIVH" are written.  A TEXT BOOK OF ELEMENTARY ASTRONOMY  By the same author A GUIDE TO THE SKY

CAMBRIDGE UNIVERSITY PRESS LONDON: BENTLEY HOUSE NEW YORK, TORONTO, BOMBAY CALCUTTA, MADRAS: MACMILLAN

All rights reserved  A TEXT BOOK OF ELEMENTARY ASTRONOMY

By ERNEST AGAR BEET B.Sc., F.R.A.S.

CAMBRIDGE AT THE UNIVERSITY PRESS 1946

Total eclipse of the Sun: Aegean Sea, 1938  CONTENTS

List of Illustrations	page vij
Preface	ix

First Edition 1945 Reprinted 1946

Chapters

I. CONCERNING LIGHT Travel in straight lines—reflection from plane and concave mirrors—refraction—atmospheric refraction—lenses—the spectrum.

II. THE EARTH Shape and size of the Earth.

III. THE ROTATION OF THE EARTH Evidence for rotation—circumpolar stars—Pole Star—the Plough.

IV. CONSTELLATIONS Cassiopeia—Andromeda—Perseus—Bull—Twins—Swan—Eagle—Vega—Orion—Sirius—Procyon—Lion.

V. THE ANNUAL MOTION OF THE EARTH Changing constellations—Signs of the Zodiac—the ellipse.

VI. TIME The meridian—solar time—sidereal time—mean time—summer time—24-hour clock—heap year.

VII. POSITION UPON THE EARTH Local time—longitude—latitude—chronometers—Nautical Almanack—sextant—methods of navigation.

VIII. THE SEASONS Plane of the ecliptic—effects of inclination—tropics—equinoxes—solstices—position of the Sun in the sky.

IX. THE MOON Motion—phases—the Moon's shadow—the shape of orbit.

X. THE STORY OF THE PLANETS The name—an ancient idea—motion of Venus—motion of Mars—Copernicus—Tycho—Kepler—Galileo.

PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS, CAMBRIDGE  vi CONTENTS

Chapters

XI. THE LAW OF GRAVITATION page 56 Newton—gravitation—tides—discovery of Uranus, Neptune and Pluto—table of the solar system.

XII. TELESCOPES 60 Simple telescope—eyepieces—equatorial—transit instrument—Greenwich Observatory—reflecting telescopes.

XIII. MORE ABOUT THE SOLAR SYSTEM 68 Moon—Mercury—Venus—Mars—Minors—Planets—Jupiter—Saturn—Uranus and Neptune—Pluto—Comets—Meteor velocity of light.

XIV. THE SUN 77 Surface—sunspots—prominences—corona—spectroheliograph—Fraunhofer's lines—magnetic storms—aurora—Zodiacal light.

XV. THE STARS 82 Magnitude—the stars—notices—distances of stars—light year—pulsar inverse square law.

XVI. THE STELLAR UNIVERSE 86 Double stars—star clusters—nebulae—Milky Way—stellar motions—completed picture--birth of the stars--life in other worlds--final problems.

Questions 95

Bibliography 106

Index 107

Illustrations

Frontispiece. Total eclipse of the Sun: Aegean Sea, 1936. Fig. 1. The laws of reflection. Effect of rotating a mirror Fig. 2. A concave mirror Fig. 3. Formation of an image by a concave mirror Fig. 4. Refraction in water Fig. 5. Refraction through a glass slab Fig. 6. Reflection of light by a prism Fig. 7. Internal reflection Fig. 8. Atmospheric refraction Fig. 9. A convex lens Fig. 10. Atmospheric refraction Fig. 11. A convex lens Fig. 12. Formation of a real image by a convex lens Fig. 13. Formation of a virtual image by a convex lens Fig. 14. Types of light Fig. 15. Types of spectra Fig. 16. The curvature of the Earth The Moon and the Sun, the Earth The ancient world Model of the rotating sky Fig. 17. The Pole Star facing 16 Fig. 18. The rotating sky facing 16 Fig. 19. The stars of summer The stars of winter The constellations of Orion The constellation of Taurus October and January positions enlarged from Fig. 25 facing 26 Circumpolar stars in the Zodiacal facing 26 To draw an ellipse facing 26 Finding the meridian facing 28 Solar time and sidereal time facing 30 Positions of the Earth at intervals of sixty days facing 31 Leaps of one day facing 33 Latitude facing 34 Altitude of the Pole Star facing 34 The altitude of the sextant facing 34 A ship's chronometer facing 36 An arc to measure altitude facing 38 To illustrate the plane of the ecliptic facing 39 The sun's path in tilt facing 40 The seasons facing 41 The path of the Sun across the sky facing 43 The phases of the Moon facing 44 An eclipse of the Moon facing 46 Why eclipses are infrequent facing 47 The two kinds of shadow facing 47

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ILLUSTRATIONS

Fig. 47.	The three types of solar eclipse
48.	A lunar eclipse
49.	The Moon's orbit
50.	Estimating the size of the Moon
51.	The phases of the Moon
52.	The path of Mars among the stars
53.	An asteroid
54.	The cause of the tides
55.	The principle of the telescope
56.	The telescope
57.	A 5-inch equatorial telescope equipped for photography
58.	A 6-inch refractor
59.	The Pleiades rising and setting
60.	Greenwich Observatory
61.	The Newtonian reflector
62.	The principle of the reflecting telescope
63.	The transit of Venus
64.	The 100-inch reflector at Mount Wilson
65.	Model of the new 200-inch telescope
66.	The telescope
67.	The Moon about third quarter
68.	The Moon about first quarter
69.	Kepler's laws of planetary motion
70.	Mars in September (1824)
71.	Photographs of Jupiter
72.	Photographs of Saturn
73.	The phases of Venus
74.	The phases of Jupiter
75.	The orbit of Halley's comet
76.	Halley's comet
77.	The measurement of the velocity of light
78.	The Sun, showing sunspots
79.	The Sun, showing the famous "anti-earth" prominence

ILLUSTRATIONS

80. Tycho Brahe's heliocentric photograph
81. The Sun, photographed in hydrogen light
82. Photographs of spectra
83. Motion of the planets around the Sun
84. The parallax of a star
85. The inverse square law
86. Mercury
87. The star cluster in Hercules
88. The Andromeda galaxy
89. The Milky Way
90. Type I supernova galaxy
91. Illustrating the birth of the stars (i) Formation of a double star by spiral nebulae (ii) Rotation of liquids forming double stars (iii) Planets produced by tidal action

PREFACE

A WIDER OUTLOOK in school science has been growing for some years, but although Astronomy is a subject often recommended it is seldom taught. The objections to Astronomy are, presumably, that it does not provide suitable experimental work and that time cannot be spared in an already overcrowded time table. With the rapid increase of General Science it is to be hoped that this section will eventually find its place, and this book more than covers the syllabus suggested by the Science Masters' Association.

The book may also have an appeal outside school work as some may wish to read it as a general introduction formal than the general reading already well catered for in the extensive literature of the subject. It will form a sequel to my former book, A Guide to the Sky, which is an observational introduction for young people.

Astronomy may be approached from a mathematical or experimental standpoint. The former has already been ably done by P.F.Burnham in his Practical Astronomy; an experimental and historical approach is made here.

Simple experimental work which forms a part of the main argument appears in its place in the text, as do some suggested demonstrations.

At the ends of the chapters there will be found other exercises and out-door work of which the importance cannot be overstressed. The questions at the end of each chapter refer to what has been said in the text.

A few elementary questions are intended to direct the thoughts before reading the chapter, B questions on the text, and C of a problem nature.

Figs. 21, 67, 68, 71, 72, 76, 79, 81, 87 and go are to be found in The Stars in their Courses by Sir James Jeans; Fig. 89 is in the same author's The Universe Around Us; Figs. 61 and 64 are reproduced from Light by A.E.E.McKenzie. For permission to use these authors are grateful to Mr J.R.Collins, who holds all rights to these figures and whose copies are to whom ascraction is made on the figures themselves.

Acknowledgements are also tendered to Dr J.L.Haughton, F.R.A.S., and the British Astronomical Association for the frontpiece; Sir Howard

---

1 The Teaching of General Science, Part II, 1938.

page 48 49 50 53 57 62 62 63 64 65 66 67 67 69 70 71 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

A page from a textbook on astronomy with illustrations and text.

Fig.

21, 67, 68, 71, 72, 76, 79, 81, 87 and go are to be found in *The Stars in their Courses* by Sir James Jeans;

Fig.

is in the same author's *The Universe Around Us*;

Figs.

61 and 64 are reproduced from Light by A.E.E.McKenzie.

For permission to use these authors are grateful to Mr J.R.Collins,

who holds all rights to these figures and whose copies are to whom ascraction is made on the figures themselves.

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Acknowledgements are also tendered to Dr J.L.Haughton, F.R.A.S., and the British Astronomical Association for the frontpiece; Sir Howard 1 *The Teaching of General Science*, Part II, 1938.

PREFACE A WIDER OUTLOOK in school science has been growing for some years, but although Astronomy is a subject often recommended it is seldom taught. The objections to Astronomy are, presumably, that it does not provide suitable experimental work and that time cannot be spared in an already overcrowded time table. With the rapid increase of General Science it is to be hoped that this section will eventually find its place, and this book more than covers the syllabus suggested by the Science Masters' Association. The book may also have an appeal outside school work as some may wish to read it as a general introduction formal than the general reading already well catered for in the extensive literature of the subject. It will form a sequel to my former book, *A Guide to the Sky*, which is an observational introduction for young people. Astronomy may be approached from a mathematical or experimental standpoint. The former has already been ably done by P.F.Burnham in his *Practical Astronomy*; an experimental and historical approach is made here. Simple experimental work which forms a part of the main argument appears in its place in the text, as do some suggested demonstrations. At the ends of the chapters there will be found other exercises and out-door work of which the importance cannot be overstressed. The questions at the end of each chapter refer to what has been said in the text. A few elementary questions are intended to direct the thoughts before reading the chapter, B questions on the text, and C of a problem nature. Fig.s 21, 67, 68, 71, 72, 76, 79, 81, 87 and go are to be found in *The Stars in their Courses* by Sir James Jeans; Fig.s is in the same author's *The Universe Around Us*; Fig.s 61 and 64 are reproduced from Light by A.E.E.McKenzie. For permission to use these authors are grateful to Mr J.R.Collins, who holds all rights to these figures and whose copies are to whom ascraction is made on the figures themselves. Acknowledgements are also tendered to Dr J.L.Haughton, and the British Astronomical Association for the frontpiece; Sir Howard --- 1 *The Teaching of General Science*, Part II, 1938.

PREFACE A WIDER OUTLOOK in school science has been growing for some years, but although Astronomy is a subject often recommended it is seldom taught. The objections to Astronomy are, presumably, that it does not provide suitable experimental work and that time cannot be spared in an already overcrowded time table. With the rapid increase of General Science it is to be hoped that this section will eventually find its place, and this book more than covers the syllabus suggested by the Science Masters' Association. The book may also have an appeal outside school work as some may wish to read it as a general introduction formal than the general reading already well catered for in the extensive literature of the subject. It will form a sequel to my former book, *A Guide to the Sky*, which is an observational introduction for young people. Astronomy may be approached from a mathematical or experimental standpoint. The former has already been ably done by P.F.Burnham in his *Practical Astronomy*; an experimental and historical approach is made here. Simple experimental work which forms a part of the main argument appears in its place in the text, as do some suggested demonstrations. At the ends of the chapters there will be found other exercises and out-door work of which the importance cannot be overstressed. The questions at the end of each chapter refer to what has been said in the text. A few elementary questions are intended to direct the thoughts before reading the chapter, B questions on the text, and C of a problem nature. Fig.s 21, 67, 68, 71, 72, 76, 79, 81, 87 and go are to be found in *The Stars in their Courses* by Sir James Jeans; Fig.s is in the same author's *The Universe Around Us*; Fig.s 61 and 64 are reproduced from Light by A.E.E.McKenzie. For permission to use these authors are grateful to Mr J.R.Collins, who holds all rights to these figures and whose copies are to whom ascraction is made on the figures themselves. Acknowledgements are also tendered to Dr J.L.Haughton, and the British Astronomical Association for the frontpiece; Sir Howard --- 1 *The Teaching of General Science*, Part II, 1938.

PREFACE A WIDER OUTLOOK in school science has been growing for some years, but although Astronomy is a subject often recommended it is seldom taught. The objections to Astronomy are, presumably, that it does not provide suitable experimental work and that time cannot be spared in an already overcrowded time table. With the rapid increase of General Science it is to be hoped that this section will eventually find its place, and this book more than covers the syllabus suggested by the Science Masters' Association. The book may also have an appeal outside school work as some may wish to read it as a general introduction formal than the general reading already well catered for in the extensive literature of the subject. It will form a sequel to my former book, *A Guide to the Sky*, which is an observational introduction for young people. Astronomy may be approached from a mathematical or experimental standpoint. The former has already been ably done by P.F.Burnham in his *Practical Astronomy*; an experimental and historical approach is made here. Simple experimental work which forms a part of the main argument appears in its place in the text, as do some suggested demonstrations. At the ends of the chapters there will be found other exercises and out-door work of which... ...the importance cannot be overstressed. The questions at... ...the end of each chapter refer... ...to what has been said... ...in... ...the text... ...A few elementary questions are intended... ...to direct... ...the thoughts... ...before reading... ...the chapter, ...B questions on... ...the text, ...and C of... ...a problem nature. ...Fig.s 21,... 67,... 68,... 71,... 72,... 76,... 79,... 81,... 87 and ...go are to be found in *The Stars in their Courses* by Sir James Jeans; Fig.s ...is in... ...the same author's *The Universe Around Us*; Fig.s ...61 and ...64 are reproduced from Light by A.E.E.McKenzie. For permission to use these authors are grateful to Mr J.R.Collins, who holds all rights to these figures and whose copies are...  X PREFACE Grubb Parsons and Co. for Figs. 57, 58 and 63; the Director of the Yerkes Observatory for Fig. 88; The New York Times for Fig. 65; Mr P. M. Ryves, F.R.A.S., and the family of the late T. E. R. Phillips for Fig. 90; Mr F. J. Sellers, F.R.A.S., for Question 72; Commander W. S. MacInwain, R.N., for question 73; Professor A. H. Bond, Ph.D., for Fig. 100; Dr W. E. Beech, F.R.Hist.S., for reading the proofs; and to many authors and friends whose ideas on teaching Astronomy have influenced mine and have thus become incorporated in this book. E. A. B. CHAPTER I CONCERNING LIGHT SIGHT is a very wonderful sense indeed. Touch and taste demand actual contact with something if they are to give us any information about it. Our sense of smell can only be used over a short distance, but sight may be used over some miles. Sight shows us things and events at distances almost too great to imagine. In a pitch-dark room you see nothing, for sight depends upon light. When a match is struck it sometimes causes disturbances called light waves and these, like water waves from a fallen stone, spread out in all directions, until they meet your eye. The eye is sensitive to light, so optic rays from a distant object fall upon the retina and you become aware that in a certain place a match is burning. This book is mainly concerned with other worlds than ours, bodies very many thousands of miles away, and our knowledge of them comes to us as light messages affecting our sense of sight. Thus a study of astronomy is closely allied with a study of light, and it is hoped that this book will further assist with the chief properties of the latter before proceeding to the former.* It is necessary to be reminded, right at the beginning, of one important property. That we cannot see around corners is a common experience, and the reason is that light by which we see travels in straight lines. Notice the beam of light entering a dim and dusty room through a window, and it immediately meets night, so daylight shining through a rift in the clouds, and there will be no doubt about the reality of these straight lines. Thus when we want to show on a diagram the direction in which light is travelling we just rule a straight line and call it a 'ray', and to show the direction in which we can see we rule such a line. Readers who have already done a course of light up to the standard of the School Certificate may skip this chapter; those who have not had any previous course may persevere with it but to read also a text book on Light, Light, by A. E. E. McKenzie (Cambridge University Press), can be recommended as being in sympathy with the present work. I  CONCERNING LIGHT and call it the 'line of sight'. It is therefore important to remember that light travels in straight lines. Reflection. When light falls on any ordinary surface, such as the page of this book, it is reflected in all directions, perhaps not quite equally, but sufficiently so for the surface to be seen from any angle. When it falls on a highly polished one, such as a mirror, it is reflected in one direction, and the laws of reflection are best understood by trying two simple experiments. Expt. 1. Project a narrow streak of light across a sheet of paper by putting a lamp behind a vertical slit in a piece of cardboard, or two rectangular objects. Let it strike a plane (i.e. flat) mirror standing up at right angles to the paper. This ray AB (Fig. 1) is the incident ray, and the ray BC is the reflected ray. Run lines along them, and along the back of the mirror if a glass one or the front if a metal one. Draw BNA at right angles to the mirror; it is called the normal. The angles ABA and BNB are the angle of incidence and angle of reflection; measure them with a protractor, and if you have done your experiment carefully they will be found to be equal. Expt. 2. Now tilt the mirror slightly so that it is no longer at right angles to the paper; what happens to the reflected ray? The paper on which you are working is a plane, and the incident and reflected rays lie in that plane. So does the normal, because it is perpendicular to the plane. But when you tilt the mirror away from the paper. When the mirror is tilted the normal is moved out of the plane, and you find that the reflected ray moves too and disappears. (^1) Simple methods of projecting rays will be found in The Science Master's Book, Series 4, Vol. 2. CONCERNING LIGHT Thus the laws of reflection are (i) the incident and reflected rays and the normal to the surface are all in the same plane, and (ii) the angle of reflection is equal to the angle of incidence. The reflection of an object in a mirror is called its image, and, as it is behind the glass and the light has not really passed through it, we say that it appears behind the glass. In other words, the image appears to be, not on the glass, but as far behind the plane mirror as the object is in front. Have you ever stood in front of a mirror and shaken hands with yourself? You use the right hand and your image uses the left, and this is another rule about a plane mirror. This changing over of right and left is called lateral inversion. Expt. 3. Set up Expt. 1 and rule along the incident and reflected rays and along the mirror. In Fig. 2 MB is the position of the mirror before rotation; MA is its position after rotation of 60° clockwise around M. Turn the light through a small angle into a new position NB and mark the new position BD of the reflected ray. Measure the angle ABD and CDB. You will find that this ray has moved twice as much as the mirror, a fact that will occur in a later chapter in connection with the sextant. A concave mirror is a part of a sphere reflecting on the inside of it, and those used in telescopes are not sharply curved, like half a tennis ball, but are nearly flat. Again it is easier to understand its properties if you can handle one, so, if such a mirror is available, here are two more simple experiments. Expt. 3. Place the mirror half way through a slot in a piece of white card, the mirror being perpendicular to the card, and project on to it several rays by passing the light through several slits or a coarse comb. Note that the reflected rays meet at one A diagram showing two rays AB and BC reflecting off a plane mirror. 1-4 Fig. 1. The laws of reflection A diagram showing two rays AB and BC reflecting off a plane mirror. 1-4 Fig. 2. Effect of rotating a mirror A diagram showing two rays AB and BC reflecting off a plane mirror. 1-4  CONCERNING LIGHT 4 point; if the incident rays are parallel (Fig. 3) the point is called the principal focus, and its distance from the mirror its focal length. Fig. 3. A concave mirror Expt. 4. Hold the mirror facing a window, and hold a piece of card so that the reflected light falls upon it. Vary the distance and you will find a position in which an inverted reproduction of the window frame appears on the card. This is called a real image, as the light really does fall on the screen. Now hold the mirror close to your face: as the object (the face) is very near the mirror the image is now upright and virtual. The formation of a real image can be illustrated by a drawing, for light rays can be represented by straight lines. In Fig. 4 C is the centre of the circle of which the mirror forms a part, and the principle of reflection is that between B and C the ray from the top of the object a ray is drawn parallel to the axis; the reflected ray will pass through the focus. A ray drawn through the centre of curvature will be at right angles to the mirror and will therefore reflect back along its own path. The three rays meet at a point; this is the head of the image. Refraction. Have you ever noticed any of these things: the appearance of your fingers through a filled tumbler in your hand; a flight of steps leading down into a swimming pool; the bottom of a clear stream seen from a boat; someone moving in the garden seen through very ordinary window glass? If so, you are already familiar with refraction, for all these various effects referred to are due to refraction, which is the bending of light as it passes from one transparent medium into another. Expt. 5. Put a coin at the bottom of a basin, move away until the coin is just hidden by the edge of the basin, and then watch carefully while a friend pours water in without disturbing the coin. The reason for the reappearance of the coin is that the light reflected from it is bent when it leaves the water and enters your eye, so that it comes from $B$ instead of $A$ (Fig. 5). Thus you see the coin apparently at $B$. It is important to note that light bends away from the normal on leaving the water and entering the less dense air; it would bend towards the normal on entering a more dense medium. The laws of refraction are not quite so simple as those of reflection, and the reader is referred to text books on light. There are a few facts about refraction which may be noted, however. When light passes through a parallel slab of glass it emerges parallel to its original direction but laterally displaced (Fig. 6). If the glass is thin and the angle of incidence is small, this displace- Fig. 5. Refraction in water Fig. 6. Refraction through a glass slab  6 CONCERNING LIGHT ment is also small. In the case of a triangular prism the light will be deviated towards the wider part of the prism (Fig. 7), the angle $D$ being called the angle of deviation. If the index of incidence in the glass is large, i.e. very oblique incidence, refraction does not occur and the light is internally reflected, shown in Fig. 8. This internal reflection is important, especially in the construction of optical instruments right-angled isosceles prisms are frequently used instead of mirrors; one way of using such a prism is shown in Fig. 9. Expt. 6. Using a ray and a sheet of paper as in Expt. 1, try to verify the phenomena illustrated in Figs. 6-8. Atmospheric Refraction. Although our study of astronomical phenomena has not yet begun, this is a convenient point at which to insert this topic; if preferred, the paragraph could be omitted until reflection and refraction have been studied on for ever; it is a layer something over 100 miles thick, and beyond it is empty space. When light from the Sun and stars enters the atmosphere it is refracted, because it is entering a denser medium, and this affects all observers on Earth. When light from a star $S$ (Fig. 10) enters the atmosphere it reaches an observer at $O$ as if the star were at $A$. Then the altitude as measured by a sextant would be $HOA$ instead of the true altitude $HOB$, and therefore sextant readings have to be corrected for refraction. Similarly when the Sun is in the direction of $C$, just below the horizon, it appears to be at $D_1$ just above the horizon; thus refraction lengthens the day. Again, during an eclipse of the Moon some Fig. 7. Refraction through a prism Fig. 8. Internal reflection Fig. 9. A reflecting prism light is refracted by the atmosphere into the Earth's shadow and illuminates the Moon enough to make it visible. Finally, refraction is partly responsible for morning and evening twilight. Needless to say, the atmosphere does not begin suddenly; the density of it becomes lower as height increases. Hence the light rays do not make one sharp turn as shown in Fig. 10, but follow a curved path and are slightly deviated when they first enter the very rare upper layer. Lenses. Most people are familiar with the common magnifying glass; it is a convex or converging lens, thicker in the middle than at the edge. Expt. 7. Repeat Expt. 3, using a convex lens in the slot. Note that the refracted rays meet at a point beyond the lens. The terms Fig. 10. Atmospheric refraction 42° and above for ordinary glass. 7  8 CONCERNING LIGHT principal focus and focal length have the same meaning as in the case of the concave mirror (Fig. 11). Expt. 8. Repeat Expt. 4 with the lens. This time a real image will be obtained by holding your screen on the side of the lens away from the window. Light from a very distant object can be regarded as being parallel; thus a real image of the Sun will be formed at the principal focus, and this gives a simple method of measuring focal length. The rays which form a "spot" given by a burning glass is not a point, but a disc of measurable size formed in the focal plane; this plane is shown dotted in Fig. 11. The formation of a real image is illustrated in Fig. 12, which is drawn as follows: a ray parallel to the axis will refract through the focus on the far side; one through the near focus will refract parallel to the axis; one through the centre of the lens will go straight on, for here the lens acts like a thin parallel plate. When a convex lens is being used as a magnifying glass the object, if placed in the focal case previously mentioned, is so close to the lens that it is within its focal length, and a virtual image is given. This is illustrated in Fig. 13, which is drawn according to the same rules as Fig. 12 except that the rays had to be produced backwards to locate the virtual image. A convex lens diagram showing rays entering and exiting a convex lens. Concave lens is thinnest in the middle and it diverges the light instead of converging it. The only kind of image that it can give by itself is a small, upright and virtual one. Dispersion. If a triangular glass prism be placed in the path of direct sunlight shining into the room, a patch of coloured light can be obtained on the wall or ceiling. The light is said to have been dispersed into a spectrum. The colours can be more conveniently examined if a strong source of light, such as a motor-car bulb, with a straight vertical filament, be placed behind a narrow vertical slit so that a narrow beam of light falls on a 60° prism (Fig. 14). A diagram showing light passing through a prism and dispersing into different colours. An important point to realise is that the prism does not actually make the colours. The colours are already in the light, and they differ from one another in the same way as when wireless transmission from different stations. Light waves were mentioned in the opening paragraph; each colour has its own particular wave-length. Concerning Light 9 Formation of a virtual image by a convex lens A concave lens is thinnest in the middle and it diverges the light instead of converging it. The only kind of image that it can give by itself is a small, upright and virtual one. Dispersion. If a triangular glass prism be placed in the path of direct sunlight shining into the room, a patch of coloured light can be obtained on the wall or ceiling. The light is said to have been dispersed into a spectrum. The colours can be more conveniently examined if a strong source of light, such as a motor-car bulb, with a straight vertical filament, be placed behind a narrow vertical slit so that a narrow beam of light falls on a 60° prism (Fig. 14). A diagram showing light passing through a prism and dispersing into different colours. An important point to realise is that the prism does not actually make the colours. The colours are already in the light, and they differ from one another in the same way as when wireless transmission from different stations. Light waves were mentioned in the opening paragraph; each colour has its own particular wave-length. A diagram showing light passing through a prism and dispersing into different colours.  10 CONCERNING LIGHT length, and when the waves fall on a prism the deviation produced depends on the wave-length. White light is a mixture of many wave-lengths, and the prism separates them into wave-lengths of a different length, sort them out and can we see the colours separately. An experiment of this kind was performed by Sir Isaac Newton in 1666, using sunlight from a hole in a shutter, and is described in his Opticks. The colours of the spectrum usually quoted are red (the least deviated), orange, yellow, green, blue, indigo (deep blue) and violet. Spectroscopes and spectrometers are instruments for producing and examining spectra; their design varies considerably according to the precise purpose for which they are to be used. If the source of light is an incandescent solid, such as an electric lamp, a gas mantle, or the hot carbon particles in a candle flame, the spectrum will be a complete band of colour, merging gradually one into the next from red to violet. This is called a continuous spectrum (see Fig. 15.1). When a lump of common salt is held in the flame of a Bunsen burner an intense yellow light is produced. The heat divides up the salt into the elements of which it is composed, and at the temperature of the flame the sodium vapour produced emits a yellow light. If this light is examined with a spectroscope, in place of the continuous spectrum, two lines appear (really two close together) as shown in Fig. 15.2. When an electric current is passed through a gas at a low pressure, light is produced, the Neon signs outside shops being a common example of this sort of lamp. This kind of light also gives lines in a spectroscopy, those due to hydrogen being illustrated. There are two very important points about these bright line spectra: (a) they are caused by incandescent gases or vapours, not by solids; and (b) they are characteristic of the element causing them, every element having its own particular group of lines that can therefore use the spectroscopy as a means of detecting elements. Suppose that an element X is being projected on to a screen, and then a piece of red glass be put in front of the slit. Will the spectrum turn red? If you can try the experiment you find that it will not, but that except for the red part the spectrum will disappear. All colours except red have been absorbed, and the result on the screen will be the absorption spectrum of that particular piece of glass. This is shown in Fig. 15.3. A similar experiment shows that of a fairly dilute solution of potassium permanganate being illustrated in Fig. 15.4. The spectroscope is a very powerful tool in the hands of the astronomer, but an account of its use of it will be deferred until we are discussing the Sun in chapter xiv; Fig. 15.5 will be explained there. When a spectrum is photographed it is found that the photograph extends beyond the violet end of the visible spectrum. This shows the existence of radiation called the ultra-violet, which has a chemical effect on the plate or film, but it is not visible to the eye. Similarly, with a special kind of plate, an extension of the spectrum at the red end can be photographed; this is called the infra-red. Infra-red radiation has no comparatively much thing and is of growing importance as a means of seeing through obscuring mists and over great distances. When light passes through a lens it is dispersed a little, and thus bright images due to a simple lens are spoilt by having coloured fringes around them. Fortunately this difficulty can be largely overcome by using lenses made up from several pieces or pairs of different kinds of glass, in contact. This arrangement is called an achromatic lens, and is the kind used as the object glass of a good quality telescope. CONCERNING LIGHT V., B., G., Y., O., R. Colour 1 Continuous 2 Sodium 3 Hydrogen 4 Absorption 5 Sunlight References G F E D CBA Fig. 15. Types of spectra 11  12 CHAPTER II THE EARTH WHAT is the shape of the earth? Your answer will probably be 'round', because you have been told so or have read about it in geography. Do you believe it? Does it look round? Except for the various indulgences that we call hills and mountains it looks flat rather than round. The various curiosities in the parlor people regarded it as such. It is so large, we cannot see it, but we cannot see its shape directly, but if we consider carefully several things that we can see we realise that it must be round. Some of this evidence that the Earth is round you may have seen in your geography books, but there is no harm in looking at it again. (i) It is possible to travel right around the world. This should need no further explanation. (ii) Ships in the distance are described as being 'hull down on the horizon'. That is, only the masts and funnels are visible, and as they come nearer more of them comes in sight. In Fig. 16 the A B C D 1 2 3 4 Fig. 16. The curvature of the Earth curved line is the surface; $AB$ is the line of sight from $A$; ship no. 1 is almost completely in view, no. 2 is 'hull down', and no. 3 is indicated only as a puff of smoke on the horizon. (iii) When you climb higher you can see farther. If there were a lighthouse at $A$ (Fig. 16), the line of sight would be $CD$ and even ship no. 4 would be plainly visible. (iv) When an eclipse of the Moon occurs (see p. 46) a shadow of the Earth is cast upon it. That this shadow is curved, though not exactly proving anything, does at least suggest that the Earth is round. (v) The apparent positions of the Sun, Moon and stars change as you travel north and south. This will be referred to again in a later chapter when you have sufficient knowledge to understand it. At the beginning of the last paragraph it was said that the curvature (i.e. roundness) of the Earth could not be seen. Nor can it by ordinary people, but the navigators of the U.S. balloon Explorer II could see it, from a height of 71,000 ft. (134 miles). One of their photographs, published in "The Graphic Magazine", shows quite distinctly that the horizon is a curve and not a straight line as in ordinary photographs. The Earth is not a perfect sphere, like a tennis or billiard ball, but is slightly flattened, more like a football (see Fig. 17). The dimensions of the Earth N.Pole S.Pole 7600 miles 7600 miles Fig. 17. The dimensions of the Earth CHAPTER III THE ROTATION OF THE EARTH ANOTHER fact about the Earth that you know, but may or may not have thought about, is that it rotates upon its axis, i.e. that it is spinning like a top. The line NS in Fig. 17 is called the axis, and if you were making a little model of this spinning Earth NS is the direction of the needle on which you would make it spin. The obvious effects of the Earth's rotation are (a) day and night, A B C D 1 2 3 4  14 THE ROTATION OF THE EARTH and (b) the Sun, Moon and stars all appear to make a daily journey around the Earth. These can be illustrated quite easily. Expt. 9. Place a geography globe some distance from a lamp; the former is the Earth and the latter the Sun. Notice that half the globe is lighted and the other half is in shadow, for light travels in straight lines and cannot get around to the back side. Now rotate the globe, and all parts will be lighted and dark alternately, just as all the Earth (except polar regions) appears to do in the sky. Expt. 10. Stand in the middle of the room and notice how various objects on the walls are placed, in front, to your right, to your left. Now slowly turn around in a direction opposite to that of the hands of a watch. Notice how the objects in front of you move away to your right and disappear, while those on the left come in front of you and new ones take their place. If you live in a room with windows, you have noticed that the Sun is to your left in the morning and to your right in the evening. Expt. 9, shows you the cause of night and day and No. 10 shows why the Sun, Moon and most of the stars rise in the east, move across the sky, and set in the west. In the far off days when people believed in a flat Earth they supposed that there was a river around it (Fig. 18). A boat carrying a fire sailed around once a day, and at night it went into a cave on the west, it went behind the mountains, which screened the world from the light of the fire until it reappeared in the east in the morning. Later on it became known that the Earth was round, and indeed it is round. The whole night and day was that the Sun moved around the Earth, as indeed it appears to do. However, the Moon and thousands of stars also move across the sky in the same way, and it is much more reasonable to suppose that they are fixed and that the Earth turns around. We know from other scientific experiments that this is true explanation. 15 THE ROTATION OF THE EARTH The rotation of the Earth makes the sky seem to rotate, and as the sky rotates from east to west we know that the motion of the Earth must be in the opposite direction, from west to east. Let us make a model of the rotating sky. Expt. 11. Put water into a round-bottomed flask, sufficient in quantity to fill the round part exactly half way when the flask is corked up and inverted. Hold this flask so that its position shown in Fig. 19 and cut it as shown by the arrows. The water represents the sea, the glass represents the sky, and the water line around the glass represents horizon. Make an ink spot at about one o'clock below it rises in the east, moves over the sky, and sets in the west. A spot at ( B ) behaves similarly, but notice that it remains above the horizon very much longer than ( A ). A spot at ( C ) never sets at all; it just describes a series of circles, at the centre of which is a spot ( D ), which does not move. This experiment reproduces almost exactly the motion of the stars in the sky. Most of them are like ( A ) and ( B ), rising and setting in the same way as the Sun, but others do not set at all. When they sink in the west they curve around near the northern horizon and then climb up again in the east. The point ( D ), about which these stars seem to revolve, is called 'the north pole' of the sky, and these stars around it, which never set, are 'the circumpolar stars'. In order to show this effect photographically it is necessary, i.e., they are too faint to show in a snapshot and the shutter must be left open for a long time, minutes or hours according to circumstances, to give the faint light time enough to make an impression on film. If such a photograph be taken with an ordinary camera in a fixed position, the stars will not appear as points but as streaks, for they have moved across the sky during exposure. Fig. 19. Model of rotating sky SUN 600  16 THE ROTATION OF THE EARTH Fig. 21 is such a photograph, taken with the camera pointed fairly high towards the northern sky, and it demonstrates very clearly that the stars in this direction do move in circles. One of the trails is brighter than the others and is very close to the centre; this is made by the Pole Star, a fairly bright star about which all the others appear to revolve, but not quite at the pole of the sky, and therefore not quite at $D$ in Expt. 11. The Pole Star is in the north, and may therefore be used as a guide to direction. Thus you should learn how to recognise it. The brightest stars are grouped in groups called constellations, and a well-known group is that called the Plough,¹ which it resembles, or the Great Bear, which it does not. This is shown in Fig. 20, and on any first night there should be no difficulty in finding it. The two stars marked $A$ and $B$ are called 'the pointers', because if you follow the direction of the arrow for about four times the distance from $A$ to $B$ you will find the Pole Star. OBSERVATIONS (1) Notice in the south the position of a bright star with respect to some landmark such as a chimney. In an hour return to the same place and look again. (2) Find the Plough and the Pole Star. (3) Notice the direction of the Plough from the Pole Star, and look again several hours later. The following are for photographers: (4) Point your camera at the Moon, open the shutter, and leave it for an hour. ¹ In America, 'the Dipper'. A diagram showing a circle with concentric rings labeled A, B, C, D, E. The outermost ring is labeled "The Plough". The innermost ring is labeled "The Pole Star". Norman Lockyer Observatory Fig. 21. The rotating sky. The straight line is a meteor trail—or chapter xii 20  THE ROTATION OF THE EARTH 17 (5) Repeat (4) for bright stars in the south on a night when there is no Moon. (6) Take a photograph like Fig. 21. Essential conditions are a clear sky, little or no wind, no Moon, no lights near the camera, and as long an exposure as possible. CHAPTER IV CONSTELLATIONS Astronomy is a subject that you cannot do entirely at your desk; you must go out and look at the sky sometimes. It is therefore necessary to be able to find your way about there, and in this chapter we shall study the map of the sky. You will have noticed that the maps given in Figs. 20 and 21 show the stars to hour and from day to day, and one map cannot always be right. The two maps given as Figs. 22, 23 are correct only on the dates and at the times mentioned below them, but between them they show all the chief constellations that can be seen during the winter evenings. The middle of the map represents the zenith, which is the point directly overhead, and the circular edge is the horizon. If you turn this map over, you will see the word 'north' towards the north you can compare it with the sky. The constellation groups were named many centuries ago, and this accounts for their peculiar names. In a few cases, such as those of the Lion and the Flying Swan, the shape of the star group does slightly resemble the subject named, while in others the ancient people imagined some form of national hero, or of the character in one of their legends. The following are names taken in this way from the old Greek stories: Cassiopeia, Perseus, Andromeda, Pegasus, Castor, Pollux and Orion. The brightest stars are said to be of the first magnitude; these are marked on the maps as larger dots, and their names are given. During the summer evenings the Great Dipper (the Big Dipper) will be found in the north, rather low in the sky, and above it, in line with the pointers, is the Pole Star. On the opposite side A page from a book showing a diagram of a constellation. 2  18 CONSTELLATIONS of the Pole Star from the Great Bear, and therefore nearly over- head at this time of year, is the constellation called Cassiopeia, shaped like a large letter W. These groups, the Great Bear and Cassiopeia, are very conspicuous in the British Isles, though stars which are a little farther than these from the Pole Star do set, and in certain seasons cannot be seen at all. A diagram showing the constellations of Cassiopeia (W) and Perseus (P). The constellation Cassiopeia is shown on the left side of the page, with its stars labeled. The constellation Perseus is shown on the right side of the page, with its stars labeled. The diagram also shows the position of the Pole Star (P) and the North Star (N). The diagram is oriented such that the top of the page is north and the bottom of the page is south. The diagram is drawn to scale, with the distance between each star being proportional to its actual distance from Earth. The diagram is labeled with the names of the stars and their positions relative to each other. CONSTELLATIONS 19 of three widely spaced stars that make Pegasus look rather like the Plough on a large scale. Return to Cassiopeia. From its eastern end there is a bright star curving and pointing towards the horizon; this is Perseus, and at the end of it is a pretty little group, like a tiny Plough, called the Pleiades. The Pleiades do not belong to Perseus but, like the first magnitude Aldebaran, A diagram showing the constellations of Perseus (P) and Andromeda (A). The constellation Perseus is shown on the left side of the page, with its stars labeled. The constellation Andromeda is shown on the right side of the page, with its stars labeled. The diagram also shows the position of the Pole Star (P) and the North Star (N). The diagram is oriented such that the top of the page is north and the bottom of the page is south. The diagram is drawn to scale, with the distance between each star being proportional to its actual distance from Earth. The diagram is labeled with the names of the stars and their positions relative to each other. SOUTH Fig. 22. The stars of autumn. Oct. 1, 11 o p.m.; Nov. 1, 9 o p.m.; Dec. 1, 7 o p.m. Imagine a line from the Pole Star to the western end of Casiopeia, and follow it on beyond the latter for about an equal distance. To do this you will have to turn around and face the south, where you will then see a large and very distinctive square called Pegasus, well above the horizon. The top left-hand corner as you are now looking at it really belongs to Andromeda, a line A diagram showing the constellations of Pegasus (P) and Andromeda (A). The constellation Pegasus is shown on the left side of the page, with its stars labeled. The constellation Andromeda is shown on the right side of the page, with its stars labeled. The diagram also shows the position of the Pole Star (P) and the North Star (N). The diagram is oriented such that the top of the page is north and the bottom of the page is south. The diagram is drawn to scale, with the distance between each star being proportional to its actual distance from Earth. The diagram is labeled with the names of the stars and their positions relative to each other. to the Bull. Close to Perseus (refer to map) is another first magnitude star, Capella, and still nearer the horizon two more, Castor and Pollux, the Twins. In the western sky, to the right of Pegasus's large cross, there lies a bright group near its head of it. This constellation is the Swan, shown in old maps with its wings outstretched and having the bright star Deneb at its A diagram showing the constellations of Perseus (P), Andromeda (A), and Swan (S). The constellation Perseus is shown on the left side of the page, with its stars labeled. The constellation Andromeda is shown on the right side of the page, with its stars labeled. The constellation Swan is shown below Andromeda, with its stars labeled. The diagram also shows the position of the Pole Star (P) and the North Star (N). The diagram is oriented such that the top of the page is north and the bottom of the page is south. The diagram is drawn to scale, with the distance between each star being proportional to its actual distance from Earth. The diagram is labeled with the names of the stars and their positions relative to each other. SOUTH Fig. 23. The stars of winter. Jan. 1, 11 o p.m.; Feb. 1, 9 o p.m.; March 1, 7 o p.m. 2-2  20 CONSTELLATIONS tail. Below the Swan is the Eagle, a bright star, Altair, with a fainter one on each side, and a little further round towards the north is another first magnitude star, Vega. After Christmas and in the depth of winter the sky has changed (Fig. 23). The Eagle and the Swan have disappeared, Pegasus is do we have such a fine display of first magnitude stars. The Great Bear is now in the north-east, tail (or handle) downwards, and if the pointers be followed away from the Pole Star you will come to the Lion, a constellation in which Regulus is one more to add to the list of brilliant winter stars. As spring comes Orion will sit, the Lion will take its place in the south, and new constellations will come up to command the summer sky. There is not space in this book to describe them, but some day the reader may consult another book, such as the author's Guide to the Sky, and study the stars of other seasons. Observations (7) Find the constellations described in this chapter and study them regularly until you can recognise them at a glance. (8) Observe how the directions in which the constellations are seen varies from month to month, observing always at the same time in each case. (9) If possible obtain a planisphere. This is a revolving star map that can be set for any hour of any day of the year. Compare it with the sky as often as possible. (Messrs Philip have them, obtainable through booksellers, at 31. 6d. each and a larger size at 6i.) CHAPTER V THE ANNUAL MOTION OF THE EARTH In chapter I we learnt that the Earth is a sphere, and in chapter II that it rotates on its axis. It also revolves around the Sun; what evidence is there for that statement? Remembering your geography books you will probably say 'seasons', and that is right, but as the seasons are due to something else besides the Earth's annual motion that phenomenon is given a chapter to itself! Some other evidence can be considered here. Eggs, tea-cups, or lamps on the table to represent the Sun, and near it a ball or globe representing the Earth. Imagine that the walls of the room represent the distant background of stars. Notice the day and night halves of the Earth; stars can be seen only from the Illustration of Orion with Betelgeuse and Rigel. ORION THE BULL Betelgeuse Rigel Aldebaran Sirius GREATER DOG Fig. 24. The constellation of Orion low in the west, while Perseus and Capella are now overhead. The southern sky is occupied by a magnificent group of stars including in all no fewer than seven of the first magnitude. The central figure in this display is Orion, separately illustrated in Fig. 24, which is based on a very old star atlas and shows the hunter's figure clearly. The three stars forming his belt are Aldebaran on left are Sirius, the brightest star in the sky, and Procyon. High in the sky above Procyon are Castor and Pollux. Only in winter  22 THE ANNUAL MOTION OF THE EARTH night half, and you will be able to see which part of the walls are providing the starry background. Now move the ball slowly around the lamp, and note that the night half is changing direction. A diagram showing the annual motion of the Earth's orbit around the Sun. The Earth is depicted as a circle with a line indicating its path around the Sun. The constellations are labeled with their names and positions on the circle. The left, such as the Archer and the Goat, are in the same direction as the Sun and therefore cannot be seen. On July 1 the conditions are reversed, the winter constellations have disappeared and the Archer and the Goat will be in the summer sky. The circumpolar constellations, such as the Great Bear and Cassiopeia, would be in a direction at right angles to the paper and are visible at any time of day. Fig. 26 shows the October and January positions enlarged. The point A is in the middle of the night half, so the time there would be midnight; at B it would be about 11 p.m. As the distance from the Earth to the Sun is very much less than that of the stars, the latter would look the same from the Sun as from the Earth, so A diagram showing "Stars rising" and "Stars setting". Stars rising is shown as a line pointing upwards from a star to a point above it, while Stars setting is shown as a line pointing downwards from a star to a point below it. The diagram also shows "South" and "North" directions. Figs. 25, 26, October and January positions enlarged from Fig. 25 imagine Fig. 26 (October 1) to be placed in the centre of the circle of constellations in Fig. 25. "Stars rising" would point between the Twins and the Bull, the latter would be between rising and setting, while the Lion would be between rising and setting, with Fig. 25 which represents the sky at 11 o'clock on October 1. A similar examination of Fig. 26 (January 1) shows that then the Twins and the Bull would be in the south and the Lion rising; look at Fig. 23. Thus the annual journey of the Earth around the Sun causes the variation in the appearance of the sky: If this were not so, during daylight we should notice that the Sun moves among them; or reason why we do not see them is simply that their feeble light is overpowered by the very much brighter sunlight. During January (Fig. 25) the Sun is in front of the constellations of the Archer and Goat, in February it 23 THE ANNUAL MOTION OF THE EARTH all the time and points towards all the walls in turn. This is why we see different constellations at different times of year, and why Figs. 22 and 23 are different. Examine Fig. 25, which shows the path, or orbit, of the Earth around the Sun, together with the directions of certain constellations. In January (Fig. 25) all but one of these constellations are on the right, the Lion, the Crab, the Twins, and the Bull, so they are among the winter constellations. The groups on A diagram showing "Stars rising" and "Stars setting". Stars rising is shown as a line pointing upwards from a star to a point above it, while Stars setting is shown as a line pointing downwards from a star to a point below it. The diagram also shows "South" and "North" directions. Feb. 26. October and January positions enlarged from Fig. 25 imagine Fig. 26 (October 1) to be placed in the centre of the circle of constellations in Fig. 25. "Stars rising" would point between the Twins and the Bull, the latter would be between rising and setting, while the Lion would be between rising and setting, with Fig. 25 which represents the sky at 11 o'clock on October 1. A similar examination of Fig. 26 (January 1) shows that then the Twins and the Bull would be in the south and the Lion rising; look at Fig. 23. Thus the annual journey of the Earth around the Sun causes the variation in appearance of the sky: If this were not so, during daylight we should notice that the Sun moves among them; or reason why we do not see them is simply that their feeble light is overpowered by the very much brighter sunlight. During January (Fig. 25) The Sun is in front of the constellations of the Archer and Goat, in February it  Dec. N 30° CHARIOTTEER PERSEUS ANDROMEDA Dec. N 30° R.A. XII XI X XIX VIII VII VI V LION CRAB Praesepe LITTLE DOG FISH -0° 0° 15° 30° Dec. S -30° Dec. S TWINS BULL ORION Pleiades RAM WHALE Fish R.A.XXXIV XXIII XXII XXI XX XIX VIII XVII XVI XV XIV XIII XII EAGLE Pis WORMS* CARRIER GOAT SERPENT BEARER Scales SCORPION VIRGIN A page from a star chart showing constellations of the zodiac. Very Bright Moderate Faint Fig. 27. Constellations of the Zodiac R.A. and Dec. explained on p. 63  26 THE ANNUAL MOTION OF THE EARTH moves into the Waterman, and so on. The twelve constellations through which it passes in this way are called the Signs of the Zodiac, and its actual path through them 'the ecliptic'. The constellations of the Zodiac are shown in Fig. 27; many of them are not given in Figs. 22 and 23. Sometimes at the head of the page in an almanack you see the appropriate constellation represented by a cut-out figure, and in the middle of the page by appropriate drawings. These signs are allotted to a month one earlier than shown in Fig. 25. This is because each year the Sun drops a bit behind its starting point among the stars, and although the amounts are so small that you will not notice the change in a lifetime, in the hundreds of years that have elapsed since the Zodiac was invented the error has amounted to a whole constellation. It is beyond the scope of this book to explain why this happens. There are two other quite important facts about the annual motion. The first is that the orbit is not really a circle, but an 'ellipse', which is a slightly flattened circle. Expt. 13. Place a sheet of paper on a drawing board and stick in two pins, A and B (Fig. 28). Put a loop of thread around the two pins and the pencil point C, and, keeping the thread tight, move the pencil round until you have drawn a closed curve. This curve is an ellipse. Try it with several different loops of thread but with different distances between A and B. The Earth's orbit is an ellipse not very different from a circle, and the Sun is at one focus. Thus during a year our distance from the Sun varies, being least early in January. The average is about 93 million miles. The second fact is closely related to this first, and it is that the speed of the Earth in its orbit also varies and is greatest when the distance from the Sun is least. Thus in January we are nearer to the Sun and travelling faster than in July. THE ANNUAL MOTION OF THE EARTH 27 OBSERVATIONS Observation 9 should be made if not already started. (10) Choose some fairly bright star in the south-west and observe how far it is from the Sun at sunset. Observe it regularly for several weeks, and notice which way the Sun appears to move among the stars. (11) Try to find objects which will serve to give you a fixed direction, such as the tops of two posts or the edges of two buildings. Find the exact time (with a watch that is right, of course) at which a star crosses this line, and repeat the observation on several nights. Does it get earlier or later? What is the daily change in minutes? CHAPTER VI TIME The rotation of the Earth gives us a natural clock and the day is our unit of time. Suppose that the place where we live is on that part of the Earth turned towards the Sun; the motion of the Earth gradually turns it away from the Sun until one day later it is towards the Sun again. Thus a day is the interval of time between two successive 'turnings towards the Sun', and that interval is divided up into hours, minutes and seconds. The term 'turning towards the Sun' is both awkward and inaccurate, and we must find a better way of saying what we mean. A line along the ground from north to south is sometimes called the meridian. When an astronomer uses the word he does not mean that line only, but also an imaginary line in the sky standing on either side of that point where it crosses any meridian (that is, north point of the horizon, passing through both poles), and therefore passing through all points on earth's surface. The meridian is really a plane, which is a flat surface including the north-south lines both on the ground and in the sky. To represent a meridian on a model of the Earth we should draw a line from the north pole to the south through the place with which we were concerned. To show what this attitude means let us imagine ourselves to be on earth's surface looking down upon it from above its centre. To do this we have to cut the sphere into two halves along the line just drawn, and then stick them together again with a sheet of cardboard. Fig. 28. To draw an ellipse. A B C  28 TIME between; the plane of the cardboard would represent the astro- nomer's meridian. Now in the last paragraph we spoke of a place being turned towards the sun, but more exact is the way that at that place the sun is on the meridian. The day, therefore, is the interval of time between two successive crossings of the meridian. The crossing of the meridian is called a transit, and the instant at which it occurs is called midday or noon. How could you find the meridian experimentally? North can be found from the Pole Star, but that has to be done at night and the Pole Star is not visible from all parts of the world. North can also be found by a compass, but this method is not accurate, as there are only a comparatively few places in the world where the compass points exactly north. South can be found by observing the Sun at midday, or at any other time by suitable use of a watch, but these methods demand knowledge of time usually not available, and incidentally it is for the purpose of correcting clocks that the meridian is needed. A repetition of Expt. 11, with a mark at a point like $A$ in Fig. 17 (p. 60), will show that when the Sun is on the meridian it is higher above the horizon than at any other time. Thus south can be found by seeing when the Sun is highest and shadows are shortest; the difficulty is that you would not know that it was highest until it had started coming down again, and then it would have passed the meridian. A method of getting over all these difficulties is to use a string tied to a post $P_1$, $AB$ is a vertical post in the ground and $BC$ a string tied to the bottom. Sometime before noon, say at about 11 o'clock, the Sun is in the direction $S_1$ and the shadow will be directly behind the post, at $BP_1$, because light travels in straight lines. Mark with a peg, or by other means, the position of $P_1$, and tie a knot $D$ in the string so that $BD$ is exactly as long as the shadow. Until noon the shadow will shorten as the Sun gets higher, and then it will lengthen again. Use the knotted string to find when the shadow is the same length as it was before, and mark its direction $BP_2$. Their directions are different because they are moving across the sky all the time. Now the shadow $BP_2$ must have been formed just as long before noon as $BP_1$ was after it, and therefore the shadow at noon would be just half way between them. The meridian is the line $NBS$ bisecting the angle $P_1BP_2$. When the meridian is known we have a means of measuring time. The period of rotation of one side of the Sun over the meridian is a solar day and an instrument such as a sundial, which divides up this interval into hours, is said to keep solar time. The appearance of a sundial is familiar to most people; the edge of the gnomon which casts the shadow is parallel to the axis of the Earth, so that the shadow moves equal angles in equal times, but the method of graduating the horizontal dial, on which the angles are not equal, makes it possible to read off one hour every day. It can also be measured by watching the transit of a star; this kind of day is called a sidereal day, and astronomers use clocks that are regulated in this way and keep sidereal time. These two methods of measuring a day are given different names because they do not give quite the same results; solar and sidereal clocks do not agree. If a star passes through your meridian once every 24 hours when the Earth has rotated exactly once, for stars are far so away that when the motion of the Earth around the Sun makes no appreciable difference to their directions. Thus one rotation takes one sidereal day. Suppose that the Earth is at $A$ (Fig. 30), and that the Sun is on the meridian at a place $\alpha$ When it has rotated once it has passed on to $B$, and so on. In this case there will be no change in $\alpha$ until it has rotated through another extra bit $\delta\alpha$, which takes about 4 minutes. Thus this solar day is 4 minutes longer than the sidereal, and astronomers' sidereal 29 Fig. 29. Finding the meridian. Approximately.  30 TIME clocks gain a minute a day on ordinary clocks. This is connected with the changes in the constellations that we see week by week, for what was the result of Observation 10 in the last chapter? If a star is on the meridian at 7.0 p.m. to-night it will be there again at 24 sidereal hours later, which will be 6.36 p.m. to-morrow. The next transit will be at 6.35, the next at 6.48, and so on, until after a year the daily 4 minutes will have added up to 24 hours and the star will once more be in its place at 7.0 p.m. You may have heard the expression 'Greenwich Mean Time', and you may have noticed that sundial is nearly always wrong. The Earth's orbit is not a perfect circle, and as a result the Earth's motion is not perfectly regular, which means that the distance $AB$ in Fig. 30 is not quite the same every day. The apparent rotation $ab$ varies a bit and solar days are not always the same length. Good clocks give us days that are all the same, an average of the solar days, and are said to give mean time, or mean solar time. The interval between solar and mean time is called the "equation of time",\footnote{The equation of time is also affected by the Earth's tilt, dealt with in chapter viii, which complicated its variation throughout the year.} and this is given a plus sign when the clock is ahead of the sundial, as it usually is in summer and winter, and minus when behind in the other two seasons. The standard mean-time clock, from which all other clocks in Britain are corrected, is kept at Greenwich Observatory, London, from which electric signals are sent out. The six pipes are a second apart, the last one being the exact time. Summer time is just Greenwich Mean Time plus 1 hour, clocks being put forward an hour in April and put back one in October. Most people are in the habit of not getting up until long after daylight break, and not going to bed until long after dark. During the Great War of 1914-18 it was realised that a great deal of gas and electricity would be saved if people would get up earlier and go to bed later than they did before. In 1927 an "hour clock" was introduced, and by putting the clocks on an hour early rising took place without affecting such habits as school at 9.0 a.m. and afternoon tea at 4-30 p.m. The extra hour of daylight in the evening, when work was over, proved so popular that summer time is now a regular custom. When the second Great War came it was decided to leave summer time for four three months each year and to put on yet another hour from April to August or September. The 24-hour clock is a means of avoiding the use of a.m. and p.m., which we must use if the numbers 1 to 12 come twice a day. The day begins at midnight and the twelve hours till midday are numbered as usual, but instead of beginning again at 1.0 it is called "midnight" again at 12.0 (Fig. 31). At 12 noon we should call 4-30 p.m. This time system is used by scientists, by the Navy, Army and Air Force, and in Continental railway time-tables. The B.B.C. used it for a few weeks in the Radio Times just to see how the British public liked the idea; they didn't—1-6-30 hours sounds such an awkward phrase for tea! Now let us consider what is meant by "a day". It is a unit of time, the year, in which the Earth makes its annual journey around the Sun. Unfortunately this journey does not take an exact number of days, and is usually quoted as $365\frac{1}{4}$. Suppose that the year begins when the Earth is at $A$ (Fig. 31); $365\frac{1}{4}$ days would be at $B$, not at $C$. If started, though another day's journey would take it past $A$. After another $365$ days the Earth would be at $C$, in three such years at $D$, and in four at $E$. The distance from $C$ to $E$ is one day's journey; so by making leap years we can make sure that Earth again starts a new year at $A$. Thus we have three years of $365$ days and then one Leap Year, of $366$, the extra day being February 29. This arrange... 31 A diagram showing a circular diagram labeled "To Sun" with two points A and B connected by lines AB and BC. Fig. 30. Sidereal and solar days A diagram showing positions of Earth at intervals during a year. Fig. 31. Positions of the Earth at intervals during a year  32 TIME ment was introduced by Julius Caesar in 46 B.C., but is not quite correct, because the extra day carries the Earth a little beyond A. To correct for this a leap year is left out every 100 years, but this correction is a bit too much so the extra one day is added every 400 years. The reason for these modifications, made by Pope Gregory in 1582, is that the century years are not leap years unless the first two figures will divide by four, i.e. 1900 was not a leap year but 2000 will be. The next leap year will be 1984, 48 being divisible by 4. OBSERVATIONS (12) Determine the position of the meridian by the method described in this chapter. (13) If a sundial is available, compare it with correct wireless clock time on as many days as possible for a year. Tabulate your results: Date Clock Sundial Difference No. Your longitude (next chapter) will cause a constant difference, but will not prevent you from detecting the variable change due to the equation of time. CHAPTER VII POSITION UPON THE EARTH Time is different in different places. Every place has its own local time, though as a matter of convenience all the places near one another, as in a small country like ours, set their clocks to some standard time. In this chapter we shall see how it is done. It is shown that Greenwich time is used all over the British Isles. In Fig. 32 the meridian at London (Greenwich) is shown pointing to the Sun, and it is midday there. The New York meridian will not point to the Sun for some hours, and actually the local time there is about 7.0 a.m., while it will be night at 10 p.m. and Vespers. You can estimate for yourself what their local time will be, if $M$ in the diagram being the place where it is midnight. Travellers must alter their clocks as they go. On an Atlantic liner steaming west the clocks are put back an hour every day, while if you travel across Europe by train you put your watch on an hour when you pass from Belgium, which keeps Greenwich Mean Time (G.M.T.), into Germany, which keeps Central European Time (C.E.T.). The world is divided into "time zones" differing by 1 hour, each zone being 15° wide with some modifications for political boundaries. This change in time is utilised to determine the position of a place on the globe, such as London. The angle between the meridian at London and that at New York is 74°, and we say that the Longitude of New York is 74° West of Greenwich, or, more simply, $56°$ W. The Earth turns once around, i.e., $360°$, in 24 hours, and in 1 hour it will turn through $15°$. Thus if we know the difference in time between the two places we can calculate their longitude. We shall find just now that when it is noon (12 o'clock) in London it is about 7.0 a.m. in New York, which is a difference of five hours, and in 5 hours the Earth would turn through $5 \times 15° = 75°$. At Long. $180°$ clock would be 12 hours fast, compared with Greenwich, on one side of the Earth; and slow on the other, so when a ship crosses the Date Line, which fixes this meridian approximately, the date must be changed by one day. A simple method for finding longitude is as follows: note the correct Greenwich time (wireless time signal) when you mark the shadow $BP_1$ (Fig. 29), and again for $BP_2$. Local noon occurs halfway between these times, and if it occurs after Greenwich noon you are west of Greenwich, before it; east. Example: $BP_1$, 11.40 a.m.; $BP_2$, 1.0 p.m. Hence local noon was at about 12 o'clock; therefore Greenwich longitude is west, and if 1 hour corresponds to $15°$ then 20 minutes will mean $5°$. The longitude is therefore $5°$ W. This illustrates the principle of Fig. 32. Longitude sea  34 POSITION UPON THE EARTH the process; in practice an almanack would have to be used in order to make allowance for the equation of time.¹ This difficulty can be overcome by timing the transit of a star abreast of the Sun, far from Greenwich, and noting the length of transit at Greenwich can be worked out and then you can compare this with its time at your own station (see Observation 14). Longitude alone does not fix your position; it only tells you how far round the Earth you are, measured east or west from Greenwich. You must also know your distance north or south, A diagram showing the relationship between latitude, longitude, and the Pole Star. and this measurement is Latitude. You almost know what the poles are. If the Earth were to be sliced in two exactly midway between them the line where the surface is cut would be the Equator (Fig. 33). At the centre of the earth the angle between either pole and any point on the Equator is 90° (Fig. 34). The latitude of a place is the angle at the centre of the earth between that place and a point on the Equator exactly north or south of it. London, Lat. 51° N., is shown on Fig. 33 and 34, and is about 7 degrees north of the Pole Star. 1 Add (or subtract if –) the equation of time to solar noon to get mean noon. If the e.t. was +5 minutes in the above example, solar noon at Greenwich would be 12:5 by the clock and the local solar noon obtained only 15 minutes behind. POSITION UPON THE EARTH 35 Equator, Lat. 51° S., is also shown in Fig. 33. All places having the same latitude lie on a circle around the Earth, such circles being called parallels of latitude. Expt. 14. Take a geography globe and read this chapter again. Find the places mentioned, and verify as far as you can all the facts stated. It would be helpful if the globe could be illuminated from one side only, preferably by lamps placed at points on the globe nearest to the hands. Notice that whereas meridians are straight lines great circles, all going right around the Earth, the parallels of latitude get smaller and smaller as you get nearer to the poles. Examine Fig. 34. OS₁ is a line from the centre of the Earth to the Pole Star, and LS₁ from his point called London to the Pole Star. As the stars are a very great distance away (the paper would not show them), we cannot see how long to get the Pole Star in the drawing); these two lines may be considered parallel. LH is the horizon at L and is at right angles to LO. Now it can be proved² that angle $S_1LH$ is equal to angle $LOE$, and therefore a simple way of finding latitude is to measure the altitude, or angle above the horizon, of the Pole Star (see Observation 15). Here again an almanack will be wanted for an accurate result, as a correction is necessary for the fact that the Pole Star is not quite above the north pole (see p. 61). Navigation. If the latitude and longitude of a place are known, its position upon the Earth's surface is fixed. Determinations of these things must be made regularly by the navigator of a ship, the Sun being the body usually observed for the whole process. The navigator's methods are different from those of his requirements when he is sailing; but they do, three things: (1) Correct Greenwich time. A ship's clock is called a chronometer; it is specially designed to keep good time in spite of the motion of the ship, and testing of these clocks is a part of the work at Greenwich Observatory. Before leaving harbour the captain must Because LS₁ and OS₁ are parallel and LO meets them at right angles (see Fig. 34), Hence the complement of $\angle S_1LOE$ = comp. of $\angle LOS_1$ or $\angle S_1LH = \angle LOE$ 3-2  36 POSITION UPON THE EARTH get the correct time, and that is why at various ports there are time guns, or time balls like the one that drops at 1 o'clock at Greenwich (visible in Fig. 60 A). The navigator used to be dependent upon the accurate running of his chronometer throughout the whole voyage, but now he can check it by wireless time signals, several times a day if he wishes. A chronometer is shown in Fig. 60 B. It consists of two pairs of mirrors, one pair being fixed to a ring which is itself pivoted on an axis at right angles to that of the first pair. It is said to be mounted on gimbals, and it will consequently remain level when the case is tilted. (A) (B) Fig. 35. The principle of the sextant (2) An almanack. The Nautical Almanack is published by the government to give mariners all the astronomical information they need, and supplying information for this book is another of the duties of the government. (3) An instrument for measuring angles in the sky. The sextant is the portable instrument used for the purpose and is illustrated diagrammatically in Fig. 35. $M_1$ can be rotated. $M_2$ is fixed, and half of it is unsilvered. From the laws of reflection we know that $H_1 M_2$ will be parallel with $H_2 M_3$, and therefore both rays will have A ship's chronometer Fig. 36. A ship's chronometer A sextant Fig. 37. A sextant  POSITION UPON THE EARTH 37 come from the same point in the distance. When the instrument is pointed to the horizon the eye will see it twice, through the clear part of $M_1$, and by reflection in the mirrors, as shown in the inset under the diagram (though without any intermediary between the two). When this is done, the Sun will reflect light from the sky instead of the horizon, and a mariner adjusts his instrument so that he sees the horizon through the clear glass and the Sun by reflection. This is illustrated in B. Now we know from Expt. 2 that the angle $\alpha$, which is the altitude of the Sun, will be twice the angle through which the mirror has been rotated. Fig. 37 shows an actual instrument, with a scale on which an arm working over a degree scale, each degree being marked as two so that the scale reading is the altitude. Note also that a small telescope is included in the instrument, and that dark glasses can be inserted in the path of the light to protect the observer's eyes. Before any observation can be used for calculation, corrections must be applied for $(a)$ parallax due to the instrument itself; $(b)$ dip of the horizon due to the observer not being at sea level; $(c)$ refraction of the atmosphere, explained in chapter I; $(d)$ parallax, due to the observer not being at the centre of the Earth, which except in the case of the stars makes an appreciable difference to the apparent position of an object; $(e)$ semi-diameter of the Sun or Moon, for while it is usually assumed that observed it is the altitude of the centre that is used in the calculation. There are several ways of finding the ship's position; the following is a brief outline of what is commonly done. In the early morning the navigator takes the altitude of the Sun and notes the time with a deck watch that can afterwards be compared with the chronometer. The navigator then refers to his chart, "Great Almanack" and specially prepared mathematical tables, gives a position line drawn upon the chart; the position of the ship is somewhere on this line. A few hours later, possibly at noon, another sight is taken, yielding another position line. The ship has now moved one interval, and knowing her course and speed she runs back one interval, and so forth until she arrives at her destination. The first position line transferred to the place it would have occupied had it referred to the same instant as the second. The intersection of the two lines  38 POSITION UPON THE EARTH is the observed position of the ship. Another method is to take sights of two or more bodies simultaneously or, more correctly, in quick succession, each of which yields a position line. As these bodies are probably stars or planets the observation is made at dawn or dusk, when the horizon is visible as well as the bodies concerned. The airman must deal with similar problems, but owing to the high speed of aircraft the result is wanted very quickly, although as a rule it need not be quite so accurate. The mathematical work is therefore simplified and he is provided with a special Air Almanac. Further, to an observer moving rapidly at a great height, parallax is negligible and preliminary extinction would be of little use, so the airman is provided with a special pattern called the bubble sextant which enables altitudes to be taken without the use of a visible horizon. OBSERVATIONS (14) Erect two thin, preferably pointed, posts on the meridian found in Observation 12. Find the time, correct to the nearest second, at which some prominent star crosses the line of the posts. The watch must be corrected by wireless time signal. From Whitaker's Almanac (in which the necessary calculation is given) find the time of its transit at Greenwich. Deduce your longitude from the difference in time (see p. 33). You can now correct for longitude in Observation 15. (15) Use the apparatus as illustrated in Fig. 38. Observe the Pole Star through the slots, and get a companion to read the angle marked by the plumb-line. This is the altitude of the star, and hence your latitude (p. 35). 39 CHAPTER VIII THE SEASONS Chapter V was devoted to the Earth's annual journey around the Sun, but one of the effects of this motion was deferred for the time being. The seasons are due to the combined effect of the uni- mual motion and the tilt of the Earth's axis. Special attention is thus paid to this fact, for such terms as 'horizontal' and 'up' and 'down' do not apply in Astronomy; 'up' in England is in the same direction as 'down' in New Zealand. The Sun appears to move around the sky, through the Signs of the Zodiac, in a year, and its path among the stars is called the ecliptic (p. 26). This path lies in the plane of the Earth's orbit, which we call its equator. 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This represents the Sun; the Earth is represented by another ball having pushed through it a needle to show the direction of the axis. The 'Earth' is floated with the axis tilted a little towards one wall of the room, and then moved around the 'Sun', the axis being pointed at the same wall all the time. The plane of the Earth's surface is parallel to that of the Earth, for the surface of the water is the plane of the ecliptic, and we can see clearly what we mean by speaking of the tilt of the axis, and by saying that the tilt is always in the same direction. That this tilt affects the condition under which we live can be shown by the experiment illustrated diagrammatically in Fig. 40. (A) shows a tilted Earth with a needle pointing towards one wall. (B) shows a similar setup but with no tilt. Fig. 40. The Earth's tilt A narrow beam of light is directed horizontally on to a geography globe so that the British Isles lie in the centre of the illuminated part. In A the axis is set towards, and in B away from, the source of light, and the difference is obvious. The beam of light is spread over a much larger area in B than in A, with the result that the British Isles are less brightly lighted. Applying this to the real Earth we find that radiation from the Sun, which includes heat as well as light, is less intense when the axis is turned away from the Sun than when turned towards it. Hence our seasons of winter and summer. Expt. 15. The room must be darkened except for one lamp, at eye level, and the apparatus required is just an old tennis ball with a steel knitting needle pushed through it to represent the axis. THE SEASONS 41 (i) Hold the 'Earth' in the summer position (Fig. 39, no. 3), i.e. with the axis slightly tilted towards the 'Sun', and slowly rotate it. Notice that the upper part of the ball, representing the northern hemisphere of the Earth, is more than half illuminated, and that the area near the north pole is light at all times (Fig. 41A). (ii) Hold the 'Earth' in the winter position (Fig. 39, no. 1), and notice that the northern hemisphere is less than half illuminated and that near the north pole it is in darkness all the time (Fig. 41B). (A) shows a tilted Earth with a needle pointing towards one wall. (B) shows a similar setup but with no tilt. (A) (B) Fig. 41. The seasons (iii) Now hold it in a position represented by 2 or 4 in Fig. 39, the axis being tilted across the direction of the light, neither towards it nor away from it. Notice that the northern hemisphere is just half illuminated, and that every part of the Earth receives light for half a rotation. This experiment illustrates several important things. In the first place, in summer we receive more than our fair share of light, and therefore our days are longer than the nights. In winter these nights are longer than our days. Notice also that at any point on earth's north pole, bounded by the Arctic Circle, where in summer it is day all the time. This means that the Sun never sets, but just skirts the northern horizon instead, and many of the pleasure cruises to the Norwegian Fjords visit the North Cape to see the 'midnight sun'. In winter, of course, the Arctic regions have perpetual night. When we say that during summer 'the Earth is tilted directly towards' or 'away from' its axis, we mean that during summer it will appear overhead at places having latitude of S°. This line is called A diagram showing two positions of Earth's tilt relative to sunlight: one tilted towards (left) and one tilted away (right). The left side has more illumination on one side due to being closer to sunlight. N E S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. E. The seasons  42 THE SEASONS the Tropic of Cancer because at the time when the condition occurs the Sun is in the Zodiacal sign of the Crab, S, in the winter diagram lies on the Tropic of Capricornus (Capricornus: the sea goat). By 'the tropics' we usually mean the zone of the Earth between these two lines and in which the Sun can be seen exactly overhead at some time during the year. Finally, in spring and autumn there is a time when the whole world is receiving equal treatment in the matter of light, and that day is somewhere the same length, about equal to that of the night. The Sun then shines vertically over the Equator. These positions are called the Equinoxes; summer and winter are called Solstices. The dates at which they occur are: Equinoxes (2 and 4 in Fig. 39) January 21-22 and September 23-24; Solstices (1 and 3) June 21-22 and December 22. How do we find the position of the Sun in the sky? A modification of Expt. 11 will explain this, but first refer again to Fig. 40. If the plane of the Equator be imagined to extend right into the sky, it will trace out a line there called the 'celestial equator'. You can find out roughly where it is by bending a piece of wire into a right angle, pointing one leg at the Pole Star, and twisting that leg until it lies along the celestial equator. Follow all the time towards the celestial equator. Notice the important fact that the angle between a point on the Equator and the pole is always 90°. Fig. 40 A shows us that in summer the Sun is above the Equator, and in winter, B, below it; we may reasonably suppose that between these two positions the Sun will be on it, and this is, in fact, the real definition of the Equinoxes, the instant when the Sun is on the Equator. Expt. 16. Take the flask filled for Expt. 11, hold it with the neck vertically downwards, and draw a chalk line around the water level to represent the Sun's path everywhere 90° from the pole O (Fig. 19). Now tilt the flask into its usual position. (i) Swing it round a minute so that it passes over the Equator and rotate the flask. Notice how it rises N. of E., passes right over the top, i.e. high in the sky, sets N. of W., and is above the horizon longer than below it. THE SEASONS 43 (ii) Equinoxes: Put the mark on the Equator. The Sun rises exactly E., does not pass over as high as in (i), sets exactly W., and is above horizon for exactly half a rotation. (iii) Winter: Put the mark below the Equator. The Sun rises S. of E., never gets far above the horizon, sets S. of W., and gives a day very much shorter than the night. These results are illustrated in Fig. 42. OBSERVATIONS (16) Use the apparatus used for Observation 14 to find the altitude of the Sun at midday. Use a dark blue, or thickly smoked glass to protect your eyes from brightness of sunlight. (17) Use this apparatus to find the exact direction in which the Sun sets. Allow for magnetic variation if you know its value. These two observations should be repeated once a week for several months in order to test the results of Expt. 16. Tabulate as under: Date Altitude of Sun at midday Sunset Time Direction Sunrise can be included with advantage if you get up in time. Fig. 42. The path of the Sun across the sky  44 CHAPTER IX THE MOON The Earth does not travel alone; it has an attendant body, or satellite, about 240,000 miles away, moving around it once a month and making the Earth a pleasant place to live in. The Moon is ever changing in appearance and adds beauty to both land and sea. A diagram showing the phases of the Moon. - The diagram is labeled "Last Quarter" at the top left. - A circle with a crescent moon is labeled "New Moon". - Another circle with a crescent moon is labeled "First Quarter". - A circle with a full moon is labeled "Full Moon". - A circle with a crescent moon is labeled "Second Quarter". - A circle with a crescent moon is labeled "Third Quarter". - A circle with a crescent moon is labeled "Fourth Quarter". - A circle with a crescent moon is labeled "Fifth Quarter". - A circle with a crescent moon is labeled "Sixth Quarter". - A circle with a crescent moon is labeled "Seventh Quarter". - A circle with a crescent moon is labeled "Eighth Quarter". - A circle with a crescent moon is labeled "Ninth Quarter". - A circle with a crescent moon is labeled "Tenth Quarter". - A circle with a crescent moon is labeled "Eleventh Quarter". - A circle with a crescent moon is labeled "Twelfth Quarter". - A circle with a crescent moon is labeled "Thirteenth Quarter". - A circle with a crescent moon is labeled "Fourteenth Quarter". - A circle with a crescent moon is labeled "Fifteenth Quarter". - A circle with a crescent moon is labeled "Sixteenth Quarter". - A circle with a crescent moon is labeled "Seventeenth Quarter". - A circle with a crescent moon is labeled "Eighteenth Quarter". - A circle with a crescent moon is labeled "Nineteenth Quarter". - A circle with a crescent moon is labeled "Twentieth Quarter". - A circle with a crescent moon is labeled "Twenty-first Quarter". - A circle with a crescent moon is labeled "Twenty-second Quarter". - A circle with a crescent moon is labeled "Twenty-third Quarter". - A circle with a crescent moon is labeled "Twenty-fourth Quarter". - A circle with a crescent moon is labeled "Twenty-fifth Quarter". - A circle with a crescent moon is labeled "Twenty-sixth Quarter". - A circle with a crescent moon is labeled "Twenty-seventh Quarter". - A circle with a crescent moon is labeled "Twenty-eighth Quarter". - A circle with a crescent moon is labeled "Twenty-ninth Quarter". - A circle with a crescent moon is labeled "Thirtyrd Quarter". The diagram shows the positions of the Moon relative to the Sun and Earth over time. The positions are numbered from 1 to 32, representing different phases of the Moon's cycle. The diagram also includes labels for each phase, such as New Moon, First Quarter, Full Moon, etc., which correspond to the positions on the diagram. The text describes the phases of the Moon and their corresponding positions on the diagram. It explains that the Moon moves through its phases as it orbits the Earth, and that these phases can be observed by looking at the Moon from different angles. The text also mentions that the Moon appears to change shape as it moves through its phases, but this change in appearance is due to the angle at which we see the Moon from Earth, rather than any actual change in the shape of the Moon itself. The text concludes by stating that the changes in the appearance of the Moon are called scintillation, and that these changes can be used to calculate the motion of the Moon and its future positions. The text also mentions that the size of the Moon's orbit around the Earth is about 200 miles in diameter, and that one half of this orbit is illuminated by the Sun. Expt. 17. The apparatus and lighting should be the same as in Expt. 15. Face the light, hold the ball at arm's length, and turn slowly round towards your left hand until you are facing again. Notice the changes that you can see in the amount of ball lighted and compare them with Fig. 43. Position no. 1 is what is really meant by 'new' Moon; it is in the eastern half of our sky, facing us on one side towards the Earth, and therefore invisible. In no. 2 most of the portion towards us is dark, but there it just a narrow crescent of light on the western side. When it reaches no. 3, a position called 'first quarter' because it is a quarter of the way around, we see half of it, and at 4, rather more than half and say that it is 'gibbous'. No. 5 shows 'full' Moon, with the whole of the lighted half towards us. From no. 6 onwards we come to see all four phases, with the western side illuminated; now we come to the 'waning' (decreasing) phases, which are similar, but with the eastern side showing, like no. 6. Remember that the waxing Moon faces the sunset and the waning Moon the sunrise; artists forget this. moves on through positions 2, 3, 4 and 5, it is moving towards the east. When at no. 3 it is on the meridian at 6 o.p.m., but at no. 6 it is on the meridian at 6 o.a.m. An interesting exercise is to note its position among the stars regularly (Observation 18) and see how long it takes to come back to the same place among them. This is a little over 27 days, and so therefore the time taken to go around among them will be nearly three months. In front of some of them, these phenomena being called scintillation. The observation and timing of disappearance and reappearance of stars in this way is very important, as results enable the motion of the Moon to be calculated, and its future positions tabulated in almanacks, with greater accuracy. The time of rotation on its axis is the same as that of its journey around the Earth, so we always see one face towards us. Fig. 43 also explains the changes in appearance of the Moon, called its phases. The Moon is not a lamp; it is solid sphere about 200 miles in diameter; one half being lighted by the Sun. When we speak of a 'new' Moon we think of a thin crescent in the western twilight just after the Sun has set. The next day it will still be in the west, but will not reach its former position until rather later in the evening. Each day it will move a little to the east among the stars until at sunset it is only just rising, and later still in the month we do not see it at all in the evening, for it rises too late. But instead we find 'the old' Moon in the west or south-west in the morning. If you are observing at 6 o.p.m., your position in Fig. 43 is at X; and you can see how, as the Moon THE MOON 45  46 THE MOON sometimes and draw the Moon in a perhaps pleasing but quite impossible position. As seen from the Moon the Earth would have phases, and just as we enjoy moonlight the imaginary inhabitants of the Moon would receive earthlight. Sometimes when the Moon is young and is but a thin crescent the remainder can be seen, looking a dim coppery colour. The bright crescent is illuminated by direct sunlight, and the remainder by light reflected by the Earth usually called earthlight. When the Moon has made one revolution around the Earth we should expect new Moon again. The Earth, however, has travelled on in its orbit, and the direction from which the sunlight now comes is shown in Fig. 43 by the dotted arrow. Thus no. 2 Fig. 44. An eclipse of the Moon is the new Moon position, and we have to wait for an extra two days for the Moon to get there. Thus a month measured by the Moon's phases is 29½ days, instead of the 27½ given by its motion among the stars. In Expt. 17 you may have found that the ball representing the Moon went exactly between you (the Earth) and the lamp (the Sun), and in another position entered the shadow of your head. Phenomena of this kind do happen sometimes and are called eclipses. They can be demonstrated with a ball like a tennis ball, or with a photography globe placed several feet from a lamp. The shadow of the ball passes over the globe; this is an eclipse of the Sun, or Solar Eclipse, and it causes a short period of darkness over that part of the Earth upon which it falls. The ball moves into the shadow of the globe; this is an eclipse of the Moon, or Lunar Eclipse, when a curved line appears across over the face of the globe; it grows dim for a time (Fig. 44). In the eclipse illustrated (1932) the Moon did not move straight through the middle of the shadow. 47 THE MOON Eclipses do not happen every month because the orbit of the Moon is not quite in the plane of the ecliptic (Fig. 39). It is near enough to that plane for the Moon to pass through the constellations of the Zodiac, but tilted at a sufficiently large angle¹ to make eclipses infrequent. In Fig. 45 note how eclipses occur only when the shadow of the Moon is south of the Earth, and full Moon when our satellite is north of the Earth's shadow. Eclipses occur only if the Moon is new or full when close to the points marked (N), where its orbit cuts the plane of the ecliptic. Fig. 45. Why eclipses are infrequent A C D B Point source Object Shadow Extended source Fig. 46. The two kinds of shadow You have probably noticed the difference between shadows due to a window (not direct sunshine) and those due to a lamp; the former are hazy and ill-defined, while the latter have sharp edges. The difference is due to the size of the sources of light (Fig. 46). ¹ About 5°. Fig. 46.  48 THE MOON Suppose that the light is coming from a point source and you are moving from $A$ to $B$. Until you reach $C$ the source is visible, from $C$ to $D$ invisible, and then visible again. The shadow $CD$ begins and ends suddenly and has sharp edges. Repeating the argument with a wide extended source, it begins to be hidden. A Total eclipse diagram showing the Moon's shadow on Earth. B Partial eclipse diagram showing the Moon's shadow on Earth. C Annular eclipse diagram showing the Moon's shadow on Earth. Fig. 47. The three types of solar eclipse when reaching $C$, but is not quite concealed until $D$ is reached. Thus from $C$ to $D$ and $E$ to $F$ there is a part shadow gradually deepening towards the dark shadow $DE$. The dark shadow is called the 'umbra' and the part shadow the 'penumbra'. The Sun is an extended source and gives this double shadow (Fig. 47). The umbra covers only a very small area of the Earth, A lunar eclipse diagram showing the Moon's shadow on Earth. Fig. 48. A lunar eclipse and therefore a total eclipse, in which the Sun is quite covered, is rather a rare occurrence in any one place. The last such eclipse in Britain was in 1927, over a belt about 30 miles wide, stretching approximately from North Wales to Hartlepool, and the next will be in 1999 in Cornwall. The general appearance of a total eclipse is seen in the frontispiece; note the darkened sky and the planet Venus showing above and to the right of the disc of the Sun. In a partial eclipse we see the Sun's disc only partly covered, as is the case in a partial eclipse (Fig. 47 B), when the umbra misses the Earth altogether. The orbit of the Moon, like that of the Earth, is an ellipse; thus the distance and apparent size vary a little. If what would have been a total eclipse had occurred, the Moon is at its greatest distance from the Earth, the umbra does not quite reach the Earth's surface (Fig. 47 C). This is called an annular eclipse, as when the Moon is exactly in front of the Sun it is too small to cover it and leaves a rim of light all around. A lunar eclipse is illustrated in Fig. 48. The penumbra in this case is of little importance, for it is the umbra shadow that we notice crossing the Moon's surface, and the 'totality' being to be total if the Moon enters it completely. One other point before we close this chapter. The Moon moves around the Earth in an ellipse, and the Earth is itself moving around the Sun in another ellipse. The Moon is therefore going around the Sun in an ellipse, but passing through it at one point but intersecting it. Fig. 49 shows a part of it, and the point to notice is that both orbits are concave towards the sun. The diagrams in some atlases are incorrect in this respect. 49 THE MOON Moon's orbit diagram showing its elliptical orbit around Earth. Earth's orbit diagram showing its elliptical orbit around Sun. Full moon diagram showing full moon phase. 3rd Qtr moon diagram showing third quarter moon phase. New moon diagram showing new moon phase. 1st Qtr moon diagram showing first quarter moon phase. Full moon diagram showing full moon phase. The Moon's orbit diagram showing its elliptical orbit around Earth. 56A 4  50 THE MOON OBSERVATIONS (18) Compare Fig. 27 with the stars near the Moon, identify the constellation in which it is situated, and decide on the exact spot on Fig. 27 at which the Moon should be inserted. Make a tracing of that part of Fig. 27 concerned and insert the position of the Moon, with its apparent motion marked. Notice this as often as possible for not less than five weeks, and so find the path taken by the Moon among the stars. From it find out the interval of time (a) for a full circuit of the sky, and (b) for a full cycle of phases, i.e. full or first quarter to first quarter. (19) If a small telescope (or good binoculars) is available, find out from Whittaker's Almanac the date and time of an occultation. Start watching for it, and when you see it try to observe the exact moment, to the nearest second with a correct watch, at which it does occur. The prediction is for Greenwich, and is slightly different in other parts of the British Isles. Fig. 50. Estimating the size of the Moon (20) Stick a halfpenny into a block of plasticine on top of a wall (Fig. 50) and then stand in such a position that the Moon is just behind it and fit it exactly. Get a friend to measure the distance (about 10 feet) from your eye to the halfpenny. By the property of similar triangles Diameter of Moon in miles = Diameter of coin in inches Distance of Moon in miles = Distance of coin in inches If the distance of the Moon is 240,000 miles, what is its diameter? CHAPTER X THE STORY OF THE PLANETS Chapter IV was devoted to the Constellations, and we saw there that the stars were mapped and named in very ancient times. There was a number of names including the Sun and Moon, which could not be mapped because they were always moving among the others, and these were called 'planets', meaning 'wanderers'. The term 'planets' no longer includes the Sun and Moon, but just refers to those which we now know to be revolving around the Sun in the same manner as the Earth. Five of these were known to the ancients. Mercury and Venus are nearer to the Sun than any other planets; Mars orbits within that of Earth. Mars, Jupiter and Saturn have larger orbits than that of the Earth, those of the last two being very much larger. The paths of these planets in the sky lie in the Zodiacal constellations and therefore their orbits, like that of the Moon, are nearly in the plane of the ecliptic. By observing the rates at which the planets moved among the stars the ancients got a very fair idea of their order in space; but they did not know that they were revolving around the Sun. The earliest ideas about the Earth were, of course, that it was flat, but by 500 b.c. men had realised that it was actually a sphere, and Eratosthenes of Alexandria (276-216 b.c.) obtained an estimate of its diameter. All the celestial bodies, however, were regarded as if they were fixed beneath us; thus all things revolving around the Earth. The Earth was supposed to be at the centre of a series of crystal (i.e. transparent) spheres. The outermost had the stars attached to it, and it resolved once a day; this did give a reasonable explanation of the observed facts. The Sun and Moon were on smaller spheres revolving, the former a little and the latter more slowly than those of the star-sphere; this did not explain the variable rate of movements seen by them subsequently modified. The spheres for the planets fell far short of explaining the facts, so let us consider how the planets do move and see what the difficulties were. 51 4-2  32 THE STORY OF THE PLANETS Probably the best known planet is Venus, the evening star. When first seen it will be low in the west just after sunset. As the weeks go on it gets higher in the sky and remains above the horizon longer, i.e. it is apparently farther from the Sun. Then its eastward motion stops and, moving more quickly this time, it returns towards the sunset and vanishes. A few weeks later it appears in the eastern sky as a morning star, just before sunrise. It rapidly reaches its maximum distance from the Sun, and then slowly returns to it. The motion of Venus can be imitated by moving a tennis ball around a lamp and watching it from a distance. It appears alternately to the left and to the right of the lamp, just as Venus appears to the left of the Sun as an evening star and to the right as a morning star. This experiment also shows that Venus has phases like those of the Moon. Fig. 51 shows the Sun and the four innermost planets. Venus is drawn in the position called "eastern elongation", because she is between Mercury and the Sun and the Sun is as great as it can be. The corresponding position on the opposite side of the Sun is, of course, "western elongation". Mercury shows a similar motion, but being nearer to the Sun never rises very high in the sky and is consequently difficult to see. It is drawn in Fig. 51 in the position called 'inferior conjunction', which is at the point S it is at 'superior conjunction'; planets in conjunction carry out their motions in the same direction as the Sun. The Earth is all the time moving in its own orbit, but the inner planets move more quickly and overtake the Earth when they are at inferior conjunction. In ancient times Venus was thought to be two planets, Lucifer in the morning light and Hesperus in the evening. When the old astronomers realised that they were not the same planet, some, at least, believed that it went around the Sun, although they would not admit that the Earth did so too. Fig. 51. The innermost planets The general motion of the other planets is similar to that of the Sun, a slow journey from west to east in the Zodiac. On careful examination, however, it is found that sometimes they stop, go backwards for a bit, and then go on again, as shown for Mars in Fig. 52. This retrograde motion puzzled the ancients gave up the crystal sphere, which would account for only direct motion only, and supposed that the planet moved in a small circle, called an epicycle, whose centre moved around the Earth (Fig. 53). Actually Fig. 51 gives all the explanation needed. Mars, in going around the Sun goes around the Earth also, because the Earth moves round its axis once every day; hence it steadily west to east motion. The Earth, however,'moves more rapidly, and from time to time overtakes Mars, causing the retrograde motion, 53 THE STORY OF THE PLANETS Fig. 52. The path of Mars among the stars TWINS 1844 Mar. RAM CEAB Twins May Little Dog Bull Orion Whale  THE STORY OF THE PLANETS 54 just as when a train in which you are travelling overtakes another going in the same direction the latter seems to be going back-wards. Jupiter and Saturn behave similarly, but as they take so long to go an extra degree (about 29°) they do not get very far between the periods of retrogression. In Fig. 51 Mars is shown in the position called 'opposition', when the Earth is just passing it and we see it on the same side as it is opposite to that of the Sun. A planet at opposition is in the middle of its retrograde path, and is nearer and brighter than before or after this date. If Mars was at C it would be in conjunction and therefore invisible. As long ago as 500 b.c. it had been suggested that the Earth went around the Sun, but this 'heliocentric system' did not receive very much support. That the Earth was at the centre of the universe was quite a natural assumption, and this was the theory that was developed by the early astronomers. It was accepted as truth for some two thousand years, until a more recent period saw the revival of Copernicus's ideas. This was not simply that there were no intelligent people, but because to question the authority of the old philosophers was just 'not done', and any who dared publicly to dispute their teaching were regarded with extreme disfavour, and sometimes ruthlessly suppressed. With the revival of learning the heliocentric system was again proposed. Copernicus (1473-1543, Poland) studied the matter in detail and in the year of his death published the book that was to set men thinking on the right lines. The next development was the work of Tycho Brahe (1546- 1601, Denmark). He was interested in the Copernican system, though he rather disproved it. His life's work was mainly observation and recording of a large number of observations of the heavenly bodies, to facilitate calculations of their motion. He was very well-to-do when he started this work, but he lost favour with the Court, left Denmark, and died, with the work yet unpublished, in rather poor circumstances in Bohemia. His tables were completed and published by his assistant, Kepler (1571-1630, Germany). The work of Tycho proved of very great importance; Copernicus gave the idea, Tycho obtained the necessary facts, and then Kepler solved the problem. Applying mathematics to the results of his former chief he deduced laws of planetary motion. The first law states that planets do not travel in circles but in ellipses, and the second showed how the speed of a planet in its orbit varies. A planet moves most quickly when in that part of the ellipse nearest to the Sun. These two laws cleared one of the difficulties which had given rise to the epicycles previously used, and then the third one gave a numerical relation between the distances of planets from the Sun and their times of revolution around the Sun. The problem had now been solved, but it remained for Galileo (1564-1642, Italy) to prove that the solution was correct. Galileo heard of the invention of an optical instrument for viewing distant objects, and after making inquiries about it he made one himself. Early in 1610 he started to use it to observe suddenly bodies moving across the sky. Only two with him mentioned here. First, he found that Jupiter had four satellites moving around the planet in just the same way as the planets were said to move around the Sun; this showed that Kepler's system could exist in fact as well as on paper. Secondly, in the experiment with the tennis ball he saw that Venus showed phases; Copernicus foretold these but Galileo saw them. Thus the telescope provided confirmation of the correctness of the theory, and the era of modern astronomy had begun. A diagram showing an epicycle around a planet orbiting around Earth. Fig. 53. An epicycle 55 (1) Every planet moves in an ellipse, with the Sun in one of its foci. (2) The straight line drawn from the centre of the Sun to the centre of the planet sweeps out equal areas in equal times. It follows that all planets are proportional to the cubes of their mean distances from the Sun. THE STORY OF THE PLANETS  THE STORY OF THE PLANETS Observation (21) Very carefully compare Fig. 27 with the sky. If you can find a star in the sky but not on the track, it is probably a planet. Mark its position and date on a tracing, as you did in Observation 18. Watch it regularly, say once a week, to see if you can detect its motion, and insert it on your tracing for as many weeks or months as it remains visible. CHAPTER XI The Law of Gravitation The next step forward was made by a very famous Englishman, Sir Isaac Newton (1643-1727). Kepler had shown how the planets moved; Newton's question was: "Why should they move like this?" It is common experience that an unsupported body falls to the ground as if the Earth were pulling it down, and Newton's idea was that the same force of gravitation held the Sun and its planets together as one family in space. The fall of an apple in his garden is said to have given him his idea and, whether it did or not, pieces of fruit fell from trees and were found to be perfectly preserved. The result of applying gravitation to Kepler's laws was the great law of gravitation, which you will find described in more detail in text books on Mechanics. The substance of the law is that the force between any two bodies is proportional to the two masses multiplied together, and inversely proportional to the square of their distance apart. In other words, the greater the course, that is the greater the body the greater the force. If you fall out of an aeroplane there is an attraction between you and it, but as the Earth is so very much more massive than the aeroplane the former wins the resulting tug-of-war and you fall. In fact the Earth is so much greater than anything on the Earth that its own gravitation holds all things down. This is why we do not fall off; the second part of the law means that the greater the distance between two bodies the very much less the force between them; double the distance—one-quarter of the force; treble the distance—one-ninth of the force. There are a number of inverse square laws like this, and another will turn up in chapter xvi of this book. The law of gravitation will be put into practice upon the hands of the astronomer, as it enabled calculations on the heavenly bodies to be made with an accuracy never before obtained, and several examples will be noticed as you go on reading. The Moon is smaller than the Earth and very much farther away; this makes its gravitational force weaker than Earth's surface weak, but it is still strong enough to cause the tides. The water on the hemisphere towards the Moon is a little nearer to that body than is the Earth beneath, so the Moon's gravitation is a little stronger, and the water is drawn slightly towards the Moon. Fig. 54. The cause of tides giving high-tide at A (Fig. 54). The Earth is nearer to the Moon than the water at B and therefore moves away slightly, giving high-tide at B also. Water flows from C and D, causing low-tides there, to provide for the heaping up at A and B. As the Earth rotates the positions of A and B are maintained by the Moon, and thus we have our two tides a day. Needless to say the theory of the tides has been worked out mathematically to fit exactly into outline of it. The Sun also tends to cause tides, and at times of full or new Moon the solar and lunar tides would both be at A and B; these tides are therefore higher than the average and are called 'spring tides'. At first or last quarter the solar tides should be at C and D, but as the water cannot do two things at once it has to choose one or other; hence we get 'neap' tides. At full Moon is the greater of the two, so the tides still occur at A and B, but are not so high and are called 'neap tides'. THE LAW OF GRAVITATION 57  THE LAW OF GRAVITATION The law of gravitation has led to the discovery of more planets, though the first addition to the six already discovered was an observation only. William Herschel, afterwards Sir William (1787-1822), who had been born in Hanover, Germany, and settled in Bath as a musician. Astronomy was his hobby and he made his own telescopes; eventually he became one of the great professional astronomers. He was observing one night at his home when he saw a star that was of rather unusual appearance. He watched it regularly and found it to be moving, and thus in 1781 the planet Uranus was discovered. The motion of this planet in its orbit, which is outside that of Saturn, provided material for further mathematical work, and it was found that its behaviour was not quite as it should be. Two mathematicians, Adams in England and Leverrier in France, quite independently tackled the problem of these variations and in 1846 they both announced their results. They concluded that Uranus was being disturbed by the gravitation of another planet farther out still, but stated just where the new planet should be situated. Quite near to its predicted place Neptune was seen for the first time by an astronomer at the Berlin Observatory. This discovery was a triumph for the gravitational work founded by Newton. History is said to repeat itself, and in this matter of planetary discovery it did. Further study of the motion of Uranus, including the effect of Neptune, was made by Percival Lowell (America; died 1917) who deduced the presence of yet another distant planet. The search at the time was unsuccessful, but in 1900 Pluto was found on photographs taken at the Lowell Observatory by another American, Clyde Tombaugh. Thus three more major planets now known, and it is, with numerical information complete, this chapter. One cannot leave the story of the planets, however, without remarking that Science knows no political boundaries. If you look through the names in these two chapters, you will see that our knowledge of the Solar System, as the Sun's family is called, has been built up step by step by representatives of Poland, Denmark, Germany, Italy, England, France and America. Table of the Solar System Period of revolution around Sun Radius from Earth Period of revolution around Sun Distance from Sun in millions of miles Name Symbol Discovery Year Year Year Year Year Year Year Year Year Year Year Uranus.                           Venus.                           Mars.                     From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth From Earth Around Earth