The sun

Front matter

IIEXLIBRIS

BY

CHARLES G. ABBOT, S.M.

Preface

Chapter II has been devoted to a description of the methods and principles employed in modern solar research, and Chapters VII to X on the relations of the sun to life upon the earth, and to the starry universe in general. Thus the book, while primarily devoted to the sun, may, I hope, serve as an introduction to the study of astrophysics for school and college use, as well as for the general reader.

In Chapters VI to IX are given many facts likely to prove of interest to the meteorologist, geologist, botanist and engineer.

Professor Young's "The Sun" is now out of print, and as it is hoped that the present work may to some extent take its place, I have been permitted to use some of his illustrations, notably in Chapter IV, and to make several quotations from his text, the longest in Chapters IV anil VI. I desire also to acknowledge my obligations to many who have given suggestions, information and illustrations. Especially I offer thanks to F. E. Fowle, S. A. Mitchell, W. W. Campbell, G. E. Hale and the staff of the Mount Wilson Solar Observatory, E. B. Frost, H. M. Chase, A. G. Eneas, Henry Holt and Company, the Superintendent of the United States Naval Observatory, M. J. Moore of the United States Patent Office, and Messrs. Briggs and Shantz of the United States Department of Agriculture.

C. G. ABBOT.

WASHINGTON, July 10/1911.

Chapter I Pages

THE SOLAR SYSTEM. THE SUN'S DISTANCE. ITS DIMENSIONS 1-30

Chapter II The Instruments And Methods Used In Solar Investi- Gation . 31-84

The Telescope. — The Coelostat. — The Spectrum and What It Indicates. — Spectroscopes. — The Spectroheliograph. — The Heliomicrometer. — The Comparator. — Nature of Radiation — Laws of Radiation. — Spectra of Different Sources. — Pyrheliometry.-^Bolometry.

Chapter III

Telescopic View. — The Photospheric Spectrum. — Rowland's Spectrum Tables. — Chemical Elements Found and not Found. — Corrections to Rowland's Wave-lengths . — Levels . — Pressures. — Convection Currents . — Limb Spectra. — The Variation of the Sun's Brightness. — Solar Temperatures. — Spectro-heliography. — The Solar Rotation.

Chapter IV Eclipses And The Outer Solar Envelopes . . 128-182

The Saros. — Eclipse Expeditions. — The Corona. — The

Chromosphere. — Jansen's and Lockyer's Discovery. —

The Spectra of tte Chromosphere and Prominences. —

vii

CONTENTS

PAGES

Prominences and the Spectroheliograph. — Recent Flash Spectrum Observations. — The Heights of Different Metals in the Chromosphere. — Mitchell's Observations of 1905. — Campbell's Observations. — Chromospheric Spectra in Full Daylight.

Chapter V

SUN-SPOTS, FACULAE AND GRANULATION . . . 183-214 Sun-spot Periodicity — Drift — The Distribution of Sunspots. — Their Formation and Life History. — The Sun-spot Level. — Langley's Typical Sun-spot. — Faculae. — Granulation. — Sun-spot Spectra. — Sun-spots and Magnetism.— Radial Motion in Spot Penumbras.

Chapter VI

Young's Views. — Halm's Views. — Schmidt's Hypothesis. — Julius' Views*. — The Author's Views.

Chapter VII

THE SUN AS THE EARTH'S SOURCE OF HEAT . . 280-330 Causes of Low Temperatures at High Altitudes. — Measurement of the Intensity of Sun Rays. — Dependence of Solar Radiation on Air Mass — The Transmission o'f the Atmosphere. — The "Solar Constant of Radiation." — The Light of the Sky.— The Dependence of the Earth's Temperature on Radiation. — The Fluctuation of Solar Emission. — Geological Temperatures.

Chapter VIII

THE SUN'S INFLUENCE ON PLANT LIFE .... 331-361 Plant Requirements. — The Assimilation of Carbon by Autotrophic Plants. — Etiolation. — Plant Geography. — Light Requirements of Plants. — Heliotropism. — Plants as Energy Accumulators.

viii

CONTENTS CHAPTER IX

PAGES

Experiments with Burning Mirrors. — The "Hot-box" Principle. — Mouchot, Pifre and Ericsson. — Eneas' Solar Engines. — Properties of Glass. — Solar Heaters and Reservoirs.— Low Temperature Solar Engines. — Solar Cooking Appliances. — Solar Metallurgy. — Resume*.— Quantity of Solar Energy Available. — Thermo-dynamic Efficiency. — Reflecting Powers of Mirror Surfaces.

Chapter X

Stellar Distances. — Magnitudes. — The Sun's Magnitude and Light Emission. — The Solar Motion. — Star Groups. — Double Stars. — Stellar Masses and Distances. — Mira Ceti and the Sun. — Stellar Spectra. — The Classification of Stellar Spectra. — Radiation Distribution. — Evolution of the Solar System. — Stellar Evolution

CONCLUSION 435-437

LIST OF PLATES AND ILLUSTRATIONS IN TEXT

LIST OF PLATES FACING

PAGE

Langley's typical sun-spot Frontispiece

PLATE I. — Smithsonian observing shelter and coelostat

PLATE II.— The Zeeman effect (King) . . . . .44

PLATE III. — Solar photograph (Ellerman) .... 86 PLATE IV. — Fig. 1. 'Spectrum of procyon (Adams); Fig. 2.

Spectrum of east and west limbs of the sun (St. John) . 88 PLATE V. — Calcium spectroheliogram, H3 (Ellerman) . .114

PLATE VI. — Hydrogen spectroheliogram, Ha (Ellerman) . 116

PLATE VII. — Calcium spectroheliogram, Ht (Ellerman) . 118

PLATE VIII. — Calcium spectroheliogram, Ha (Ellerman) . 120

PLATE IX. — Calcium spectroheliogram, H3 (Ellerman) . 122

PLATE X. — Hydrogen spectroheliogram, Hy (Ellerman) . 124

PLATE XI. — Hydrogen spectroheliogram, Ha (Ellerman) . 126 PLATE XII.— Solar corona, 1900, May 28 . . .132

PLATE XIII.— Solar corona, 1905, August 30 ... 134 PLATE XIV. — Spectroheliograms of solar prominences (Slo-

PLATE XV.— Flash spectra, 1905, August 30 (S. A. Mitchell) 174

PLATE XVI. — Photographs of a portion of the sun (Jansen) 202 PLATE XVII. — Spectra of photosphere and sun-spot (Mount

Wilson Solar Observatory) 210

PLATE XVIII. — Effect of pressure on gaseous spectra (Gale) 248

PLATE XIX.— The Pleiades (Ritchey) 398

PLATE XX A.— Stellar spectra (Campbell) . . . .406

PLATE XX B.— Stellar spectra (Campbell) .... 408

PLATE XXL— Stellar spectra (Hale and Ellerman) . . 410

xi

PLATES AND ILLUSTRATIONS IN TEXT

FACING PAGE

PLATE XXII.— The great nebula in Orion (Ritchey) . . • 418

PLATE XXIII.— Nebula N. G. C. 6992 Cygni (Ritchey) . 420

PLATE XXIV. — The great nebula in Andromeda (Ritchey) 422 PLATE XXV. — Spiral Nebula M. 51 Canum Venaticorum

(Ritchey) 424

PLATE XXVI.— Fig. 1. Nebula H. V. 24 (Ritchey); Fig. 2.

Ring nebula in Lyra (Ritchey) 426

LIST OF ILLUSTRATIONS IN TEXT

PAGE

1. — Relative distances of planets 5

2. — Geometrical parallax method 10

3.— Velocity of light (Fizeau) 19

4.— Velocity of light (Foucault) 20

5. — Determination of constant of gravitation .... 29

6. — Projecting the solar image 32

7. — HerschePs solar eye-piece . 33

8. — Shade glasses . . . 34

9. — Polarizing eye-piece 34

10. — Rapid exposing solar shutter . . . . . . 35

11. — Prismatic refraction of light 47

12. — Prismatic spectroscope 50

13.— Diffraction of light ....'.... 51

14. — Plane grating spectroscope 53

15. — Concave grating spectroscope 54

16.— The 150-foot tower (Mount Wilson) .... 58

17. — Energy-spectra of the sun and the perfect radiator . 69

18.— Pouillet's pyrheliometer 73

19. — Abbot's silver disk pyrheliometer 76

20. — Angstrom's pyrheliometer 77

21. — Angstrom's pyrheliometer. Details 77

22. — Abbot's water flow pyrheliometer 79

23.— The bolometer 81

24. — Holographs of the solar spectrum 83

25. — Brightness on solar disk .106

26. — Energy spectra on solar disk 109

xii

PLATES AND ILLUSTRATIONS IN TEXT

FIG. PAGE

27. — Huggin's first observation of a prominence in full sunshine 143

28. — Double reversal of the D-lines 147

29.— Double reversal of C-line 148

30. — " Arrow-head " spectrum 148

31. — Opened slit of the spectroscope 149

32 . — Chromosphere and prominences as seen in the spectrum . 151

33. — Relative frequency of protuberances and sun-spots . 153

34-39. — Eruptive prominences 157

40-45. — Quiescent prominences 159

46-51. — Forms of prominences 163

52. — Motion indicated by prominence spectra . . .165

53. — Sun-spots and terrestrial magnetism 187

54.' — Sun-spots and terrestrial temperatures and magnetism . 191

55. — Spoerer's curves of sun-spot latitude 194

56.— Solar diagram (Young) 216

57. — Normal and anomalous dispersion 233

58.— Michelson's hypothesis 260

59. — Displacement diagram 261

60. — March of insolation (Mount Wilson) .... 285

61. — Holographs of the solar spectrum 292

62. — Atmospheric transmission plats 294

63. — Insolation and terrestrial temperatures . . . .316 64. — Apparent variations of the sun's radiation (Smithsonian

observations) 321

65. Hypothetical temperature diagram 325

66.— Stomata (Schwendener) 338

67. — Promotion of carbon assimilation by light, and absorption of light 343

68. — Eneas' solar engine 367

69. — Boiler of Eneas' solar engine 368

70. — Adams' solar cooker 380

71. — Intensity of sun rays (Mount Wilson and Washington) 384 72. — Intensity of solar radiation (Different latitudes and

elevations) 385

LIST OF TABLES

TABLE PAGE

I. — Principal data of the solar system .... 3

II. — Velocity of light in different media .... 46

III. — Principal solar spectrum lines 90

IV. — Chemical elements found in the sun ... 91

V. — Chemical elements doubtfully occurring in the sun 92

VI. — Corrections to Rowland's wave-lengths ... 96

VII. — Distribution of radiation over the sun's disk . . 107

VIII. — Energy spectrum relations over the sun's disk . 110

IX. — Daily rotation of the sun's surface .... 126

X. — Measures of ninety-two lines in the flash spectrum

XI. — Years of sun-spot maxima and minima and maximum intensities 186

XII. — Hydrogen spectrum in sun-spots .... 206

XIII. — Spectrum lines affected in sun-spots . . . 206

XIV. — Sun-spot, hot arc and cool arc spectra . . . 209 XV. — Moissan's experiments on the vaporization of the

elements of the iron family .... 238

XVI. — Differences between observed and computed values

of atmospheric transmission .... 242

XVII. — Observed intensity of solar radiation, Mount Wilson, July 6, 1910 . . . . . . .2,87

XVIII. — The intensity of radiation in different parts of the

solar spectrum 288

XIX. — Transmission for total solar radiation . . . 296

XX. — Atmospheric transmission for homogeneous rays 297

XXI.— Sunlight and sky light (Exner) .... 301

XXII.— Sunlight and sky light (Roscoe) .... 302

xv

LIST OF TABLES

TABLE PAGE

XXIII. — Sky light on a vertical surface (Exner, Schramm) 303 XXIV. — Sun and sky light. Relative brightness for different wave-lengths (Mount Wilson) . . 305 XXV. — Average brightness of sky zones. Flint Island

and Mount Wilson 306

XXVI.— Ratio of total radiations: Sky to sun . . .307 XXVII. — Yearly means and mean daily temperature departures 311

XXVIII. — Composition of food products 333

XXIX. — Economy of Helianthus Annuus .... 361

XXX. — Percentage reflecting powers of various reflectors 3 88 XXXI. — Classification of stellar spectra . . . .410 XXXII. — Intensities in stellar spectra (Wllsing and Schei-

XXXIII. — Spectroscopic binaries. Spectral types, periods and

eccentricities (Campbell) 422

XXXIV. — Spectral types and velocities in space (Kapteyn) . 430

INTKODUCTION

WE depend on the sun for life, warmth, light, and all mechanical and electrical powers. Its constant supply of heat is necessary to prevent the oceans and even the air from freezing. The supply of coal which we are now using is but an evidence of the sun's light in former ages. To pass to the enumeration of the comforts and luxuries and beauties we owe to the solar rays would lead us far astray, and is indeed wholly unnecessary because all men acknowledge and many worship the sun as the source of these benefits. It would be a gross neglect to omit the closer investigation of such unique relations as those the sun maintains to life. Yet the study of the means of increasing the usefulness of the sun has been neglected, and it is rather in the investigation of its curious features that solar researches have gone farthest.

The enormous brilliance and heat of the solar rays suggestive of temperatures far above any which can be produced on the earth; the marked dimness and brown shade of the edge or limb of the sun relative to the center; the fluctuating march of spots across the disk; the variable rates of rotation of the sun's surface in different latitudes; the brilliant markings 2 xvii called faculse which accompany the spots; the weird and highly beautiful phenomena of total solar eclipses; all these have long been the objects of minute study. In the last half century the development of the spectroscope has led to great progress in the more intimate and satisfactory knowledge of the sun; so that we now know many of the chemical elements of which it is composed; the approximate temperature of its surface ; the motion of the vapors at and near the surface; the approximate pressure under which they lie; the magnetic character and cyclonic structure of sun spots; their relative coolness as compared with their surroundings; besides many other details hardly to be credited as known of a body situated nearly ninety-three millions of miles away.

By bonds unseen yet altogether stronger than a bar of steel thousands of miles in diameter the sun holds to itself the moving family called the solar system, comprising the earth and moon, the seven other great planets with their satellites, half a thousand asteroids, or minor planets, besides numerous comets and meteorites. It has required the lifelong labors of many men of exceptional genius, like Newton, coupled with centuries of no less praiseworthy if less brilliant accumulations of accurate observations to have given us the full knowledge which we now enjoy of the distances, dimensions, masses and orbits of the solar system.

Although the distance from the sun to the orbit of Neptune is 2,800,000,000 miles, the solar system is

xviii but a speck in the vast universe of the stars. In the year 1901 there flared up in the constellation Perseus a new star which for a few days rivaled the brightest stars of the heavens in its brilliancy, and then slowly faded away into insignificance. To dwellers on the earth this sight was new in 1901, but in reality that new star was so far away that its sudden burst of light, traveling toward us 186,000 miles a second, had been on the journey since the days of Cromwell, and the star had faded away nearly three centuries ago. At such enormous distances are the stars that, although some of them are believed to be millions of miles in diameter, they present no real disks even in the largest telescopes, so that the details of their surfaces cannot be examined. Nevertheless, by the powerful aid of the spectroscope, much is known of the chemical constitutions of the stars; and many of them have been shown to belong to revolving systems, the components of which, though separated in some instances by greater distances than is Jupiter from the sun, are separately indistinguishable to the telescope. Still we might despair of knowing much more of the physics of the stars if it were not that the spectroscope shows also that the sun is but one of them close by, and that a large class among the stars is probably in a similar condition as to temperature, and made up of the same chemical substances as the sun.

Both telescopic and spectroscopic observations have shown that the solar system is moving at a rapid

xix rate towards the constellation Hercules, although no change in the aspect of the heavens sensible to the naked eye would accumulate for an immense period of years. By means of the displacement of the earth in its orbit around the sun, amounting to over 180 millions of miles, semi-annually, it has been possible to obtain with fair accuracy the distances of many of the individual stars, and from these by statistical methods to go further and estimate the average distances of all the stars of a given brightness. These various examples indicate the important place of the sun in stellar investigations; and indeed the study of the sun as a typical star, though quite recently developed, seems bound to throw much more light on the subject of the nature of the universe.

Considering the sun as the fountain of light and heat upon the earth, perhaps the first question which suggests itself is this: How much radiant energy reaches the earth from the sun in a given time? This utilitarian branch of solar investigation has been comparatively neglected. No more striking proof of the neglect need be cited than to say that the foremost text-book on meteorology, published since 1900, states various determinations of the intensity of solar radiation at the earth's mean distance which range from 1.76 to 4.06 calories per square centimeter per minute. Of these the author of the text-book prefers one which is confessedly the mean of such divergent numbers as 2.63 and 3.50, one of which numbers was thought by its originator to be

xx too low, and the other too high! As will be shown later, there can be little question now (1910) that the true value is about 1.95 calories; but how remarkable it is that one of the fundamental constants of Nature should have been uncertain within such wide limits, so late as the beginning of the twentieth century. Imagine, for analogy, that it had been stated in a standard work on astronomy, published in 1905, that the sun's distance (which is of no greater importance than the constant of radiation) might be anything between 80 millions and 200 millions of miles so far as known, and that it was generally supposed to be 140 millions!

Some of the more important questions connected with the sun's action as the fountain of light and heat are the following: Is the solar radiation uniform or variable? What losses does it suffer in the earth's atmosphere? Are there changes of transparency in the sun's outer layers sufficient to alter the earth's supply of radiation appreciably? How much solar radiation does the earth reflect, unused, to space? How does the earth's temperature depend on solar radiation and on the transparency of the air? If there should be variations of solar radiation, how great changes of temperature of different stations on the surface of the earth ought to follow, and how long would such responses be delayed? In short, are solar studies applicable to weather prediction? What methods, if any, can be economically used to store and employ the sun's energy for power or heat-

xxi ing? What influences do changes in the intensity or color of the light falling on different plants produce on their growth and fruitage? May advantageous variations of plants be promoted by the control of their radiation supply? What can be done with solar rays for the promotion of health?

In the pages which follow the sun will be considered in these three aspects: First as the controlling member of the solar system; second, as an object of inquiry, interesting in itself, but still more so as the nearest star, and typical of a large class of stars; third, as the fountain of light and heat, and through them of life on the earth. It is indispensable to any satisfactory understanding of the second and third branches to be familiar with the methods and principles which are now being employed in solar investigations. For the convenience of the reader a general account of these is given in Chapter II, which therefore has to do directly with physics, and only secondarily with the sun, but which forms the groundwork of the chapters relating directly to solar phenomena. Illustrated descriptions of some of the instruments used in solar research will also be found in Chapter II, and appropriate references to these descriptions and to the statements of the general relations will be found in the text of subsequent chapters.

To avoid premature discussion, the various solar phenomena will be described first without much attention to their explanation, except as seems nec-

xxii essary to fix attention upon significant facts. Solar theories are dealt with in Chapter VI. One principal exception to this course is in the frequent noting of applications of Kirchhoff s discoveries on the relations of temperature, radiation, and absorption. It may be that future writers on the sun will attribute to anomalous dispersion many of the phenomena here set down as due to absorption and motion. But although anomalous dispersion hypotheses are so strongly advocated by Julius, the writer feels confident that his own preference for the older views is still shared by most students of solar physics.

What, after all, is the sun, and how can we best explain the principal solar phenomena? No doubt many will find the views here advanced heretical, but for the writer the existence of the cloudy photosphere, so firmly believed in by most solar observers, seems so highly improbable that he has ventured to advocate the view of a purely gaseous sun. But in doing so it is not Schmidt's refraction theory to which he turns to explain the sharp solar boundary. According to Lord Rayleigh our own atmosphere, if freed from dust, would still scatter light by the action of the gases themselves. Schuster and Natanson have computed this effect, independently, and both find that the purely gaseous scattering goes far to explain in full the observed weakening of the direct beam of the sun above Mount Wilson for rays which are not selectively absorbed. This weakening amounts to several per cent. If then the gases of

xxiii the atmosphere of the earth, which extend, in density sufficient to scatter light appreciably, perhaps only fifty miles in altitude, suffice to scatter several per cent, of a beam of light, it seems probable that we can see at the most not more than a very few thousand miles into the gaseous body of the sun, which, at the layer producing the Fraunhofer lines, seems to be under several atmospheres of pressure. Admitting this, how deep, measured radially, can one see near the sun's edge, where the few thousand miles above mentioned will lie along a line of sight nearly tangent to the sun? It would-seem that at the sun's edge a shell of gas of only a few hundred miles in thickness must suffice to fully veil all that lies below. Viewed from the earth this would correspond to a fraction of a second of arc, so that a gaseous sun at 93,000,000 miles away would present an apparently sharp boundary. From these considerations depend various consequences adapted to the explanation of solar phenomena. To be sure there are several apparently powerful objections to this view of a purely gaseous sun, but they seem not to be insuperable.

My good friend, Prof. J. C. Kapteyn, has encouraged me to set down several hypotheses which can be regarded as only slenderly founded. Among these are the hypotheses of the causes of some strange phenomena of geological climates, touched upon in Chapter VI, and more fully discussed in Chapter VII ; the hypotheses of the causes of some peculiar-

xxiv ities of stellar evolution given in Chapter X; and as some readers may be disposed to think, even the explanation of solar phenomena already mentioned which occupies a large part of Chapter VI. Professor Kapteyn is of the opinion that a bushel of chaff is worth searching by a Crusoe if it contains some grains of corn that will sprout, and so my defense for my temerity in including such speculations is that they may interest some readers to begin some more fruitful researches.

Chapter I

THE SOLAR SYSTEM. THE SUN'S DISTANCE. ITS DIMENSIONS

THE objects which appear to move among the stars, namely the sun, planets, minor planets, moons, meteors and comets,1 compose the solar system. Formerly it was believed that all the heavenly bodies revolve about the earth. But now the theory of Copernicus is fully verified, arid the earth is known to be only a planet, of much smaller size than Jupiter, Saturn, Uranus or Neptune, though larger than Mars, Venus or Mercury, and like the other planets it revolves about the sun. Galileo was threatened with torture and forced to perjure himself because he believed this, which shows how fortunate we are to live in the present age.

The moon has actually only -— as great a diameter

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as the sun, although they appear to be about equal. It is the immense distance by which the sun and planets are separated from the earth in comparison with the distances we are accustomed to travel over

1 Not all the comets remain permanently attached to the solar system, but many of them do.

d with the distance of the moon, which prevents us from immediately realizing the great bulks of these distant bodies. In the following table is a summary of the approximate dimensions and principal characteristics of the larger members of the solar system. The means of determining the sun's distance, dimensions and rotation will be given later.

GRAVITATION

Accustomed as we are to regard inches and feet as ordinary, miles as considerable, and thousands of miles as very great distances, it may seem almost incredible that there should be any bond between the the sun and Neptune, situated as they are 2,800,000,- 000 miles apart. There is, however, a bond between them so strong that it would require the strength of a bar of steel 500 miles in diameter to take its place in preventing the escape of Neptune from the sun. This bond we call gravitation. Every body in the universe is believed to attract every other body in the universe with a force proportional to the mass or quantity of matter the body contains, and inversely proportional to the square of the distance between their centers of gravity. On the one hand, this law of gravitation applies between all bodies on the earth as well as between the earth itself and any one of them; and, on the other hand, there is evidence that it holds also among the fixed stars. The weight of a stone is the measure of the attraction between it and

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The attraction of gravitation between the sun and Neptune amounts to 8 x 1016 (8 followed by sixteen ciphers) tons. If there was nothing opposed to this force, Neptune obviously would fall into the sun. It is the motion of the planet in its orbit, at right angles to the line leading towards the sun, which maintains the distance between them.

Kepler's laws of planetary motion are as follows:

I. The orbit of each -planet is an ellipse, with the sun in one of its foci.

II. The radius vector of each planet describes equal areas in equal times.

III. The squares of the periods of revolution of the planets are proportional to the cubes of their mean distances from the sun.

There is but little difference between the major and minor axes of the elliptical orbits of most of the planets, or, in other words, their orbits are nearly circular.

THE SOLAR SYSTEM

But this is not true of the orbits of Mercury and Mars, as is shown in Table 1.

It may be surprising to some readers that Kepler could have possessed so much knowledge of the distances of the planets from the sun as to enable him to verify the third law, while as yet the actual distances in miles were not even roughly known. But only the ratios of the distances of the planets were required by Kepler, and these could be fixed independently of the actual distances by the following method, known since the days of Hipparchus, which I quote from Young's "The Sun."

" First, observe the date when the planet comes to its opposition, i.e., when sun, earth, and planet are in line, as in the figure, where the planet and earth are represented by M and E.

Next, after a known number of days, say one hundred, when the

planet has advanced to M'and the earth to E', observe the planet's elongation from the sun, i.e., the angle M'E'S. Now, since we know the periodic times of both the earth and planet, we shall know both the angle MSM' moved over by the planet in one hundred days, and also ESE', described in the same time by the earth. The difference is M'SE, often called the synodic angle. We have, therefore, in the triangle M'SE', the angle at E' measured, and the angle

M'SE' known as stated above, and hence by the ordinary processes of trigonometry we can find the relative values of its three sides."

Thus, by means of comparatively simple astronomical observations, all the relative distances in the solar system can be fixed with high accuracy. It is a work of far greater difficulty, as we shall see, to measure any of these distances absolutely.