THE BOOK WAS
DRENCHED
CO > 00
a: ft
62941
ca
THE GREAT TELESCOPE OF THE UNITED STATES NAVAL OBSERVA
TORY, WASHINGTON.
CONSTRUCTED BY ALVAN CLAIIK AND SONS, 1873.
POPULAR ASTRONOMY.
BY
SIMON NBWCOMB, LL.IX,
PROFESSOR, U. S. NAVAL OBSERVATORY.
WITH ONE HUNDRED AND TWELVE ENGRAVINGS,
AND FIVE MAPS OF THE STARS.
HP #n b a n :
MACMILLAN AND CO.
1878.
LONDON:
PRINTED BY WILLIAM CLOWES AND SONS,
STAMFORD STREET AND CHAUINO CROSS.
PREFACE.
To prevent a possible misapprehension in scientific quar-
ters, the author desires it understood that the present work
is not designed either to instruct the professional investi-
gator or to train the special student of astronomy. Its main
object is to present the general reading public with a con-
densed view of the history, methods, and results of astro-
nomical research, especially in those fields which are of most
popular and philosophic interest at the present day, couched
in such language as to be intelligible without mathematical
study. He hopes that the earlier chapters will, for the most-
part, be readily understood by any one having clear geomet-
rical ideas, and that the later ones will be intelligible to all.
To diminish the difficulty which the reader may encounter
from the unavoidable occasional use of technical terms, a
Glossary has been added, including, it is believed, all that
are used in the present work, as well as a number of others
which may be met with elsewhere.
Respecting the general scope of the work, it may be said
that the historic and philosophic sides of the subject have
been treated with greater fulness than is usual in works of
this character, while the purely technical side has been pro-
portionately condensed. Of the four parts into which it is
divided, the first two treat of the methods by which the mo-
vi PREFACE.
tions and the mutual relations of the heavenly bodies have
been investigated, and of the results of such investigation,
while in the last two the individual peculiarities of those
bodies are considered in greater detail. The subject of the
general structure and probable development of the universe,
which, in strictness, might be considered as belonging to the
first part, is, of necessity, treated last of all, because it re-
quires all the light that can be thrown upon it from every
available source. Matter admitting of presentation in tabular
form has, for the most part, been collected in the Appendix,
where will be found a number of brief articles for the use
of both the general reader and the amateur astronomer.
The author has to acknowledge the honor done him by
several eminent astronomers in making his work more com-
plete and interesting by their contributions. Owing to the
great interest which now attaches to the question of the con-
stitution of the sun, and the rapidity with which our knowl-
edge in this direction is advancing, it was deemed desirable
to present the latest views of the most distinguished investi-
gators of this subject from their own pens. Four of these
gentlemen Rev. Father Secchi, of Rome ; M. Faye, of Paris ;
Professor Young, of Dartmouth College ; and Professor Lang-
ley, of Allegheny Observatory have, at the author's request,
presented brief expositions of their theories, which will be
found in their own language in the chapter on the sun.
An Addendum gives the basis of the remarkable modifi-
cation of the theory of the solar spectrum proposed by Dr.
Henry Draper, which appeared while the sheets were passing
through the press.
CONTENTS.
PART I.
THE SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
PAGIt
INTRODUCTION 1
CHAPTER I.
THE ANCIENT ASTRONOMY, OR THE APPARENT MOTIONS OF THE HEAV-
ENLY BODIES 7
& 1. The Celestial Sphere 7
2. The Diurnal Motion 9
3. Motion of the Sun among the Stars 13
~ 4. Precession of the Equinoxes. The Solar Year 19
5. The Moon's Motion 21
^6. Eclipses of the Sun and Moon 24
7. The Ptolemaic System 32
/ 8. The Calendar 44
CHAPTER II.
THE COPERNICAN SYSTEM, OR THE TRUE MOTIONS OF THE HEAVENLY
BODIES 51
1. Copernicus * 51
2. Obliquity of the Ecliptic ; Seasons, etc. ; on the Copernican Sys-
tem 61
3. Tycho Brahe 66
4. Kepler. His Laws of Planetary Motion 68
5. From Kepler to Newton 71
viii CONTENTS.
CHAPTER III. PAGE
UNIVERSAL GRAVITATION 74
1. Newton. Discovery of Gravitation 74
2. Gravitation of Small Masses. Density of the Earth 81
3. Figure of the Earth 86
4. Precession of the Equinoxes 88
5. The Tides 90
< 6. Inequalities in the Motions of the Planets produced by their
Mutual Attraction 93
7. Relation of the Planets to the Stars 101
PAKT II.
PRACTICAL ASTRONOMY.
INTRODUCTORY REMARKS 103
CHAPTER I.
THE TELESCOPE 106
1. The First Telescopes 106
2. The Achromatic Telescope 114
3. The Mounting of the Telescope 118
4. The Reflecting Telescope 121
5. The Principal Great Reflecting Telescopes of Modem Times... 125
6. Great Refracting Telescopes 135
7. The Magnifying Powers of the Two Classes of Telescopes 139
CHAPTER II.
APPLICATION OP THE TELESCOPE TO CELESTIAL MEASUREMENTS 146
1. Circles of the Celestial Sphere, and their Relations to Positions
/ on the Earth 146
^2. The Meridian Circle, and its Use 152
3. Determination of Terrestrial Longitudes 157
4. Mean, or Clock, Time 162
CONTENTS i x
CHAPTER ITT. PAGR
MEASURING DISTANCES IN THE HEAVENS 165
1. Parallax in General 165
-' 2. Measures of the Distance of the Sun j[7l
3. Solar Parallax from Transits of Venus 175
4. Other Methods of "Hotel-mining the Sun's Distance, and their
Results 194
5. Stellar Parallax 201
CHAPTER IV.
THE MOTION OF LIGHT 210
CHAPTER V.
THE SPECTROSCOPE 222
PAET III.
THE SOLAR SYSTEM.
CHAPTER I.
GENERAL STRUCTURE OF THE SOLAR SYSTEM 231
CHAPTER II.
THE SUN 237
1. The Photosphere 237
2. The Solar Spots and Rotation 242
3. Periodicity of the Spots 248
4. Law of Rotation of the Sun 249
5. The Sun's Surroundings. Phenomena of Total Eclipses 251
6. Physical Constitution of the Sun 258
7. Views of Distinguished Students of the Sun on the Subject of
its Physical Constitution 265
X CONTENTS.
CHAPTER III. PAOE
THE INNER GROUP OF PLANETS 283
1. The Planet Mercury 283
2. The Supposed Intra-Mercurial Planets 28G
3. The Planet Venus 289
4. The Earth 298
5. The Moon 30G
6. The Planet Mars 320
7. The Small Planets 323
CHAPTER IV.
THE OUTER GROUP OF PLANETS 331
1. The Planet Jupiter 331
2. The Satellites of Jupiter 336
3. Saturn and its System, Physical Aspect, Belts, Rotation 338
4. The Rings of Saturn 341
5. Constitution of the Ring . 349
6. The Satellites of Saturn 351
7. Uranus and its Satellites 353
8. Neptune and its Satellite 358
CHAPTER V.
COMETS AND METEORS 365
1. Aspects and Forms of Comets 365
2. Motions, Origin, and Number of Comets 369
3. Remarkable Comets 374
4. Encke's Comet, and the Resisting Medium 381
5. Meteors and Shoo ting- stars 384
6. Relations of Comets and Meteoroids 391
7. The Physical Constitution of Comets 398
8. The Zodiacal Light 405
PAET IV.
THE STELLAR UNIVERSE.
INTRODUCTORY REMARKS 407
CONTENTS. xi
CHAPTER I. PAQE
THE STARS AS THEY ARE SEEN 410
1. Number and Orders of Stars and Nebulae 410
2. Description of the Principal Constellations 417
3. New and Variable Stars 42G
4. Double Stars 436
5. Clusters of Stars 441
6. Nebulas 444
7. Proper Motions of the Stars 452
CHAPTER II.
THE STRUCTURE OF THE UNIVERSE 460
1. Views of Astronomers before Herschel 461
2. Researches of Herschel and his Successors 465
3. Probable Arrangement of the Visible Universe 478
4. Do the Stars really form a System? 483
CHAPTER III.
THE COSMOGONY 491
1. The Modern Nebular Hypothesis 493
2. Progressive Changes in our System 499
3. The Sources of the Sun's Heat 505
4. Secular Cooling of the Earth 511
5. General Conclusions respecting the Nebular Hypothesis 514
(>. The Plurality of Worlds 516
ADDENDUM TO PART III., CHAPTER II 520
APPENDIX.
I. LIST OF THE PRINCIPAL GREAT TELESCOPES OF THE WORLD 521
II. LlST OF THE MORE REMARKABLE DOUBLE STARS 523
III. LlST OF THE MORE INTERESTING AND REMARKABLE NEBULAE AND
STAR CLUSTERS 525
IV. PERIODIC COMETS SEEN AT MORE THAN ONE RETURN 527
xii CONTENTS.
PAGE
V. ELEMENTS OP THE ORBITS OP THE EIGHT MAJOR PLANETS FOR 1850. 528
ELEMENTS OP THE SATELLITES OF JUPITER 529
ELEMENTS OP THE SATELLITES OF SATURN 529
ELEMENTS OF THE SATELLITE OF NEPTUNE 529
ELEMENTS OP THE SATELLITES OF URANUS 529
VI. ELEMENTS OP THE SMALL PLANETS 530
VII. DETERMINATIONS OF STELLAR PARALLAX 535
VIII. SYNOPSIS OF PAPERS ON THE SOLAR PARALLAX, 1854-'77 538
IX. LIST OP ASTRONOMICAL WORKS, MOST OP WHICH HAVE BEEN CON-
SULTED AS AUTHORITIES IN THE PREPARATION OF THE PRESENT
WORK , 542
X. GLOSSARY OF TECHNICAL TERMS OF FREQUENT OCCURRENCE IN
ASTRONOMICAL WORKS 549
INDEX 559
ADDENDUM II. THE SATELLITES OP MARS 565
EXPLANATION OF THE STAR MAPS 15(38
LIST OF ILLUSTRATIONS.
FIG. PAGE
THE GREAT TELESCOPE OF THE UNITED STATES NAVAL OBSERVATO-
RY, WASHINGTON Frontispiece
1. SECTION OF THE IMAGINARY CELESTIAL SPHERE 8
2. MAP ILLUSTRATING THE DlURNAL MOTION ROUND THE POLE 10
3. THE CELESTIAL SPHERE AND DIURNAL MOTION 12
4. MOTION OF THE SUN PAST THE STAR REGULUS 15
5. SHOWING THE SUN TO BE FARTHER THAN THE MOON , 22
6. ANNULAR ECLIPSE OF THE SUN 26
7. PARTIAL ECLIPSE OF THE SUN 26
8. ECLIPSE OF THE SUN, THE SHADOW OF THE MOON FALLING ON THE
EARTH 26
9. ECLIPSE OF THE MOON, IN THE SHADOW OF THE EARTH 27
10. SHOWING THE APPARENT ORB^T OF A PLANET 88
11. APPARENT ORBITS OF JUPITER AND SATURN 39
12. ARRANGEMENT OF THE SEVEN PLANETS IN THE PTOLEMAIC SYSTEM... 41
13. THE ECCENTRIC 42
14. SHOWING THE ASTROLOGICAL DIVISION OF THE SEVEN PLANETS
AMONG THE DAYS OF THE WEEK 46
15. APPARENT ANNUAL MOTION OF THE SUN EXPLAINED 55
16. SHOWING now THE APPARENT EPICYCLIC MOTION OF THE PLANETS
IS ACCOUNTED FOR 56
17. RELATION OF THE TERRESTRIAL AND CELESTIAL POLES AND EQUATORS. 62
18. CAUSES OF CHANGES OF SEASONS ON THE COPERNICAN SYSTEM 63
19. ENLARGED VIEW OF THE EARTH, SHOWING WINTER IN THE NORTH-
ERN HEMISPHERE, AND SUMMER IN THE SOUTHERN 65
20. ILLUSTRATING KEPLER'S FIRST Two LAWS OF PLANETARY MOTION... 69
21. ILLUSTRATING THE FALL OF THE MOON TOWARDS THE EARTH 78
22. BAILY'S APPARATUS FOR DETERMINING THE DENSITY OF THE EARTH. 83
23. VIEW OF BAILY'S APPARATUS 84
24. DIAGRAM ILLUSTRATING THE ATTRACTION OF MOUNTAINS 85
25. PRECESSION OF THE EQUINOXES 88
xiv LIST OF ILLUSTRATIONS.
FIG. PACK
26. ATTRACTION OF THE MOON TENDING TO PRODUCE TIDES 91
27. ARMILLARY SPHERE AS DESCRIBED BY PTOLEMY 105
28. THE GALILEAN TELESCOPE 108
29. FORMATION or AN IMAGE BY A LENS 109
30. GREAT TELESCOPE OF THE SEVENTEENTH CENTURY 112
31. REFRACTION THROUGH A COMPOUND PRISM 114
32. SECTION OF AN ACHROMATIC OBJECTIVE 115
33. SECTION OF EYE-PIECE OF A TELESCOPE 118
34. MODE OF MOUNTING A TELESCOPE 119
35. SPECULUM BRINGING RAYS TO A SINGLE Focus BY REFLECTION 122
36. HERSCIIELIAN TELESCOPE 123
37. HORIZONTAL SECTION OF A NEWTONIAN TELESCOPE 123
38. SECTION OF THE GREGORIAN TELESCOPE 124
39. HERSCHEL'S GREAT TELESCOPE 127
40. LORD ROSSE'S GREAT TELESCOPE 130
41. MR. LASSELL'S GREAT FOUR-FOOT REFLECTOR 132
42. THE NEW PARIS REFLECTOR , 134
43. THE GREAT MELBOURNE REFLECTOR 136
44. CIRCLES OF THE CELESTIAL SPHERE... 147
45. THE WASHINGTON TRANSIT CIRCLE 153
46. SPIDER LINES IN FIELD OF VIEW OF A MKRIWAN CIRCLE 154
47. DIAGRAM ILLUSTRATING PARALLAX 165
48. DIAGRAM ILLUSTRATING PARALLAX 166
49. VARIATION OF PARALLAX WITH THE ALTITUDE 167
50. APPARENT PATHS OF VENUS ACROSS THE SUN 176
51. VENUS APPROACHING INTERNAL CONTACT ON THE FACE OF THK SUN. 178
52. INTERNAL CONTACT OF LIMB OF VENUS WITH THAT OF THE SUN.... 178
53. THE BLACK DROP, OR LIGAMENT 179
54. METHOD OF PHOTOGRAPHING THE TRANSIT OF VKNUS 186
55. ARTIFICIAL TRANSIT OF VENUS 188
56. MAP OF THE EARTH, SHOWING THE AREAS OF VISIBILITY OF THE
TRANSIT OF 1874 191
57. MAP OF THE WORLD, SHOWING THE REGIONS IN WHICH THE TRAN-
SIT OF VENUS WILL BE VISIBLE ON DECEMBER GTII, 1882 195
58. EFFECT OF STELLAR PARALLAX 202
59. ABERRATION OF LIGHT 212
60. REVOLVING WHEEL FOR MEASURING THE VELOCITY OF LIGHT 216
61. ILLUSTRATING FOUCAULT'S METHOD OF MEASURING THE VELOCITY
OF LIGHT 218
62. COURSE OF RAYS THROUGH A SPECTROSCOPE 224
LIST OF ILLUSTRATIONS. XV
F1Q. PAGE
63. RELATIVE SIZE OF SUN AND PLANETS 232
64. ORBITS OF THE PLANETS FROM THE EARTH OUTWARD 23G
65. MAN HOLDING TELESCOPE, TO SHOW SUN ON SCREEN 243
66. SOLAR SPOT, AFTER SECCHI 244
67. CHANGES IN THE ASPECT OF A SOLAR SPOT AS IT CROSSES THE SUN'S
DISK 246
68. TOTAL ECLIPSE OF THE SUN, AS SEEN AT DES MOINES, IOWA, AU-
GUST TTH, 1869 253
69. SPECIMENS OF SOLAR PROTUBERANCES, AS DRAWN BY SKCGHI 256
70. THE SUN, WITH ITS CHROMOSPHERE AND RED FLAMES, ON JULY
23D, 1871 2G1
71. ILLUSTRATING SECCHI'S THEORY OF SOLAR SPOTS 269
72. SOLAR SPOT, AFTER LANGLEY 281
73. ORBITS OF THE FOUR INNER PLANETS, ILLUSTRATING THE ECCEN-
TRICITY OF THOSE OF MERCURY AND MARS 283
74. PHASES OF VENUS 291
75. SHOWING THE THICKNESS OF THE EARTH'S CRUST 299
76. DISTRIBUTION OF AURORAS ; 302
77. VIEW OF AURORA 303
78. SPECTRUM OF Two OF THE GREAT AURORAS OF 1871 305
79. RELATIVE SIZE OF EARTH AND MOON 306
80. VIEW OF MOON NEAR THE THIRD QUARTER 313
81. LUNAR CRATER "COPERNICUS" 315
82. THE PLANET MARS ON JUNE 23D, 1875 322
83. MAP OF MARS 322
84. NORTHERN HEMISPHERE OF MARS , 323
85. SOUTHERN HEMISPHERE OF MARS 323
86. JUPITER, AS SEEN WITH THE GREAT WASHINGTON TELESCOPE, MARCH
21ST, 1876 331
87. VIEW OF JUPITER, AS SEEN IN LORD ROSSE'S GREAT TELESCOPE,
FEBRUARY 27TH, 1861 333
88. VIEW OF SATURN AND HIS RINGS. 339
89. SPECIMENS OF DRAWINGS OF SATURN BY VARIOUS OBSERVERS 343
90. VIEWS OF ENCKE'S COMET IN 1871 367
91. HEAD OF DONATI'S GREAT COMET OF 1858 368
92. PARABOLIC AND ELLIPTIC ORBIT OF A COMET 370
93. ORBIT OF HALLEY'S COMET 377
94. GREAT COMET OF 1858 380
95. METEOR PATHS, ILLUSTRATING THE RADIANT POINT 390
96. ORBIT OF NOVEMBER METEORS AND THE COMET OF 18G1 391
tvi LIST OF ILLUSTRATIONS.
ie. PAGE
97. ORBIT OF THE THIRD COMET OP 1862 395
98. MEASURE OF POSITION ANGLE OF DOUBLE STAR 438
99. DISTANCE OF COMPONENTS OF DOUBLE STAR 438
00. DIAGRAM TO ILLUSTRATE POSITION ANGLE 438
01. TELESCOPIC VIEW OF THE PLEIADES 442
02. CLUSTER OF 47 TOUCANI 444
03. CLUSTER u> CENTAURI 444
04. THE GREAT NEBULA OF ORION 446
05. THE ANNULAR NEBULA IN LYRA 448
06. THE OMEGA NEBULA 450
07. NEBULA HERSCHEL 3722 451
08. THE LOOPED NEBULA; HERSCHEL 2941 451
09. HERSCHEL'S VIEW OF THE FORM OF THE UNIVERSE 469
10. ILLUSTRATING HERSCHEL'S ORDERS OF DISTANCE OF THE STARS.... 471
11. PROBABLE ARRANGEMENT OF THE STARS AND NEBULAE VISIBLE
WITH THE TELESCOPE 481
12. DIAGRAM ILLUSTRATING ELLIPTIC ELEMENTS OF A PLANET 551
STAR MAPS.
IAP I. THE NORTHERN CONSTELLATIONS WITHIN 50
OF THE POLE ..........................................
" II. SOUTHERN CONSTELLATIONS VISIBLE IN AU-
TUMN AND WINTER ..................................
" HI. SOUTHERN CONSTELLATIONS VISIBLE IN WIN-
TER AND SPRING .....................................
" IV. SOUTHERN CONSTELLATIONS VISIBLE IN SPRING
AND SUMMER.. .........................................
" V. SOUTHERN CONSTELLATIONS VISIBLE IN SUM-
MER AND AUTUMN ...................................
At End of Book.
POPULAR ASTRONOMY.
PART I. THE SYSTEM OF THE WORLD
HISTORICALLY DEVELOPED.
INTRODUCTION.
ASTRONOMY is the most ancient of the physical sciences, be-
ing distinguished among them by its slow and progressive
development from the earliest ages until the present time.
In no other science has each generation which advanced it
been so much indebted to its predecessors for both the facts
and the ideas necessary to make the advance. The conception
of a globular and moving "ea^th pursuing her course through
the celestial spaces among her sister planets, which we see as
stars, is one to the entire evolution of which no one mind and
no one $,ge can lay claim. It was the result of a gradual
process of* education, of which the subject was not an indi-
vidual, But the human race. The great astronomers of all
ages have built upon foundations laid by their predecessors;
and when we attempt to search out the first founder, we find
ourselves lost in the mists of antiquity. The theory of uni-
versal gravitation was founded by Newton upon the laws of
Kepler, the observations and measurements of his French con-
temporaries, and the geometry of Apollonius. Kepler used
as his material the observations of Tycho Brahe, and built
upon the theory of Copernicus. When w$ seek the origin of
*;he instruments used by 'Tycho, we soon find ourselves among
2
2 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
the mediaeval Arabs. The discovery of the true system of
the world by Copernicus was only possible by a careful study
of the laws of apparent motion of the planets as expressed in
the epicycles of Ptolemy and Hipparchus. Indeed, the more
carefully one studies the great work of Copernicus, the more
surprised he will be to find how completely Ptolemy furnished
him both ideas and material. If we seek the teachers and
predecessors of Hipparchus, we find only the shadowy forms
of Egyptian and Babylonian priests, whose names and writings
are all entirely lost. In the earliest historic ages, men knew
that the earth was round ; that the sun appeared to make an
annual revolution among the stars; and that eclipses were
caused by the moon entering the shadow of the .earth, or the
earth that of the moon.
Indeed, each of the great civilizations of the ancient world
seems to have had its own system of astronomy strongly
marked by the peculiar character of the people among whom
it was found. Several events recorded in the annals of China
show that the movements of the sun and the laws of eclipses
were studied in that country at a very early age. Some of
these events must be entirely mythical; as, for instance, the
despatch of astronomers to the four points of the compass for
the purpose of determining the equinoxes and solstices. But
there is another event which, even if we place it in the same
category, must be regarded as indicating a considerable amount
of astronomical knowledge among the ancient Chinese. We
refer to the tragic fate of Hi and Ho, astronomers royal to one
of the ancient emperors of that people. It was part of the
duty of these men to carefully study the heavenly movements,
and give timely warning of the approach of an eclipse or other
remarkable phenomenon. But, neglecting this duty, they gave
themselves up to drunkenness and riotous living. In conse-
quence, an eclipse of the sun occurred without any notice being
given ; the religious rites due in such a case were not performed,
and China was exposed to the anger of the gods. To appease
their wrath, the unworthy astronomers were seized and sum-
marily executed by royal command. Some historians have
INTRODUCTION. 3
gone so far as to fix the date of this occurrence, which is vari-
ously placed at from 2128 to 2159 years before the Christian
era. If this is correct, it is the earliest of which profane his-
tory has left us any record.
In the Hindoo astronomy we see the peculiarities of the
contemplative Hindoo mind strongly reflected. Here the,
imagination revels in periods of time which, by comparison,
dwgrjE even the measures of the celestial spaces made by mod-
ern astronomers. In this, and in perhaps other ancient sys-
tems, we find references to a supposed conjunction of all the
planets 3102 years before the Christian era. Although we
have every reason for believing that this conjunction was
learned, not from any actual record of it, but by calculating
back the position of the planets, yet the very fact that they
were able to make this calculation shows that the motions of
the planets must have been observed and recorded during
many generations, either by the Hindoos themselves, or some
other people from whom they acquired their knowledge. As
a matter of fact, we now know from our modern tables that
this conjunction was very far from being exact; but its error
could not be certainly detected by the rude observations of the
times in question.
Among a people so prone as the ancient Greeks to speculate
upon the origin and nature of things, while neglecting the ob-
servation of natural phenomena, we cannot expect to find any-
thing that can be considered a system of astronomy. But there
are some ideas attributed to Pythagoras which are so frequent-
ly alluded to, and so closely connected with the astronomy of
a subsequent age, that we may give them a passing mention.
He is said to have taught that the heavenly bodies were set
in a number of crystalline spheres, in the common centre of
which the earth was placed. In the outer of these spheres
were set the thousands of fixed stars which stud the firma-
ment, while each of the seven planets had its own sphere. The
transparency of each crystal sphere was perfect, so that the
bodies set in each of the outer spheres were visible through
all the inner ones. These spheres all rolled round on each
4: SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
other in a daily revolution, thus causing the rising and setting
of the heavenly bodies. This rolling of the spheres on each
other made a celestial music, the "music of the spheres,"
which filled the firmament, but was of too elevated a char-
acter to be heard by the ears of mortals.
It must be admitted that the idea of the stars being set in a
hollow sphere of crystal, forming the vault of the firmament,
was a very natural one. They seemed to revolve around the
earth every day, for generation after generation, without the
slightest change in their relative positions. If there were no
solid connection between them, it does not seem possible that
a thousand bodies could move around their vast circuit for
such long periods of time without a single one of them vary-
ing its distance from one of the others. It is especially diffi-
cult to conceive how they could all move around the same
axis. But when they are all set in a solid sphere, every one is
made secure in its place. The planets could not be set in the
same sphere, because they change their positions among the
stars. This idea of the sphericity of the heavens held on to
the minds of men with remarkable tenacity. The funda-
mental proposition of the system, both of Ptolemy and Coper-
nicus, was that the universe is spherical, the latter seeking to
prove the naturalness of the spherical form by the analogy
of a drop of water, although the theory served him no pur-
pose whatever. Faint traces of the idea are seen here and
there in Kepler, with whom it vanished from the mind of the
race, as the image of Santa Glaus disappears from the mind of
the growing child.
Pythagoras is also said to have taught in his esoteric lect-
ures that the sun was the real centre of the celestial move-
ments, and that the earth and planets moved around it, and it
is this anticipation of the Copernican system which constitutes
his greatest glory. But he never thought proper to make a
public avowal of this doctrine, and even presented it to his
disciples somewhat in the form of an hypothesis. It must
also be admitted that the accounts of his system which have
reached us are so vague and so filled with metaphysical specu-
INTRODUCTION. 5
lation that it is questionable whether the frequent application
of his name to the modern system is not more pedantic than
justifiable.
The Greek astronomers of a later age not only rejected the
vague speculations of their ancestors, but proved themselves
the most careful observers of their time, and first made astron-
omy worthy the name of a science. From this Greek astrono-
my the astronomy of our own time may be considered as coin-
ing by direct descent. Still, were it not for the absence of his-
toric records, we could probably trace back both their theories
and their system of observation to the plains of Chaldea. The
zodiac was mapped out and the constellations named many
centuries before they commenced their observations, and these
works marked quite an advanced stage of development. This
prehistoric knowledge is, however, to be treated by the histo-
rian rather than the astronomer. If we confine ourselves to
men whose names and whose labors have come down to us,
We must Concede to HjpI^LE-h 115 flip, frminr af ViPincr J;]IA fafkoy
of astronomy. Not only do his observations of the heavenly
bodies appear to have been far more accurate than those of
any of his predecessors, but he also determined the laws of the
apparent motions of the planets, and prepared tables by which
these motions could be calculated. Probably he was the first
propounder of the theory of epicyclic motions of the planets,
commonly called after the name of his successor, Ptolemy, who
lived three centuries later.
Commencing with the time of Ilipparchus, the general
theory of the structure of the universe, or "system of the
world," as it is frequently called, exhibits three great stages of
development, each stage being marked by a system quite dif-
ferent from the other two in its fundamental principles. These
are:
1. The so-called Ptolemaic system, which, however, really
belongs to Ilipparchus, or some more ancient astronomer. In
this system the motion of the earth is ignored, and the appar-
ent motions of the stars and planets around it are all regarded
as real.
6 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
2. The Copernican system, in which it is shown that the sun
is really the centre of the planetary motions, and that the earth
is itself a planet, both turning on its axis and revolving round
the sun.
3. The Newtonian system, in which all the celestial motions
are explained by the one law of universal gravitation.
This natural order of development shows the order in which
a knowledge of the structure of the universe can be most
clearly presented to the mind of the general reader. We
shall therefore explain this structure historically, devoting a
separate chapter to each of the three stages of development
which we have described. We commence with what is well
known, or, at least, easily seen by every one who will look at
the heavens with sufficient care. We imagine the observer
out-of-doors 011 a starlit night, and show him how the heav-
enly bodies seern to move from hour to hour. Then, we show
him what changes he will see in their aspects if he contin-
ues his watch through months and years. By combining the
apparent motions thus learned, he forms for himself the an-
cient, or Ptolemaic, system of the world. Having this system
clearly in mind, the passage to that of Copernicus is but a
step. It consists only in showing that certain singular oscilla-
tions which the sun and planets seem to have in common are
really due to a revolution of the earth around the sun, and
that the apparent daily revolution of the celestial sphere arises
from a rotation of the earth on its own axis. The laws of
the true motions of the planets being perfected by Kepler,
they are shown by Newton to be included in the one law of
gravitation towards the sun. Such is the course of thought to
which we first invite the reader.
THE CELESTIAL SPHERE.
CHAPTER I.
THE ANCIENT ASTRONOMY, OK THE APPARENT MOTIONS OF THE
HEAVENLY BODIES.
1. The Celestial Sphere.
IT is a fact with which we are familiar from infancy, that
all the heavenly bodies sun, moon, and stars seem to be set
in an azure vault, which, rising high over our heads, curves
down to the horizon on every side. Here the earth, on which
it seems to rest, prevents our tracing it farther. But if the
earth were out of the way, or were perfectly transparent, we
could trace the vault downwards on every side to the point
beneath our feet, and could see sun, moon, and stars in every
direction. The celestial vault above us, with the correspond-
ing one below us, would then form a complete sphere, in the
centre of which the observer would seem to be placed. This
has been known in all ages as the celestial sphere. The direc-
tions or apparent positions of the heavenly bodies, as well as
their apparent motions, have always been defined by their ^it-
nation and motions on this sphere. The fact that it is purely
imaginary does not diminish its value as enabling us to form
distinct ideas of the directions of the heavenly bodies from us.
It matters not how large we suppose this sphere, so long as
we always suppose the observer to be in the centre of it, so
that it shall surround him on all sides at an equal distance.
But in the language and reasoning of exact astronomy it is
always supposed to be infinite, as then the observer may con-
ceive of hi-mself as transported to any other point, even to one
of the heavenly bodies themselves, and still be, for all practical
purposes, in the centre of the sphere. In this case, however,
the heavenly bodies are not considered as attached to the cir-
8
SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
cumf erence of the infinite sphere, but only as lying on the line
of sight extending from the observer to some point of the
sphere. Their relation to it may be easily understood by the
observer conceiving himself to be luminous, and to throw out
rays in every direction to the infinitely distant sphere. Then
the apparent positions of the various heavenly bodies will be
those in which their shadows strike the sphere. For instance,
the observer standing on the earth and looking at the moon,
FIG. 1. Section of the imaginary celestial sphere. The observer at 0, looking at the
' Btnrs or other bodies, marked p t 7, r, s, t, w, v, will imagine them situated at P, Q, #, &',
T, (7, V, on the surface of the sphere, where they will appear projected along the
straight pP t qQ, etc.
the shadow of the latter will strike the sphere at a point on a
straight line drawn from the observer's eye through the centre
of the moon, and continued till it meets the sphere. The point
of meeting will represent the position of the moon as seen by
the observer. Now, suppose the latter transported to the moon.
Then, looking back at the earth, he will see it projected on the
sphere in a point diametrically opposite to that in which lie
formerly saw the moon. To whatever planet he might trans-
THE DIUKNAL MOTION. 9
port himself, he would see the earth and the other planets pro-
jected on this imaginary sphere precisely as we always seem
to see the heavenly bodies so projected.
This is all that is left of the old crystalline spheres of Py-
thagoras by modern astronomy. From being a solid which
held all the stars, the sphere has become entirely immaterial,
a mere conception of the mind, to enable it to define the di-
rections in which the heavenly bodies are seen. Ey examin-
ing the figure it will be clear that all bodies which lie in the
same straight line from the observer will appear on the same
point of the sphere. For instance, bodies at the three points
marked t will all be seen as if they were at T.
2. The Diurnal Motion.
If we watch the heavenly bodies for a few hours we shall
always find them in motion, those in the east rising upwards,
those in the south moving towards the west, and those in the
west sinking below the horizon. We know that this motion
is only apparent, arising from the rotation of the earth on its
axis ; but as we wish, in this chapter, only to describe things
as they appear, we may speak of the motion as real. A few
days' watching will show that the whole celestial sphere seems
to revolve, as on an axis, every day. It is to this revolution,
carrying the sun alternately above and below the horizon, that
the alternations of day and night are due. The nature and
effects of this motion can best be studied by watching the ap-
parent movement of the stars at night. We should soon learn
from such a watch that there is one point in the heavens, or
on the celestial sphere, which does not move at all. In our
latitudes this point is situated in the north, between the zenith
aiid the horizon, and is called the pole. Around this pole, as
a fixed centre, all the heavenly bodies seem to revolve, each
one moving in a circle, the size of which depends on the dis-
tance of the body from the pole. There is no star situated
exactly at the pole, but there is one which, being situated lit-
tle more than a degree distant, describes so small a circle that
the unaided eye cannot see any change of place without mak-
10 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
ing some exact and careful observation. This is therefore
called the pole star. The pole star can nearly always be very
readily found by means of the pointers, two stars of the con-
stellation Ursa Major, the Great Bear, or, as it is familiarly
called, the Dipper. By referring to the figure, the reader will
readily find this constellation, by the dotted line from the pole
and thence the pole star, which is near the centre of the map.
FIG. 2. Map of the priiicipal stars of the northern sky, showing the constellations which
never set in latitude 40, but revolve round the pole star every day in the direction
shown by the arrows. The two lower stars of Ursa Major, on the left of the map,
point to the pole star in the centre.
The altitude of the pole is equal to the latitude of the place.
In the Middle States the latitude is generally not far from
forty degrees ; the pole is therefore a little nearer to the hori-
zon than to the zenith. In Maine and Canada it is about half-
way between these points, while in England and Northern
Europe it is nearer the zenith.
THE DIURNAL MOTION. 11
Now, to see the effect of the diurnal motion near the pole,
let us watch any star in the north between the pole and the
horizon. We shall soon see that, instead of moving from east
to west, as we are accustomed to see the heavenly bodies move,
it really moves towards the east. After passing the north
point, it begins to curve its course upwards, until, in the north-
east, its motion is vertical. Then it turns gradually to the
west, passing as far above the pole as it did below it, and, sink-
ing down on the west of the pole, it again passes under it.
The passage above the pole is called the upper culmination,
and that below it the lower one. The course around the pole
is shown by the arrows on Fig. 2. We cannot with the naked
eve follow it all the way round, on account of the intervention
of daylight ; but by continuing our watch every clear night for
a year, we should see it in every point of its course. A star
following the course we have described never sets, but may be
seen every clear night. If we imagine a circle drawn round
the pole at such a distance as just to touch the horizon, all the
stars situated within this circle will move in this way ; this is
therefore called the circle of perpetual apparition.
As we go away from the pole we shall find the stars mov-
ing in larger circles, passing higher up over the pole, and lower
down below it, until we reach the circle of perpetual appari-
tion, when they will just graze the horizon. Outside this circle
every star must dip below the horizon for a greater or less
time, depending on its distance. If it be only a few degrees
outside, it will set in the north-west, or between north and
north-west ; and, after a few hours only, it will be seen to rise
again between north and north-east, having done little more
than graze the horizon. The possibility of a body rising so
soon after having set does not always occur to those who live
in moderate latitudes. In July, 1874, Coggia's comet set in
the north-west about nine o'clock in the evening, and rose
again about three o'clock in the morning ; and some intelligent
people who then saw it east of the pole supposed it could not
be the same one that had set the evening before.
Passing outside the circle of perpetual apparition, we find
12 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
that the stars pass south of the zenith at their upper culmina-
tion, that they set more quickly, and that they are a longer
time below the horizon. This may be seen in Fig. 3 5 the por-
tion of the sphere to which we refer being between the celes-
tial equator and the line LN. When we reach the equator
one-half the course will be above and one-half below the hori-
Z
FIG. 3. The celestial sphere and diurnal motion. S is the south horizon, N the north hori-
zon, Z the zenith. The circle LN around the north pole contains the stars shown in
Fig. 2 ; and the observer at O, in the centre of the sphere, looking to the north, sees the
stars as they are depicted in that figure. The arrows show the direction of the diurnal
motion in the west.
zon. South of the equator the circles described by the stars
become smaller once more, and more than half their course is
below the horizon. Near the south horizon the stars only show
themselves above the horizon for a short time, while below it
there is a circle of perpetual disappearance, the stars in which,
to us, never rise at all. This circle is of the same magnitude
MOTION OF THE SUN AMONG THE STARS. 13
with that of perpetual apparition, and the south pole is situated
in its centre, just as the north pole is in the centre of the other.
If we travel southward we find that the north pole gradually
sinks towards the horizon, while new stars come into view above
the south horizon ; consequently the circles of perpetual appari-
tion and of perpetual disappearance both grow smaller. When
we reach the earth's equator the south pole has risen to the
south horizon, the north pole has sunk to the north hori-
zon ; the celestial equator passes from east to west directly
overhead ; and all the heavenly bodies in their diurnal revolu-
tions describe circles of which one half is above and the other
half below the horizon. These circles are all vertical.
South of the equator only the south pole is visible, the north
one, which we see, being now below the horizon. Beyond the
southern tropic the sun is north at noon, and, instead of mov-
ing from left to right, its course is from right to left.
The laws of the diurnal motion which we have described
may be summed up as follows :
1. The celestial sphere, with the sun, moon, and stars, seems
to revolve daily around an inclined axis passing through the
point where we may chance to stand.
2. The upper end of this axis points (in this hemisphere) to
the north pole ; the other end passes into the earth, and points
to the south pole, which is diametrically opposite, and therefore
below the horizon.
3. All the fixed stars during this revolution move together,
keeping at the same distance from each other, as if the revolv-
ing celestial sphere were solid, and they were set in it.
4. The circle drawn round the heavens half-way between
the two poles being the celestial equator, all bodies north of
this equator perform more than half their revolution above
the horizon, while south of it less than half is above it.
3. Motion of the Sun among the Stars.
The most obvious classification of the heavenly bodies which
we see with the naked eye is that of sun, moon, and stars.
But there is also this difference among the stars, that while the
14 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
great mass of them preserve the same relative position on the
celestial sphere, year after year and century after century, there
are five which constantly change their positions relatively to
the others. Their names are Mercury, Venus, Mars, Jupiter,
and Saturn. These five, with the sun and moon, constitute the
seven planets, or wandering stars, of the ancients, the motions
of which are next to be described. Taking out the seven
planets, the remaining heavenly bodies visible to the naked
eye are termed the Fixed Stars, because they have no appar-
ent motion, except the regular diurnal revolution described in
the last section. But if we note the positions of the sun,
moon, and planets among the stars for a number of successive
nights, we shall find certain slow changes among them which
we shall now describe, beginning with the sun. In studying
this description, the reader must remember that we are not
seeking for the apparent diurnal motion, but only certain
much slower motions of the planets relative to the fixed stars,
such as would be seen if the earth did not rotate on its axis.
If we observe, night after night, the exact hour and minute
at which a star passes any point by its diurnal revolution, we
shall find that passage to occur some four minutes earlier
every evening than it did the evening before. The starry
sphere therefore revolves, not in 24 hours, but in 23 hours
56 minutes. In consequence, if we note its position at the
same hour night after night, we shall find it to be farther and
farther to the west. Let us take, for example, the brightest
star in the constellation Leo, represented on Map III., and
commonly known as Regulus. If we watch it on the 22d of
March, we shall find that it passes the meridian at ten o'clock
in the evening. On April 22d it passes at eight o'clock, and
at ten it is two hours west of the meridian. On the same day
of May it passes at six, before sunset, so that it cannot be seen
on the meridian at all. When it first becomes visible in the
evening twilight, it will be an hour or more west of the me-
ridian. In June it will be three hours west, and by the end of
July it will set during twilight, and will soon be entirely lost
in the rays of the sun. Tins shows that during the months in
MOTION OF THE SUN AMONG THE STARS. 15
question the sun has been approaching the star from the west,
and in August has got so near it that it is no longer visible.
Carrying forward our computation, we find that on August
21st the star crosses the meridian at noon, and therefore at
nearly the same time with the sun. In September it crosses
at ten in the morning, while the sun is on the eastern side.
The sun has therefore passed from the west to the east of the
star, and the latter can be seen rising in the morning twilight
before the sun. It constantly rises earlier and earlier, and
therefore farther from the sun, until February, when it rises
at sunset and sets at sunrise ; and is therefore directly opposite
the sun. In March the star would cross the meridian at ten
o'clock once more, showing that in the course of a year the
sun and star had resumed their first position. But, while the
sun has risen and set 365 times, the star has risen and set 366
times, the sun having lost an entire revolution by the slow
backward motion we have described.
If the stars were visible in the daytime (as they would be
but for the atmosphere), the apparent motion of the sun among
them could be seen in the course of a single day. For in-
stance, if we could have seen Eegulus rise on the morning of
August 20th, 1876, we should have seen the sun a little south
and west of it, the relative position of the sun being as shown
by the circle numbered 1 in the figure. ^
Watching the star all day, we should find
that at sunset it was north from the sun,
as from circle No. 2. The sun would "
during the day have moved nearly its own about August 26th of
T , -vr , i i T i every year.
diameter. JNext morning we should have
seen that the sun had gone past the star into position 3, so
that the latter would now rise before the former. By sun-
set it would have advanced to position 4y&nd so forth. The
path which the sun describes among th6 stars in his annual
revolution is called the ecliptic. It ij/marked down on Maps
II., III., IV., and V., and the months in which the sun passes
through each portion of the ecliptic are also indicated. A
belt of the heavens, extending a few degrees on each side of
16 SYSTEM OF THE WOULD HISTOEICALLY DEVELOPED.
the ecliptic, is called the zodiac. The poles of the ecliptic are
two opposite points, each in the centre of one of the two hemi-
spheres into which the ecliptic divides the celestial sphere.
The determination of the solar motion around the ecliptic
may be considered the birth of astronomical science. The
prehistoric astronomers divided the ecliptic and zodiac into
twelve parts, now familiarly known as the signs of the zodiac.
This proceeding was probably suggested by the needs of agri-
culture, and of the chronological reckoning of years. A very
little observation would show that the changes of the seasons
are due to the variations in the meridian altitude of the sun,
and in the length of the day; but it was only by a careful
study of the position of the ecliptic, and the motion of the sun
in it, that it could be learned how these variations in the daily
course of the snn were brought about. This study showed
that they were due to the fact that the ecliptic and equator
did not coincide, but were inclined to each other at an angle
of between twenty-three and twenty-four degrees. This in-
clination is known as the obliquity of the ecliptic. The two
circles, equator and ecliptic, cross each other at two opposite
points, the positions of which among the stars may be seen by
reference to Maps II. -V. When the sun is at either of
these points, it rises exactly in the east, and sets exactly in the
west ; one-half its diurnal course is above the horizon, and the
other half below. The days and nights are therefore of equal
length, from which the two points in question are called the
Equinoxes.
The vernal equinox is on the right-hand edge of Map II.
Leaving that equinox about March 21st, the sun crosses over
the region represented by the map in the course of the next
three months, working northward as it does so, until June 20th,
when it is on the left-hand edge of the map, 23^ north of the
equator. This point of the ecliptic is called the summer solstice,
being that in which the sun attains its greatest northern declina-
tion. When near this solstice, it rises north of east, culmi-
nates at a high altitude (in our latitudes), and sets north of
west As explained in describing the diurnal motion of an
MOTION OF THE SUN AMONG THE STARS. 17
object north of the celestial equator, more than half the daily
course of the sun is now above our horizon, so that our days
are longer than our nights, while the great meridian altitude
of the sun produces the heats of summer.
The portion of the ecliptic represented on Map II., com-
mencing at the vernal equinox, where the sun crosses the equa-
tor, was divided by the early astronomers into the three signs
of Aries, the Ram ; Taurus, the Bull ; and Gemini, the Twins.
It will be seen that these signs no longer coincide with the
constellations of the same name : this is owing to a change in
the position of the equator, which will be described presently.
Turning to Map III., we see that during the three months,
from June to September, the sun works downwards towards
the equator, reaching it about September 20th. The point of
crossing marks the autumnal equinox, found also on the right
hand of Map IV. The days and nights are now once more of
equal length.
During the next six months the sun is passing over the re-
gions represented on Maps IV. and V., and is south of the
equator, its greatest southern declination, or " the southern
solstice," being reached about December 21st. More than
half its daily course is then below the horizon, so that in our
latitudes the nights are longer than the days, and the -low
noonday altitude of the sun gives rise to the colds of winter.
We have no historic record of this division of the zodiac
into signs, and the ideas of the authors can only be inferred
from collateral circumstances. It has been fancied that the
names were suggested by the seasons, the agricultural opera-
tions, and so on. Thus the spring signs (Aries, the Ham ; Tau-
rus, the Bull ; and Gemini, the Twins) are supposed to mark the
bringing forth of young by the flocks and herds. Cancer, the
Crab, marks the time when the sun, having attained its great-
est declination, begins to go back towards the equator; and the
crab having been supposed to move backwards, his name was
given to this sign. Leo, the Lion, symbolizes the fierce heat?
of summer ; and Virgo, the Virgin, gleaning corn, symbolizes
the harvest. In Libra, the Balance, the day and night balance
3
18 SYSTEM OF THE WOELD HISTORICALLY DEVELOPED.
each other, being of equal length. Scorpius, the Scorpion, is
supposed to have marked the presence of venomous reptiles in
October ; while Sagittarius, the Archer, symbolizes the season
of hunting. The explanation of Capricornus, the Goat, is more
fanciful, if possible, than that of Cancer. It was supposed that
tliis animal, ascending the hill as he feeds, in order to reach
the grass more easily, on reaching the top, turns back again, so
that his name was used to mark the sign in which the sun,
from going south, begins to return to the north. Aquarius,
the Water-bearer, symbolizes the winter rains ; and Pisces, the
Fishes, the season of fishes.
All this is, however, mere conjecture; the only coincidences
at all striking being Virgo and Libra. The names of the con-
stellations were probably given to them several centuries, per-
haps even thousands of years, before the Christian era ; and in
that case the zodiacal constellations would not have correspond-
ed to the seasons we have indicated. An attempt has even been
made to show that the names of the zodiacal constellations were
intended to commemorate the twelve labors of Hercules; but
this theory rests on no better foundation than the other.
The zodiacal constellations occupy quite unequal spaces in
the heavens, as may be seen by inspection of the maps. In
the beginning they were simply twelve houses for the sun,
which that luminary occupied in the course of the year. Ilip-
parchus found this system entirely insufficient for exact astron-
omy, and therefore divided the ecliptic and zodiac into twelve
equal parts, of 30 each, called signs of the zodiac. He gave
to these signs the names of the constellations most nearly cor-
responding to them. Commencing at the vernal equinox, the
first arc of 30 was called the sign Aries, the second the sign
Taurus, and so forth. The mode of reckoning positions on
the ecliptic by signs was continued until the last century, but
is no longer in use among professional astronomers^ owing to
its inconvenience. The whole ecliptic is now divided into
360, like any other circle, the count commencing at the vernal
equinox, and following the direction of the sun's motion all the
way round to 360.
PRECESSION OF THE EQUINOXES. 19
4. Precession of the Equinoxes. The Solar Year.
By comparing his own observations with those of preceding
astronomers, Hipparchus found that the equinoxes were slowly
shifting their places among the stars, the change being at least
a degree in a century towards the west. His successors deter-
mined it with greater exactness, and it is now known to be
nearly a degree in seventy years. Careful study of the change
shows that it is due mainly to a motion of the equator, which
again arises from a change in the direction of the pole. The
position of the ecliptic among the stars varies so slowly that the
change can be seen only by the refined observations of modern
times. In the explanation of the diurnal motion, it was stated
that there was a certain point in the heavens around which all
the heavenly bodies seem to perform a daily revolution. This
point, the pole of the heavens, is marked on the centre of Map
L, and is also in the centre of Fig. 2, page 10. It is little more
than a degree distant from the pole star. Now, precession real-
ly consists in a very slow motion of this pole around the pole
of the ecliptic, the rate of motion being such as to carry it all
the way round in about 25,300 years. The exact time has
never been calculated, and would not always be the same, ow-
ing to some small variations to which the motion is subject;
but it will never differ much from this. There is a very slight
motion to the ecliptic itself, and therefore to its pole ; and this
fact renders the motion of the pole of the equator around it
somewhat complicated ; but the curve described by the latter
is very nearly a circle 46 in diameter. In the time of Hip-
parchus, our present pole star was 12 from the pole. The pole
has been approaching it steadily ever since, and will continue
to approach it till about the year 2100, when it will slowly
pass by it at the distance of less than half a degree. The
course of the pole during the next 12,000 years is laid down
on the map, and it will be seen that at the end of that time
it will be near the constellation Lyra. Since the equator is
always 90 distant from the pole, there will be a correspond-
ing motion to it, and hence to the point of its crossing the
20 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
ecliptic. To show this, the position of the equator 2000 years
ago, as well as its present position, is given on Map II.
The reader will, of course, understand that the various ce-
lestial movements of which we have spoken in this chapter are
only apparent motions, and are due to the motion of the earth
itself, as will be explained in the chapter on the Copernican
system. The diurnal revolution of the celestial sphere is due
to the rotation of the earth on its axis, while precession is real-
ly a change in the direction of that axis.
One important effect of precession is that one revolution of
the sun among the stars does not accurately correspond to the
return of the same seasons. The latter depend upon the posi-
tion of the sun relative to the equinox, the time when the sun
crosses the equator towards the north always marking the sea-
son of spring (in the northern hemisphere), no matter where
the sun may be among the stars. If the equator did not move,
the sun would always cross it at nearly the same point among
the stars. But when, starting from the vernal equinox, it
makes the circuit of the heavens, and returns to it again, the
motion of the equator has been such that the sun crosses it
20 minutes before it reaches the same star. In one year, tin's
difference is very small; but by its constant accumulation, at
the rate of 20 minutes a year, it becomes very considerable
after the lapse of centuries. We must, therefore, distinguish
between the sidereal and the tropical year, the former being
the period required for one revolution of the sun among the
stars, the latter that required for his return to the same equi-
nox, whence it is also called the equinoctial year. The exact
lengths of these respective years are :
Days. Days. Hours. Min. Sec.
Sidereal year 365.25636 = 365 699
Tropical year 365.24220 = 365 5 48 46
Since the recurrence of the seasons depends on the tropical
year, the latter is the one to be used in forming the calendar,
and for the purposes of civil life generally. Its true length is
11 minutes 14 seconds less than 365J days. Some results of
this difference will be shown in explaining the calendar.
THE MOON. 21
5. The Moons Motion.
Every one knows that the moon makes a revolution in the
celestial sphere in about a month, and that during its revolu-
tion it presents a number of different phases, known as u new
moon," "first quarter," "full moon," and so on, depending
on its position relative to the sun. A study of these phases
during a single revolution will make it clear that the moon is
a globular dark body, illuminated by the light of the sun, a
fact which has been evident to careful observers from the re-
motest antiquity. This may be illustrated by taking a large
globe to represent to moon, painting one half white, to rep-
resent the half on which the sun shines, arid the other half
dark. Viewing it at a proper distance, and turning it into
different positions, it will be found that the visible part of the
white half may be made to imitate the various appearances of
the moon.
As the sun makes a revolution around the celestial sphere
in a year, so the moon makes a similar revolution among the
stars in a little more than 27 days. This motion can be seen
on any clear night between first quarter and full moon, if the
moon happens to be near a bright star. If the position of the
moon relatively to the star be noted from hour to hour, it will
be found that she is constantly working towards the east by a
distance equal to her own diameter in an hour. The follow-
ing night she will be found from 12 to 14 east of the star,
and will rise, cross the meridian, and set from half an hour to
an hour later than she did the preceding night. At the end
of 27 days 8 hours, she will be back in the same position
among the stars in which she was first seen. -
If, however, starting from one new moon, we count forwards
this period, we shall find that the moon, although she has re-
turned to the same position among the stars, has not got back
to new moon again. The reason is that the sun has moved
forwards, in virtue of his apparent annual motion, so far that
it will require more than two days for the moon to overtake
him. So, although the moon really revolves around the earth
22 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
in 27^ days, the average interval between one new moon and
the next is 29 days.
A comparison of the phases of the moon with her direction
will show that the sun is many times more distant than the
moon. In Fig. 5, let E be the position of an observer on the
earth, M the moon, and S the sun, illuminating one half of it.
When the observer sees the moon in her first quarter that is,
when her disk appears exactly half illuminated the angle at
FIG. 5 Showing the sun to be farther than the moon.
the moon, between the observer and the sun, must be a right
angle. If the sun were only about four times as far as the
moon, as in the figure, the observer, by measuring the angle
SEM between the sun and moon, would find it to be 75 ; and
the nearer the sun, the smaller he would iind it. But actual
measurement would show it to be so near 90 that the dif-
ference would be imperceptible with ordinary instruments.
Hence, the sun is really at the point where the dotted line and
the line MS continued meet each other, which is many times
the distance EM to the moon.
This idea was applied by Aristarchus, who flourished in the
third century before Christ, preceding both Hipparchus and
Ptolemy, to determine the distance of the sun, or, more ex-
actly, how many times it exceeded the distance of the moon.
He found, by measurement, that, in the position represented
in the figure, the distance between the directions of the sun
and moon was 87, and that the sun was therefore something
like twenty times as far as the moon. We. now know that this
result was twenty times too small, the angle being really so
near 90 that Aristarchus could not determine the difference
with certainty. In principle, the method is quite correct and
THE MOON. 23
very ingenious, but it cannot be applied in practice. The one
insuperable difficulty of the method arises from the impossi-
bility of seeing when the moon is exactly half illuminated,
the uncertainty arising from the inequalities in the lunar sur-
face being greater than the whole angle to be measured.
Watching and mapping down the path of the moon among
the stars, it is found not to be the same with that of the sun,
being inclined to it about 5. The paths cross each other in
two opposite points of the heavens, called the moon's nodes.
The path of the moon in the middle of the year 1877 is
marked on star Maps 1L-V. Ref erring to Map III., it will
be seen that the descending node of the moon is in the con-
stellation Leo, very near the star Regulus. Here the moon
passes south of or below the ecliptic, and continues below it
over the whole of Map IV. On Map V., it approaches the
ecliptic again, crossing to the north of it in the constellation
Aquarius, and continuing* on that side till it reaches Eegulus
once more.
Such is the moon's path in July, 1877. But it is con-
stantly changing in consequence of a motion of the nodes
towards the west, amounting to more than a degree in every
revolution. In order that the line drawn on the map may
continue to represent the path of the moon, we must suppose
it to slide along the ecliptic towards the right at the rate of
about 20 a year, so that a slightly different path will be de-
scribed in every monthly revolution. The path will always
cross the ecliptic at the same angle, but the moon will not
always pass over the same stars. In August, 1877, she will
cross the ecliptic a little farther to the right (west), and will
pass a little below Regulus. The change going on from
month to month and from year to year, in a little less than
ten years the ascending node will be found in Leo ; and the
other node, now in Leo, will have gone back to Aquarius.
In a period of eighteen years and seven months, the nodes
will have made a complete revolution, and the path of the
moon will have resumed the position given on the map.
24 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
6. Eclipses of the Sun and Moon.
The early inhabitants of the world were, no doubt, terrified
by the occasional recurrence of eclipses many ages before
there were astronomers to explain their causes. But the mo-
tions of the sun and moon could not be observed very long
without the causes being seen. It was evident that if the
moon should ever chance to pass between the earth and the
sun, she must cut off some or all of his light. If the two bodies
followed the same track in the heavens, there would be an
eclipse of the sun every new moon; but, owing to the incli-
nation of the two orbits, the moon will generally pass above
or below the sun, and there will be no eclipse. If, however,
the sun happens to be in the neighborhood of the moon's node
when the moon passes, then there will be an eclipse. For an
example, let us refer to Map 'III. We see that the sun passes
the moon's descending node about August 25th, 1877, and is
within 20 of this node from early in August till the middle
of September. The moon passes the sun on August 8th and
September 6th of that year, which arc, therefore, the dates of
new moon. At the first date, the moon passes so far to the
north that, as seen from the centre of the earth, there is no
eclipse at all; but in the northern part of Asia the moon
would be seen to cut off a small portion of the sun.
While the moon is performing another circuit, the sun has
moved so far past the node, that the moon passes south of it,
and there is only a small eclipse, and that is visible only
around the region of Cape Horn. Thus, there are two solar
eclipses while the sun is passing this node in 1877, but both
are very small. Indeed, every time the sun crosses a node;
the moon is sure to cross his path, either before he reaches
the node, or before he gets far enough from it to be out of
the way. As he crosses both nodes in the course of the year,
there must be at least two solar eclipses every year to some
points of the earth's surface.
The cause of lunar eclipses might not have been so easy to
guess as was that of solar ones; but a great number could
ECLIPSES OF THE SUN AND MOON. 25
not have been observed, and their times of occurrence record-
ed, without its being noticed that they always occurred at full
moon, when the earth was opposite the sun. The idea that
the earth cast a shadow, and that the moon passed into it,
could then hardly fail to suggest itself; and we find, accord-
ingly, that the earliest observers of the heavens were perfectly
acquainted with the cause of lunar eclipses.
The reason why eclipses of the moon only occur occasion-
ally is of the same general nature with that of the rare occur-
rence of solar eclipses. The centre of the earth's shadow is
always, like the sun, in the ecliptic ; and unless the moon hap-
pens to be very near the ecliptic, and therefore very near one
of her nodes &t the time of full moon, she will fail to strike
the shadow, passing above or below it. Owing to the great
magnitude of the sun, the earth's shadow is, at the distance of
the moon, much smaller than the earth itself. The result of
this is, that the moon must be decidedly nearer her node to
produce a lunar than to produce a solar eclipse. Sometimes
a whole year passes without there being any eclipse of the
moon.
The nature of an eclipse will vary with the positions and
apparent magnitudes of the sun and moon. Let us suppose,
lirst, that, in a solar eclipse, the centre of the moon happens
to pass exactly over the centre of the sun. Then, it is clear
that if the apparent angular diameter of the moon exceed that
of the sun, the latter will be entirely hidden from view. This
is called a total eclipse of the sun. It is evident that such an
eclipse can occur only when the observer is near the line join-
ing the centres of the sun and moon. If, under the same cir-
cumstances, the apparent magnitude of the moon is less than
that of the sun, it is evident that the whole of the latter cannot
be covered, but a ring of light around his edge will still be visi-
ble. This is called an annular eclipse. If the moon does riot
pass centrally over the sun, then it can cover only a portion of
the latter on one side or the other, and the eclipse is said to be
partial. So with the moon : if the latter is only partially im-
mersed in the earth's shadow, the eclipse of the moon is called
20 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
partial y if she is totally immersed in it, so that no direct sun-
light can reach her, the eclipse is said to be total. An an-
Fio. G. Annular eclipse of the sun.
Fi. 7. Partial eclipse of the eun.
nular eclipse of the moon is impossible, because the earth's
shadow always exceeds the diameter of the moon in breadth.
Some points respecting eclipses will be seen more clearly
by reference to the accompanying figures, in which /S repre-
sents the sun, E the earth, and J!^the moon. Referring to the
first figure, it will be seen that an observer at either of the
points marked 0, or indeed anywhere outside the shaded por-
tions, will see the whole of the sun, so that to him there will
be no eclipse at all. Within the lightly shaded regions, marked
PJP, the sun will be partially eclipsed, and more so as the ob-
server is near the centre. This region is called the penumbra.
FUJ. S Eclipse of the sun, the shadow of the moou falling on the eartfc.
Within the darkest parts between the two letters P is a region
where the sun is totally hidden by the moon. This is the
shadow, and its form is that of a cone, with its base on the
moon, and its point extending towards the earth. Now, it
happens that the diameters of the sun and moon are very
nearly proportional to their respective mean distances, so that
the point of this shadow almost exactly reaches the surface of
the earth. Indeed, so near is the adjustment, that the dark
shadow sometimes reaches the earth, and sometimes does not
ECLIPSES OF THE SUN AND MOON.
owing to the small changes in the distance of the sun and
moon. When the shadow reaches the earth, it is comparative-
ly very narrow, owing to its being so near its sharp point; but
if an observer can station himself within it, he will see a total
eclipse of the sun during the short time the shadow is passing
over him. If the reader will study the figure, he will see why
a total eclipse of the sun is so rare at any one place on the
earth. The shadow, when it reaches the earth, is so near down
to a point that its diameter is not generally more than a hun-
dred miles ; consequently, each total eclipse is visible only
along a belt which may not average more than a hundred
miles across.
In most eclipses, the shadow comes to a point before it
reaches the earth ; in this case, the apparent angular diameter
of the moon is less than that of the sun, and there can be no
total eclipse. But if an observer places himself in a line with
the centre of the shadow, he will see an annular eclipse, the
sun showing itself on all sides of the moon.
The next figure shows us the form of the earth's shadow.
FIG. 9. Eclipse of the moon, the latter being io the shadow of the earth.
The earth being much larger than the moon, its shadow ex-
tends far beyond it; and where it reaches the moon, it is al-
ways so much larger than the latter that she may be wholly
immersed in it, as shown in the figure. Now, suppose the
moon, in her course round the earth, to pass centrally through
the shadow, and not above or below it, as she commonly does ;
then, when she entered the shaded region, marked jP, which
is called the penumbra, an observer on her surface would see
a partial eclipse of the sun caused by the intervention of the
28 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
earth. The time when this begins is given in the almanacs,
being expressed by the words, " Moon enters penumbra."
Some of the sunlight is then cut off from the moon, so that
the latter is not so bright as usual; but the eye does not
notice any loss of light until the moon almost reaches the
dark shadow. As she enters the shadow, a portion of her sur-
face seems to be cut off and to disappear entirely, and her vis-
ible portion continually grows smaller, until, in case of a total
eclipse, her whole disk is immersed in the shadow. When this
occurs, it is found that she is not entirely invisible, but still
faintly shines with a lurid copper-colored light. This light is
refracted into the shadow by the earth's atmosphere, and its
amount may be greater or less, according to the quantity of
clouds and vapor in the atmosphere around that belt of the
earth which the sunlight must graze in order to reach the moon.
In about half of the lunar eclipses, the moon passes so far
above or below the centre of the shadow that part of her body
is in it, and part outside, at the time of greatest eclipse. This
is called & partial eclipse of the moon. The magnitude of a
partial eclipse, whether of the sun or moon, was measured by
the older astronomers in digits. The diameter of the solar or
lunar disk was divided into twelve equal parts, called digits;
and the magnitude of the eclipse was said to be equal to the
number of digits cut off by the shadow of the earth in case of
a lunar eclipse, or by the moon in case of a solar eclipse. The
most ancient astronomers were in the habit of measuring the
digits by surface : when the moon was said to be eclipsed four
digits, it meant that one -third of her surface, and not one-
third her diameter, was eclipsed. (
The duration of an eclipse varies between very wide limits,
according to whether it is nearly central or the contrary. The
duration of a solar eclipse depends upon the time required for
the moon to pass over the distance from where she first comes
into apparent contact with the sun's disk, until she separates
from it again ; and this, in the case of eclipses which are pret-
ty large, may range between two and three hours. In a total
eclipse, however, the apparent disk of the moon exceeds that
ECLIPSES OF THE SUN AND MOON. 29
of the sun by so smalFan amount, that it takes her but a short
time to pass far enough to uncover some part of the sun's
disk; the time is rarely more than five or six minutes, and
sometimes only a few seconds. A total eclipse of the moon
may, however, last nearly two hours, and the partial eclipses
on each side of the total one may extend the whole duration
of the eclipse to three or four hours.
Total eclipses of the sun afford very rare and highly prized
opportunities for studying the operations going on around that
luminary. Of these we shall speak in a subsequent chapter.
Returning, now, to the apparent motions of the sun and
moon around the celestial sphere, we see that since the moon's
orbit has two opposite nodes in which it crosses the ecliptic,
and the sun passes through the entire course of the ecliptic in
the course of the year, it follows that there are two periods in
the course of a year during which the sun is near a node, and
eclipses may occur. Roughly speaking, these periods are each
about a month in duration, and we may call them seasons of
eclipses. For instance, it will be seen on Map V. that the
sun passes one node of the moon's orbit towards the end of
February, 1877. A season of eclipses for that year is there-
fore February and the first half of March. Actually, there is
a total eclipse of the moon on February 27th, and a very small
eclipse of the sun on March 14th, of that year, visible only in
Northern Asia.* From this time, the sun is so far from the
node that there can be no eclipses until he approaches the
other node in August. Then we have the two eclipses of the
sun already mentioned, and, between, them, a total eclipse of
the moon on August 23d. Thus, in the year 1877, the first
season of eclipses is in February and March, and the second
in August and September.
We have said that the length of each eclipse season is about
a month. To speak with greater accuracy, the average season
for eclipses of the sun extends 18 days before and after the)
* There is an extraordinary coincidence between this eclipse and that of Au-
gust 8th of the same year, both being visible from nearly the same region in Cen-
tral Siberia.
30 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
sun's passage through the node, while that for lunar eclipses
extends 11 days on each side of the node. The total season
is, therefore, 36 days for solar, and 23 days for lunar eclipses.
Owing to the constant motion of the moon's node already
described, the season of eclipses will not be the same from
year to year, but will occur, on the average, about 20 days
earlier each year. We have seen that the sun passed the de-
scending node of the moon marked on Map III. on August
24th, 1877; but during the year following the node will have
moved so far to the west that the sun will again reach it on
August 5th, 1878. The effect of this constant shifting of the
nodes and seasons of eclipses is that in 1887 the August sea-
son will be shifted back to February, and the February season
to August. The reader who wishes to find the middle of the
eclipse seasons for twenty or thirty years can do so by starting
from March 1st and August 24th, 1877, and subtracting 19f
days for eacli subsequent year.
There is a relation between the motions of the sun and
inoon which materially assisted the early astronomers in the
prediction of eclipses. We have said that the moon makes
one revolution among the stars in about 27-J- days. Since the
node of the orbit is constantly moving back to meet the moon,
as it were, she will return to her node in a little less than this
period namely, as shown by modern observations, in a mean
interval of 27.21222 days. The sun, after passing any node
of the orbit, will reach the same node again in 346.6201 days.
The relation between these numbers is this : 242 returns of
the moon to a node take very nearly the same time with 19
returns of the sun, the intervals being
242 returns of the moon to her node 6585.357 days;
19 " " sun to moon's node 6585.780 "
Consequently, if at any time the sun and moon should start
out together from a node, they would, at the end of 6585
days, or 18 years and 11 days, be again found together very
near the same node. During the interval, there would have
been 223 new and full moons, but none so near the node as
ECLIPSES OF THE SUN AND MOON, 31
tliis. The exact time required for 223 lunations is 6585.3212
days; so that, in the case supposed, the 223d conjunction of
the sun and moon would happen a little before they reached
the node, their distance from it being, by calculation, a little
less than one of their diameters, or, more exactly, 28'. If,
instead of being exactly at the node, they are any given dis-
tance from it, say 3 east or west, then, in the same period,
they will be again together within half a degree of the same
distance from the node.
The- period just found was called the Saros, and may be ap-
plied in this way : Let us note the exact time of the middle
of any eclipse, either of the moon or of the sun ; then let us
count forwards 6585 days, 7 hours, 42 minutes, and we shall
find another eclipse ot very nearly the same kind, Reduced
to years, the interval will be 18 years and 10 or 11 days, ac-
cording to whether the 29th of February has intervened four
or five times during the interval. This being true of every
eclipse, if we record all the eclipses which occur during a
period of 18 years, we shall find the same series after 10 or
11 days to begin over again ; but the new series will not gen-
erally be visible at the same places with the old ones, or, at
least, will riot occur at the same time of day, since the mid-
dle will be nearly eight hours later. Not till the end of three
periods will they recur near the same meridian ; and then,
owing to the period not being exact, the eclipse will not be
precisely of the same magnitude, and, indeed, may fail entire-
ly. Every successive recurrence of an eclipse at the end of
the period being 28' farther back relatively to the node, the
conjunction must, in process of time, be so far back from the
node as not to produce an eclipse at all. During nearly every
period it will be found that some eclipse fails, and that some
new one enters in. A new eclipse of the moon thus entering
will be a very small one indeed. At every successive recur-
rence of its period it will be larger, until, about its thirteenth
recurrence, it will be total. It will be total for about twenty-
two or twenty-three recurrences, when it will become partial
once more, but on the opposite side of the moon from that on
32 SYSTEM OF THE WORLD HISTOIHCALLY DEVELOPED.
which it was first seen. There will then be about thirteen par-
tial eclipses, each smaller than the last, until they fail entirely.
The whole interval of time over which the recurrence of a
lunar eclipse thus extends will be about 48 periods, or 865J
years. The solar eclipses, occurring farther from the node,
will last yet longer, namely, from 65 to 70 periods, or over
1200 years.
As a recent example of the Saros, we may cite some total
eclipses of the sun well known in recent times ; for instance,
1842, July 8th, l h 8 A.M., total eclipse, observed in Europe ;
1860, July 18th, 9 h A.M., total eclipse America and Spain ;
1878, July 29th, 4 h 2 P.M., one visible in Colorado and on the Pacific Coast.
A yet more remarkable series of total eclipses of the sun
occurs in the years 1850, 1868, 1886, etc., the dates being
1850, August 7th, 4 h 4 P.M., in the Pacific Ocean?
1868, August 17th, 12 h P.M., in India ;
1886, August 29th, 8 h A.M., in the Central Atlantic Ocean and Southern Africa;
1904, September 9th, noon, in South America.
This series is remarkable for the long duration of totality,
amounting to some six minutes.
It must be understood that the various numbers we have
given in this section are not accurate for all cases, because the
motions both of the sun and moon are subject to certain small
irregularities which may alter the times of eclipses by an hour
or more. We have given only mean values, which are, how-
ever, always quite near the truth.
7. The Ptolemaic System.
There is still extant a work which for fourteen centuries
was a sort of astronomical Bible, from which nothing was
taken, and to which nothing material in principle was added.
This is the "Almagest" of Ptolemy, composed about the mid-
dle of the second century of our era. Nearly all we know of
the ancient astronomy as a science is derived from it. Frag-
ments of other ancient authors have come down to us, and
most of the ancient writers make occasional allusions to astro-
nomical phenomena or theories, from which various ideas re-
THE PTOLEMAIC SYSTEM. 38
specting the ancient astronomy have been gleaned; but the
work of Ptolemy is the only complete compendium which we
possess. Although his system is in several important points
erroneous, it yet represents the salient features of the apparent
motions of the heavenly bodies with entire accuracy. Defec-
tive as it is when measured by our standard, it is a marvel of
ingenuity and research when measured by the standard of the
times.
The immediate object of the present chapter is to explain
the apparent movements of the planets, which can be most
easily done on the Ptolemaic system. But, on account of its
historic interest, we shall begin with a brief sketch of the
propositions on which the system rests, giving also Ptolemy's
method of proving them. His fundamental doctrines are that
the heavens are spherical in form, and all the heavenly mo-
tions spherical or in circles; that the earth is also spherical,
and situated in the centre of the heavens, or celestial sphere,
where it remains quiescent, and that it is in magnitude only a
point when compared with the sphere of the stars. We shall
give Ptolemy's views of these propositions, and his attempts
to prove them, in their regular order.
1st. The Heavenly Bodies move in Circles. Here Ptole-
my refers principally to the diurnal motion, whereby every
heavenly body is apparently carried around the earth, or ? rath-
er, around the pole of the heavens, in a circle every day. But
all the ancient and mediaeval astronomers down to the time
of Kepler had a notion that, the circle being the most perfect
plane figure, all the celestial motions must take place in cir-
cles ; and as it w T as found that the motions were never uni-
form, they supposed these circles not to be centred on the
earth. Where a single circle did not suffice to account for
the motion, they introduced a combination of circular motions
in a manner to be described presently.
2d. The Earth is a Sphere. That the earth is rounded
from east to west Ptolemy proves by the fact that the sun,
moon, and stars do not rise and set at the same moment to all
the inhabitants of the earth. The times at which eclipses of
4
34 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
the moon are seen in different countries being compared, it is
found that the farther the observer is west, the earlier is the
hour after sunset. As the time is really the same everywhere,
this shows that the sun sets later the farther we go to the west.
Again, if the earth were not rounded from north to south, a
star passing the meridian in the north or south horizon would
always pass in the horizon, however far to the north or south
the observer might travel. But it is found that when an ob-
server travels towards the south, the stars in the north ap-
proach the horizon, and the circles of their diurnal motion cut
below it, while new stars rise into view above the south hori-
zon. This shows that the horizon itself changes its direction
as the observer moves. Finally, from whatever direction we
approach elevated objects from the sea, we see that their bases
are first hidden from view by the curvature of the water, and
gradually rise into view as we approach them.
3d. The Earth is in the Centre of the Celestial Sphere.
If the earth were displaced from the centre, there would be
various irregularities in the apparent daily motion of the ce-
lestial sphere, the stars appearing to move faster on the side
towards which the earth was situated. If it were displaced
towards the east, we should be nearer the heavenly bodies
when they are rising than when they are setting, arid they
would appear to move more rapidly in the east than in the
west. The forenoons would therefore be shorter than the af-
ternoons. Towards whatever side of the turning sphere it
might be moved, the heavenly bodies would seem to move
more rapidly on that side than on the other. No such irreg-
ularity being seen, but the diurnal motion taking place with
perfect uniformity, the earth must be in the centre of mo-
tion.
4th. The Earth has no Motion of Translation Because
if it had it would move away from the centre towards one
side of the celestial sphere, and the diurnal revolution of the
stars would cease to be uniform in all its parts. But the uni-
formity of motion just described being seen from year to year,
the earth must preserve its position in the centre of the sphere.
THE PTOLEMAIC SYSTEM. 35
It will be interesting to analyze these propositions of Ptole-
my, to see what is true and what is false. The first proposi-
tion that the heavenly bodies move in circles, or, as it is
more literally expressed, that the heavens move spherically-
is quite true, so far as the apparent diurnal motion is con-
cerned. What Ptolemy did not know was that this motion is
only apparent, arising from a rotation of the earth itself on its
axis. The second proposition is perfectly correct, and Ptole-
my's proofs that the earth is round are those still found in our
school-books at the end of seventeen hundred years. Most
curious, however, is the mixture of truth and falsehood in the
third and fourth propositions, that the earth remains quies-
cent. We cannot denounce it as unqualifiedly false, because,
in a certain sense, and indeed in the only sense in which there
is any celestial sphere, the earth may be said to remain in the
centre of the sphere. What Ptolemy did not see is that this
sphere is only an ideal one, which the spectator carries witli
him wherever he goes. His demonstration that the centre of
revolution of the sphere is in the earth is, in a certain sense,
correct ; but what he really proves is that the earth revolves
on its own axis. He did not see that if the earth could carry
the axis of revolution with it, his demonstration of the quies-
cence of the earth would fall to the ground.
Considerable insight into Ptolemy's views is gained by his
answers to two objections against his system. The first is the
vulgar and natural one, that it is paradoxical to suppose that
a body like the earth could remain supported on nothing, and
still be at rest. These objectors, he says, reason from what
they see happen to small bodies around them, and not from
what is proper to the universe at large. There is neither up
nor down in the celestial spaces, for we cannot conceive of it
in a sphere. What we call down is simply the direction of
our feet towards the centre of the earth, the direction in
which heavy bodies tend to fall. The earth itself is but a
point in comparison with the celestial spaces, and is kept fixed
by the forces exerted upon it on all sides by the universe,
which is infinitely larger than it, and similar in all its parts.
36 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
This idea is as near an approach to that of universal gravita-
tion as the science of the times would admit of.
He then says there are others who, admitting this reason-
ing, pretend that nothing hinders us from supposing that the
heavens' are immovable, and that the earth itself turns round
its own axis once a day from west to east. It is certainly
singular that one who had risen so far above the illusions of
sense as to demonstrate to the world that the earth was round ;
that up and down were only relative ; and that heavy bodies
fell towards a centre, and not in some unchangeable direction,
should riot have seen the correctness of this view.
To refute the doctrine of the earth's rotation, he proceeds
in a way the opposite of that which he took to refute those
who thought the earth could not rest on nothing. lie said of
the latter that they regarded solely what was around them on
the earth, and did not consider what was proper to the uni-
verse at large. To those who maintained the earth's rotation,
lie says, if we consider only the movements of the stars, there
is nothing to oppose their doctrine, which he admits has the
merit of simplicity ; but in view of what passes around us and
in the air, their doctrine is ridiculous. He then enters into a
disquisition on the relative motion of light and heavy bodies,
which is extremely obscure ; but his conclusion is that if the
earth really rotated with the enormous velocity necessary to
carry it round in a day, the air would be left behind. If they
say that the earth carries round the air with it, he replies that
this could not be true of bodies floating in the air ; and hence
concludes that the doctrine of the earth's rotation is not tena-
ble. It is clear, from this argument, that if Ptolemy and his
contemporaries had devoted to experimental physics half the
careful observation, research, and reasoning which we find in
their astronomical studies, they could not have failed to estab-
lish the doctrine of the earth's rotation.
In the Ptolemaic system, all the celestial motions are repre-
sented by a series of circular motions. We have already ex-
plained the motions of the sun and moon among the stars, the
first describing a complete circuit of the heavens from west to
THE PTOLEMAIC SYSTEM. 37
east in a year, and the second a similar circuit in a month.
Though not entirely uniform, these movements are always for-
ward. But it is not so with the five planets Mercury, Ve-
nus, Mars, Jupiter, and Saturn. These move sometimes to the
east and sometimes to the west, and are sometimes stationary.*
On the whole, however, the easterly movements predominate ;
and the planets really oscillate around a certain mean point
itself in regular motion towards the east. Let us take, for in-
stance, the planet Jupiter. Suppose a certain fictitious Jupi-
ter performing a circuit of the heavens among the stars every
twelve years with a regular easterly motion, just as the sun
performs such a circuit every year; then the real Jupiter will
be found to oscillate, like a pendulum, on each side of the fic-
titious planet, but never swinging more than 12 from it. The
time of each double oscillation is about thirteen months that
is, if on January 1st we find it passing the fictitious planet
towards the west, it will continue its westerly swing about
three months, when it will gradually stop, and return with a
somewhat slower motion to the fictitious planet again, passing
to the cast of it the middle of July. The easterly swing will
continue till about the end of October, when it will return
towards the west. The westerly or backward motion is called
retrograde, and the easterly motion direct. Between the two
is a point at which the planet appears stationary once more.
The westerly motions are called retrograde because they are
in the opposite direction both to the motion of the snn among
the stars, and to the average direction in which all the planets
move. It was seen by Ilipparchus, who lived three centuries
before Ptolemy, that this oscillating motion could be repre-
sented by supposing the real Jupiter to describe a circular or-
bit around the fictitious Jupiter once in a year. This orbit is
called the epicycle, and thus we have the celebrated epicyclic
theory of the planetary motions laid down in the " Almagest."
The movement of the planet on this theory can be seen by
* It may not be amiss to remind the reader once more that we here leave the
diurnal motion of the stars entirely out of sight, and consider only the motions of
the planets relative to the stars.
38 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
Fig. 10. E is the earth, around which the fictitious Jupiter
moves in the dotted circle, 1, 2, 3, 4, etc. To form the epicycle
in which the real planet moves, we must suppose an arm to be
constantly turning round the fictitious planet once a year, on
the end of which Jupiter is carried. This arm will then be in
the successive positions, II 7 , 22', 3 3', etc., represented by the
light dotted lines. Drawing a line through the successive po-
sitions 1', 2', 3', etc., of the real Jupiter, we shall have a series
of loops representing its apparent orbit.
FIG. 10. Showing the apparent orbit of a planet, regarding the earth as at rest.
It will be seen that although it requires only a year for the
arm carrying the real Jupiter to perform a complete revolu-
tion and return to its primitive direction, it requires about
thirteen months to form a complete loop, because, owing to
the motion of the fictitious planet in its orbit, the arm must
move more than a complete revolution to finish the loop. For
instance, referring again to Fig. 10, comparing the positions
1 1 7 and 8 8', it will be seen that the arm, being in the same
direction, has performed a complete revolution ; but, owing to
the curvature of the orbit, it does not reach the middle of the
second loop until it attains the position 99'.
THE PTOLEMAIC SYSTEM. 39
The planets of which the radius of the epicycle makes an
annual revolution in this way are Mars, Jupiter, and Saturn.
The complete apparent orbits of the last two planets are shown
in the next figure, taken from Arago. By the radius of the
epicycle we mean the imaginary revolving arm which, turn-
ing round the fictitious planet, carries the real planet at its
FIG. 11. Apparent orbits of Jupiter and Saturn, 1708-1737, after Cassini.
end. The law of revolution of this arm is, that whenever the
planet is opposite the sun, the arm points towards the earth,
as in the positions 1 1 7 , 9 9', in which cases the sun will be on
the side of the earth opposite the planet ; while, whenever the
planet is in conjunction with the sun, the arm points from the
earth. This fact was well known to the ancient astronomers,
and their calculations of the motions of the planets were all
40 SYSTEM OF TEE WORLD HISTORICALLY DEVELOPED.
founded upon it; but they do not seem to have noticed the
very important corollary from it, that the direction of the
radius of the epicycle of Mars, Jupiter, and Saturn is always
the same with that of the sun from the earth. Had they
done so, they could hardly have failed to see that the epicycles
could be abolished entirely by supposing that it was the earth
which moved round the sun, and not the sun round the earth.
The peculiarity of the planets Mercury and Venus is that
the fictitious centres around which they oscillate are always in
the direction of the sun, or, as we now know, the sun himself
is the centre of their motions. They are never seen more than
a limited distance from that luminary, Venus oscillating about
45 on each side of the sun, and Mercury from 16 to 29. It
is said that the ancient Egyptians really did make the sun the
centre of the motion of these two planets ; and it is difficult to
see how any one could have failed to do so after learning the
laws of their oscillation. Yet Ptolemy rejected this system,
placing their orbits between the earth and sun without assign-
ing any good reason for the course.
The arrangement of the planets on the Ptolemaic system is
shown in Fig. 12. The nearest planet is the moon, of which
the ancient astronomers actually succeeded in roughly meas-
uring the distance. The remaining planets are arranged in
the same order with their real distance from the sun, except
that the latter takes the place assigned to the earth in the
modern system. Thus we have the following order :
The Moon,
Mercury,
Venus,
The Sun,
Mars,
Jupiter,
Saturn.
Outside of Saturn was the sphere of the fixed stars.
This order of the planets must have been a matter of opin-
ion rather than of demonstration, it being correctly judged
by the ancient astronomers that those which seemed to move
THE PTOLEMAIC SYSTEM.
Fro. 12. Arrangement of the seven planets iu the Ptolemaic system. The orbits, as
marked, are those of the fictitious planets, the real planets being supposed to describe
a series of loops.
more slowly were the more distant. This system made it
quite certain that the moon was the nearest planet, and Mars,
Jupiter, and Saturn, in their order, the most distant ones. But
the relative positions of the Sun, Mercury, and Venus were
more in doubt, since they all performed a revolution round
the celestial sphere in a year. So, while Ptolemy, as we have
just said, placed Mercury and Venus between the earth and
the sun, Plato placed them beyond the sun, the order being,
Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn.
Hipparclms and Ptolemy made a series of investigations re-
specting the times of revolution of the planets, and the inequal-
ities of their motions, of which it is worth while to give a brief
4:2 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
summary. The former was no doubt an abler astronomer than
Ptolemy; but as he was, so far as we know, the first accurate
observer of the celestial motions, he could not make a suf-
ficiently long series of observations to determine all the peri-
ods of the planets. Ptolemy had the advantage of being able
to combine his own observations with those of Hipparchus,
three centuries earlier.
Imperfect though their means of observation were, these
observers found that the easterly movements of the planets
among the stars were none of them uniform. This held true
not only of the sun and moon, but of the fictitious planets
already described. Hence they
invented the eccentric, and sup-
posed the motions to be really cir-
cular and uniform, but in circles
not centred in the earth. In Fig.
13, let E be the earth, and C the
centre around which the planet
really revolves. Then, when the
planet is passing the point P,
which is nearest the earth, its an-
gular motion would seem more
rapid than the average, because
FIG. 13. The eccentric. Shows how . ^ ,-, - i .,
the ancients represented the unequal general the angular velocity
apparent velocities of the planets o a moving bo'dv is greater the
when their real motion was supposed . . . , .->
uniform, by placing the earth away nearer the Observer IS tO it, while
from the centre of motion, at E. w j ien p ass i n g ft w {\\ seem to be
more slow than the average. The angular velocity being
always greatest in one point of the orbit, and least in a point
directly opposite, changing regularly from the maximum to
the minimum, the general features of the movement are cor-
rectly represented by the eccentric. By comparing the angu-
lar velocities in different points of the orbit, Hipparchus and
Ptolemy were able to determine the supposed distance of the
earth from the centre, or rather the proportion of this distance
to the distance of the planet. The distance thus determined
is double its true amount. The point P is called the Perigee,
THE PTOLEMAIC SYSTEM. 43
and A the Apogee. The distance CE from the earth to the
centre of motion is the eccentricity. As there was no way of
determining the absolute dimensions of the orbit, it was neces-
sary to take the ratio of CE to the radius of the orbit CP or
CE for the eccentricity.' 34 '
In determining the motions of the moon, Hipparchus and
Ptolemy depended almost entirely on observations of lunar
eclipses. The first of these, it is said, was observed at Babylon
in the first year of Mardocempad, between the 29th and 30th
days of the Egyptian month Thoth. It commenced a little
more than an hour after the moon rose, and was total. The
date, in our reckoning, was B.C. 720, March 19th. The series
of eclipses extended from this date to that of Ptolemy him-
self, who lived between eight and nine centuries later. If the
observations of these eclipses had been a little more precise,
they would still be of great value to us in fixing the mean
motion of the moon. As it is, we can now calculate the cir-
cumstances of an ancient eclipse from our modern tables of
the sun and moon almost as accurately as any of the ancient
astronomers could observe it.
Notwithstanding the extremely imperfect character of the
observations, both Hipparchus and Ptolemy made discoveries
respecting the peculiarities of the moon's motions which show
a most surprising depth of research. By comparing the inter-
vals between eclipses, they found that her motion was not uni-
form, but that, like the sun, she moved faster in some parts of
her orbit than in others. To account for this, they supposed
her orbit eccentric, like that of the sun ; that is, the earth, in-
stead of being in the centre of the circular orbit of the moon,
was supposed to be displaced by about a tenth part the whole
distance of that body. So far the orbit of the moon was like
that of the sun and the fictitious planets, except that its eccen-
tricity was greater. But a long series of observations showed
* Compared with the modern theory of the elliptic motion, approximately treat-
ed, the distance CE is double the eccentricity of the ellipse. One-half the appar-
ent inequality is really caused hy the orbit being at various distances from the
earth or sun, but the other half is real.
44 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
that the perigee and apogee did not, as in the case of the situ
and planets, remain in the same points of the orbit, but moved
forwards at such a rate as to carry them round the heavens in
nine years ; that is, supposing Fig. 13 to represent the orbit of
the moon, the centre of the circle O revolved round the earth
in nine years, and the orbit changed its position accordingly.
It was also found by Ptolemy, by measuring the apparent
angle between the moon and sun in various points of the
orbit of the former, that there was yet another inequality in
her motion. This has received the name of the evection. In
consequence of this inequality, the moon oscillates more than
a degree on each side of her position as calculated from the
eccentric, in a period not differing much from her revolution
round the earth. To represent this motion, Ptolemy had to
introduce a small additional epicycle, as in the case of the
planets, only the radius was so small that there was no looping
of the orbit. In consequence, his theory of the moon's motion
was quite complicated; yet he managed to represent this mo-
tion, within the limits of the errors of his observations, by a
combination of circular motions, and thus saved the favorite
theory of the times, that all the celestial motions were circular
and uniform.
8. The Calendar.
One of the earliest purposes of the study of the celestial
motions was that of finding a convenient measurement of
time. Tills application of astronomy, being of great antiquity,
having been transmitted to us without any fundamental altera-
tion, and depending on the apparent motions of the sun and
moon, which we have studied in this chapter, is naturally con-
sidered in connection with the ancient astronomy.
The astronomical divisions of time are the day, the month,
and the year. The week is not such a division, because it does
not correspond to any astronomical cycle, although, as we shall
presently see, a certain astronomical signification was said to
have been given to it by the ancient astrologers. Of these
divisions the day is the most well-marked and strikin^ through-
THE CALENDAR. 45
out the habitable portion of the globe. Had a people lived at
or near the poles, it would have been less striking than the year.
But wherever man existed, there was a regular alternation of
da} 7 and night, with a corresponding alternation in his physical
condition, both occurring with such regularity and uniformity
as to furnish in all ages the most definite unit of time. For
merely chronological purposes the day would have been the
only unit of time theoretically necessary; for if mankind had
begun at some early age to number every day by counting
from 1 forwards without limit, and had every historical event
been recorded in connection with the number of the day on
which it happened, there would have been far less uncertain-
ty about dates than now exists. But keeping count of such
large numbers as would have accumulated in the lapse of cen-
turies would have been very inconvenient, and a simple count
of time by days has never been used for the purposes of civil
life through any greater period than a single month.
Next to the day, the most definite and striking division of
time is the year. The natural year is that measured by the
return of the seasons. All the operations of agriculture are
so intimately dependent on this recurrence, that man must
have begun to make use of it for measuring time long before
lie had fully studied the astronomical cause on which it de-
pends. The years in the lifetime of any one generation not
being too numerous to be easily reckoned, the year was found
to answer every purpose of measuring long intervals of time.
The number of days in the year is, however, too great to
be conveniently kept count of; an intermediate measure was
therefore necessary. This was suggested by the motion and
phases of the moon. The " new moon " being seen to emerge
from the sun's rays at intervals of about 30 days, a measure
of very convenient length was found, to which a permanent
interest was attached by the religious rites connected with the
reappearance of the moon.
The week is a division of time entirely disconnected with
the month and year, the employment of which dates from the
Mosaic dispensation. The old astrologers divided the seven
46 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
days of the week among the seven planets, not in the order of
their distance from the sun, but in one shown by the follow-
ing figure. If we go round the circle in the direction of the
hands of a watch, we shall find the names of the seven plan-
ets of the ancient astronomy, in the order of their supposed
distances ;* while, if we follow the lines drawn in the circle
from side to side, we shall have the days of the week in their
order.
itrtiv* Xf
S&SU*
Pro. 14. Showing the astrological division of the seven planets among the days of the
week.
If the lunar month had been an exact number of days, say
30, and the year an exact number of months, as 12, there
would have been no difficulty in the use of these cycles for
the measurement of time. But the former is several hours
less than 30 days, while the latter is nearly 12 lunar months.
In the attempt to combine these measures, the ancient calen-
* See pages 40, 41.
THE CALENDAR. 47
dars were thrown into a confusion which made them very per-
plexing, and which we see to this day in the irregular lengths
of our months. To describe all the devices which we know to
have been used for remedying these difficulties would be very
tedious ; we shall therefore confine ourselves to their general
nature.
The lunar month, or the mean interval between successive
new moons, is very nearly 29J days. In counting months by
the moon, it was therefore common to make their length 29
and 30 days, alternately. But the period of 29 J days is really
about three-quarters of an hour too short. In the course of
three years the count will therefore be a day in error, and it
will be necessary to add a day to one of the months. When
lunar months were used, the year, comprising 12 such months,
would consist of only 354 days, and would therefore be 11
days too short. Nevertheless, such a year was used both by
the Greeks and Romans, and is still used by the Mahome-
tans ; the Romans, however, in the calendar of Numa, adding
22 or 23 days to every alternate year by inserting the inter-
calary month Mercedonius between the 23d and 24th of Feb-
ruary.
The irregularity and inconvenience of reckoning by lunar
months caused them to be very generally abandoned, the only
reason for their retention being religious observances due at
the time of new moon, which, among the Jews and other an-
cient nations, were regarded as of the highest importance. Ac-
cordingly, we find the Egyptians counting by months of 30
days each, and making every year consist of 12 such mouths
and five additional days, making 365 days in all. As the true
length of the year was known to be about six hours greater
than this, the equinox would occur six hours later every year,
and a month later after the lapse of 120 years. After the lapse
of 1460 years, according to the calculations of the time, each
season would have made a complete course through the twelve
months, and would then have returned once more at the same
time of year as in the beginning. This was termed the Sothic
Period; but the error of each year being estimated a little
48 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
too great, as we now know, the true length of the period
would have been about 1500 years.
The confusion in the Greek year was partly remedied
through the discovery by Meton of the cycle which has since
borne his name. This cycle consists of 19 solar years, during
which the moon changes 235 times. The error of this cycle
is very small, as may be seen from the following periods, com-
puted from modern data :
Days. Hours. Min.
23/5 lunations require in the mean 6939 16 ,31
19 true solar years (tropical). 6939 14 27
19 Julian years of 36, r > days 6939 18
Hence, if we take 235 lunar months, and divide them up as
nearly evenly as is convenient into 19 years, the mean length
of these years will be near enough right for all the purposes
of civil reckoning. The years of each cycle were numbered
from 1 to 19, and the number of the year was called the Gold-
en Number, from its having been ordered to be inscribed on
the monuments in letters of gold.
The Golden Number is still used in our church calendars
for finding the date of Easter Sunday. This is the solitary
religious festival which, in Christian countries, depends on the
motion of the moon. The nominal rule for determining East-
er is that it is the Sunday following the first new moon which
occurs after the 21st of March. The dates of the new moon
correspond to the Metonic Cycle; that is, after the lapse of 19
years they recur on or about the same day of the year. Con-
sequently, if we make a list of the dates on which the Paschal
new moon occurs, we shall find no two dates to be the same
for nineteen successive years ; but the twentieth will occur on
the same day with the first, or, at most, only one day different,
and then the whole series will be repeated. Consequently,
the Golden Number for the year shows, with sufficient exact-
ness for ecclesiastical purposes, on what day, or how many
days after the equinox, the Paschal new moon occurs. The
church calculations of Easter Sunday are, however, founded
upon very old tables of the moon, so that if we fixed it by the
THE CALENDAR. 49
actual moon, we should often find the calendar feast a week
in error.
The basis of the calendars now employed throughout Chris-
tendom was laid by Julius Caesar. Previous to his time, the
Roman calendar was in a state of great confusion, the nomi-
nal length of the year depending very largely on the caprice
of the ruler for the time being. It was, however, very well
known that the real length of the solar year was about 365J
days ; and, in order that the calendar year might have the same
mean length, it was prescribed that the ordinary year should
consist of 365 days, but that one day should be added to every
fourth year. The lengths of the months, as we now have them,
were finally arranged by the immediate successors of Csesar.
The Julian calendar continued unaltered for about sixteen
centuries ; and if the true length of the tropical year had been
365^ days, it would have been in use still. But, as we have
seen, this period is about 11J minutes longer than the solar
year, a quantity which, repeated every year, amounts to an en-
tire day in 128 years. Consequently, in the sixteenth century,
the equinoxes occurred 11 or 12 days sooner than they should
have occurred according to the calendar, or on the 10th in-
stead of the 21st of March. To restore them to their original
position in the year, or, more exactly, to their position at the
time of the Council of Nice, was the object of the Gregorian
reformation of the calendar, so called after Pope Gregory
XIILj by whom it was directed. The change consisted of
two parts :
1. The 5th of October, 1582, according to the Julian calen-
dar, was called the 15th, the count being thus advanced 10
days, and the equinoxes made once more to occur about March
21st and September 21st.
2. The closing year of each century, 1600, 1700, etc., in-
stead of being each a leap-year, as in the Julian calendar,
should be such only when the number of the century was di-
visible by 4. While 1600, 2000, 2400, etc., were to be leap-
years, as before, 1700, 1800, 1900, 2100, etc., were to be re<
duced to 365 days each.
50 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
This change in the calendar was soon adopted by all Catho-
lic countries, and, more slowly, by Protestant ones England,
among the latter, holding out for more than a century, but
finally entering into the change in 1752. In Kussia it was
never adopted at all, the Julian calendar being still continued
in that country. Consequently, the Russian reckoning is now
12 days behind ours, the 10 days' difference during the six-
teenth and seventeenth centuries being increased by the days
dropped from the years 1700 and 1800 in the new reckoning.
The length of the mean Gregorian year is 365 d 5 h 49 m 12 s ;
while that of the tropical year, according to the best astronom-
ical determination, is 365 d 5 h 48 m 46 s . The former is, there-
fore, still 26 seconds too long, an error which will not amount
to an entire day for more than 3000 years. If there were
any object in having the calendar and the astronomical years
in exact coincidence, the Gregorian year would be accurate
enough for all practical purposes during many centuries. In
fact, however, it is difficult to show what practical object is to
be attained by seeking for any such coincidence. It is im-
portant that summer and winter, seed-time and harvest, shall
occur at the same time of the year through several successive
generations ; but it is not of the slightest importance that
they should occur at the same time now that they did 5000
years ago, nor would it cause any difficulty to our descendants
of 5000 years hence if the equinox should occur in the middle
of February, as would be the case should the Julian calendar
have been continued.
The change of calendar met with much popular opposition,
and it may hereafter be conceded that in this instance the
common sense of the people was more nearly right than the
wisdom of the learned. An additional complication was in-
troduced into the reckoning of time without any other real
object than that of making Easter come at the right time.
As the end of the century approaches, the question of making
1900 a leap-year, as usual, will no doubt be discussed, and it is
possible that some concerted action may be taken on the part of
leading nations looking to a return to the old mode of reckoning.
COPERNICUS. 51
CHAPTER II.
THE COPERNICAN SYSTEM, OB THE TRUE MOTIONS OF THE HEAV-
ENLY BODIES.
1. Copernicus.
IN the first section of the preceding chapter we described
the apparent diurnal motion of the heavens, whereby all the
heavenly bodies appear to be carried round in circles, thus
performing a revolution every day. Any observer of this mo-
tion who should suppose the earth to be flat, and the direction
we call downward everywhere the same, would necessarily re-
gard it as real. A very little knowledge of geometry would,
however, show him that the appearance might be accounted
for by supposing the earth to revolve. The seemingly fatal
objection against this view would be that, if such were the
case, the surface of the earth could not remain level, and ev-
ery thing would slide away from its position. But it was im-
possible for men to navigate the ocean without perceiving the
rotundity of its surface, and we have no record of a time when
it was not known that the earth was round. We have seen
that Ptolemy not only was acquainted with the true figure of
the earth, but knew that in magnitude it was so much smaller
than the celestial spaces, or sphere of the heavens, as to be only
a point in comparison. He had, therefore, all the knowledge
necessary to enable him to see that the moving body was much
more likely to be the earth than to be the sphere of the heav-
ens. Nevertheless, he rejected the theory on obscure physical
grounds, as shown in the last chapter, the untenability of which
would have been proved him by a few very simple physical ex-
periments. And although it is known that the doctrine of the
earth's motion was sustained by others in his age, notably by
Tirnocharis, yet the weight of his authority was so great as
52 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
not only to override all their arguments, but to carry his views
through fourteen centuries of the intellectual history of man.
The history of astronomy during these centuries offers hard-
ly anything of interest to the general reader. There was no
telescope to explore the heavens, and no genius arose of suffi-
cient force to unravel the maze of their mechanism. It was
mainly through the Arabs that any systematic knowledge of
the science was preserved for the use of posterity. The as-
tronomers of this people invented improved methods of ob-
serving the positions of the heavenly bodies, and were thus
able to make improved tables of their motions. They meas-
ured the obliquity of the ecliptic, and calculated eclipses of
the sun and moon with greater precision than the ancient
Greeks could do. The predictions of the science thus gradu-
ally increased in accuracy, but no positive step was taken in
the direction of discovering the true nature of the apparent
movements of the heavens.
The honor of first proving to the world what the true theory
of the celestial motions is belongs almost exclusively to Coper-
nicus. It is true that we have some reason to believe that
Pythagoras taught that the sun, and not the earth, was the
centre of motion, and that he was, therefore, the first to solve
the great problem. But he did not teach this doctrine public-
ly, and the very vague statements of his private teachings on
this point which have been handed down to us are so mixed
up with the speculations which the Greek philosophers com-
bined with their views of nature, that it is hard to say with
precision whether Pythagoras had or had not fully seized the
truth. It is certain that no modern would receive the credit
of any discovery without giving more convincing proofs of the
correctness of his views than we have any reason to suppose
that Pythagoras gave to his disciples.
The great merit of Copernicus, and 'the basis of his claim to
the discovery in question, is that he was not satisfied with a
mere statement of his views, but devoted a large part of the
labor of a life to their demonstration, and thus placed them in
such a light as to render their ultimate acceptance inevitable.
COPERNICUS. 53
Apart from all questions of the truth or falsity of his theory,
the great work in which it was developed, "De Revolutionibus
Orbium Codestium" would deservedly rank as the most im-
portant compendium of astronomy which had appeared since
Ptolemy. Few books have been more completely the labor of
a lifetime than this. Copernicus was born at Thorn, in Prus-
sia, in 1473, twenty years before the discovery of America,
but studied at the University of Cracow. He became an ec-
clesiastical dignitary, holding the rank of canon during a large
portion of his life, and finding ample leisure in this position
to pursue his favorite studies. He is said to have conceived of
the true system of the world as early jas 1507. He devoted the
years of his middle life to the observations and computations
necessary to the perfection of his system, and communicated
his views to a few friends, but long refused to publish them,
fearing the popular prejudice which might thus be excited.
In 1540, a brief statement of them was published by his friend
Eheticus ; and, as this was favorably received, he soon con-
sented to the publication of his great work. The first printed
copy was placed in his hands only a few hours before his
death, which occurred in May, 1543.
The fundamental principles of the Copernican system are
embodied in two distinct propositions, which have to be proved
separately, and one of which might have been true without
the other being so. They are as follows :
1. The diurnal revolution of the heavens is only an appar-
ent motion, caused by a diurnal revolution of the earth on an
axis passing through its centre.
2. The earth is one of the planets, all of which revolve
round the sun as the centre of motion. The true centre of
the celestial motions is therefore not the earth, but the sun.
For this reason the Copernican system is frequently spoken of
in historical discussions as the " heliocentric theory."
The first proposition is the one with the proof of which Co-
pernicus begins. He explains how an apparent motion may
result from a real motion of the person seeing, as well as from
a motion of the object seen, and thus shows that the diurnal
54 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
motion may be accounted for just as well by a revolution of
the earth as by one of the heavens. To sailors on a ship sail-
ing on a smooth sea, the ship, and every thing in it, seems to be
at rest and the shore to be in motion. Which, then, is more
likely to be in motion, the earth or the whole universe outside
of it ? In whatever proportion the heavens are greater than
the earth, in the same proportion must their motion be more
rapid to carry them round in twenty -four hours. Ptolemy
himself shows that the heavens were so immense that ,the
earth was but a point in comparison, and, for any thing that
is known, they may extend into infinity. Then we should re-
quire an infinite velocity of revolution. Therefore, it is far
more likely that it is this comparative point that turns, and
that the universe is fixed, than the reverse.
The second principle of the Copernican system that the
apparent annual motion of the sun among the stars, described
in 3 of the preceding chapter, is really due to an annual revo-
lution of the earth around the sun rests upon a very beautiful
result of the laws of relative motion. This movement of the
earth explains not only this apparent revolution of the sun,
but the apparent epicyclic motion of the planets described in
treating of the Ptolemaic system.
In Fig. 15, let S represent the suu,AJBCD the orbit of the
earth around it, and the figures 1, 2, 3, 4, 5, 6, six successive
positions of the earth. These positions would be about two
weeks apart. Also, let EFGH represent the apparent sphere
of the fixed stars. Then, an observer at 1, viewing the sun in
the direction 1$, will see him as if he were in the celestial
sphere at the point 1', because, having no conception of the
actual distance, the sun will appear to him as if actually among
the stars at V which lie in the same straight line with him.
When the earth, with the observer on it, reaches 2, he will see
the sun in the direction 2$2', that is, as if among the stars in
2'. That is, during the two weeks' interval, the sun will ap-
parently have moved among the stars by an angle equal to the
actual angular motion of the earth around the sun. So, as the
earth passes through the successive positions 3, 4, 5, 6, the sun
COPERNICUS.
55
will appear in the positions 3', 4', 5', 6', and the motion of the
earth continuing all the way round its orbit, the sun will ap-
pear to move through the entire circle EFGII. Thus we
have, as a result of the annual motion of the earth around the
sun, the annual motion of the sun around the celestial sphere
already described in the third section of the preceding chapter.
FIG. 15. Apparent annual motion of the sun explained.
Let us now see how this same motion abolishes the compli-
cated system of epicycles by which the ancient astronomers
represented the planetary motions. A theorem on which this
explanation rests is this : If an observer in unconscious mo-
tion sees an object at rest> that object will seem to him to be
moving in a direction opposite to his own, and with an equal
velocity. A familiar instance of this is the apparent motion
56 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
of objects on shore to passengers on a steamer. In Fig. 16,
let us suppose an observer on the earth carried around the
sun Siu the orbit ABCDEF,
^^"' ' \ but imagining himself at rest
x \ v in the centre of motion S. Sup-
pose that he observes the ap-
c parent motion of the planet P,
which is really at rest. How
will the planet appear to move ?
To show this, we represent ap-
parent directions and motions
by dotted lines. Let us begin
with the observer at A, from
which position he really sees
the planet in the direction and
Distance AP. But, imagining
himself at S, he thinks he sees
the planet at the point a, the
distance and direction of which
Sa is the same with AP. As
F he passes unconsciously from A
to jff, the planet seems to him to
move past from a to b in the op-
posite direction ; and, still think-
ing himself at rest in 8, he sees
the planet in #, the line Sb be-
FIG. 16.-Showing how the apparent epi- j ng equal and parallel to JSP.
cyclic motion of the planets is accounted A , j i?
for by the motion of the earth round the As he recedes from the plan-
sun - et through the arc BCD, the
planet seems to recede from him through bed. While he
moves from left to right through DE^ the planet seems to
move from right to left through de. Finally, as he approaches
the planet through the arc EFA^ the planet will seem to ap-
proach him through efa, and when he gets back to A he
will locate the planet at a, as in the beginning. Thus, in
consequence of the motion of the observer around the circle
ABCDEF, the planet, though really at rest, will seem to him
COPERNICUS. 57
to move through a corresponding circle, abcdef. If there are
a number of planets, they will all seem to describe correspond-
ing circles of the same magnitude.
If the planet P, instead of being at rest, is in motion, the
apparent circular motion will be combined with the forward
motion of the planet, and the latter will now describe a circle
around a centre which is in motion. Thus we have the appar-
ent motion of the planets around a moving centre, as already
described in the Ptolemaic system. We have said, in 7 of
the preceding chapter, that by this system the motions of the
planets are represented by supposing a fictitious planet to re-
volve around the heavens with a regular motion, while the
real planet revolves around this fictitious one as a centre once
a year. Here, the progressive motion of the fictitious planet
is (in the case of the outer planets Mars, Jupiter, and Sat-
urn} the motion of the real planet around the sun, while the
circle which the real planet describes around this moving cen-
tre is only an apparent motion due to the observer being car-
ried around the sun on the earth. If the reader will com-
pare the epicyclic motion of Ptolemy, represented in Figs. 10
and 11 with the motion explained in Fig. 16, he will find that
they correspond in every particular. In the case of the inner
planets, Mercury and Venus, which never recede far from the
sun, the epicyclic motion by which they seem to vibrate from
one side of the sun to the other is due to their orbital motion
around the sun, while the progressive motion with which they
follow the sun is due to the revolution of the earth around
the sun.
We may now see clearly how the retrograde motion and
stationary phases of the planets are explained on the Coper-
nican system. The earth and all the planets are really mov-
ing round the sun in a direction which we call east on the
celestial sphere. When the earth and an outer planet are
on the same side of the sun, they are moving in the same
direction; but the earth is moving faster than the planet.
Hence, to an observer on the earth, the planet seems to be
west, though its real motion is east. As the earth
58 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
passes to the opposite side of the sun from the planet, it
changes its motion to a direction the opposite of that of the
planet, and thus the westerly motion of the latter appears to
be increased by the whole motion of the earth.* Between
these two motions there is a point at which the planet does
not seem to move at all. This is called the stationary point.
If the planet we consider is not an outer, but an inner one,
Mercury or Venus, and we view it when between us and the
sun, its motion to us is reversed, because we see it from the
side opposite the sun. Hence it seems to move west to us,
and it is retrograde. The earth is indeed moving in the same
real direction; but since the planet moves faster than the
earth, its retrograde motion seems to predominate. As the
planet passes round in its orbit, it first appears stationary,
and then, passing to the opposite side of the sun, it seems
direct.
Let us now dwell for a moment on some considerations
which will enable us to do justice to the Ptolemaic system, as
it is called, by seeing how necessary a step it was in the evo-
lution of the true theory of the universe. The great merit of
that system consisted in the analysis of the seemingly compli-
cated motions of the planets into a combination of two circular
motions, the one that of a fictitious planet around the celestial
sphere, the other that of the real planet around the fictitious
one. Without that separation, the constant oscillations of the
planets back and forth could not have suggested any idea
whatever, except that of a motion too complicated to be ex-
plained on mechanical principles. But when, leaving out of
sight the regular forward motion of the mean or fictitious
planet, the attention was directed to the epicyclic motion
alone, one could not fail to see the remarkable correspondence
between this latter motion and the apparent annual motion
of the sun. Seeing this, it took a very small step to see that
* It must not be forgotten that the direction east in the heavens is a curved di-
rection, as it were, and is opposite on opposite sides of the sun or celestial sphere.
For instance, the motions of the stars as they rise and as they set are opposite,
but both are considered west.
COPERNICUS. 59
the sun, and not the earth, was the centre of planetary motion.
Then nothing but the illusions of sense remained to prevent
the acceptance of the theory that the earth was itself a planet
moving round the sun, and that both the annual motion of the
sun and the epicyclic motion of the planets were not real, but
apparent motions, due to the motion of the earth itself; and
in no other way than this could the heliocentric theory have
been developed. >
The Copernican system affords the means of determining
the proportions of the solar system, or the relative distances of
the several planets, with great accuracy. That is, if we take
as our measuring -rod the distance of the earth from the sun,
we can determine how many lengths of this rod, or what frac-
tional parts of its length, will give the distance of each planet,
although the length of the rod itself may remain unknown.
This determination rests on the principle that the apparent
circle or epicycle described by the planet in Fig. 16 is of the
same magnitude with the actual orbit described by the earth
around the sun. Hence, the nearer the observer is to this cir-
cle, the larger it will appear. The apparent epicycle described
by Neptune is rather less than two degrees in radius ; that is,
the true planet Neptune is seen to swing a little less than two
degrees on each side of its mean position in consequence of
the annual motion of the earth round the sun. This shows
that the orbit of the earth, as seen from Neptune, subtends an
angle of only two degrees. On the other hand, the planet
Mars generally swings more than 40 on each side; sometimes,
indeed, more than 45. From this a trigonometrical calcula-
tion shows that its mean distance is only about half as much
again as that of the earth; and the fact that the apparent
swing is variable shows the distance to be different at different
times.
As it will be of interest to see how nearly Copernicus was
able to determine the distances of the planets, we present his
results in the following table, together with what we now
know to be the true numbers. The numbers given are deci-
mal fractions,* expressing the least and greatest distance of
60 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
each planet from the sun, the distance of the earth being taken
as unity.*
Planets.
LEAST DISTANCE.
GREATEST DISTANCE.
Copernicus,
Modern.
Copernicus.
Modern.
Mercury
0.326
0.709
1.373
5.453
9.76
0.308
0.718
1.382
5.454
10.07
0.405
0.730
1.666
4.980
8.66
0.467
0.728
1.666
4.952
9.00
Venus
Mars
Jupiter
Saturn. ...
Considering the extremely imperfect means of observation
which the times afforded, these results of Copernicus come
very near the truth. The greatest proportional deviation is in
the case of Mercury, the most difficult of all the planets to
observe, even to the present day. It is said that Copernicus
died without ever seeing this planet.
The eccentricities of the orbits were represented by Coper-
nicus in a way which agrees exactly with the modern formulae
when only a rough approximation is sought for. Like Ptole-
my, he supposed the orbits of the planets not to be centred on
the sun, but to be displaced by a small quantity termed the
eccentricity. But it had long been known that the theory of
uniform motion in an eccentric circle, though it might make
the irregularities in the planet's angular motion come out all
right, would make the changes of distance double their true
value. He therefore took for the eccentricity a mean between
that which would satisfy the motion in longitude, and that
which would give the changes of distance, and added a small
epicycle of one-third this eccentricity ; and, by supposing the
planet to make two revolutions in this epicycle for every
revolution around the sun, he represented both irregulari-
ties.!
* I have deduced these numbers from the tables given in Book V. of "De
Revolutionibus Orbium Oelestium." They are probably the most accurate that
Copernicus was able to obtain.
t The mathematical form of this theory of Copernicus is as follows : Putting
OBLIQUITY OF THE ECLIPTIC. 61
The work of Copernicus was the greatest step ever taken in
astronomy. But he still took little more than the single step
of showing what apparent motions in the heavens were real,
and what were due to the motion of the observer. Not only
was his work in other respects founded on that of Ptolemy,
but he had many of the notions of the ancient philosophy re-
specting the fitness of things. Like Ptolemy, he thought the
heavens as well as the earth to be spherical, and all the celes-
tial motions to be circular, or composed of circles. He argues
against Ptolemy's objections to the theory of the earth's mo-
tion, that that philosopher treats of it as if it were an enforced
or violent motion, entirely forgetting that if it exists it must
be a natural motion, the laws of which are altogether different
from those of violent motion. Thus, part of his argument was
really without scientific foundation, though his conclusion was
correct. Still, Copernicus did about all that could have been
done under the circumstances. His hypothesis of a small epi-
cycle one-third the eccentricity represented the motions of the
planets around the sun with all the exactness that observation
then admitted of, while, in the absence of any knowledge of
the laws of motion, it was impossible to frame any dynamical
basis for the motions of the planets.
2. Obliquity of the Ecliptic ; Seasons, etc. / on the Coper-
nican System.
We have next to explain the relations of the ecliptic and
equator on the new system. Since, on this system, the ce-
lestial sphere does not revolve at all, what is the significance
of the pole and axis around which it seems to revolve ? The
e for his eccentricity, and g for the mean anomaly of the planet, he represented its
rectangular coordinates in the form
x = a (cos. g e + $e cos. 2g\
y~a (sin. g + %e sin. Zg) ;
while the approximate modern formulae of the elliptic motion are
x a (cos. g \e, -f $e cos. 2g),
y = a (sin. g + \e sin. 2#),
which agree exactly when we put e = |e.
62 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
answer is, that the celestial poles are the points among the stars
towards which the axis of the earth is directed. Here the
stars are supposed to be infinitely distant, and the axis of the
earth to be continued in an infinite straight line to meet them.
Since this point appears to the unassisted sight to be the same
during the entire year, it follows that as the earth moves round
the sun, its axis keeps pointing in the same absolute direction,
as will be shown in Fig. 18. But in the preceding chapter we
showed that there is a slow but constant change in the position
of the pole among the stars, called precession, which the an-
cient astronomers discovered by studying observations extend-
FIG. 17. Relation of the terrestrial and celestial poles and equators,
ing through several centuries, and this shows that on the Co-
pernican system the direction of the earth's axis is slowly
changing.
To conceive of the celestial equator on the Copernican sys-
tem, we must imagine the globular earth to be divided into
two hemispheres by a plane intersecting the earth around its
equator, and continued out on all sides till it reaches the ce-
lestial sphere. This may, perhaps, be better understood by
referring to Fig. 17, representing the earth in the centre of the
OBLIQUITY OF THE ECLIPTIC. 63
imaginary celestial sphere. The dotted lines passing from the
poles of the earth to the points P and S mark the poles of that
sphere. It is evident that as the earth turns on this axis, the
celestial sphere, no matter how great it may seem to be, will
appear to turn on the same axis in the opposite direction.
Again, ep being the earth's equator, dividing it into two equal
parts, we have only to imagine it to be extended to E and Q,
all round the celestial sphere, to cut the latter into two equal
parts.
Let us next examine more closely the relation of the earth
to the sun. We have already shown that as the earth moves
around the sun, the latter seems to move around the celestial
sphere, and the circle in which he seems to move is called the
ecliptic. But the ecliptic and the celestial equator are in-
clined to each other by an angle of about 23^. This shows
that the axis of the earth is not perpendicular to its orbit, but
D
FIG. 18.- Causes of changes of seasons on the Copemican system.
is inclined 23| to that perpendicular, as shown in Fig. 18,
which represents the annual course of the earth round the
sun. It is of necessity drawn on a very incongruous scale,
because the distance of the sun from the earth being near-
ly 12,000 diameters of the latter and 110 that of the sun, both
bodies would be almost invisible if they were not greatly mag-
nified in the figure. A difficulty which may suggest itself is,
that the present figure represents the earth as moving away
64 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
from its position in the centre of the sphere. There are two
ways of avoiding this difficulty. One is to suppose that the
observer carries the imaginary celestial sphere with him as he
is carried around the sun ; the other is to consider the sphere
as nearly infinite in diameter. The latter is probably the
easiest mode of conception for the general reader. He must,
therefore, in the last figure suppose the sphere to extend out
to the fixed stars, which are so distant that the whole orbit of
the earth is but a point in comparison ; and the different points
of the sphere towards which the poles and the equator of the
earth point, as the latter moves round the sun, are so far as to
appear always the same. It now requires but an elementary
idea of the geometry of the sphere to see that these two great
circles of the celestial sphere the ecliptic, around which the
sun seems to move, and the equator, which is everywhere
equally distant from the points in which the earth's axis in-
tersects the sphere will appear inclined to each other by the
same angle by which the earth's axis deviates from the per-
pendicular to the ecliptic.
Next, we have to see how the changes of the seasons, the
equinoxes, etc., are explained on the Copernican theory. In
the last figure the earth is represented in four different posi-
tions of its annual orbit around the sun. In the position A,
the south pole is inclined 23 towards the sun, while the
north pole, and the whole region within the arctic circle, is
enveloped in darkness. Hence, in this position, the sun nei-
ther rises to the inhabitants of the arctic zone, nor sets to
those of the antarctic zone. Outside of these zones, he rises
and sets, and the relative lengths of day and night at any
place can be estimated by studying the circles around which
that place is carried by the diurnal turning of the earth on its
axis. To facilitate this, we present on the following page a
magnified picture of the earth at A, showing more fully the
hemisphere in which it is day and that in which it is night.
The seven nearly horizontal lines on the globe are examples
of the circles in question. We see that a point on the arctic
circle just grazes the dividing-line between light and darkness
THE SEASONS. 65
once in its revolution, or once a day; that is, the sun just
shows himself in the horizon once a day. Of the next circle
towards the south about two-
thirds is in the dark, and one-
third in the light hemisphere.
Tins shows that the days are
about twice as long as the
nights. This circle is near that
around which London is carried
by the diurnal revolution of the
earth on its axis. As we go
south, we see that the propor-
tion of light on the diurnal cir-
cles Constantly increases, while FIG. 10. Enlarged view of the earth in
_ .., the position A of the preceding figure,
that OI darkness diminishes, UIl- showing winter in the northern herai-
til we reach the equator, where 8phere ' aud 8Uramer in the 80Uthem -
they are equal. When we pass into the southern hemisphere,
we see the light covering more than half of each circle, the
proportion of light to darkness constantly increasing, at the
same rate that the opposite proportion would increase in going
to the north. When we reach the antarctic circle, the whole
circle is in the light hemisphere, the observer just grazing the.
dividing-line at midnight. Inside of that circle the observer
is in sunlight all the time, so that the sun does not set at all.
We see, then, that at the equator the days and nights are al-
ways of the same length, and that the inequality increases as
we approach either pole.
We now go on three months to the position B^ which the
earth occupies in March. Here 'the plane of the terrestrial
equator being continued, passes directly through the sun ; the
latter, therefore, seems to be in the celestial equator. All the
diurnal circles are here one-half in the illuminated, and one-
half in the unilluminated hemisphere, the latter being invisi-
ble in the figure, through its being behind the earth. The
days and nights are, therefore, of equal length all over the
globe, if we call it night whenever the sun is geometrically
below the horizon. In the position (7, which the earth takes
6
66 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
in June, everything is the same as in position A, except that
effects are reversed in the two hemispheres. The northern
hemisphere now has the longest days, and the southern one
the longest nights. At />, which the earth reaches in Sep-
tember, the days and nights are equal once more, for the same
reason as in J3. Thus, all the seemingly complicated phenom-
ena which we have described in the preceding chapter are
completely explained in the simplest way on the new system.
We have next to see how the details of the system were filled
in by the immediate successors of Copernicus.
3. T.ycho Brake.
We have said that no great advance could be made upon
the Copernican system, without either a better knowledge of
the laws of motion or more exact observations of the positions
of the heavenly bodies. It was in the latter direction that
the advance was first made. The leader was Tycho Brahe,
who was born in 1546, three years after the death of Coperni-
cus. His attention was first directed to the study of astron-
omy by an eclipse of the sun on August 21st, 1560, which was
total in some parts of Europe. Astonished that such a phe-
nomenon could be predicted, he devoted himself to a study of
the methods of observation and calculation by which the pre-
diction was made. In 1576 the King of Denmark founded
the celebrated Observatory of Uraniberg, at which Tycho
spent twenty years, assiduously engaged in observations of the
positions of the heavenly bodies with the best instruments that
could then be made. This was just before the invention of
the telescope, so that the astronomer could not avail himself
of that powerful instrument. Consequently, his observations
were superseded by the improved ones of the centuries fol-
lowing, arid their celebrity and importance are principally due
to their having afforded Kepler the means of discovering his
celebrated laws of planetary motion.
As a theoretical astronomer, Tycho was unfortunate. He
rejected the Copernican system, for a reason which, in his day,
had some force, namely, the incredible distance at which it
TTCHO BBAHE. 67
was necessary to suppose the fixed stars to be situated if that
system were accepted. We have shown how, on the Coperni-
can system, the outer planets seem to describe an annual revo-
lution in an epicycle, in consequence of the annual revolution
of the earth around the sun. The fixed stars, which are sit-
uated outside the solar system, must appear to move in the
same way, if the system be correct. But no observations,
whether of Tycho or his predecessors, had shown any such
motion. To this the friends of Copernicus could only reply
that the distance of the fixed stars must be so great that the
motion could not be seen. Since a vibration of three or four
minutes of arc might have been detected by Tycho, it would
be necessary to suppose the stellar sphere at least a thousand
times the distance of the sun, and a hundred times that of Sat-
urn, then the outermost known planet. That a space so vast
should intervene between the orbit of Saturn and the fixed
stars seemed entirely incredible: to the philosophers of the
day it was an axiom that nature would not permit the waste of
space here implied. At the same time, the proofs given by
Copernicus that the sun was the centre of the planetary mo-
tions were too strong to be overthrown. Tycho, therefore,
adopted a system which was a compound of the Ptolemaic
and the Copernican; he supposed the five planets to move
around the sun as the centre of their motions, while the sun
was itself in motion, describing an annual orbit around the
earth, which remained at rest in the centre of the universe.
Perhaps it is fortunate for the reception of the Copernican
system that the astronomical instruments of Tycho were not
equal to those of the beginning of the present century. Had
he found that there was no annual parallax among the stars
amounting to a second of arc, and therefore that, if Coperni-
cus was right, the stars must be at least 200,000 times the dis-
tance of the sun, the astronomical world might have stood
aghast at the idea, and concluded that, after all, Ptolemy must
be right, and Copernicus wrong.
Tycho never elaborated his system, and it is hard to say
how lie would have answered the numerous objections to it.
68 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
He never had any disciples of eminence, except among the
ecclesiastics ; in fact, the invention of the telescope did away
with the last remaining doubts of the Correctness of the Co-
pernican system before a new one would have had time to
gain a foothold.
4. Kepler. His Laws of Planetary Motion.
Kepler was born in 1571, in Wiirternberg. He was for a
while the assistant of Tycho Erahe in his calculations, but was
too clear-sighted to adopt the curious system of his master.
Seeing the truth of the Copernican system, he set himself to
determine the true laws of the motion of the planets around
the sun. We have seen that even Copernicus had adopted the
ancient theory, that all the celestial motions are compounded
of uniform circular motions, and had thus been obliged to in-
troduce a small epicycle to account for the irregularities of
the motion. The observations of Tycho were so much more
accurate than those of his predecessors, that they showed Kep-
ler the insufficiency of this theory to represent the true mo-
tions of the planets around the sun. The planet most favora-
ble for this investigation was Mars, being at the same time
one of the nearest to the earth, and one of which the orbit
was most eccentric. The only way in which Kepler could
proceed in his investigation was to make various hypotheses
respecting the orbit in which the planet moved, and its velocity
in various points of its orbit, and from these hypotheses to cal-
culate the positions and motions of the planet as seen from
the earth, and then compare with observations, to see whether
the observed and calculated positions agreed. As our modern
tables of logarithms by which such calculations are immensely
abridged were not then in existence, each trial of an hypothe-
sis cost Kepler an immense amount of labor. Finding that
the form of the orbit was certainly not circular, but elliptical,
he was led to try the effect of placing the sun in the focus of
the ellipse. Then, the motion of the planet would be satisfied
if its velocity were made variable, being greater the nearer
it was to the sun. Thus lie was at length led to the first two
KEPLER.
69
of his three celebrated laws of planetary motion, which are as
follows :
1. The orbit of each planet is an ellipse, having the sun in
one focus.
2. As the planet moves round the sun, its radius-vector (or
the line joining it to the sun) passes over equal areas in
equal times.
To explain these laws, let PA (Fig. 20) be the ellipse in
which the planet moves. Then the sun will not be in the ceii-
FIG. 20. Illustrating Kepler's first two laws of planetary motion.
tre of the ellipse, but in one focus, say at S, the other focus
being empty. When the planet is at P 9 it is at the point near-
est the sun; this point is therefore called the perihelion. As
it passes round to the other side of the sun, it continues to re-
cede from him till it reaches the point A, when it attains its
greatest distance. This point is the aphelion. Then it begins
to approach the sun again, and continues to do so till it reaches
P once more, when it. again begins to repeat the same orbit.
It thus describes the same ellipse over and over.
Now, suppose that, starting from P 9 we mark the position
of the planet in its orbit at the end of any equal intervals of
time, say 30 days, 60 days, 90 days, 120 days, and so on. Let
a, b, c, d be the first four of these positions between each of
which the planet has required 30 days to move. Draw lines
from each of the five positions of the planet, beginning at JP,
70 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
to the sun at 8. We shall thus have four triangular spaces,
over each of which the radius-vector of the planet has swept
in 30 days. The first of Kepler's laws means that the areas
of all of these spaces will be equal.
The old theory that the motions of the heavenly bodies must
be circular and uniform, or, at least, composed of circular and
uniform motions, was thus done away with forever. The el-
lipse took the place of the circle, and a variable motion the
place of a uniform one.
Another law of planetary motion, not less important than
these two, was afterwards discovered by Kepler. Copernicus
knew, what had been surmised by the ancient astronomers,
that the more distant the planet, the longer it took it to per-
form its course around the sun, and this not merely because it
had farther to go, but because its motion was really slower.
For instance, Saturn is about 9^ times as far as the earth, and
if it moved as fast as the earth, it would perform its revolu-
tion in 9J years ; but it actually requires between 29 and 30
years. It does not, therefore, move one-third so fast as the
earth, although it has nine times as far to go. Copernicus,
however, never detected any relation between the distances
and the periods of revolution. Kepler found it to be as fol-
lows :
Third law of planetary motion. The square of the time
of revolution of each planet is proportional to the cube of
its mean distance from the sun.
This law is shown in the following table, which gives (1)
the mean distance of each planet known to Kepler, expressed
in astronomical units, each unit being the mean distance of
Planets.
(i)
Distance.
(2)
Cube of Dis-
tance.
(3)
Period
(Years).
(4)
Square of
Period.
Mercury
0.387
0.058
0.241
0.058
Venus
0.723
0.378
0.615
378
Earth
1.000
1.000
1.000
1 OOP
Mars
1.524
3.540
1.881
3 538
Jupiter
5.203
140.8
11.86
140.66
1) 539
868.0
21) 46
867 9
FROM KEPLER TO NEWTON. 71
the earth from the sun; (2) the cube of this quantity; (3) the
time of revolution in years ; and (4) the square of this time.
The remarkable agreement between the second and fourth
columns will be noticed.
5. From Kepler to Newton.
So far as the determination of the laws of planetary motion
from observation was concerned, we might almost say that
Kepler left nothing to be done. Given the position and
magnitude of the elliptic orbit in which any planet moved,
and the point of the orbit in which it was found at any
date, and it became possible to calculate the position of the
planet in all future time. More than that science could not
do. It is true that the places of the planet thus predicted
were not found to agree exactly with observation ; and had
Kepler had at his command observations as accurate as those
of the present day, lie would have found that his laws could
not be made to perfectly represent the motion of the planets.
Not only would the elliptic orbit have been found to vary its
position from century to century, but the planets would have
been found to deviate from it, first in one direction and then
in the other, while the areas described by the radius- vector
would have been sometimes larger and sometimes smaller.
Why should a planet move in an elliptic orbit? Why should
its radius -vector describe areas proportional to the time?
Why should there be that exact relation between their dis-
tances and times of revolutions ? Until these questions were
answered, it would have been impossible to say why the plan-
ets deviated from Kepler's laws; arid they were questions
which it was impossible to answer until the general laws of
motion, unknown in Kepler's time, were fully understood.
>* The first important step in the discovery of these laws was
taken by Galileo, the great contemporary of Kepler, one of
the inventors of the telescope, and the first who ever pointed
that instrument at the heavens. From a scientific point of
view, as inventor of the telescope, founder of the science of
dynamics, teacher and upholder of the Copernican system, and
72 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
sufferer at the hands of the Inquisition, for promulgating what
he knew to be the truth, Galileo is perhaps the most interest-
ing character of his time. If any serious doubt could remain
of the correctness of the Copernican system, it was removed
by the discoveries made b.y the telescope. The phases of
Venus showed that she was a dark globular body, like the
earth, and that she really revolved around the sun. In Jupi-
ter and his satellites, the solar system, as described by Coperni-
cus, was repeated on a small scale with a fidelity which could
not fail to strike the thinking observer. There was no longer
any opposition to the new doctrines from any source entitled
to respect. The Inquisition forbade their promulgation as
absolute truths, but were perfectly willing that they should be
used as hypotheses, and rather encouraged men of science in
the idea of investigating the interesting mathematical prob-
lems to which the explanation of the celestial motions by the
Copernican system might give rise. The only restriction was
that they must stop short of asserting or arguing the hypothe-
ses to be a reality. As this assertion was implicitly contained
in several places in the great work of Copernicus, they con-
demned this work in its original form, and ordered its revi-
sion.* Probably the decree of the Inquisition was entirely
without effect in stopping the reception of the Copernican
system outside of Italy and Spain.
It will be seen, from what has been said, that the next step
to be taken in the direction of explaining the celestial motions
must be the discovery of some general cause of those motions,
or, at least, their reduction to some general law. The first
attempt to do this was made by Descartes in his celebrated
theory of vortices, which for some time disputed the field with
Newton's theory of gravitation. This philosopher supposed
the sun to be immersed in a vast mass of fluid, extending in-
definitely in every direction. The sun, by its rotation, set the
* The order for this revision was made at the time of condemning Galileo's
work, but I am not aware that it was ever executed. An edition of Copernicus,
revised to satisfy the Inquisition, would certainly be an interesting work to the
astronomical bibliopole at the present time.
FMOM KEPLER TO NEWTON. 73
parts of the fluid next to it in rotation ; these communicated
their motions to the parts still farther out, and so on, until
the whole mass was set in rotation like a whirlpool. The
planets were carried around in this ethereal whirlpool. The
more distant planets moved more slowly because the ether
was less affected by the rotation of the sun the more distant
it was from him. In the great vortex of the solar system
were smaller ones, each planet being the centre of one ; and
thus the satellites, floating in the ether, were carried round
their primaries. Had Descartes been able to show that the
parts of his vortex must move in ellipses having the sun in
one focus, that they must describe equal areas in equal times,
and that the velocity must diminish as we recede from the
sun, according to Kepler's third law, his theory would so far
have been satisfactory. Failing in this, it cannot be regarded
as an advance in science, but rather as a step backwards. Yet,
the great eminence of the philosopher and the number of his
disciples secured a wide currency for his theory, and we find
if supported by no less an authority than John Bernoulli.
After Galileo, the man who, perhaps, did most to prepare
the way for gravitation was Huyghens. As a mathematician,
a mechanician, and an observer, he stood in the first rank.
He discovered the laws of centrifugal force, and if he had
simply applied these laws to the solar system, he would have
been led to the result that the planets are held in their orbits
by a force vailing as the inverse square of their distance from
the sun. Having found this, the road to the theory of gravita-
tion could hardly have been missed. But the great discovery
seemed to require a mind freshly formed for the occasion.
74 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
CHAPTER III.
UNIVERSAL GRAVITATION.
1. Newton. Discovery of Gravitation.
THE real significance of Newton's great discovery of univer-
sal gravitation is fully appreciated by but few. Gravitation
is generally thought of as a mysterious force, acting only be-
tween the heavenly bodies, and first discovered by Newton.
Had gravitation itself been discovered by Newton as some
new principle to account for the motions of the planets, it
would not have been so admirable a discovery as that which
he actually made. Gravitation, in a somewhat limited sphere,
is known to all men. It is simply the force which causes
all heavy bodies to fall, or to tend towards the centre of the
earth. Every one who had ever seen a stone fall, or felt it to
be heavy, knew of the existence of gravitation. What New-
ton did was to show that the motions of the planets were
determined by a universal force, of which the force which
caused the apple to fall was one of the manifestations, and
thus to deprive the celestial motions of all the mystery in
which they had formerly been enshrouded. To his predeces-
sors, the continuous motion of the planets in circles or ellipses
was something so completely unlike any motion seen on the
surface of the earth, that they could not imagine it to be gov-
erned by the same laws ; and, knowing of no law to limit the
planetary motions, the idea of the heavenly bodies moving in
a manner which set all the laws of terrestrial motion at de-
fiance was to them in no way incredible.
The idea of a cosmical force emanating from the sun or the
earth, and causing the celestial motions, did not originate with
Newton. We have seen that even Ptolemy had an idea of a
force which, always directed towards the centre of the earth,
NEWTON. DISCOVERY OF GRAVITATION. 75
or, which was to him the same thing, towards the centre of
the universe, not only caused heavy bodies to fall, but bound
the whole universe together. Kepler also maintained that the
force which moved the planets resided in, and emanated from,
the sun. But neither Ptolemy nor Kepler could give any ade-
quate explanation of the force on the basis of laws seen in ac-
tion around us; nor was it possible to form any conception of its
true nature without a knowledge of the general laws of motion
and force, to which neither of these philosophers ever attained.
The great misapprehension which possessed the minds of
nearly all mankind till the time of Galileo was, that the con-
tinuous action of some force was necessary to keep a moving
body in motion. That Kepler himself was fully possessed of
this notion is shown by the fact that he conceived a force act-
ing only in the direction of the sun to be insufficient for keep-
ing up the planetary motions, and to require to be supplement-
ed by some force which should constantly push the planet
ahead. The latter force, he conceived, might arise from the
rotation of the sun on his axis. It is hard to say \vlio was the
first clearly to see and announce that this notion was entirely
incorrect, and that a body once set in motion, and acted on by
no force, would move forwards forever so gradually did the
great truth dawn on the minds of men. It must have been
obvious to Leonardo da Vinci ; it was implicitly contained in
Galileo's law of falling bodies, and in Huyghens's theory of
central forces; yet neither of these philosophers seems to have
clearly and completely expressed it. We can hardly be far
wrong in saying that Newton was the first who clearly laid
down this law in connection with the correlated laws which
cluster around it. The basis of Newton's discovery were these
three laws of motion :
First law. A body once set in motion and acted on by no force
will move forwards in a straight line and with a uniform velocity
forever.
Second law. If a moving body be acted on by any force, its de-
viation from the motion defined in the first law will be in the direc-
tion of the force, and proportional to it.
76 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
Third law. Action and reaction are equal, and in opposite di-
rections ; that is, whenever any one body exerts a force on a second
one, the latter exerts a similar force on the first, only in the opposite
direction.
The first of these laws is the fundamental one. The cir-
cumstance which impeded its discovery, and set man astray
for many centuries, was that there was no body on the earth's
surface acted on by no force, and therefore no example of a
body moving in a continuous straight line. Every body on
which an experiment could be made was at least acted on by
the gravitation of the earth that is, by its own weight and,
in consequence, soon fell to the earth. Other forces which im-
peded its motion were friction and the resistance of the air.
It needed research of a different kind from what the prede-
cessors of Galileo had given to physical problems to show that,
but for these forces, the body would move in a straight line
without hinderance.
We are now prepared to understand the very straightfor-
ward and simple way in which Newton ascended from what
he saw on the earth to the great principle with which his
name is associated. We see that there is a force acting all
over the earth by which all bodies are drawn towards the
earth's centre. This force extends without sensible diminu-
tion, not only to the tops of the highest buildings, but of the
highest mountains. How much higher does it extend ? Why
should it not extend to the moon ? If it does, the moon would
tend to drop to the earth, just as a stone thrown from the
hand does. Such being the case, why should not this simple
force of gravity be the force which keeps the moon in her
orbit, and prevents her from flying off in a straight line under
the iirst law of motion ? To answer this question, it was nec-
essary to calculate what force was requisite to retain the moon
in her orbit, and to compare it with gravity. It was at that
time well known to astronomers that the distance of the moon
was sixty sernidiameters of the earth. Newton at first sup-
posed the earth to be less than 7000 miles in diameter, and
consequently his calculations failed to lead him to the right
NEWTON. DISCOVERY OF GRAVITATION. 77
result. This was in 1665, when he was only twenty -three
years of age. He laid aside his calculations for nearly twenty
years, when, learning that the measures of Picard, in France,
showed the earth to be one-sixth larger than he had supposed,
he again took up the subject. He now found that the deflec-
tion of the orbit of the moon from a straight line was such as
to amount to a fall of sixteen feet in one minute, the same dis-
tance which a body falls at the surface of the earth in one
second. The distance fallen being as the square of the time,
it followed that the force of gravity at the surface of the earth
was 3600 times as great as the force which held the moon in
her orbit. This number was the square of 60, which expresses
the number of times the moon is more distant than we are
from the centre of the earth. Hence, the force which holds the
moon in her orbit is the same as that which makes a stone fall, only
diminished in the inverse square of the distance from the centre of
the earth. >.,
To the mathematician the passage from the gravitation of an
apple to that of the moon is quite simple ; but the non-mathe-
matical reader may not, at first sight, see how the moon can be
constantly falling towards the earth without ever becoming any
nearer. The following illustration will make the matter clear :
any one can understand the law of falling bodies, by which a
body falls sixteen feet the first second, three times that distance
the next, five times the third, and so on. If, in place of falling,
the body be projected horizontally, like a cannon-ball, for ex-
ample, it will fall sixteen feet out of the straight line in which
it is projected during the first second, three times that distance
the next, and so on, the same as if dropped from a state of
rest. In the annexed figure, let AB represent a portion of
the curved surface of the earth, and AD a straight line hori-
zontal at A, or the line along which an observer at A would
sight if he set a small telescope in a horizontal position.
Then, owing to the curvature of the earth, the surface will
fall away from this line of sight at the rate of about eight
inches in the first mile, twenty-four inches more in the second
mile, and so on. In five miles the fall will amount to sixteen
78 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
feet. In ten miles, in addition to this sixteen feet, three times
that amount will be added, and so on, the law being the same
ff
FIG. 21. Illustrating the fall of the moon towards the earth.
with that of a falling body. Now, let AC be a high steep
mountain, from the summit of which a cannon-ball is fired in
the horizontal direction CIS. The greater the velocity with
which the shot is fired, the farther it will go before it reaches
the ground. Suppose, at length, that we should fire it with
a velocity of five miles a second, and that it should meet with
no resistance from the air. Suppose e to be the point on the
line five miles from C. Since it would reach this point in one
second, it follows, from the law of falling bodies just cited,
that it will have dropped sixteen feet below e. But we have
just seen that the earth itself curves away sixteen feet at this
distance. Hence, the shot is no nearer the earth than when it
was fired. During the next second, while the ball would go to
E, it would fall forty-eight feet more, or sixty-four feet in all.
But here, again, the earth has still been rounding off, so the
distance DB is sixty-four feet. Hence, the ball is still no near-
er the earth than when it was fired, although it has been drop-
ping away from the line in which it was fired exactly like a
falling body. Moreover, meeting with no resistance, it is still
going on with undiminished velocity ; and, just as it has been
falling for two seconds without getting any nearer the earth,
so it can get no nearer in the third second, nor in the fourth,
nor in any subsequent second ; but the earth will constantly
curve away as fast as the ball can drop. Thus the latter will
pass clear round the earth, and come back to the first point (7,
NEWTON.DISCOVERY OF GRAVITATION. 79
from which it started, in the direction of the arrow, without
any loss of velocity. The time of revolution will be about an
hour and twenty-four minutes, and the ball will thus keep on
revolving round the earth in this space of time. In other
words, the ball will be a satellite of the earth, just like the
moon, only much nearer, and revolving much faster.
Our next step is to extend gravitation to other bodies than
the earth. The planets move around the sun as the moon
does around the earth, and must, therefore, be acted on by a
force directed towards the sun. This force can be no other
than the gravitation of the sun itself. A very simple calcula-
tion from Kepler's third law shows that the force with which
each planet thus gravitates towards the sun is inversely as the
square of the mean distance of the planet.
Only one more step is necessary. What sort of an orbit
will a planet describe if acted on by a force directed towards
the sun, and inversely as the square of the distance ? A very
simple demonstration will show that, no matter what the law
of force, if it be constantly directed towards the sun, the radi-
us-vector of the planet will sweep over equal areas in equal
times. And, conversely, it cannot sweep over equal areas in
equal times if the force acts in any other direction than that
of the sun. Hence it follows, from Kepler's second law, that
the force is directed towards the sun itself.
The problem of determining what form of orbit would be
described was one with which very few mathematicians of
that day were able to grapple. Newton succeeded in proving,
by a rigorous demonstration, that the orbit would be an el-
lipse, a parabola, or a hyperbola, according to circumstances,
having the sun in one of its foci, which, in the case of the
ellipse, was Kepler's first law. Thus, all mystery disappeared
from the celestial motions, and the planets were shown to be
simply heavy bodies moving according to the same laws we
see acting all around us, only under entirely different circum-
stances. All three of Kepler's laws were expressed in the sin-
gle law of gravitation towards the sun, with a force acting in-
versely as the square of the distance.
80 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
Very beautiful is the explanation which gravity gives of
Kepler's third law. We have seen that if we take the cubes
of the mean distances of the several planets, and divide them
by the square of the times of revolution, the quotient will be
the same for each planet of the system. If we proceed in the
same way with the satellites of Jupiter, cubing the distance
of each satellite from Jupiter, and dividing the cube by the
square of the time of revolution, the quotient will be the same
for each satellite, but will not be the same as for the planets.
This quotient, in fact, is proportional to the mass or weight of
the central body. In the case of the planets it is 1050 times
as great as in the case of the satellites of Jupiter. This shows
that the sun is 1050 times as heavy as Jupiter. We thus have
a very convenient way of "weighing" such of the planets as
have satellites, by measuring the orbits of the satellites, and
determining the times of their revolution. But the weight is
not thus expressed in tons, but only in fractions of the mass
of the sun.
The law, however, is not yet complete. The attraction be-
tween the suri and planets must, by the third law of motion,
be mutual. If the earth attracts the moon, she must, if the
law be a general one, attract the planets also, and the planets
must attract each other, and thus alter their motions around
the sun. Now, it is known from observation that the planets
do not move in exact accordance with Kepler's laws. The
final question, then, arises whether the attraction of the plan-
ets on each other fully and exactly accounts for the deviations.
This question Newton could answer only in an imperfect way,
the problem being too intricate for his mathematics. He was
able to show that the attraction of the sun would cause ine-
qualities in the motion of the moon of the same nature as
those observed, but he could not calculate their exact amount.
Still, the general correspondence of his theory with the mo-
tions of the heavens was so striking that there ought riot to
be any doubt of its truth. Very remarkable, therefore, is it
to see the French Academy of Sciences, as late as 1732 more
than forty years later awarding a prize to John Bernoulli, the
GRAVITATION OF SMALL MASSES. 81
celebrated mathematician, for a paper in which the motions
of the planets were explained on the theory of vortices. It
should not be inferred from this that that justly celebrated
body still considered that theory to be correct ; but we may
infer that they still considered it an open question whether
the theory of gravitation was correct.
To express Newton's theory with completeness, it is not suf-
ficient to say simply that the sun, earth, and planets attract
each other. Divide matter as finely as we may, we find it
still possessing the power of attraction, because it has weight
Since the earth attracts the smallest particles, they must, by
the third law of motion, attract the earth' with equal force.
Hence we conclude that the power of attraction resides, not
in the earth as a whole, but in each individual particle of the
matter composing it ; that is, the attraction of the earth upon
a stone is simply the sum total of the attractions between the
stone and all the particles composing the earth.
There is no known limit to the distance to which the at-
traction of gravitation extends. The attraction of the sun
upon the most distant known planets, Uranus and Neptune,
shows not the slightest variation from the law of Newton.
But, owing to the rapid diminution with the distance to which
the law of the inverse square gives rise when we take distances
so immense as those which separate us from the fixed stars,
the gravitation even of the sun is so small that a million
years would be required for it to produce any important ef-
fect. We are thus led to the law of universal gravitation, ex-
pressed as follows :
Every particle of matter in the universe attracts every other par-
tide with a force directly as their masses, and inversely as the
square of the distance which separates them.
2. Gravitation of Small Masses. Density of the Earth.
To make perfect the proof that gravity does really reside
in each particle of matter, it was desirable to show, by actual
experiment, that isolated masses did really attract each other,
as required by Newton's law. This experiment has been
7
82 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
made in various ways with entire success, the object, howev-
er, being not to prove the existence of the attraction, but to
measure the mean density of the earth, which admits of be-
ing thus determined. The attraction of a sphere upon a point
at its surface is shown, mathematically, to be the same as if
the entire mass of the sphere were concentrated in its centre.
It is, therefore, directly as the total amount of matter in the
sphere, that is, its weight, and inversely as the square of its
radius. Let us, then, compare the attraction of two spheres of
the same material, of which the diameter of the one is double
that of the other. The larger will have eight times the bulk,
and therefore eight times the mass, of the smaller. But
against this is the disadvantage that a particle on its surface
is twice as far from its centre as in the case of the smaller
sphere, which causes a diminution of one -fourth. Conse-
quently, it will attract such a particle with double the force
that the smaller sphere will ; that is, the attractions are direct-
ly as the diameters of the spheres, if the densities are equal.
If the densities are not equal, the attraction is proportional to
the product of the density into the diameter.
The diameter of the earth is, in round numbers, forty millions
of feet. Consequently, the attraction of a sphere of the same
mean density as the earth, but one foot in diameter, will be
40 ooo ooo part the attraction of the earth; that is, 4o O oo ooo
the weight of the body attracted. Consequently, if we should
measure the attractioii of such a sphere of lead, and find that
it was just 40 ooo ooo that of the weight of the body attracted,
we would conclude that the mean density of the earth was
equal to that of lead. But the attraction is actually found
to be nearly twice as great as this ; consequently, a leaden
sphere is nearly twice as dense as the average of the mat-
ter composing the earth. Such a determination of the density
of the earth is known as the Cavendish experiment, from the
name of the physicist who first executed it.
The method in which a task seemingly so hopeless as meas-
uring a minute force like this is accomplished is shown in the
following figures. It consists primarily of a torsion balance ;
GRAVITATION OF SMALL MASSES.
83
that is, a very light rod, e, with a weight at each end, suspend-
ed horizontally by a fine fibre of silk. In order to protect it
against currents of air, it must be completely enclosed in a
case. In Fig. 22, the balance eb is suspended from the end
FIG. 22 Baily'e apparatus for determining the density of the earth by the Cavendish ex-
periment. The left-hand ball b is hidden behind the weight W.
of the arm KF by the fine fibre of silk, FE. The weights to
be attracted are at the two ends, Ib. When thus suspend-
ed, the balance will swing round in a horizontal direction,
twisting the silk fibre, by a very small force. The attracting
masses consist of a pair of leaden balls, WW> as large as the
experimenter can procure and manage, which are supported
on the turn-table, T. In Fig. 23, a view of the apparatus from
above is given, showing the relative positions of the leaden
balls, and the suspended weights which they are to attract.
It will be seen that in the position in which the weights are
represented in the figure their attraction tends to make the
torsion balance turn in the direction opposite that of the hands
of a watch. The effect of placing the leaden balls in this posi-
tion is, that the balance begins to turn as described, and, being
carried by its momentum beyond the position of equilibrium,
at length comes to rest by the twisting of the silk thread by
which it is suspended, and then is carried part of the way
84 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
back to its original position. It makes several vibrations,
each requiring some minutes, and at length comes to rest in a
position different from its original one. The attracting balls
are then placed in the reverse position, corresponding to the
FIG. 23. View of Baily's apparatus from above.
dotted lines, so that thfcy tend to make the balance swing in
the opposite direction, and the motions of the balance are
again determined. These motions are noted by a small mi-
croscope, viewed through the enclosure in which the whole
apparatus is placed, and from these motions the attractions of
the balls can be computed.
Since this experiment was first made by Cavendish, it has
been repeated by several other physicists ; first by Professor
Eeich, of Freiberg, in 1838, and again by Francis Baily, Esq.,
of London. The latter repetition forms one of the most elab-
orate and exhaustive series of experiments ever made; we
have therefore chosen Baily's apparatus for the purpose of
illustration. The results for the mean density of the earth
obtained by these several experiments are :
Cavendish (his own result) 5.48
" (Hutton's revision).... 5.32
Reich 5.44
Baily 5.66*
* Memoirs of the Royal Astronomical Society, vol. xix.
DENSITY OF THE EARTH. 85
The same problem has been attacked by attempting to de-
termine the attraction of mountains, or portions of the crust
of the earth. In fact, the first attempt
of the sort ever made was by Maske-
lyne, Astronomer Koyal of England
from 1766 to 1811, who determined
the attraction of the mountain Sche-
hallien, in Scotland, by observing its
effect on the plumb-line. The princi-
ple of this is very clear : on whichever
eide of a steep isolated mountain we
hang a plumb - line, the attraction of Flo< 24t
the mountain will cause it to incline towards it, the direction
of gravity, or the apparent vertical, being changed from AB
(Fig. 24) to AE, and from CD to CG. The density of the
earth thus obtained was 4.71, a quantity much smaller than
that afterwards given by the leaden balls. But this method
is necessarily extremely uncertain, owing to the fact that the
earth immediately beneath the mountain will probably not be
of the same density as at a distance from it, and it is impos-
sible to determine and allow for this difference.
A third method is to determine the diminution of gravity
as we descend into the earth. We have said that the attrac-
tion of the earth upon a point outside of it is the same as if
the whole mass of the earth were concentrated in its centre.
Hence, as we rise above the surface of the earth, thus receding
from the centre, the forcfe of gravity diminishes. If this force
all resided in the centre of the earth, it would continue to in-
crease as we go below the surface. But such is not the case,
because, once inside the earth, we have matter round and
above us the attraction of which tends to lessen the gravity
towards the centre. If we could actually reach the centre,
the attraction would be nothing, because a point there would
be equally attracted in every direction. If the density of the
earth were uniform, the force of gravity would diminish with
perfect uniformity from the surface to the centre. If the den-
sity increases as we approach the centre, the diminution of
86 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
gravity will be less rapid.* A determination of the density of
the earth by the diminution of gravity in a mine was made
by Professor Airy, at tlje Harton Colliery, in Wales, in 1855.
His result was 6.56. This method is subject to uncertainty,
from the difficulty of determining the density of that portion
of the earth the attraction of which causes the gravity of bodies
in the bottom of the mine to be diminished.
3. Figure of the Earth.
If the earth did not revolve, the mutual attraction of all its
parts would tend to make it assume a spherical form. If the
cohesion of the solid parts prevented the spherical form from
being accurately assumed, nevertheless the surface of the
ocean, or of any fluid covering the earth, would assume that
form. If, now, we set such a spherical earth in rotation
around an axis, a centrifugal force will be generated towards
the equatorial regions, which will cause the ocean to move
from the poles towards the equator, so that the surface will
tend to assume the form of an oblate spheroid, the longest di-
ameter passing through the equator, and the shortest through
the poles. A computation of the centrifugal force at the
equator shows it to be -^ the force of gravity itself. Conse-
quently, the oblateness ought to be easily measurable in geo-
detic operations. Yet another result was that, in consequence
of the centrifugal force at the equator, bodies would be light-
er, and a clock regulated to northern latitudes would lose
time when taken thither.
This last result accorded with the experience of Eicher,
sent by the French Academy to Cayenne, in 1672, to make ob-
servations on Mars. After that, to deny the oblate figure of
the earth was not so much to deny Newton's theory of gravity
* The general law which regulates the force of gravity within the earth is this :
The total attraction of the shell of earth, which is outside the attracted point ex-
tending all around the globe, is nothing, while the remainder of the globe, being
a sphere with the point on its surface, attracts as if it were all concentrated at
the centre. But this presupposes that the whole earth is composed of spherical
layers, each of uniform density, which is not strictly the case.
FIGURE OF THE EARTH. 87
as to deny that mechanical forces produced their natural effect
in changing the form of the surface of the ocean. Neverthe-
less, the French astronomers long refused their assent, because
the geodetic operations they had undertaken in France seemed
to indicate that the earth was elongated rather than flattened
in the direction of the poles. The real cause of this result
was, that the distance measured in France was so short that
the effect of the earth's ellipticity was entirely masked by the
unavoidable errors of the measures, yet it long delayed the en-
tire acceptance of the Newtonian theory by the French astron-
omers. We must, however, give the latter, or, speaking of
them individually, their successors of the next generation, the
Credit of taking the most thorough measures to settle the ques-
tion. Their government sent one expedition to Peru, to meas-
ure the length of a degree of latitude at the equator, and an-
other to Lapland, to measure one as near as possible to the
pole. The result was entirely in accord with the theory of
Newton, and gave it a confirmation which had in the mean
time become entirely unnecessary.
Newton was unable to determine the exact figure which the
earth ought to assume under the influence of its own attrac-
tion and the centrifugal force of rotation, though he could see
that its meridian lines would be curves not very different from
an ellipse. The complication of the problem arises from the
fact that, as the earth changes its form in consequence of the
rotation, the direction and force of attraction at the various
points of its surface chenge also; and this, in its turn, leads
to a different figure. It was not until the middle of the last
century that the problem of the form of a rotating fluid mass
was solved, and the answer found to be an ellipsoid.
The figure of the earth is, however, not an exact ellipsoid,
there being two causes of deviation. (When we speak of the
figure or dimensions of the earth, we mean those of the ocean
as they would be if the ocean covered the entire earth.) One
cause of Deviation is that the density of the earth increases
as we approach its centre. The other cause is that there are
great irregularities in the density of its superficial portions.
88 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
In consequence of this, the real figure of the water-line is full
of small deviations, which are rendered very evident by the
refined determinations pf modern times, and which are very
troublesome to all who are engaged in exact geodetic opera-
tions.
4:. Precession of the Equinoxes.
Yet another, mysterious phenomenon which gravity com-
pletely explained was that of the precession of the equinoxes.
We have already described this as a slow change in the posi-
tion of the pole of the celestial sphere among the stars, lead-
ing to a corresponding change in the position of the celestial
equator. But the Copernican theory shows the celestial polg
to be purely fictitious, because the heavens do not revolve at
all, but the earth. The pole of the celestial sphere is only
that point of the heavens towards which the axis of the earth
points. Hence, when we come to the Copernican system, we
see that precession must be in the earth, and not in the heav-
ens, and must consist simply in a change in the direction of
the earth's axis, in virtue of which it describes a circle in the
heavens in about 25,800 years. This effect was traced by
Newton to the attraction of the sun and moon on the protu-
berance produced, as just described, by the centrifugal force
at the earth's equator. In the present case the effect is much
the same as if the earth, being itself spherical, were enveloped
by a huge ring extending round its equator. In Fig. 25 let
S
Fio. 25.
AB represent this ring revolving around the sun, S; the cen-
trifugal force at its centre, c, will then balance the attraction of
the sun at the same point*. But the point A being nearer the
sun, his attraction will be greater than at c, and the centrif u-
PRECESSION OF THE EQUINOXES. 89
gal force will be less, so that there will be a surplus force
pulling A towards the sun. At B, on the other hand, the at-
tractive force of the sun is less, and the centrifugal force is
greater. Consequently, there is a surplus force tending to
draw B from the sun. The ring being oblique towards the
sun, the effect of these surplus forces would be to make the
ring turn round at c until the line AB pointed towards the
sun. The spherical earth being fastened in the ring, as just
supposed, would very slowly be turned round with the ring, so
that its equator would be directed towards the sun. But this
effect is prevented by the earth's rotation on its axis, which
makes it act like a gyroscope, or like a spinning-top. Instead
of being brought down towards the sun, a very slow motion, at
right angles to this direction, is produced, and thus we have
the motion of precession. The nature of this motion may be
best seen by Fig. 17, where the north pole of the earth is rep-
resented as constantly inclined to the right of the observer as
the earth moves round the sun, so that the solstices are at A
and C, and the equinoxes at B and D. The effect of the at-
traction of the sun and moon on the protuberance at the
equator is, that in 6500 years the axis of the earth will incline
towards the observer of the picture, with nearly the inclina-
tion of 23 ; so that the solstices will be at B and Z>, and the
equinoxes at A and C. In 6500 years more the north pole
will be pointed towards the left instead of the right, as in the
figure; in 6500 more it \\i\\ be directed from the observer;
and, finally, at the end of a fourth period it will be once more
near its present position.
The effects we have described would not occur if the plane
of the ring, AB, passed through the sun, because then the
forces which draw A towards the sun and B from it, would act
directly against each other, and so destroy each other's effect.
Now, this is the case twice a year, namely, when the sun is on
the equator. Therefore, the motion of precession is not uni-
form, but is much greater than the average in June and De-
cember, when the sun's declination is greatest ; and is less in
March and September, when the sun is on the plane of the
90 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED.
equator. Moreover, in December the earth is nearer the sun
than in June, and the force greater, so that we have still an-
other inequality from this cause.
Precession is not produced by the sun alone. The moon is
a yet more powerful agent in producing it, its smaller mass
being more than compensated by its greater proximity to us.*
The same causes which make the action of the sun variable
make that of the moon variable also, and we have the addi-
tional cause that, owing to the revolution of the moon's node,
the inclination of the moon's orbit to the plane of the earth's
equator is subject to an oscillation having a period of 18.6
years, producing an inequality of this same period in the pre-
cession. The several inequalities in the precession which we
have described are known as nutation of the earttis axis, and
are all accurately computed and laid down in astronomical
tables.
5. The Tides.
It has been known to seafaring nations from a remote an-
tiquity that there was a singular connection between the ebb
and flow of the tides, and the diurnal motion of the moon.
Caesar's description of his passages across the English Channel
shows that he was acquainted with the law. In describing
the motion of the moon, it was shown that, owing to her revo-
lution in a monthly orbit, she rises, passes the meridian, and
sets about fifty minutes later every day. The tides ebb and
flow twice a day, but the corresponding tide is always later
than the day before, by the same amount, on the average, that
the moon is later. Hence, at any one place, the tides always
occur when the moon is near the same point of her apparent
diurnal course.
* This may need some explanation, as the attractive force of the sun upon the
earth is more than a hundred times that of the moon. The force which produces
precession is proportional to the difference of the attractions on the two sides of
the earth, or on A and B in Fig. 25, and this difference is greater in the case of
the moon's attraction. In fact, it varies inversely as the cube of the distance of
the attracting body.
THE TIDES. 91
The cause of this ebb and flow of the sea, and its relation
to the moon, was a mystery until gravitation showed it to be
due to the attraction of the moon on the waters of the ocean.
The reason why there are two tides a day will appear by
studying the case of the moon's revolution around the earth.
Let M be the rnoon, JFthe earth, and EM the line joining their
centres. Now, strictly speaking, the earth does not revolve
around the moon, any more than the moon around the earth;
but, by the principle of action and reaction, both move around
their common centre of gravity. The earth being eighty
times as heavy as the moon, this centre is situated within the
former, about three-fourths of the way from its centre to its
surface, at the point G in the figure. The manner in which
J?
A
FIG. 26. Attraction of the moon tending to produce tides.
the moon produces the tides is much the same as that in
which precession is produced. Near the centre of the earth,
E, the gentrjfiigal force of the earth's monthly rotation around
(7, and the attraction of the moon, counterbalance each other,
so that a point there has no disposition to move under the influ-
ence of these combined forces. As we pass from E to J9, the
part of the earth's surface opposite the moon, the centrifugal
force around G keeps increasing, owing to our greater distance
from the centre, while the attraction of the moon diminishes.
Hence, at D the centrifugal force predominates, and tends to
throw the waters of the ocean out, as shown in the figure.
Again, as we pass from the centre E to (7, the centrifugal force
constantly diminishes till we reach the centre of revolution,
#, when it vanishes, and, beyond (7, begins to act in the oppo-
site direction. Hence, at C the attraction of the moon and
the small centrifugal force around G both combine to throw
92 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
the waters of the ocean out in the direction of the moon.
Thus, there is a force causing the waters to rise at D and (7,
land therefore to fall at A and B; and there are, therefore, two
tides to each apparent diurnal revolution of the moon.
If the waters everywhere yielded immediately to the at-
tractive force of the moon, it would always be high -water
when the moon was on the meridian, low- water when she was
rising or setting, and high-water again when she was in the
middle of that portion of her course which is under the hori-
zon. But, owing to the inertia of the water, some time lis
necessary for so slight a force to set it in motion, and, once in
motion, it continues so after the force has ceased, and until' it
has acted some time in the opposite direction. Therefore, if
the motion of the water were unimpeded, it would ndt be
high-water until some hours after the moon had passed the
meridian. Yet another circumstance interferes with the free
motion of the water namely, the islands and continents.
These deflect the tidal wave from its course in such a way that
it may, in some cases, be many hours behind its time, or even
a whole day. Sometimes two waves may meet each other,
and raise an extraordinarily high tide. At other times the
tides may have to run up a long bay, where the motion of a
long mass of water will cause an enormous tide to be raised.
In thqJBay: of ,JFundy botlijof these causes are combined. A
tidul wave coming up the Atlantic coast meets the ocean
wave from the east, and, entering the bay with their com-
bined force, the water at the head of it is forced up to the
height of sixty or seventy feet, on the principle seen in the
hydraulic ram. J
The sun produces a tide as well as the moon, the force
which it exerts on the two sides of the earth being the same,
which, acting on the equatorial protuberance of the earth,
produces precession. The tide-producing force of the sun is
about -nj- of that of the moon. At new and full moon the two
bodies unite their forces, and the result is that the ebb and
flow are greater than the average, and we have the "spring-
tides." When the moon is in her first or third quarterTnie
INEQUALITIES IN THE MOTIONS OF THE PLANETS. 93
two forces act against each other ; the tide-producing force is
the difference of the two, the ebb and flow are less than the
average, and we have the " neap-tides."
6. Inequalities in the Motions of the Planets produced by their
Mutual Attraction.
The profoundest question growing out of the theory of
gravitation is whether all the inequalities in the motion of the
moon and planets admit of being calculated from their mut-
ual attraction. This question can be completely answered
only by actually making the calculation, and seeing whether
the resulting motion of each planet agrees exactly with that
observed. The problem of computing the motion of each
planet under the influence of the attraction of all the others
is, however, one of such complexity that no complete and per-
fect solution has ever been found. Stated in its most general
form, it is as follows : Any number of planets of which the
masses are known are projected into space, their positions, ve-
locities, and directions of motion all being given at some one
moment. They are then left to their mutual attractions, ac-
cording to the law of gravitation. It is required to find gen-
eral algebraic formulae by which their position at any time
whatever shall be determined. In this general form, no ap-
proximation to an entire solution has ever been found. But
the orbits described by the planets around the sun, and by the
satellites around their primaries, are nearly circular; and this
circumstance affords the means of computing the theoretical
place of the planet as accurately as we please, provided the
necessary labor can be bestowed upon the work.
What makes the problem so complex is that the forces
which act upon the planets are dependent on their motions,
and these again are determined by the forces which act on
them. If the planets did not attract each other at all, the
problem could be perfectly solved, because they would then
all move in ellipses, in exact accordance with Kepler's laws.
Supposing them to move in ellipses, their positions and dis-
tances at any time could be expressed in algebraic formulae,
94: SYSTEM OF THE WOELD HISTORICALLY DEVELOPED.
and their attractions on each other could be expressed in the
same way. But, owing to these very attractions, they do not
move in ellipses, and therefore the formulae thus found will
not be strictly correct. To put the difficulty into a nut-shell,
the geometer cannot strictly determine the motion of the plan-
et until he knows the attractions of all the other planets on it,
and he cannot determine these without first knowing the posi-
tion of the planet, that is, without having solved his problem.
The question how to surmount these difficulties has, to a
greater or less extent, occupied the attention of all great math-
ematicians from the time of Newton till now ; and although
complete success has not attended their efforts, yet the mar-
vellous accuracy with which sun, moon, and planets move in
their prescribed orbits, and the certainty with which the laws
of variation of those orbits through countless ages past and to
come have been laid down, show that their labor has not been
in vain. Newton could attack the problem only in a geomet-
rical way ; he laid down diagrams, and showed in what way
the forces acted in various parts of the orbits of the two plan-
ets, or in various positions of the sun and moon. He was thus
enabled to show how the attraction of the sun upon the moon
changes the orbit of the latter around the earth, and causes its
nodes to revolve from east to west, as observations had shown
them to do, and to calculate roughly one or two of the inequal-
ities in the motion of the moon in her orbit.
When the Continental mathematicians were fully convinced
of the correctness of Newton's theory, they immediately at-
tacked the problem of planetary motion with an energy and
talent which placed them ahead of the rest of the world.
They saw the entire insufficiency of Newton's geometrical
method, and the necessity of having the forces which moved
the planets expressed by the algebraic method, and, by adopt-
ing this system, were enabled to go far ahead both of New-
ton and his countrymen. The last half of the last century
was the Golden Age of mathematical astronomy. Five il-
lustrious names of this period outshine all others : Clairaut,
D'Alembert, Euler, Lagrange, and Laplace, all, except Euler,
INEQUALITIES IN THE MOTIONS OF THE PLANETS. 95
French by birth or adoption. The great works which closed
it were the " Mecanique Celeste " of Laplace, and the " M6-
canique Analytique" of Lagrange, which embody the sub-
stance of all that was then Mown of the subject, and form the
basis of nearly everything that has since been achieved. We
shall briefly mention some of the results of these works, .and
those of their successors which may interest the non- mathe-
matical reader.
Perhaps the most striking of these results is that of the sec-
ular variations of the planetary orbits. Copernicus and Kep-
ler had found, by comparing the planetary orbits as observed
by themselves with those of Ptolemy, that the forms and posi-
tions of those orbits were subject to a slow change from cen-
tury to century. The immediate successors of Newton were
able to trace this change to the mutual action of the planets,
and thus arose the important question, Will it continue for-
ever ? For, should it do so, it would end in the ultimate sub-
version of the solar system, and the destruction of all life on
our globe. The orbit of the earth, as well as of the other plan-
ets, would become so eccentric that, approaching near the sun at
one time, and receding far from it at another, the vicissitudes
of temperature would be insupportable. Lagrange, however,
was enabled to show by a mathematical demonstration that
these changes were due to a regular system of oscillations ex-
tending throughout the whole planetary system, the periods of
which were so immensely long that only a progressive motion
could be perceived during all the time that men had observed
the planets. The number of these combined oscillations is
equal to that of the planets, and their periods range from
50,000 years all the way up to 2,000,000" Great clocks of
eternity, which beat ages as ours beat seconds." In conse-
quence of these oscillations, the perihelia of the planets will
turn in every direction, and the orbits will vary in eccentricity,
but will never becoind so eccentric as to disturb the regularity
of the system. About 18,000 years ago, the eccentricity of the
earth's orbit was about .019; it has been diminishing ever
since, and will continue to diminish for 25,000 years to come,
96 SYSTEM OF THE WOELD HISTORICALLY DEVELOPED.
when it will be more nearly a circle than any orbit of our sys-
tem now is.
Some of the questions growing out of the moon's motion
are not completely settled yet. Early in the last century it
was found by Halley, from a comparison of ancient eclipses
with modern observations of the moon, that our satellite was
accelerating her motion around the earth. She was, in fact,
about a degree ahead of where she ought to have been had
her motion been uniform from the time of Hipparchus and
Ptolemy. The existence of this acceleration was fully estab-
lished in the time of Lagrange and Laplace, and was to them
a source of great perplexity, because they had conceived them-
selves to have shown mathematically that the mutual attrac-
tions of the planets or satellites could never accelerate or re-
tard their mean motions in their orbits, and thus the motion
of the moon seemed to be affected by some other force than
gravitation. After several vain attempts to account for the
motion, it was found by Laplace that, in consequence of the
secular diminution of the eccentricity of the earth's orbit, the
action of the sun on the moon was progressively changing in
such a manner as to accelerate its motion. Computing the
amount of the acceleration, he found it to be about 10 sec-
onds in a century, and its action on the moon being like that
of gravity on a falling body, the total effect would increase as
the square of the time ; that is, while in one century the moon
would be 10 seconds ahead, in two centuries she would be 40
seconds ahead, in three centuries 90 seconds, and so on.
This result agreed so well with the observed acceleration,
as determined by a comparison of ancient eclipses with mod-
ern data, that no one doubted its correctness till long after the
time of Laplace. But, in 1853, Mr. J. 0. Adams, of England,
celebrated as one of the two mathematicians who had calcu-
lated the position of Neptune from the motions of Uranus, un-
dertook to recompute the effect of the variation of the earth's
eccentricity on the mean motion of the moon. He was sur-
prised to find that, carrying his process farther than Laplace
had done, the effect in question was reduced from 10 seconds,
INEQUALITIES IN THE MOTION OF THE MOON. 97
the result of Laplace, to 6 seconds. On. the other hand, the
farther examination of ancient and modern observations
seemed to show that the acceleration as given by them was
even greater than that found by Laplace, being more nearly
12 seconds than 10 seconds ; that is, it was twice as great as
that computed by Mr. Adams from the theory of gravitation.
The announcement of this result by Mr. Adams was at^flrst
received with surprise and incredulity, and led to one of the
most remarkable of scientific discussions. Three of the great
astronomical mathematicians of the day Hansen, Plana, and
De Pontecoulant disputed the correctness of Mr. Adams's
result, and maintained that that of Laplace was not affected
with any such error as Mr. Adams had found. In fact, Hansen,
by a method entirely different from that of his predecessors,
had found a result of 12 seconds, which was yet larger than
that of Laplace. On the other hand, Delaunay, of Paris, by a
new and ingenious method of his own, found a result agreeing
exactly with Mr. Adams's. Thus, the five leading experts of
the day were divided into two parties on a purely mathemat-
ical question, and several years were required to settle the dis-
pute. The majority had on their side not only the facts of
observation, so far as they went, but the authority of Laplace;
and, if the question could have been settled either by observa-
tion or by authority, they must have carried the day. But the
problem was altogether one of pure mathematics, depending
on the computation of the effect which the gravitation of the
sun ought to produce on the motion of the moon. Both par-
ties were agreed as to the data, and but one correct result was
possible, so that an ultimate decision could be reached only by
calculation.
The decision of such a question could not long be delayed.
There was really no agreement among the majority as to what
the supposed error of Mr. Adams consisted in, or what the ex-
act mathematical expression for the moon's acceleration was.
On the other hand, Mr. Adams showed conclusively that the
methods of De Pontecoulant and Plana were fallacious; and the
more profoundly the question was examined, the more evident
98 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
it became that he was right. Mr. Cayley made a computation
of the result by a new method, and Delaunay by yet another
method, and both agreed with Mr. Adams's. Although their
antagonists never formally surrendered, they tacitly abandon-
ed the field, leaving Delaunay and Adams in its undisturbed
possession.*
Mow, however, there was a discrepancy between the theo-
retical and observed acceleration, the cause of which was to
be investigated. A possible cause happened to be already
known : the friction of the tidal wave must constantly retard
the diurnal motion of the earth on its axis, though it is impos-
sible to say how much this retardation may amount to. The
consequence would be that the day would gradually, but un-
ceasingly, increase in length, and our count of time, depend-
ing on the day, would be always getting too slow. The moon
would, therefore, appear to be going faster, when really it was
only the earth which was moving more slowly. So long as
theory had agreed with the observed acceleration of the moon,
there had been no need to invoke this cause ; but, now that
there was a discrepancy, it afforded the most plausible expla-
nation. The amount of retardation necessary to account for
the excess of the apparent acceleration over that computed is
about ten seconds in a century; that is, we must suppose that
the diurnal rotation of the earth, at the end of one hundred
years, is ten seconds behind what it would have been if it had
rotated uniformly at the rate it had at the beginning of the
century. This change is so minute that there is no way of de-
tecting it except by celestial observations ; and we are not yet
in a position to pronounce upon it with certainty.
The secular acceleration is not the only variation in the
moon's mean motion which has perplexed the mathematicians.
About the close of the last century, it was found by Laplace
that the moon had, for a number of years, been falling behind
* The writer has reason to believe it an historical fact that Hansen, on revising
his own calculations, and including terms he at first supposed to be insensible,
found that he would be led substantially to the result of Adams, although he
never made any formal publication of this fact.
INEQUALITIES IN fHE MOTION OF THE MOON. 99
her calculated place, a result which seemed to show that there
was some oscillation of long period which had been overlooked.
He made two conjectural explanations of this inequality, but
both were disproved by subsequent investigators. The ques-
tion, therefore, remained without any satisfactory solution till
1846, when Hansen announced that the attraction of Venus
produced two inequalities of long period in the moon's mo-
tion, which had been previously overlooked, and that these
fully accounted for the observed deviations of the moon's po-
sition. These terms were recomputed by Delaunay, and he
found for one of them a result agreeing very well with Han-
sen's. But the second came out so small that it could never be
detected from observations, so that here was another mathe-
matical discrepancy. There was not room, however, for much
discussion this time. Hansen himself admitted that he had
been unable to determine the amount of this inequality in a
satisfactory manner from the theory of gravitation, and had
therefore made it agree with observation, an empirical process
which a mathematician would never adopt if he could avoid
it. Even if observations were thus satisfied, doubt would still
remain. But it has lately been found that this empirical
term of Hansen's no longer agrees with observation, and that
it does not satisfactorily agree with observations before 1700.
In consequence, there are still slow changes in the motion of
our satellite which gravitation has not yet accounted for. We
are, apparently, forced to the conclusion either that the motion
of the moon is influenced by some other cause than the gravi-
tation of the other heavenly bodies, or that these inequalities
are only apparent, being really due to small changes in the
earth's axial rotation, and in the consequent length of the day.
If we admit the latter explanation, it will follow that the
earth's rotation is influenced by some other cause than the
tidal friction ; and that, instead of decreasing uniformly, it va-
ries from time to time in an irregular manner. The observed
inequalities in the motion of the moon may be fully accounted
for by changes in the earth's rotation, amounting in the ag-
gregate to half a minute or so of time changes which could
100 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
be detected by a perfect clock kept going for a number of
years. But, as it takes many years for these changes to occur,
no clock yet made will detect them.
Yet another change not -entirely accounted for on the the-
ory of gravitation: occurs in the motion of the planet Mercury.
From a discussion of all the observed transits of this planet
across the disk of the sun, Leverrier has found that the mo-
tion of the perihelion of Mercury is about 40 seconds in a
century greater than that computed from the gravitation of
the other planets. This he attributes to the action of a group
of small planets between Mercury and the sun. In this form,
however, the explanation is not entirely satisfactory. In the
first place, it seems hardly possible that such a group of plan-
ets could exist without being detected during total eclipses of
the sun, if not at other times. In the next place, granting
them to exist, they must produce a secular variation in the
position of the orbit of Mercury, whereas this variation seems
to agree exactly with theory. Leverrier explains this by sup-
posing the group of asteroids to be in the same plane with the
orbit of Mercury, but it is exceedingly improbable that such
a group would be found in this plane. There is, however, an
allied explanation which is at least worthy of consideration.
The phenomenon of the zodiacal light, to be described here-
after, shows that there is an immense disk of matter of some
kind surrounding the sun, and extending out to the orbit of
the earth, where it gradually fades away. The nature of this
matter is entirely unknown, but it may consist of a swarm of
minute particles, revolving round the sun, and reflecting its
light, like planets. If the total mass of these particles is equal
to that of a very small planet, say a tenth the mass of the
earth, it would cause the observed motion of the perihelion of
Mercury. The evidence on this subject will be considered
more fully in treating of Mercury.
With the exceptions just described, all the motions in the
solar system, so far as known, agree perfectly with the results
of the theory of gravitation. The little imperfections which
still exist in the astronomical tables seem to proceed mainly
RELATION OF THE PLANETS AND STARS. 101
from errors in the data from which the mathematician must
start in computing the motion of any planet. The time of
revolution of a planet, the eccentricity of its orbit, the position
of its perihelion, and its place in the orbit at a given time, can
none of them be computed from the theory of gravitation, but
must be derived from observations alone. If the observations
were absolutely perfect, results of any degree of accuracy
could be obtained from them; but the imperfections of all
instruments, and even of the human sight itself, prevent ob-
servations from attaining the degree of precision sought after
by the theoretical astronomer, and make the considerations of
"errors of observation" as well as of "errors of the tables"
constantly necessary.
7. Relation of the Planets to the Stars.
In Chapter I., 3, it was stated that the heavenly bodies
belong to two classes, the one comprising a vast multitude of
stars, which always preserved their relative positions, as if they
were set in a sphere of crystal, while the others moved, each
in its own orbit, according to laws which have been described.
We now know that these moving bodies, or planets, form a
sort of family by themselves, known as the Solar System.
This system consists of the sun as its centre, with a number of
primary planets revolving around it, and satellites, or second-
ary planets, revolving around them. Before the invention of
the telescope but six primary planets were known, including
the earth, and one satellite, the rnoon. By the aid of that in-
strument, two great primary planets, outside the orbit of Sat-
urn, and an immense swarm of smaller ones between the or-
bits of Mars and Jupiter, have been discovered; while the
four outer planets Jupiter, Saturn, Uranus, and Neptune
are each the centre of motion of one or more satellites. The
sun is distinguished from the planets, not only by his immense
mass, which is several hundred times that of all the other bod-
ies of his system combined, but by the fact that he shines by
his own light, while the planets and satellites are dark bodies,
shining only by reflecting the light of the sun.
102 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED.
A remarkable symmetry of structure is seen in this system,
in that all the large planets and all the satellites revolve in
orbits which are nearly circular, and, the satellites of the two
outer planets excepted, nearly in the same plane. This family
of planets are all bound together, and kept each in its respec-
tive orbit, by the law of gravitation, the action of which is of
such a nature that each planet may make countless revolutions
without the structure of the system undergoing any change.
Turning our attention from this system to the thousands of
fixed stars which stud the heavens, the first thing to be consid-
ered is their enormous distance asunder, compared with the
dimensions of the solar system, though the latter are them-
selves inconceivably great. To give an idea of the relative
distances, suppose a voyager through the celestial spaces could
travel from the sun to the outermost planet of our system in
twenty-four hours. So enormous would be his velocity, that it
would carry him across the Atlantic Ocean, from New York
to Liverpool, in less than a tenth of a second of the clock.
Starting from the sun with this velocity, he would cross the
orbits of the inner planets in rapid succession, and the outer
ones more slowly, until, at the end of a single day, he would
reach the confines of our system, crossing the orbit of Neptune.
But, though he passed eight planets the first day, he would
pass none the next, for he would have to journey eighteen or
twenty years, without diminution of speed, before he would
reach the nearest star, and would then have to continue his
journey as far again before he could reach another. All the
planets of our system would have vanished in the distance, in
the course of the first three days, and the sun would be but an
insignificant star in the firmament. The conclusion is, that
our sun is one of an enormous number of self-luminous bodies
scattered at such distances that years would be required to
traverse the space between them, even when the voyager went
at the rate we have supposed. The solar and the stellar sys-
tems thus offer us two distinct fields of inquiry, into which we
shall enter after describing the instruments and methods by
which they are investigated*
PART IL PRACTICAL ASTRONOMY.
INTRODUCTORY REMARKS.
SHOULD the reader ask what Practical Astronomy is, the
best answer might be given him by a statement of one of its
operations, showing how eminently practical our science is.
"Place an astronomer on board a ship; blindfold him ; carry
him by any route to any ocean on the globe, whether under
the tropics or in one of the frigid zones; land him on the
wildest rock that can be found; remove his bandage, and give
him a chronometer regulated to Greenwich or Washington
time, a transit instrument with the proper appliances, and the
necessary books and tables, and in a single clear night he can
tell his position within a hundred yards by observations of the
stars." This, from a utilitarian point of view, is one of the
most important operations of Practical Astronomy. When we
travel into regions little known, whether on the ocean or on
the Western plains, or when we wish to make a map of a
country, we have no way of finding our position by reference
to terrestrial objects. Our only course is to observe the heav-
ens, and find in what point the zenith of our place intersects
the celestial sphere at some moment of Greenwich or Wash-
ington time, and then the problem is at once solved. The in-
struments and methods by which this is done may also be ap-
plied to celestial measurements, and thus we have the art and
science of Practical Astronomy. To speak more generally,
Practical Astronomy consists in the description and investiga-
tion of the instruments and methods employed by astronomers
in the work of exploring and measuring the heavens, and of
104 PRACTICAL ASTRONOMY.
determining positions on the earth by observations of the heav-
enly bodies. The general construction of these instruments,
and the leading principles which underlie their use and em-
ploymejit, can be explained with the aid of a few technical
terms which we shall define as we have occasion for them.
The instruments employed by the ancients in celestial ob-
servations were so few and simple that we may dispose of
them very briefly. The only ones we need mention at pres-
ent are the gnomon and the astrolabe, or armillary sphere.
The former was little more than a large sun-dial of the sim-
plest construction, by which the altitude and position of the
sun were determined from the length and direction of the
shadow of an upright pillar. If the sun were a point to the
sight, this method would admit of considerable accuracy, be-
cause the shadow would then be sharply defined. In fact,
however, owing to the apparent size of the solar disk, the shad-
ow of any object at the distance of a few feet becomes ill-de-
fined, shading off so gradually that it is hard to say where it
ends. No approach to accuracy can therefore be attained by
the gnomon.
Notwithstanding the rudeness of this instrument, it seems
to have been the one universally employed by the ancients
for the determination of the times when the sun reached
the equinoxes and solstices. The day when the shadow was
shortest marked the summer solstice, and a comparison of
the length of the shadow with the height of the style gave,
by a trigonometric calculation, the altitude of the sun. The
day when the shadow was longest marked the winter solstice ;
and the day when the altitude of the sun was midway between
the altitudes at the two solstices marked the equinoxes. Thus
this rude instrument served the purpose of determining the
length of the year with an accuracy sufficient for the purposes
of daily life. But so immensely superior are our modern
methods in accuracy, that the astronomer can to-day compute
the position of the sun at any hour of any day 2000 years ago
with far greater accuracy than it could have been observed
with a gnomon.
INTRODUCTORY REMARKS.
105
The armillary sphere consisted of a combination of three
circles, one of which could be set in the plane of the equator
or the ecliptic; that is, an arm moving around this circle
would always point towards some part of the equator or the
ecliptic, according to the way the instrument was set. The
circle in question, being divided into degrees, served the pur-
pose of measuring the angular distance of any two bodies in
or near the ecliptic, as the sun and moon, or a star and planet.
It was by such measures that Hipparchus and Ptolemy were
able to determine the larger inequalities in the motions of the
sun, moon, and planets.
E
FIG. 27. Armillary sphere, as described by Ptolemy, and used by him and by Hipparchus.
The circle El is eet in the plane of the ecliptic, the line PP being directed towards its
pole. The circle ApMp passes through the poles of both the ecliptic and the equator.
The inner pair of circles turn on the axis PP, and are furnished with sights which may
be directed on the object to be observed. The latitude and longitude of the object are
then read off by the position of the circles.
106 PRACTICAL ASTRONOMY.
CHAPTER I.
THE TELESCOPE.
1. The First Telescopes.
THE telescope is so essential a part of every instrument in-
tended for astronomical measurement, that, apart from its own
importance, it must claim the first place in any description of
astronomical instruments. The question, Who made the first
telescope ? was long discussed, and, perhaps, will never be con-
clusively settled. If the question were merely, Who is entitled
to the credit of the invention under the rules according to
which scientific credit is now awarded ? we conceive that the
answer must be, Galileo. The first publisher of a result or
discovery, supposing such result or discovery to be honestly
his own, now takes the place of the first inventor ; and there
is little doubt that Galileo was the first one to show the world
how to make a telescope. But Galileo himself says that it
was through hearing that some one in France or Holland had
made an instrument which magnified distant objects, and
brought them nearer to the view, that he was led to inquire
-how such a result could be reached. He seems to have ob-
tained from others the idea that the instrument was possible,
but no hint as to how it was made.
As a historic fact, however, there is no serious question that
the telescope originated in Holland ; but the desire of the in-
ventors, or of the authorities, or both, to profit by the posses-
sion of an instrument of such extraordinary powers, prevented
the knowledge of its construction from spreading abroad. The
honor of being the originator has befcn claimed for three men,
each of whom has had his partisans. Their names are Metitis,
THE FIRST TELESCOPES. 107
Lipperhey, and Jansen ; the last two being spectacle-makers
in the town of Middleburg, and the first a professor of mathe-
matics.
The claims of Jansen were sustained by Peter Borelli, au-
thor of a small book* on the subject, and on the strength of
his authority Jansen was long held to be the true inventor.
His story was that Jansen had shown a telescope sixteen inches
long to Prince Maurice and the Archduke Albert, who, per-
ceiving the importance of the invention in war, offered him
money to keep it a secret. If this story be true, it would be
interesting to know on what terms Jansen was induced to sell
out his right to immortality. But Borelli's case rests on the
testimony of two or three old men who had known Jansen in
their youth, taken forty-five or fifty years after the occurrence
of the events, when Jansen had long been dead, and has there-
fore never been considered as fully proved.
About 1830, documentary evidence was discovered which
showed that Hans Lipperhey, whom Borelli claims to have
been a second inventor of the telescope, made application to
the States-general of Holland, on November 2d, 1608, for a
patent for an instrument to see with at a distance. About
the same time a similar application was made by James Me-
tius. The Government refused a patent to Lipperhey, on the
ground that the invention was already known elsewhere, but
ordered several instruments from him, and enjoined him to
keep their construction a secret.
It will be seen from this that the historic question, Who
made the first telescope? does not admit of being easily an-
swered; but that the powers of the instrument were well
known in Holland in 1608 seems to be shown by the refusal
of a patent to Lipperhey. The efforts made in that country
to keep the knowledge of the construction a secret were so
far successful that we must go from Holland to Italy to find
how that knowledge first became public property. About six
months after the petitions of Lipperhey arid Metius, Galileo
"I)e Vero TPelescopii Inventore," The Hague, 1655.
108 PRACTICAL ASTRONOMY.
was in Venice on a visit, and there received a letter from
Paris, in which the invention was mentioned. He at once set
himself to the reinvention of the instrument, and was so suc-
cessful that in a few days he exhibited a telescope magnify-
ing three times, to the astonished authorities of the city. Re-
turning to his home in Florence, he made other and larger
ones, which revealed to him the spots on the sun, the phases
of Venus, the mountains on the moon, the satellites of Jupiter,
the seeming handles of Saturn, and some of the myriads of
stars, separately invisible to the naked eye, whose combined
light forms the milky-way. But the largest of these instru-
ments magnified only about thirty times, and was so imper-
fect in construction as to be far from showing as much as
could be seen with a modern telescope of that power. The
Galilean telescope was, in fact, of the simplest construction,
consisting of the combination of a pair of lenses, of which the
larger was convex and the smaller concave, as shown in the
following figure :
FIG. 28. The Galilean telescope. The dotted lines show the course of the rays through
the lenses.
The distance of the lenses was such that the rays of light
from a star passing through the large convex lens, or object-
glass, OB, met the concave lens, _/?, before reaching the focus.
The position of this concave lens was such that the rays
should emerge from it nearly parallel. This form of tele-
scope is still used in opera -glasses, because it can be made
shorter than any other.
The improvements in the telescope since Galileo can be
best understood if we give a brief statement of the princi-
ples on which all modern telescopes are constructed. The
properties of every such instrument depend on the power pos-
sessed by a lens or by a concave mirror of forming an im-
age of any distant object in its focus. This is done in the
THE FIRST TELESCOPES. 109
case of the lens by refracting the light which passes through
it, and in the case of the mirror by reflecting back the rays
which strike it. In order to form an image of a point, it is
necessary that a portion of the rays of light which emanate
from the point shall be collected and made to converge to
some other point. For instance, in the following figure, the
FIG. 29. Formation of an image by a lens.
nearly parallel rays emanating from a distant point in the di-
rection from which the arrow is coming strike the lens, L,
and as they pass through it are bent out of their course, and
made to converge to a point, F. Continuing their course,
they diverge from F exactly as if F itself were a luminous point,
a cone of light being formed with its apex at F. An observer
placing his eye within this cone of rays, and looking at F,
will there seem to see a shining point, although really there
is nothing there. This apparent shining point is, in the lan-
guage of astronomy, called the image of the real point. The dis-
tance, OF, is called the focal length of the lens.
If, instead of a simple point, we have an object of some
apparent magnitude, as the moon, a house, or a tree, then the
light from each point of the objpct will be brought to a cor-
responding point near F. To find where this corresponding
point is, we have only to draw a line from each point of an
object through the centre of the lens, and continue it as far as
the focus. Each point of the object will then have its own
point in the image. These points, or images, will be spread
out over the surface, EFE, which is called the focal plane, and
will make up a representation, or image, of the entire object
on a small scale, but in a reversed position, exactly as in the
camera of a photographer. An eye at B within the cone of
rays will then see all or a part of the object reversed in the
focal plane. The image thus formed may be viewed by the
110 PRACTICAL ASTRONOMY.
eye as if it were a real object; and as a minute object may be
viewed by a magnifying lens, so such a lens may be used to
view and magnify the image formed in the focal plane. In
the large lens of long focus to form the image in the focal
plane, and the small lens to view and magnify this image, we
have the two essential parts of a refracting telescope. The
former lens is called the objective, or object-glass, and the latter
the eye-piece, eye-lens, or ocular.
The magnifying power of a telescope depends upon the rel-
ative focal lengths of the objective and ocular. The greater
the focal length of the former that is, the greater the distance
OF the larger the image will be ; and the less the focal length
of the eye-lens, the nearer the eye can be brought to the im-
age, and the more the latter will be magnified. The magnify-
ing power is found by dividing the focal length of the objec-
tive by that of the eye-lens. For instance, if the focal length
of an objective were 36 inches, and that of the eye-lens were
three-quarters of an inch, the quotient of these numbers would
be 48, which would be the magnifying power. If the focal
lengths of these lenses were equal, the telescope would not
magnify at all. By simply turning a telescope end for end,
and looking in at the objective, we have a reversed telescope,
which diminishes objects in the same proportion that it mag-
nifies them when not reversed.
From the foregoing rule it follows that we can, theoretical-
ly, make any telescope magnify as much as we please, by sim-
ply using a sufficiently small eye -lens. If, for instance, we
wish our telescope of 36 inches focal length to magnify 3600
times, we have only to apply to it an eye-lens of yj^ of an inch
focal length. But, in attempting to do this, a difficulty arises
with which astronomers have always had to contend, and
which has its origin in the imperfection of the image formed
by the object-glass. No lens will bring all the rays of light
to absolutely the same focus. When light passes through a
prism, the various colors are refracted unequally, red being
refracted thfe least, and violet the most. It is the same
when light is refracted by a lens, and the consequence is that
THE FIKST TELESCOPES. 113
the red rays will be brought to the farthest focus, and the vio-
let to the nearest, while the intermediate colors will be scat-
tered between. As all the light is not brought to the same
focus, it is impossible to get any accurate image of a star or
other object at which the telescope is pointed, the eye seeing
only a confused mixture of images of various colors. When
a sufficiently low magnifying power is used, the confusion will
be slight, the edges of the object being indistinct, and made
up of colored fringes. When the magnifying power is in-
creased, the object will indeed look larger, but these confused
fringes will look larger in the same proportion j so that the
observer will see no more than before. This separation of the
light in a telescope is termed chromatic aberration.
Such was the difficulty which the successors of Galileo en-
countered in attempting to improve the telescope, and which
they found it impossible to obviate. They found, however,
that they could diminish it by increasing the length of the tel-
escope, and the consequent size of the confused image. If
they made an object-glass of any fixed diameter, say six inches,
they found that the image was no more confused when the
focal length was sixty feet than when it was six, and the same
eye-lens could therefore be used in both cases. But the im-
age in the focus of the first was ten times as large as in the
second, and thus using the same eye-lens would give ten times
the magnifying power. Huyghens, Cassini, Hevelius, and oth-
er astronomers of the latter part of the seventeenth century,
made telescopes a hundred feet or upwards in length. Some
astronomers then had to dispense with a tube entirely ; the ob-
jective being mounted by Cassini on the top of a long pole,
while the ocular was moved along near the ground. Hevelius
kept his objective and ocular connected by a long rod which
replaced the tube. Very complicated and ingenious arrange-
ments were sometimes used in managing these huge instru-
ments, of which we give one specimen, taken from the work
of Blanchini, "Hesperi et Phosphori Nova Phenomena" in which
that astronomer describes his celebrated observations on the
rotation of Venus.
9
PRACTICAL ASTRONOMY.
2. The Achromatic Telescope.
A century and a half elapsed from the time when Galileo
showed his first telescope to th6 authorities of Venice before
any method of destroying the chromatic aberration of a lens
was discovered. It is to Dollond, an English optician, that the
practical construction of the achromatic telescope is due, al-
though the principle on which it depends was first published
by Euler, the German mathematician. The invention of Dol*
lond consists in the combination of a convex and concave lens
of two kinds of glass in such a way that their aberrations
shall counteract each other. How this is effected will be best
seen by taking the case of refraction by a prism, where the
same principle comes into play. The separation of the light
into its prismatic colors is here termed dispersion. Suppose,
now, that we take two prisms of glass, ABC and ACD, (Fig.
31), and join them in the manner shown in the figure. If a
Jfr-
FIG. 31. Refraction through a compound prism.
ray, SS 9 pass through the two, their actions on it will tend
to counteract each other, owing ,to the opposite directions in
which their angles are turned, and tie ray will be refracted
only by the difference of the refractive powers, and dispersed
by the difference of the dispersive powers. If the dispersive
powers are equal, there will be no dispersion at all, the ray
passing through without any separation of its colors. If the
two prisms are made of the same kind of glass, their dispersive
powers can be ma4e equal only by making them of the same
angle, and then their refractive powers will be equal also, and
the ray will pass through without any refraction. As our ob-
THE ACHEOMATIC TELESCOPE. 115
ject is to have refraction without dispersion, a combination of
prisms of the same kind of glass cannot effect it.
The problem which is now presented to ns is, Can we make
two prisms of different kinds of glass such that their disper-
sive powers shall be equal, but their refractive powers un-
equal ? The researches of Euler and Dollond answered this
question in the affirmative by showing that the dispersive
power of dense flint-glass is double that of crown-glass, while
its refractive power is nearly the same. Consequently, if we
make the prism ABO of crown glass, and the prism ACD of
flint, the angle of the flint at being half that of the crown
at A, the two opposite dispersions will neutralize each other,
and the rays will pass through without being broken up into
the separate colors. But the crown prism, with double the an-
gle, will have a more powerful refractive power than the flint ;
so that, by combining the two, we shall have refraction without
dispersion, which solves the problem.
The manner in which this principle is applied to the con-
struction of an object-glass is this : a convex lens of crown is
combined with a concave lens of flint of about half the cur-
vature. No exact rule respecting the ratio of the two curva^
tures can be given, because the refractive powers of different
specimens of glass differ greatly, and the proper ratio must,
therefore, be found by trial in each case. Having found it,
the two lenses will then have equal aberrations, but in oppo-
site directions, while the crown refracting more powerfully
than the flint, the rays will be brought to a focus at a dis-
tance a little iftore than double the focal distance of the former.
A combination of this sort is called an achromatic objective.
Some of the earlier achromatic objectives were made of three
lenses, a double concave lens of flint glass being fitted be*
tween two double convex ones of crown. At present, how*
ever, but two lenses are used, the forms of
which, as used in the smaller European tele-
scopes, and in all the telescopes of Mr. Alvan -
Clark, are shown in Fig. 32. The crown- Fia ^ ectionofan
glass is here a double convex lens, and the achromatic objective.
116 PRACTICAL ASTRONOMY.
curvatures of the two faces are equal. The curvature of the
inside face of the flint is the same as that of the crown, so
that the two faces fit accurately together, while the outer face
is nearly flat. If the dispersive power of the flint were just
double that of the crown, this face would have to be flat
to produce achromatism ; but this is not generally the case.
The fact is that, as no two specimens of glass made at dif-
ferent meltings have exactly the same refractive and disper-
sive powers, the optician, in making a telescope, must find the
ratios of dispersion of his two glasses, and then give the outer
face of his flint such a degree of curvature as to neutralize
the dispersion of his crown glass. Usually, this face will have
to be slightly concave.
When the inner faces of the glasses are thus made to fit, it
is not uncommon to join the glasses together with a transpar-
ent balsam, in order to diminish the loss of light in passing
through the glass. Whenever light falls upon transparent
glass, between three and four per cent, of it is reflected back,
and when, after passing through, it leaves again, about the
same amount is reflected back into the glass. Consequently,
about seven per cent, of the light is lost in passing through
each lens. But when the two lenses are joined with balsam
or castor-oil, the reflection from the second surface of the flint
and the first surface of the crown is greatly diminished, and a
loss of perhaps six per cent, of the light is avoided.*
As larger and more perfect achromatic telescopes were
made, a new source of aberration was discovered, no practical
method of correcting which is yet known. It arises from the
fact that flint glass, as compared with crown, disperses the blue
end of the spectrum more than the red end. If we make
* When there is no balsam, another inconvenience sometimes arises from a
double reflection of light from the inner surfaces of the glass. Of the light re-
flected back from the first surface of the crown, four per cent, is again reflected
from the second surface of the flint, and sent down to the focus of the telescope
with the direct rays. If there be the slightest misplacement of one of the lenses,
the reflected rays will come to a different focus from the direct ones, and every
bright star will seem to have a small companion star along-side of it.
THE ACHROMATIC TELESCOPE. 117
lenses of flint and crown having equal dispersive power, we
shall find that the red end is longest in the crown-glass spec-
trum, and the blue eod in the flint-glass spectrum. The con-
sequence is that when we join a pair of prisms in reversed
positions, as shown in Fig. 31, the two dispersions cannot be
made to destroy each other entirely. Instead of the refracted
light being all joined in one white ray, the spectrum will be
folded over, as it were, the red and indigo ends being joined
together, the faint violet light extending out by itself, while
the yellow and green are joined at the opposite end. This
end will, therefore, be of a yellowish green, while the other
end is purple.
The spectrum thus formed by the combination of a flint
and crown prism is termed the secondary spectrum. It is very
much shorter than the ordinary spectra formed by either the
crown or the flint glass, and a large portion of the light is con-
densed near the yellowish-green end. The effect of it is that
the refracting telescope is not perfectly achromatic, though
very nearly so. In a small telescope the defect is hardly no-
ticeable, the only drawback being that a bright star or other
object is seen surrounded by a blue or violet areole, formed by
the indigo rays thrown out by the flint-glass. If the eye-piece
is pushed in, so that the star is seen, not as a point, but as a
small disk, the centre of this disk will be green or yellow,
while the borderwill be reddish purple. But, in the immense
refractors of two-feet aperture or upwards, of which a number,
have been produced of late years, the secondary aberration
constitutes the most serious optical defect; and it is a defect
which, arising from the properties of glass itself, no art can
diminish. The difficulty may be lessened in the same way
that the chromatic aberration was lessened in the older tele-
scopes, namely, by increasing the length of the instrument.
In doing this, however, with glasses of such large size, engi-
neering difficulties are encountered which soon become insur-
mountable. We must, therefore, consider that, in the great
refractors of recent times, the limit of optical power for such
instruments has been very nearly attained.
118 PRACTICAL ASTRONOMY.
The eye-piece of a telescope, as well as its objective, con-
sists of two glasses, A single lens will, indeed, answer all
the purposes of seeing an object in the centre of the field
of view, but the field itself will be narrow and indistinct at
the edges. An additional lens, term-
ed the field - lens, is therefore placed
very near the image, for the purpose
of refracting the outer rays into the
proper direction to form a distinct
image with the aid of the eye -lens.
F '- **Sr-*~ ^ Kg- 33 such an eye-piece is rep-
resented, in which the field- lens is
between the imagef and the eye. This is called & positive
eye-piece. In the negative eye-piece the rays pass through
the field-lens just before coming to a focus, so that the image
is formed just within that lens. The positive eye -piece is
used when it is required to use a micrometer in the focal
plane ; but for mere looking the negative ocular is best. All
telescopes are supplied with a number of eye -pieces, by
changing which the magnifying power may be altered to suit
the observer.
The astronomical telescope used with these eye-pieces al-
ways shows objects upside down and right side left. This
causes no inconvenience in celestial observations. But for
viewing terrestrial objects the eye-piece must have two pairs
of lenses, the first of which forms a new image of the object
restored to its proper position, which image is viewed by the
eye -piece formed of the second pair. This combination is
called an erecting or terrestrial eye-piece.
3. The Mounting of the Telescope.
If the earth did not revolve, so that each heavenly body
would be seen hour after hour and day after day in nearly
the same direction, the problem of using great telescopes
would be much simplified. The objective and the eye-piece
could be fixed so as to point at the object, and the observer
could scrutinize it at his leisure. But actually, when we use
THE MOUNTING OF THE TELESCOPE.
119
a telescope, the diurnal revolution of the earth is apparently
increased in proportion to the magnifying power of the in-
strument; and if the latter is fixed, and a high power is used,
the object passes by with such rapidity that it is impossible to
scrutinize it. Merely to point a telescope at an object needs
many special contrivances, because, unless the pointing is ac-
curate, the object cannot be found at all. With a telescope,
and nothing more, an observer might spend half an hour in
vain efforts to point it at Sirius so accurately that the image
of the star should be brought into the field of view; and then,
before he got one good look, it might flit away and be lost
again. If this is the case with a bright star, how much harder
must it be to point at the planet Neptune, an object invisible
to the naked eye, which is not in the same direction two min-
utes in succession ! It will readily be understood that, to make
any astronomical use of a large telescope, two things are abso-
lutely necessary : first, the means of pointing the telescope at
any object, visible or invisible ; and, second, the means of mov-
ing the telescope so that
it shall follow the object
in its diurnal motion,
and thus keep its image
in the field of view. The
following are the me-
chanical contrivances by
which these objects are
effected :
The object-glass is
placed in one end of a
tube, OE) the length of
the tube being nearly
equal to the focal length
of the objective. The
eye-piece is fitted into a
projection at the lower
end of the tube, E. The
object of the tube is to
Fio. 34. Mode of mounting a telescope so as to fol-
low^ star in its diurnal motion.
120 PRACTICAL ASTRONOMY.
keep the glasses in their proper relative positions, and to pro-
tect the eye of the observer from stray light.
The tube has an axis, AB, firmly fastened to it at A near its
middle, which axis passes through a cylindrical case, (7, into
which it neatly fits, and in which it can turn. By turning the
telescope on this axis, the end E can be brought towards the
reader,- and' from him, or vice versa. This axis is called the
declination axis. The case, (7, is firmly fastened to a second
axis, DE, supported at D and E called the polar axis. This
axis points to the pole of the heavens, and, by turning it, the
whole telescope, with the part, A (7, of the case, may be brought
towards the observer, w y hile the end B will recede from him,
or vice versa. In order that the weight of the telescope may
not make it turn on the polar axis, it is balanced by a weight
at B, on the other end of the declination axis. This weight
is commonly divided, a part being carried by the axis, and a
part by the case, C. The polar axis is carried by a frame, I\
well fastened on top of a pier of masonry.
Such is the general nature of the mechanism by which an
astronomical telescope is mounted. The essential point is
that there shall be two axes one fixed, and pointing at the
pole, and one at right angles to it, and turning with it. In
the arrangement of these axes there are great differences in
the telescopes of different makers; but Fig. 34 shows what
is essential in the plan of mounting now very generally
adopted.
In the figure the telescope is represented as east of the spec-
tator, and as pointed at the pole, and therefore parallel to the
polar axis. Suppose now that the telescope be turned on the
declination axis, AB, through an arc of 90, the eye-piece, E,
being brought towards the spectator ; the object end will then
point towards the east horizon, and therefore towards the celesr
tial equator, the eye end pointing directly towards the spec-
tator. Then let the whole instrument be turned on the polar
axis, the eye-piece being brought downwards. The telescope
will then move along the celestial equator, or the path of a
star, 90 from the pole. And at whatever distance from the
THE REFLECTING TELESCOPE. 121
pole we set it by turning it on the declination axis, if we
turn it .on the polar axis it will describe a circle having the
pole at its centre ; that is, the same circle which a star follows
by its diurnal motion. So, to observe a star with the telescope,
we have first to turn it on the declination axis to the polar dis-
tance of the star, and then on the polar axis till it points at
the star. This pointing is effected by circles divided into de-
grees and minutes, not shown in the figure, by which the dis-
tance which the telescope points from the pole and from the
meridian may be found at any time.
In order that the star, when once found, may be kept in the
field of view, the telescope is furnished with a system of clock-
work, by which the polar axis is slowly turned at the rate of
one revolution a day. By starting this clock-work, the tele-
scope is made to follow the star in its diurnal motion ; or, to
speak with greater astronomical precision, as the earth turns
on its axis from west to east, the telescope turns from east to
west with the same angular velocity, so that the direction in
which it points in the heavens remains unaltered.
In order to facilitate the finding or recognition of an object,
the telescope is furnished with a " finder," T, consisting of a
small telescope of low power pointing in the same direction
with the larger one. An object can be seen in the small tel-
escope without the pointing being so accurate as is necessary
in the case of, the large one; and, when once seen, the tele-
scope is moved until the object is in the middle of the field
of view, when it is also in the field of view of the large one.
4. The Reflecting Telescope.
Two radically different kinds of telescopes are made : the
one just described, known as the refracting telescope, because
dependent on the refraction of light through glass lenses ; and
the other, the reflecting telescope, so called because it acts by
reflecting the light from a concave mirror. The name of the
first inventor of this instrument is disputed; but Sir Isaac
Newton was among the first to introduce it. It was designed
by him to avoid the difficulty growing out of the chromatic
122 PRACTICAL ASTRONOMY.
aberration of the refracting telescopes of his time, which, it
will be remembered, were not achromatic. If parallel rays of
light from a distant object fall upon a concave mirror, as shown
in Fig. 35, they will all be reflected back to a focus, F, half-
way between the centre of curvature, (7, and the surface of
FIG. 35. Speculum bringing rays to a single focus by reflection.
the mirror. In order that the rays may be all reflected to
absolutely the same focus, the section of the mirror must be
a parabola, and the point where the rays meet will be the
focus of the parabola. If the rays emanate from the various
points of an object, an image of this object will be formed
in and near the focus, as in the case of a lens. This image
is to be viewed with a magnifying eye-piece like that of a
refracting telescope. Such a mirror is called a speculum.
Here, however, a difficulty arises. The image is formed on
the same side of the mirror on which the object lies; and in or-
der that it may be seen directly, the eye of the observer and
the eye-piece must be between F and #, directly in the rays
of light emanating from the object. By placing the eye here,
not only would a great deal of the light be cut off by the body
of the observer, but the definition of the image would be great-
ly injured by the interposition of so large an object. Three
plans have been devised for evading this difficulty, which are
due, respectively, to Gregory, Newton, and Herschel.
The Herschelian Telescope. In this form of telescope the
mirror is slightly tipped, so that the image, instead of being
formed in the centre of the tube, is formed near one side of
it, as in Fig. 36. The observer can then view it without put-
ting his head inside the tube, and, therefore, without cutting
off any material portion of the light. In observation, he must
stand at the upper, or outer, end of the tube, and look into it,
his back being turned towards the object. From his looking
THE REFLECTING TELESCOPE.
123
directly into the mirror, it was also called the "front-view"
telescope. The great disadvantage of this arrangement is that
FIG. 36. Herschelian telescope.
the rays cannot be brought to an exact focus when they are
thrown so far to one side of the axis, and the injury to the
definition is so great that the front- view plan is now entirely
abandoned.
The Newtonian Telescope. The plan proposed by Sir Isaac
Newton was to place a small plane mirror just inside the fo-
cus, inclined to the telescope at an angle of 45, so as to throw
the rays to the side of the tube, where they come to a focus,
and form the image. An opening is made in the side of the
tube, just below where the image is formed in which the eye-
piece is inserted. This mirror cuts off some of the light, but
not enough to be a serious defect. An improvement which
lessens this defect has been made by Professor Henry Draper.
FIG. 37. Horizontal section of a Newtonian telescope. This section shows how the lumi-
nous rays reflected from the parabolic mirror M meet a small rectangular prism m n,
which replaces the inclined plane mirror used in the old form of Newtonian telescope.
After undergoing a total reflection from m ?i, the rays form at a & a very small image
of the heavenly body.
The inclined mirror is replaced by a small rectangular prism,
by reflection from which the image is formed very near the
prism. 'A pair of lenses are then inserted in the course of
124 PRACTICAL ASTRONOMY.
the rays, by which a second image is formed at the opening
in the side of the tube, and this second image ik viewed by
an ordinary eye -piece. The four lenses together form an
erecting eye-piece.
T/ie Gregorian Telescope. This is a form proposed by James
Gregory, who probably preceded Newton as an inventor of the
reflecting telescope. Behind the focus, F, a small concave
mirror, R y is placed, by which the light is reflected back again
FIG. 38. Section of the Gregorian telescope.
down the tube. The larger mirror, M, has an opening through
its centre, and the small mirror, -R, is so adjusted as to form a
second image of the object in this opening. This image is
then viewed by an eye-piece which is screwed into the opening.
The Cassegminian TelescopeIn principle the same with the
Gregorian, differs from it only in that the small mirror, -ft, is
convex, and is placed inside the focus, F, so that the rays are
reflected from it before reaching the focus, and no image is
formed until they reach the opening in the large mirror.
This form has an advantage over the Gregorian in that the
telescope may be made shorter, and the small mirror can be
more easily shaped to the required figure. It has therefore
entirely superseded the original Gregorian form.
Optically, these forms of telescope are inferior to the New-
tonian. But the latter is subject to the inconvenience that the
observer must be stationed at the upper end of the telescope,
where he looks into an eye-piece screwed into the side of the
tube. If the telescope is a small one, this inconvenience is
not felt ; but with large telescopes, twenty feet long or up-
wards, the case is entirely different. Means must then be pro-
vided by which the observer may be carried in the air at a
height equal to the length of the instrument, and this requires
considerable mechanism, the management of which is often
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 125
very troublesome. On the other hand, the Cassegrainian tele-
scope is pointed directly at the object to be viewed, like a re-
fractor, and the observer stands at the lower end, and looks in
at the opening through the large mirror. This is, therefore,
the most convenient form of all in management. Dne draw-
back is, that there are two mirrors to be looked after, and, un-
less the figure of both is perfect, the image will be distorted.
Another is the great size of the image, which forces the ob-
server to use either a high magnifying power, or an eye-piece
of corresponding size.* But these defects are of little impor-
tance compared with the great advantage of convenient use.
5. The Principal Great Reflecting Telescopes of Modern Times.
The reflecting telescopes made by Newton and his contem-
poraries were very small indeed, none being more than a few
inches in diameter. Though vastly more manageable than the
immensely long refractors of Huyghens, they do not seem to
have exceeded them in effectiveness. We might, therefore,
have expected the achromatic telescope to supersede the re-
flector entirely, if it could be made of large size. But in the
time of Dollond it was impossible to produce disks of flint-glass
of sufficient uniformity for a telescope more than a very few
inches in diameter. An achromatic of four inches aperture
was then considered of extraordinary size, and good ones of
more than two or three inches were rare. Consequently, for
the purpose of seeing the most faint and difficult objects, the
earlier achromatics were little, if any, better than the long
telescopes of Huyghens and Cassini. As there were no such
obstacles to the polishing of large mirrors, it was clear that it
was to the reflecting telescope that recourse must be had for
any great increase in optical power. Before the middle of
the last century the reflectors were little larger than the re-
fractors, and had not exceeded them in their optical perform-
ance. But a genius now arose who was to make a wonderful
improvement in their construction.
The Melbourne telescope has an eye-lens six inches in diameter.
126 PRACTICAL ASTRONOMY.
William Herschel, in 1766, was a church-organist and teach-
er of music of very high repute in Bath, who spent what little
leisure he had in the study of mathematics, astronomy, and
optics. By accident a Gregorian reflector two feet long? fell
into his hands, and, turning it to the heavens, he was so enrapt-
ured with the views presented to him that he sent to London
to see if he could not purchase one of greater power. The
price named being far above his means, lie resolved tcyfnake
one for himself. After many experiments with m^j^tic al-
loys, to learn which would reflect most light, airiPCmny efforts
to find the best way of polishing his rairrorJjuid giving it a
parabolic form, he produced a five-foot NewJbnian reflector,
which revealed to him a number of interest!^; qelestial phe-
nomena, though, of course, nothing that was not* already known.
Determined to aim at nothing less than the largest telescope
that could be made, he attempted vast numbers k>f mirrors of
constantly increasing size. The large majority of the individ-
ual attempts were failures but among the results of the suc-
cessful attempts were telescopes of constant!^ Increasing size,
until he attained the hitherto un though t-of apfffee of two feet,
with a length of twenty feet. With one of fiese he discov-
ered the planet Uranus. The fame of the musician-astrono-
mer reaching the ears of King George J$L, that monarch gave
him a pension of 200 per annum, $ enable him to devote
his life to a career of astronomical discovery. He now made
the greatest stride of all by completing a reflector four feet
in diameter and forty feet long, with which he discovered two
new satellites of Saturn.
Herschel now found that he had attained the limit of man-
ageable size. The observer had to be suspended perhaps thir-
ty or forty feet in the air, in a room large enough to hold, not
only himself, but all the means necessary for recording his
observations ; and this room had to follow the telescope as it
moved, to keep a star in the field. To this was added the
difficulty of keeping the mirror in proper figure, the mere
change of temperature in the night operating injuriously in
this respect. We need not, therefore, be surprised to learn
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 127
FIG. 39. Herschers great telescope.
that Herschel made very little use of this instrument, and pre-
ferred tho twenty-foot.even in scrutinizing the most difficult
objects.*
* Herschel's great instrument is still preserved, but is not mounted for use ;
indeed, it is probable that the mirror lost all its lustre long years ago. In 1839,
Sir John Herschel dismounted it, laid it in a horizontal position, and closed it up
after a family celebration inside the tube, at which the following song was sung :
THE OLD TELESCOPE.
[To be sung on New-year's-eve, 1839-'40 t by Papa, Mamma, Madame Gerlach, and all the Little
Bodies in the Tube thereof assembled.)
In the old Telescope's tube we sit,
And the shades of the past around ns flit ;
His requiem sing we with shout and din,
While the old year goes ont, and the new comes in.
Chorus. Merrily, merrily let us all sing,
And make the old telescope rattle and ring I
128 PRACTICAL ASTRONOMY.
The only immediate successor of Sir William Herschel in
the construction of great telescopes was his son, Sir John Her-
schel. But the latter made none to equal the largest of his
father's in size, and it is doubtful whether they exceeded them
in optical power.
The first decided advance on the great telescope was the
celebrated reflector of the Earl of Kosse,* at Parsonstown, Ire-
Full fifty years did he laugh at the storm,
And the blast could not shake his majestic form ;
Now prone he lies, where he once stood high,
And searched the deep heaven with his broad, bright eye.
Chorus. Merrily, merrily, etc., etc.
There are wonders no living sight has seen,
Which within this hollow have pictured been ;
Which mortal record can never recall,
And are known to Him only who made them all.
Chorus. Merrily, merrily, etc., etc.
Here watched our father the wintry night,
And his gaze has been fed with preadamite light.
His labors were lightened by sisterly love,
And, united, they strained their vision above.
Chorus. Merrily, merrily, etc., etc.
He has stretched him quietly down, at length,
To bask in the starlight his giant strength ;
And Time shall here a tough morsel find
For his steel-devouring teeth to grind.
Chorus. Merrily, merrily, etc., etc.
He will grind it at last, as grind it he must,
And its brass and its iron shall be clay and rust ;
But scathless ages shall roll away,
And nurture its frame, and its form's decay.
Chortw. Merrily, merrily, etc., etc.
A new year dawns, and the old year's past ;
God send it, a happy one like the last
(A little more sun and a little less rain
To save us from cough and rheumatic pain).
Chorus. Merrily, merrily, etc., etc.
God grant that its end this group may find
In love and in harmony fondly joined !
And that some of us, fifty years hence, once more
May make the old Telescope's echoes roar.
Chorus. Merrily, merrily, etc., etc.
* William Parsons, third Earl of Rosse, the original constructor of this tele-
scope, died in 1867. The work of the instrument is continued by his son, the pres-
ent earl.
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 131
land. The speculum of this telescope is six feet in diameter,
and about fifty-four feet focal length, and was cast in 1842.
One of the great improvements made by the Earl of Eosse
was the introduction of steam machinery for grinding and
polishing the great mirror, an instrumentality of which Her-
schel could not avail himself. The mounting of this telescope
is decidedly different from that adopted by Herschel. The
telescope is placed between two walls of masonry, which only
allow it to move about 10 on each side of the meridian, and
it turns on a pivot at the lower end of the tube. It is moved
north and south in the meridian by an ingenious combination
of chains, and may thus be set at the polar distance of any
star which it is required to observe. It is then moved slowly
towards the west, so as to follow the star, by a long screw
driven by an immense piece of clock-work. It is commonly
used as a Newtonian, the observer looking into the side of the
tube near the upper end. To enable him to reach the mouth
of the tube, various systems of movable platforms and staging
are employed. One of the platforms is suspended south of
the piers ; it extends east and west by the distance between
the walls, and may be raised by machinery so as to be directly
under the mouth of the telescope so long as the altitude of the
latter is less than 45. When the altitude is greater than this,
the observer ascends a stairway to the top of one of the walls,
where he mounts one of several sliding stages, by which he
can be carried to the mouth of the telescope, in any position
of the latter. This instrument has been employed principal-
ly in making drawings of lunar scenery and of the planets
and nebulae. Its great light-gathering power peculiarly fits it
for the latter object.
Other Reflecting Telescopes. Although no other reflector ap-
proaching the great one of the Earl of Kosse in size has ever
been made, some others are worthy of notice, on account of
their perfection of figure and the importance of the discov-
eries made with them. Among these the first place is due to
the great reflectors of Mr. William Lassell, of England. This
gentleman made a reflector of two feet aperture about the
132
PRACTICAL ASTRONOMY.
same time that Rosse constructed his immense six-foot. The
perfection of figure of the mirror was evinced by the discov-
ery of two satellites of Uranus, which had been previously un-
known and unseen, unless, as is possible, Herschel and Struve
caught glimpses of them on a few occasions. He afterwards
made one of four feet .aperture, which, in 1863, he took to the
island of Malta, where he made a series of observations on
satellites and nebulae.
FIG. 41. Mr. Lassell's great four-foot reflector, as mounted at Malta.
In 1870, a reflecting telescope four feet in diameter, on the
Cassegrainian plan, was made by Thomas Grubb & Son, of
Dublin, for the Observatory of Melbourne, Australia. This
instrument .is remarkable, not only for its perfection of figure,
but as being probably the most easily managed large reflector
ever made.
Fio. 42. The new Paris reflector.
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 135
The only American who has ever successfully undertaken
the construction of large reflecting telescopes is Professor Hen-
ry Draper, of New York, who has one of twenty-eight inches
aperture, the work of his own hands. This instrument was
mounted about 1872 in the owner's private observatory at
Hastings, on the Hudson. The mirror is not of speculum
metal, but of silvered glass, and is almost perfect in figure.
This telescope has been principally employed in making pho-
tographs of celestial objects, and can be used either as a New-
tonian or a Cassegrainian.
An attempt has recently been made at the Paris Observa-
tory to construct a reflecting telescope with a mirror of sil-
vered glass, as large as the great specula of Lassell and the
Melbourne Observatory. The diameter of the glass is 120
centimetres, a fraction of an inch short of four English feet.
It was figured, polished, and silvered at the Paris Observa-
tory by M. Martin, using the methods devised by Foucault.
It was mounted in 1875; but, unfortunately, the proper meas-
ures were not taken to prevent the glass from bending under
its own weight, and thus destroying the perfection of the
parabolic figure which M. Martin had succeeded in obtain-
ing. It was therefore taken from its tube to have this defect
of mounting remedied. The machinery for supporting and
moving this telescope being in some respects peculiar, we pre-
sent a view of it in Fig. 42, on page 134-.
6. Great Refracting Telescopes.
We have already remarked that, in the early days of the
achromatic telescope, its progress was hindered by the diffi-
culty of making large disks of flint-glass. About the begin-
ning of the present century, Guinand, a Swiss mechanic, after
a long series of experiments, discovered a method by which
he could produce disks of flint-glass of a size before unheard
of. The celebrated Fraunhofer was then commencing busi-
ness as an optician in Munich, and hearing of Gninand's suc-
cess induced him to come to Munich and commence the man-
ufacture of optical glass. Fraunhofer was a physicist of a
136
PRACTICAL ASTRONOMY.
Fio. 43 The great Melbourne reflector. T, the tube containing the great mirror near its
lower eud. Y, the small mirror throwing the light back to the eye-piece, y. C N, the
polar axis. U, the counterpoise at the end of the declination axis. Z, the clock-work
which moves the telescope by the jointed rods z e e E, and the clamp F.
high order, and made a more careful and exhaustive study of
the optical qualities of glass, and the conditions for making
the best telescope, than any one before him had ever attempted.
With the aid of the large disks furnished by Guinand, he was
able to carry the aperture of his telescopes up to ten inches.
Dying in 1826, his successors, Merz and Mahler, of Munich,
made two telescopes of fifteen inches aperture, which were
then considered most extraordinary. One of these belongs
GREAT REFRACTING TELESCOPES. 137
to the Pulkowa Observatory, in Russia ; and the other was
purchased by a subscription of citizens of Boston for the ob-
servatory of Harvard University.
No rival of the house of Fraunhofer in the construction of
great refractors arose until he had been dead thirty years, and
then it arose where least expected. In 1846, Mr. Alvan Clark
was a citizen of Cainbridgeport, Massachusetts, unknown to
fame, who made a modest livelihood by pursuing the self-
taught art of portrait -painting, and beguiled his leisure by
the construction of small telescopes. Though without the
advantage of a mathematical education, he had a perfect
knowledge of optical principles to just the extent necessary
to enable him to make and judge a telescope. Having been
led by accident to attempt the grinding of lenses, he soon pro-
duced objectives equal in quality to any ever made, and, if
he had been a citizen of any other civilized country, would
have found no difficulty in establishing a reputation. But
lie had to struggle ten years with that neglect and incre-
dulity which is the common lot of native genius in this coun-
try ; and, extraordinary as it may seem, it was by a foreigner
that his name and powers were first brought to the notice
of the astronomical world. Rev. W. K. Dawes, one of the
leading amateur astronomers of England, and an active mem-
ber of the Royal Astronomical Society, purchased an object-
glass from Mr. Clark in 1853. He found it so excellent that
in the course of the next two or three years he ordered several
others, and, finally, an entire telescope. He also made several
communications to the Astronomical Society, giving lists of
difficult double stars detected by Mr. Clark with telescopes of
his own construction, and showing that Mr. Clark's objectives
were almost perfect iri definition.
The result of this was that the American artist began to be
appreciated in his own country ; and in 1860 he received an
order from the University of Mississippi, of which Dr. F. A.
P. Barnard* was then president, for a refractor of eighteen
* Now President of Columbia College, New York City.
138 PRACTICAL ASTRONOMY.
inches aperture, which was three inches greater than the larg-
est that had then been made. Before the glass was finished,
it was made famous by the discovery of the companion of
SirinSj a success for which the Lalande medal was awarded
by the French Academy of Sciences. While this telescope
was in progress, the civil war broke out, and prevented the
party originally ordering it from taking it; but it was soon
sold to the Astronomical Society of Chicago, in which city it
was mounted in 18B3. The definition of this telescope is very
fine ; but the defects of the dome in which it is mounted, and
the want of means to support an astronomer, have greatly
interfered with its efficiency.
This instrument did not long retain its supremacy. The
firm of Thomas Cooke & Sons, of York, England, in 1870,
mounted a refractor of twenty-five inches clear aperture for
K. S. Newall, Esq., of Gateshead, England, of which the defi-
nition is very good. This instrument was intended by its
owner to be transported to some finer climate than that of
England; but this project lias not been put into execution.
In the summer of 1874: it was used by Mr. Lockyer, in a study
of Coggia's comet.
During the time that these immense telescopes were being
made on every hand, and after it was proved that telescopes of
more than two feet aperture could be made, the National Ob-
servatory of the United States had nothing better than an old
Munich refractor of nine and a half inches, such as Fraunho-
fer used to make early in the century. The attention of Con-
gress was so forcibly called to this deficiency, and to the abili-
ties of the firm of Alvan Clark & Sons to remedy it, that, in
1870, a bill was passed authorizing the superintendent of the
observatory to contract for a telescope of the largest size of
American manufacture. The aperture agreed on was twenty-
six inches, exceeding that of Mr. Newall's telescope by only
one inch. It proved extremely difficult to obtain disks of
rough glass even of this size, and more than a year elapsed
after Messrs. Chance & Co. received the order from Mr. Clark
before they were able to complete good disks of the required
MAGNIFYING POWERS OF TELESCOPES. 139
size. The glass arrived in December, 1871, and work was com-
menced in January following. The labor of polishing the
glasses was completed in October, 1872 ; the whole instrument
was completed in a year more, and was finally mounted and
ready for observation in November, 1873. The figure of this
glass is almost perfect, its principal defect arising from the
secondary aberration which is inseparable from a large re-
fractor. It has been principally employed in observing the
satellites of Saturn, Uranus, and Neptune, with the view of de-
termining the masses of these planets.
7. The Magnifying Powers of the Two Classes of Telescopes.
Questions which now very naturally arise are, Which of the
two classes of telescopes we have described is the more power-
ful, the reflector or the refractor ? and is there any limit to the
magnifying power of either ? To these questions it is difficult
to return a decided answer, because each class has its peculiar
advantages, and in each class many difficulties lie in the way
of obtaining the highest magnifying power. The fact is, that
very exaggerated ideas of the magnifying power of great tele-
scopes are entertained by the public. It will, therefore, be
instructive to state what the circumstances are which prevent
these ideas from being realized, and what the conditions are
on which the seeing power of telescopes depends.
We note, first, that when we look at a luminous point a star,
for instance without a telescope, we see it by the aid of the
cone of light which enters the pupil of the eye. The diameter
of the pupil being about one-fifth of an inch, as much light
from the star as falls on a circle of this diameter is brought to
a focus on the retina, and unless this quantity of light is suffi-
cient to be perceptible, the star will not be seen. Now, we
may liken the telescope to a " Cyclopean eye," of which the
object-glass is the pupil, because, by its aid, all the light which
falls on the object-glass is brought to a focus on the retina,
provided that a sufficiently small eye-piece is used. Of course,
we must except that portion of the light which is lost in pass-
ing through the glasses. Since the quantity of light which
140 PRACTICAL ASTRONOMY.
falls on a surface is proportional to the extent of the surface,
and therefore to the square of its diameter, it follows that,
because a telescope of one -inch clear aperture has live times
the diameter of the pupil, it will admit 25 times the light; a
six-inch will admit 900 times the light which the pupil will ;
and so with any other aperture. A star viewed with the
telescope will, therefore, appear brighter than to the naked
eye in proportion to the square of the apertiire of the in-
strument. But the star will not be magnified like a planet,
because a point is only a point, no matter how often we mul-
tiply it. It is true that a bright star in the telescope some-
times appears to have a perceptible disk; but this is owing to
various imperfections of the image, having their origin in the
air, the instrument, and the eye, all of which have the effect of
slightly scattering a portion of the light which comes from the
star. Hence, with perfect vision the apparent brilliancy of a
star will be proportional to the square of the aperture of the
telescope. It is said that Sir William Herschel, at a time when
by accident his telescope was so pointed that Sirius was about
to enter its field of view, was first apprised of what was corn-
ing by the appearance of a dawn like the morning. The light
increased rapidly, until the star itself appeared with a dazzling
splendor which reminded him of the rising sun. Indeed, .in
any good telescope of two feet aperture or upwards, Sirius is
an almost dazzling object to an eye which has rested for some
time in darkness.
But in order that all the light which falls on the object-
glass, or mirror, of a telescope may enter the pupil of the eye,
it is necessary that the magnifying power be at least equal to
the ratio which the aperture of the telescope bears to that of
the pupil. The latter is generally about one-fifth of an inch.
We must, therefore, employ a magnifying power of at least
five for every inch of aperture, or we will not get the full ad-
vantage of our object-glass. The reason of this will be appar-
ent by studying Fig. 29, p. 109, from which it will be seen that
a pencil of parallel rays falling on the object-glass, and pass-
ing through the eye-piece, will be reduced in diameter in the
MAGNIFYING POWERS OF TELESCOPES. 141
ratio of the focal distance of the objective to that of the eye-
piece, which is the same as the magnifying power. For in-
stance, if to a twenty-four-inch telescope we attached an eye-
piece so large that the magnifying power was only 48, and
pointed it at a bright star, the " emergent pencil " of rays from
the eye-piece would be half an inch in diameter, and the whole
of them could not possibly enter the pupil. By increasing the
magnifying power, we would increase the apparent brilliancy
of the star, until we reached the power 120, after which no
further increase of brilliancy would be possible.
All this supposes that we are viewing a star or other lumi-
nous point. If the object has a sensible surface, like the moon,
or a large nebula, and we consider its apparent superficial
brilliancy, the case will be in part reversed. The object will
then appear equally illuminated, with all powers below five
for each inch of aperture, but will begin to grow darker when
we pass above that limit. The reason of this is, that as we
increase the magnifying power the light is spread over a larger
surface of the retina, and is thus enfeebled. So long as our
magnifying power is below the limit, the increased quantity
of light which enters the pupil by an increase of magnifying
power just compensates for the greater surface over which it
is spread, so that the brilliancy is constant. Above the limit
of five to the inch, the surface over which the light is spread,
or the apparent magnitude of the object, still increases with
the magnifying power, but there is no increase of light ; hence,
the object looks fainter. What may at first sight seem para-
doxical is, that the degree of illumination to which we now
refer can never be increased by the use of the telescope, but,
at the best, will be the same as to the naked eye. Indeed,
as some light is necessarily lost in passing through any tele-
scope, the illumination is always less with the telescope. With
the best reflectors of speculum metal, the illumination will be
reduced to one-half, or less, if the polish is not perfect ; and
with refractors it will be reduced to seven or eight tenths. As
examples of these conclusions, the sky can never be made to
appear as bright through a telescope as to the naked eye ; the
142 PRACTICAL ASTRONOMY.
moon or a large nebula will appear more brightly illuminated
through a refracting telescope than through a reflector. If
the object is a very brilliant one, like the sun or Venus, the
loss of brilliancy by magnifying, which we have described, will
not cause any inconvenience ; but the outer planets and many
of the nebulas are so faintly illuminated that a magnifying
power many times exceeding the limit cannot be used with
advantage.
Still another cause which places a limit to the power of
telescopes is diffraction. When the " emergent pencil " is
reduced below -$ of an inch in diameter that is, when the
magnifying power is greater than 50 for every inch of aper-
ture of the object-glass the outlines of every object observed
become confused and indistinct, no matter how bright the il-
lumination or how perfect the glass may be. The effect is the
same as if we looked through a small pin-hole in a card, an
experiment which anyone may try. This effect is owing to
the diffraction of the light at the edge of the object-glass or
mirror, and it increases so rapidly with the magnifying power
that when we carry the latter above 100 to the inch, the in-
crease of indistinctness neutralizes the increase of power. If,
then, we multiply the aperture of the telescope in inches by
100, we shall have a limit beyond which there is no use in
magnifying. Indeed, it is doubtful if any real advantage is
gained beyond 60 to the inch. In a telescope of two feet (24
inches) aperture this limit would be 2400. Such a limit can-
not be set with entire exactness; but, even under the most fa-
vorable circumstances, the advantage in attempting to surpass
a power of 70 to the inch will be very slight.
The foregoing remarks apply to the most perfect telescopes,
used under the most favorable circumstances. But the best
telescope has imperfections which would nearly always pre-
vent the use of the highest magnifying powers in astronomical
observations. In the refracting telescope the principal defect
arises from the secondary aberration already explained, which,
arising from an inherent quality of the glass itself, cannot be
obviated by perfection of workmanship. In the case of the re
MAGNIFYING POWERS OF TELESCOPES. 143
fleeter, the corresponding difficulty is to keep the mirror in per-
fect figure in every position. As the telescope is moved about,
the mirror is liable to bend, through its own weight and elas-
ticity, to such an extent as greatly to injure or destroy the im-
age in the focus ; and, though this liability is greatly dimin-
ished by the plan now adopted, of supporting the mirror on a
system of levers or on an air-cushion, it is generally trouble-
some, owing to the difficulty of keeping the apparatus in order.
If we compare the refracting and reflecting telescopes which
have hitherto been made, it is easy to make a summary of
their relative advantages. If properly made and attended to,
the refractor is easy to manage, convenient in use, and al-
ways in order for working with its full power. If its greatest
defect, the secondary spectrum, cannot be diminished by skill,
neither can it be increased by the want of skill on the part of
the observer. So important is this certainty of operation, that
far the greater part of the astronomical observations of the
present century have been made with refractors, which have
always proved themselves the best working instruments. Still,
the defects arising from the secondary spectrum are inherent
in the latter, and increase with the aperture of the glass to
such an extent that no advantage can ever be gained by carry-
ing the diameter of the lenses beyond a limit which may be
somewhere between 30 and 36 inches. On the other hand,
when we consider mere seeing-power, calculation at least gives
the preference to the reflector. It is easy to compute that
Lord Rosse's " Leviathan," and the four-foot reflectors of Mr.
Lassell and of the Paris and Melbourne observatories, must
collect from two to four times the light of the great Washing-
ton telescope. But when, instead of calculation, we inquire
what difficult objects have actually been seen with the two
classes of instruments, the result seems to indicate that the
greatest refractor is equal in optical power to the great reflect-
ors. No known object seen with the latter is too faint to be
seen with the former. Why this discrepancy between the
calculated powers of the great reflectors and their actual per-
formance ? The only causes we can find for it are imperfec-
144 PRACTICAL ASTRONOMY.
tions in the figure and polish of the great mirrors. The great
refractors are substantially perfect in their workmanship ; the
reflectors do not appear to be perfect, though what the imper-
fections may be, it is impossible to say with entire certainty.
Whether the great telescope of the future shall belong to the
one class or the other must depend upon whether the imper-
fections of the reflecting mirror can be completely overcome.
Mr. Grubb, the maker of the great Melbourne telescope, thinks
he has completely succeeded in this, so as to insure a mirror
of six, seven, or even eight feet in diameter which shall be as
perfect as an object-glass. If he is right and there is no
mechanician whose opinion is entitled to greater confidence
then he has solved the problem in favor of the reflector, so far
as optical power is concerned. But so large a telescope will
be so difficult to manipulate, that we must still look to the re-
fractor as the working instrument of the future as well as of
the past; though, for the discovery and examination of very
faint objects, it may be found that the advantage will all be
on the side of the future great reflector.
The great foe to astronomical observation is one which
people seldom take into account, namely, the atmosphere.
When we look at a distant object along the surface of the
ground on a hot summer day, we notice a certain waviness of
outline, accompanied by a slight trembling. If we look with
a telescope, we shall find this waving and trembling magnified
as much as the object is, so that we can see little better with
the most powerful telescope than with the naked eye. The
cause of this appearance is the mixing of the hot air near the
ground with the cooler air above, which causes an irregular
and constantly changing refraction, and the result is that as-
tronomical observations requiring high magnifying power can
very rarely be advantageously made in the daytime. By
night the air is not so much disturbed, yet there are always
currents of air of slightly different temperatures, the crossing
and mixing of which produce the same effects in a small de-
gree. To such currents is due the twinkling of the stars;
and we may lay it down as a rule, that when a star twinkles
MAGNIFYING POWERS OF TELESCOPES. 145
the finest observation of it cannot be made with a telescope of
high power. Instead of presenting the appearance of a bright,
well-defined point, it will look like a blaze of light flaring
about in every direction, or like a pot of molten boiling metal ;
and the higher the magnifying power, the more it will flare
and boil. The amount of this atmospheric disturbance varies
greatly from night to night, but it is never entirely absent.
If no continuous disturbance of the image could be seen with
a power of 400, most astronomers would regard the night as a
very good one ; and nights on which a power of more than
1000 can be advantageously employed are quite rare, at least
in this climate.
It has sometimes been said that Sir William Herschel em-
ployed a power as high as 6000 with one of his great tele-
scopes, and, on the strength of this, that the moon may have
been brought within an apparent distance of forty miles. If
such a power was used on the moon, we must suppose, not
merely that the moon was seen as if at the distance of forty
miles, even if Herschel used his largest telescope that of
four feet aperture but that the vision would be the same as
if he had looked through a pin-hole y^ of an inch in diam-
eter, and through several yards of running water, or many
miles of air. It is doubtful whether the moon has ever been
seen with any telescope so well as it could be seen with the
naked eye at a distance of 500 miles. If such has been the
case, we may be sure that the magnifying power did not ex-
ceed 1000.
If seeing depended entirely on magnifying power, we could
not hope to gain much by further improvement of the tele-
scope, unless we should mount our instrument in some place
where there is less atmospheric disturbance than in the re-
gions where observatories have hitherto been built. It is sup-
posed that, on the mountains or table-lands in the western and
so titlT- western regions of North America, the atmosphere is
clear and steady in an extraordinary degree ; and if this sup-
position is entirely correct, a great gain to astronomy might
result from establishing an observatory in that region.
11
14:6 PRACTICAL ASTRONOMY.
CHAPTER II.
APPLICATION OF THE TELESCOPE TO CELESTIAL MEASUEEMENTS.
1. Circles of the Celestial Sphere, and their Relations to Positions
on the Earth.
IN the opening chapter of this work it was shown that all
the heavenly bodies seem to lie and move on the surface of a
sphere, in the interior of which the earth and the observer are
placed. The operations of Practical Astronomy consist large-
ly in determining the apparent positions of the heavenly bod-
ies on this sphere. These positions are defined in a way anal-
ogous to that in which the position of a city or a ship is de-
fined on the earth, namely, by a system of celestial latitudes
and longitudes. That measure which, in the heavens, corre-
sponds most nearly to terrestrial longitude is called Right As-
cension, and that which corresponds to terrestrial latitude is
called Decimation.
In Fig. 45 let the globe be the celestial sphere, represented
as if viewed from the outside by an observer situated towards
the east, though we necessarily see the actual sphere from the
centre. Pis the north pole, AB the horizon, Q the south pole
(invisible in northern latitudes because below the horizon), EF
the equator, Z the zenith. The meridian lines radiate from
the north pole in every direction, cross the equator at right
angles, and meet again at the south pole, just like meridians
on the earth. The meridian from which right ascensions are
counted, corresponding in this respect to the meridian of
Greenwich on the surface of the earth, is that which passes
through the vernal equinox, or point of crossing of the equa-
tor and ecliptic. It is called the first meridian. Three bright
CIRCLES OF THE CELESTIAL SPHERE.
147
stars near which this meridian now passes may be seen during
the autumn: they are a Andromedse and y-Pegasi, on Maps
II. and V., and /3 Cassiopeise, on Map I. The right ascension
of any star on this meridian is zero, and the right ascension
of any other star is measured by the angle which the merid-
ian passing through it makes with the first meridian, this angle
being always counted towards the east. For reasons which
will soon be explained, right ascension is generally reckoned,
not in degrees, but in hours, minutes, and seconds of time.
FIG. 44. Circles of the celestial sphere.
TJ is the ecliptic, crossing the equator at its point of inter-
section with the first meridian, and making an angle of 23%
with it. The declination of a star is its distance from the
celestial equator, whether north or south, exactly as latitude
on the earth is distance from the earth's equator. Thus, when
the right ascension and declination of a heavenly body are
given, the astronomer knows its position in the celestial sphere,
just as we know the position of a city on the earth when its
longitude and latitude are given.
It must be observed that the declinations of the heavenly
148 PRACTICAL ASTRONOMY.
bodies are, in a certain sense, referred to the earth. In as-
tronomy the equator is regarded as a plane passing through
the centre of the earth, at right angles to its axis, and dividing
it into two hemispheres. The line where this plane intersects
the surface of the earth is our terrestrial, or geographical, equa-
tor. If an observer standing on the geographical equator im-
agines this plane running east and west, and cutting into and
through the earth, where he stands he will have the astro-
nomical equator, which differs from the geographical equator
only in being the plane in which the latter is situated. Now
imagine this plane continued in every direction without limit
till it cuts the infinite celestial sphere as in Fig. 17, page 62.
The circle in which it intersects this sphere will be the celes-
tial equator. It will pass directly over the head of the ob-
server at the equator.
There is a general correspondence between latitude on the
earth and declination in the heavens, which may be seen by
referring to the same figure. Here the reader must conceive
of the earth as a globe, ep, situated in the centre of the celes-
tial sphere, EPQ8, which is infinitely larger than the earth.
The plane represented by EQ is the astronomical equator, di-
viding both the earth and the imaginary celestial sphere into
two equal hemispheres. Suppose, now, that the observer, in-
stead of standing under the equator, is standing under some
other parallel, say that of 45 N. (Being in this latitude means
that the plumb-line where he stands makes an angle of 45
with the plane of the equator.) The point over his head will
then be in 45 celestial declination. If we imagine a pencil
of infinite length rising vertically where the observer stands
so that its point shall meet the celestial sphere in his zenith,
and if, as the earth performs its diurnal revolution on its axis,
we imagine this pencil to leave its mark on the celestial sphere,
this mark will be the parallel of 45 N. declination, or a cir-
cle everywhere equally distant from the equator and from the
pole. The same observer will see the celestial pole at an eleva-
tion equal to his latitude, that is, at the angle 45. We have now
the following rules for determining the latitude of a place :
CIRCLES OF THE CELESTIAL SPHERE. 149
1. The latitude is equal to the declination of the observer's zenith.
2. It is also equal to the altitude of the pole above his horizon.
Hence, if the astronomer at any unknown station wishes to
determine his latitude, he has only to find what parallel of
declination passes through his zenith, the latter being marked
by the direction of the plumb-line, or by the perpendicular to
the surface of still water or quicksilver. If he finds a star
passing exactly in his zenith, and knows its declination, he has
his latitude at once, because it is the same as the stars dec-
lination. Practically, however, an observer will never find a
known star exactly in his zenith ; he must therefore find at
what angular distance from the zenith a known star passes his
meridian, and by adding or subtracting this distance from the
star's declination he has his latitude. If he does not know
the declination of any star, he measures the altitudes above
the horizon at which any star near the pole passes, the merid-
ian, both above the pole and under the pole. The mean of
the two gives the latitude.
Let us now consider the more complex problem of deter-
mining longitudes. If the earth did not revolve, the observ-
er's longitude would correspond to the right ascension of his
zenith in the same fixed manner that his latitude corresponds
to its declination. But, owing to the diurnal motion, there is
no such fixed correspondence. It is therefore necessary to
have some means of representing the constantly varying rela-
tion.
Wherever on the earth's surface an observer may stand, his
meridian, both terrestrial and celestial, is represented astronom-
ically by an imaginary plane similar to the plane of the equa-
tor. This plane is vertical to the observer, and passes through
the poles. It divides the earth into two hemispheres, and is
perpendicular to the equator. In Fig. 17, the celestial and ter-
restrial spheres are supposed to be cut through by this plane ;
it cuts the earth when the observer stands in a line running
north and south from pole to pole, and thus forms a terrestrial
meridian. The same plane intersects the celestial sphere in a
great circle, which, rising above the observer's horizon in the
150 PEACTICAL ASTRONOMY.
north, passes through the pole and the zenith, and disappears at
the south horizon. Two observers north and south of each
other have the same meridian ; but in different longitudes they
have different meridians, which, however, all pass through each
pole.
In consequence of the earth's diurnal motion, the meridian
of every place is constantly moving among the stars in such a
way as to make a complete revolution in 23 hours 56 minutes
4.09 seconds. The reader will find it more easy to conceive
of the celestial sphere as revolving from east to west, the ter-
restrial meridian remaining at rest; the effect being geomet-
rically the same whether we conceive of the true or the ap-
parent motion. There are, then, two sets of meridians on
the celestial sphere. One set (that represented in Fig. 45) is
fixed among the stars, and is in constant apparent motion
from east to west with the stars, while the other set is fixed
by the earth, and is apparently at rest.
As differences of latitude are measured by angles in the
heavens, so differences of terrestrial longitude are measured by
the time it takes a celestial meridian to pass from one terres-
trial meridian to another ; while differences of right ascension
are measured by the time it takes a terrestrial meridian to
move from one celestial meridian to another. Ordinary solar
time would, however, be inconvenient for this measure, because
a revolution does not take place in an exact number of hours.
A different measure, known as sidereal time, is therefore in-
troduced. The time required for one revolution of the celes-
tial 'meridian is divided into 24 hours, and these hours are
subdivided into minutes and seconds. Sidereal noon at any
place is the moment at which the vernal equinox passes the
meridian of that place, and sidereal time is counted round
from hour to 24 hours, when the equinox will have returned
to the meridian, and the count is commenced over again.
Since right ascensions in the heavens are counted from the
equinox, when it is sidereal noon, or hour, all celestial ob-
jects on the meridian of the place are in of right ascension.
At 1 hour sidereal time, the meridians have moved 15, and
CIRCLES OF THE CELESTIAL SPHERE.
151
objects now on the meridian are in 15 of right ascension.
Throughout its whole diurnal course the right ascension of the
meridian constantly increases at the rate of 15 per hour, so
that the right ascension is always found by multiplying the
sidereal time by 15. To avoid this constant multiplication, it
is customary in astronomy to express both right ascensions and
terrestrial longitudes by hours. Thus the Pleiades are said to
be in 3 hours 40 minutes right ascension, meaning that they are
on the meridian of any place at 3 hours 40 minutes sidereal
time. The longitude of the Washington Observatory from
Greenwich is 77 3'; but in astronomical language the longi-
tude is said to be 5 hours 8 minutes 12 seconds, meaning that
it takes 5 hours 8 minutes 12 seconds for any celestial merid-
ian to pass from the meridian of Greenwich to that of Wash-
ington. In consequence, when it is hour, sidereal time at
Washington, it is 5 hours 8 minutes 12 seconds sidereal time
at Greenwich.
About March 22d of every year, sidereal hour occurs very
nearly at noon. On each successive day it occurs about 3 min-
utes 56 seconds earlier, which in the course of a year brings
it back to noon again. Since the sidereal time gives the posi-
tion of the celestial sphere relatively to the meridian of any
place, it is convenient to know it in order to find what stars
are on the meridian. The following table shows the sidereal
time of mean, or ordinary civil, noon at the beginning of each
month :
January
February 20 47
March 22 37
April 40
May 2 38
June 4 40
lira. Min. Hr 8 . Min.
18 45 July 6 38
August 8 40
September 10 43
October 12 41
November 14 43
December 16 42
The sidereal time at any hour of the year may be found
from the preceding table by the following process within a
very few minutes: To the number of the preceding table
corresponding to the month add 4 minutes for each day of
the month, and the hour past noon. The sum of these num-
152 PRACTICAL ASTRONOMY.
bers, subtracting 24 hours if the sum exceeds that quantity,
will give the sidereal time. As an example, let it be required
to find the sidereal time corresponding to November 13th at
3 A.M. This is 15 hours past noon. So we have
Hra. Min.
November, from table. 14 43
13 dajsX4 52
Past noon 15 Q
Sum yo 35
Subtract 24
Sidereal time required 6 35
The sidereal time obtained in this way will seldom or never
be more than five minutes in error during the remainder of
this century. In every observatory the principal clock runs
by sidereal time, so that by looking at its face the astronomer
knows what stars are on or near the meridian. Having the
sidereal time, the stars which are on the meridian may be
found by reference to the star maps, where the right ascen-
sions are shown on the borders of the maps.
2. The Meridian Circle, and its Use.
As a complete description of the various sorts of instru-
ments used in astronomical measurements, and of the modes
of using them, would interest but a small class of readers,
we shall confine ourselves for the present to one which may
be called the fundamental instrument of modern astronomy,
the application of which has direct and immediate reference
to the circles of the celestial sphere described in the preceding-
section. This one is termed the Meridian Circle, or Transit Cir-
cle. Its essential parts are a moderate-sized telescope balanced
on an axis passing through its centre, with a system of fine
lines in the eye-piece ; one or two circles fastened on the axis,
revolving with the telescope, and having degrees and subdi-
visions cut on their outer edges; and a set of microscope mi-
crometers for measuring between the lines so cut. It is abso-
lutely necessary that every part of the instrument shall be of
the most perfect workmanship, and that the masonry piers on
THE MERIDIAN CIRCLE, AND ITS USE.
153
which it is mounted shall be as stable as it is possible to make
them.
There are many differences of detail in the construction
and mounting of different meridian circles, but they all turn
on an east and west horizontal axis, and therefore the telescope
moves only in the plane of the meridian. Fig. -45 shows the
FIG. 45. The Washington transit circle.
construction of the great circle in the Naval Observatory,
Washington. The marble piers, PP, are supported on a mass
of masonry under the floor, the bottom of which is twelve feet
below the surface of the ground. The middle of the telescope
is formed of a large cube, about fifteen inches on eaclj side.
From the east and west side of this cube extend the trunn-
ions, which are so large next the cube as to be nearly conical
in shape. The outer ends terminate in finely ground steel
pivots two and a half inches in- diameter, which rest on brass
V's firmly fixed to heavy castings set into the piers with hy-
154
PRACTICAL ASTRONOMY.
draulic cement. In order that the delicate pivots may not
be worn by the whole weight of the instrument resting on
them, the counterpoises, BB, support all the weight except 30
or 40 pounds. Near the ends of the axis are the circles, seen
edgewise, which are firmly screwed on the trunnions, and there-
fore turn with the instrument. Each pier carries four arms,
and each of these arms carries a microscope, marked m, hav-
ing in its focus the face of the circle on which the lines are
cut. These lines divide the circle into 360, and each degree
into thirty spaces of two minutes each, so that there are 10,800
lines cut on the circle. They are cut in a silver band, and are
so fine as to be invisible to the naked eye unless the light is
thrown upon them in a particular way. On each side of the
instrument, in a line with the axis, is a lamp which throws
light into the telescope so as to illuminate the field of view.
Reflecting prisms inside of the pier throw some of the light
upon those points of the circle which are viewed by the mi-
croscopes, so as to illuminate the fine divisions on the circle.
Being thus limited in its movements, an object can be seen
with the telescope only when on, or very near, the meridian.
The sole use of the instrument is to observe the exact times
at which stars cross the meridian, and their altitudes above
the horizon, or distances from the zenith, at the time of cross-
ing. To give precision to these observations, the eye-piece of
the instrument is supplied with a system of fine black lines,
usually made of spider's web, as
shown in Fig. 46. These lines
are set in the focus, so that the
image of a star crossing the me-
ridian passes over them. The
middle vertical spider line marks
the meridian ; and to find the
time of meridian transit of a star
it is only necessary to note the
moment of passage of its image
lliffll111 ^ over this line. But, to cive great-
T IG . 46. Spider lines in field of view of t t ' p CD w ** u
a meridian circle. er precision and certainty to his
THE MERIDIAN CIRCLE, AND ITS USE, 155
observation, the astronomer generally notes the moments of
transit over five or more lines, and takes the average of them
all.
Formerly the astronomer had to find the times of transit by
listening to the beat of his sidereal clock, counting the sec-
onds, and estimating the tenths of a second at which the tran-
sit over a line took place. If, for instance, he should find that
the star had not reached the line when the tick of twenty-
three seconds was heard, but crossed before the twenty-fourth
second was ticked, he would know that the time was twenty-
three seconds and some fraction, and would have to estimate
what that fraction was. A skilful observer will generally
make this estimate within a tenth of a second, and will only
on rare occasions be in error by as much as two tenths.
Shortly after the introduction of the electric-telegraph, the
American astronomers of that day introduced a much easier
method of determining the time of transit of a star, by means
of the electro-chronograph. As now made, this instrument con-
sists of a revolving cylinder, having a sheet of paper wrapped
around it, and making one revolution per minute. A pen
or other marker is connected with a telegraphic apparatus in
such a way that whenever a signal is sent to the pen it makes
a mark on the moving paper. This pen moves lengthwise of
the cylinder at the rate of about an inch in ten minutes, so
that, in consequence of the turning of the cylinder on its axis,
the marks of the pen will be along a spiral, the folds of which
are one-tenth of an inch apart. The galvanic circuit which
works the pen is connected with the sidereal clock, so that the
latter causes the pen to make a signal every second. The
same pen may be worked by a telegraphic key in the hand
of the observer. The latter, looking into his telescope, and
watching the approach of the image of the star to each wire,
makes a signal at the moment at which the star crosses. This
signal is recorded on the chronograph in its proper place
among the clock signals, from which it may be distinguished
by its greater strength. The record is permanent, and the
sheet may be taken off and read at leisure, the exact tenth of
156 PRACTICAL ASTRONOMY.
a second at which each signal was made being seen by its
position among the clock signals. The great advantages of
this method are, that great skill and practice are not required
to make good observations, and that the observer need not see
either the clock or his book, and can make a' great number of
observations in the course of the evening which may be read
off at leisure. In the case of the most skilful observers there
is no great gain in accuracy, for the reason that they can esti-
mate the fraction of a second by the eye and ear with nearly
the same accuracy that they can give the signal.
The zenith distance of the star, from which its declination
is determined, is observed by having in the reticule a hori-
zontal spider line which is made to bisect the image of the
star as it passes the meridian line. The observer then goes to
the microscopes, ascertains what lines cut on the circle are un-
der them, and what number of seconds the nearest line is from
the proper point in the field of the microscope. The mean of
the results from the four microscopes is called the circle-reading,
and can be determined within two or three tenths of a second
of arc, or even nearer, if all the apparatus is in the best order.
The minuteness of this angle may be judged by the circum-
stance that the smallest round object a keen eye can see sub-
tends an angle of about forty seconds.
We have described only the leading operations necessary in
determinations with a meridian circle. To complete the de-
termination of the position of a star as accurately as a prac-
tised observer can bisect it with the spider line is a much more
complicated matter, owing to the unavoidable errors and im-
perfections of his instrument. It is impossible to set the lat-
ter in the meridian with mathematical precision, and, if it were
done, it would not remain so a single day. When the astron-
omer comes to tenths of seconds, he has difficulties to contend
with at ev$ry step. The effects of changes of temperature
and motions of the solid earth on the foundations of his in-
strument are such as to keep it constantly changing; his clock
is so far from going right that he never attempts to set it per-
fectly right, but only determines its error from his observa-
DETERMINATION OF TERRESTRIAL LONGITUDES. 157
tions. Every observation must, therefore, be corrected for a
number of instrumental errors before the result is accurate,
an operation many times more laborious than merely making
the observation.
3. Determination of Terrestrial Longitudes.
The telegraphic mode of recording observations, described
in the last section, affords a method of determining differences
of longitude between places connected by telegraph of ex-
traordinary elegance and perfection. We have already shown
that the difference of longitude between two points is meas-
ured by the time it takes a star to move from the meridian of
the easternmost point to that of the westernmost point. We
have also explained in the last section how an observer with a
meridian circle determines and records the passage of a star
over his meridian within a tenth of a second. Since the ze-
nith distance of the star is not required in this observation, the
circles and microscopes may be dispensed with, and the instru-
ment is then much simpler in construction, and is termed a
Transit Instrument. When the observer makes a telegraphic
record of the moment of transit of a star by striking a key in
the manner described, it is evident that the electro -chrono-
graph on which his taps are recorded may be at any distance
to which the electric current can carry his signal. It may,
therefore, be in a distant city. There is no difficulty in a
Washington observer recording his observations in Cincinnati.
On this system, the mode of operation is about as follows :
the Washington and Cincinnati stations each has its transit in-
strument, its observer, and its chronograph ; but the chrono-
graphs are connected by telegraph, so that any signal made
by either observer is recorded on both chronographs. As
the Washington observer sees a star previously agreed on pass
over the lines in the focus of his instrument, h' makes sig-
nals with his telegraphic key, which are recorded both on his
own chronograph and on that of Cincinnati. When the star
readies the meridian of the latter city, the observer there sig-
nals the transit of the star in like manner, and the moment
158 PRACTICAL ASTRONOMY.
of passage over each line in the focus of his instrument is
recorded, both in Cincinnati and Washington. The elapsed
time is then found by measuring off the chronograph sheets.
The reason for having all the observations recorded on both
chronographs is that the results may be corrected for the time
it takes the electric current to pass between the two cities,
which is quite perceptible at great distances. In consequence
of this " wave-time," the Washington observation will be re-
corded a little too late at Cincinnati, so that the difference of
longitude on the Cincinnati chronograph will be too small.
The Cincinnati observation, which comes last, being recorded
a little too late at Washington, the difference of time on the
Washington chronograph will be a little too great. The mean
of the results on the two chronographs will be the correct
longitude, while their difference will be twice the time it takes
the electric current to pass between the two cities. The re-
sults thus obtained for the velocity of electricity are by no
means accordant, but the larger number do not differ very
greatly from 8000 miles per second.
A celestial meridian moves over the earth's surface at the
rate of fifteen degrees an hour, or a minute of arc in four sec-
onds of time. More precisely, this is the rate of rotation of
the earth. The length of a minute of arc in longitude de-
pends on the latitude. It is about 6000 feet, or a mile and a
sixth at the equator, but diminishes whether we go north or
south, owing to the approach of the meridians on the globular
earth, as can be seen on a globe. In the latitude of our Mid-
dle States it is about 4600 feet, so that the surface of the earth
there moves over 1150 feet a second. At the latitude of
Greenwich it is 3800 feet, so that the motion is 950 feet per
second. Two skilful astronomers, by making a great num-
ber of observations, can determine the time it takes the stars
to pass from one meridian to another within one or two hun-
dredths of a second of time, and can therefore make sure of
the difference of longitude between two distant cities within
six or eight yards.
Of late the telegraphic method of determining longitudes
DETERMINATION OF TERRESTRIAL LONGITUDES. 159
has been applied in a way a little different, though resting on
the same principles. Instead of recording the transits of stars
on both chronographs, each observer determines the error of
his clock by transits of stars of which the right ascension has
been carefully determined. Each clock is then connected with
both chronographs by means of the telegraphic lines, and made
to record its beats for the space of a few minutes only. Thus
the difference between the sidereal times at the two stations
for the same moment of absolute time can be found, and this
difference is the difference of longitude in time. A few years
ago, when the difference of longitude between points on the
Atlantic and Pacific coasts was determined by the Coast
Survey, a clock in Cambridge was made to record its beats on
a chronograph in San Francisco, and vice versa. In 1866, as
soon as the Atlantic cable had been successfully laid, Dr. B. A.
Gould went to Europe, under the auspices of the Coast Survey,
to determine the difference of longitude between Europe and
America. Owing to the astronomical importance of this de-
termination, it has since been twice repeated, once under the
direction of Mr. Dean, and, lastly, under that of Mr. Hilgard,
both of the Survey. These three campaigns gave the follow-
ing separate results for the difference of longitude between
the Royal Observatory, Greenwich, and the Naval Observato-
ry, Washington :
Hrs. Min. Sec.
Dr. Gould, 1867 5 8 12.11
Mr. Dean, 1870 5 8 12.16
Mr. Hilgard, 1872 5 8 12.09
The extreme difference, it will be seen, is less than a tenth of
a second, and would probably have been smaller but for the
numerous difficulties attendant on a determination through a
long ocean cable, which are much greater than through a land
line.
The use of the telegraph for the determination of longitude
is necessarily limited, and other methods must therefore gen-
erally be used. The general problem of determining a longi-
tude, whether that of a ship upon the ocean or of a station
160 PRACTICAL ASTRONOMY.
upon the land, depends on two requirements : (1) a knowledge
of the local time at the station, and (2) a knowledge of the
corresponding time at Greenwich, Washington, or some other
standard meridian. The difference of these two represents
the longitude.
The first determination, that of the local time, is not a diffi-
cult problem when the utmost accuracy is not required. We
have already shown how it is determined with a transit instru-
ment. But this instrument cannot be used at all at sea, and
is somewhat heavy to carry and troublesome to set up on the
land. For ships and travellers it is, therefore, much more con-
venient to use a sextant, by which the altitude of the sun or of
a star above the horizon can be measured with very little time
or trouble. To obtain the time, the observation is made, not
when the object is on the meridian, but when it is as nearly as
practicable east or west. Having found the altitude, the calcu-
lation of a spherical triangle from the data given in the Nau-
tical Almanac at once gives the local time, or the error of the
chronometer on local time.
The difficult problem is to determine the Greenwich time.
So necessary to navigation is some method of doing this, that
the British Government long had a standing offer of a reward
of 10,000 to any one who would find a successful method
of determining the longitude at sea. When the office of As-
tronomer Royal was established, which was in 1675, the duty
of the incumbent was declared to be " to apply himself with
the most exact care and diligence to the rectifying the Ta-
bles of the Motions of the Heavens, and the places of the
Fixed Stars, in order to find out the so much desired Longi-
tude at Sea for the perfecting the Art of Navigation." The
reward above referred to was ultimately divided between an
astronomer, Tobias Mayer, who made a great improvement in
the tables of the moon, and a watch-maker who improved the
marine chronometer.
The moon, making her monthly circuit of the heavens, may
be considered a sort of standard clock from which the astron-
omer can learn the Greenwich time, in whatever part of the
DETERMINATION OF TERRESTRIAL LONGITUDES. 161
world he may find himself. This he does by observing her po-
sitions among the stars. The Nautical Almanac gives the pre-
dicted distance of the moon from certain other bodies sun,
planets or bright stars for every three hours of Greenwich
time; and if the astronomer or navigator measures this dis-
tance with a sextant, he has the means of finding at what
Greenwich time the distance was equal to that measured. Un-
fortunately, however, this operation is much like that of deter-
mining the time from a clock which has nothing but an hour-
hand. The moon moves among the stars only about 13 in
a day, and her own diameter in an hour. If the observer wants
his Greenwich time within half a minute, he must determine
the position of the moon within the hundred and twentieth of
her diameter. This is about as near as an ordinary observer
at sea can come with a sextant; and yet the error would be 7^
miles of longitude. Even this degree of exactness can be ob-
tained only by having the moon's place relatively to the stars
predicted with great accuracy ; and here we meet with one of
the most complex problems of astronomy, the efforts to solve
which have already been mentioned.
In addition to the uncertainty of which we have spoken,
this method is open to the objection of being difficult, owing
to the long calculation necessary to free the measured distance
from the effects of the refraction of both bodies by the atmos-
phere, and of the parallax of the moon. On ordinary voyages
navigators prefer to trust to their chronometers. The error of
the chronometer on Greenwich time and its daily rate are
determined at ports of which the longitude is known, and the
navigator can then calculate this error on the supposition that
the chronometer gains or loses the same amount every day.
On voyages between Europe and America a good chronome-
ter will not generally deviate more than ten or fifteen seconds
from its calculated rate, so that it answers all the purposes of
navigation.
Still another observation by which Greenwich time may be
obtained to a minute in any part of the world is that of the
eclipses of Jupiter's first satellite. The Greenwich or Wash-
12
162 PRACTICAL ASTRONOMY.
ington times at which the eclipses are to occur are given in
the Nautical Almanac, so that if the traveller can succeed in
observing one, he has his Greenwich time at once, without any
calculation whatever. But the error of his observation may
be half a minute, or even an entire minute, so that this meth-
'od is not at all accurate.
Where an astronomer can fit up a portable observatory, the
observation of the moon affords him a much more accurate
longitude than it does the navigator, because he can use better
instruments. If he has a transit instrument, he determines
from observation the right ascension of the moon's limb as
she passes his meridian, and then, referring to the Nautical
Almanac, he finds at what Greenwich time the limb had this
right ascension. A single transit would, if the moon's place
were correctly predicted, give a longitude correct within six
or eight seconds of time. It is found, however, that, owing to
the errors of the moon's tables, it is necessary for the astron-
omer to wait for corresponding observations of the moon at
some standard observatory before he can be sure of this de-
gree of accuracy.
4. Mean, or Clock, Time.
We have hitherto described only sidereal time, which corre-
sponds to the diurnal revolution of the starry sphere, or, more
exactly yet, of the vernal equinox. Such a measure of time
would not answer the purposes of civil life, and even in astron-
omy its use is generally confined to the determination of right
ascensions. Solar time, regulated by the diurnal motion of the
sun, is almost universally used in astronomical observations as
well as in civil life. Formerly, solar time was made to con-
form absolutely to the motion of the sun ; that is, it was noon
when the sun was on the meridian, and the hours were those
that would be given by a sundial. If the interval between
two consecutive transits of the sun were always the same,
this measure would have been adhered to. But there are two
sources of variation in the motion of the sun in right ascen-
sion, the effect of which is to make these intervals unequal :
MEAN, OR CLOCK, TIME. 163
1. The eccentricity of the earth's orbit. In consequence
of this, as already explained, the angular motion of the ear%
round the sun is more rapid in December, when the earth is
nearest the sun, than in June, when it is farthest. The aver-
age, or mean, motion is such that the sun is 3 minutes 56 sec-
onds longer in returning to the meridian than a star is. But,
owing to the eccentricity, this motion is actually one-thirtieth
greater in December, and the same amount less in June ; so
that it varies from 3 minutes 48 seconds to 4 minutes 4 sec-
onds.
2. The principal source of the inequality referred to is the
obliquity of the ecliptic. When the sun is near the equinoxes,
his motion among the stars is oblique to the direction of the
diurnal motion; while the latter motion is directly to the
west, the former is 23^ north or south of east. If, then, sun
and star cross the meridian together one day near the equinox,
he will not be 3 minutes 56 seconds later than the star in
crossing the next day, but about one -twelfth less, or 20 sec-
onds. Therefore, at the times of the equinoxes, the solar days
are about 20 seconds shorter than the average. At the sol-
stices, the opposite effect is produced. The sun, being 23^
nearer the pole than before, the diurnal motion is slower, and
it takes the sun 20 seconds longer than the regular interval of
3 minutes 56 seconds for that motion to carry the sun over
the space which separates him from the star which culminat-
ed with him the day before. The days are then 20 seconds
longer than the average, from this cause.
So long as clocks could not be made to keep time within
20 seconds a day, these variations in the course of the sun
were not found to cause any serious inconvenience. But
when clocks began to keep time better than the sun, it be-
came necessary either to keep putting them ahead when the
sun went too fast, and behind when he went too slow, or to
give up the attempt to make them correspond. The latter
course is now universally adopted, where accurate time is re-
quired ; the standard sun for time being, not the real sun, but
a " mean sun," which is sometimes ^head of the real one, and
164: PRACTICAL ASTRONOMY.
sometimes behind it. The irregular time depending on the
motion of the true sun, or that given by a sundial, is called
Apparent Time, while that given by the mean sun, or by a
clock going at a uniform rate, is called Mean Time. The two
measures coincide four times in a year ; during two interme-
diate seasons the mean time is ahead, and during two it is
behind. The following are the dates of coincidence, and of
maximum deviation, which vary but slightly from year to
year :
February 10th True sun 15 minutes slow.
April 15th
May 14th
June 14th
July 25th ,
August 31st
November 2d ...
December 24th.
correct.
4 minutes fast.
correct.
6 minutes slow.
correct.
16 minutes fast,
correct.
When the sun is slow, it passes the meridian after mean noon,
and the clock is faster than the sundial, and vice versa. These
wide deviations are the result of the gradual accumulations of
the deviations of a few seconds from day to day, the cause of
which has just been explained. Thus, during the interval be-
tween November 2d and February 12th, the sun is constantly
falling behind the clock at an average rate of 18 or 19 seconds
a day, which, continued through 100 days, brings it from 16
minutes fast to 15 minutes slow.
This difference between the real and the mean sun is called
the Equation of Time. One of its effects, which is frequently
misunderstood, is that the interval from sunrise until noon, as
given in the almanacs, is not the same as that between noon
and sunset. This often leads to the inquiry whether the fore-
noons can be longer or shorter than the afternoons. If by
" noon " we meant the passage of the real sun across the me-
ridian, they could not; but the noon of our clocks being some-
times 15 minutes before or after noon by the sun, the former
may be half an hour nearer to sunrise than to sunset, or vice
versa.
PARALLAX IN GENERAL. 165
CHAPTEK III.
MEASURING DISTANCES IN THE HEAVENS.
1. Parallax in General.
THE determination of the distances of the heavenly bodies
from us is a much more complex problem than merely deter-
mining their apparent positions on the celestial sphere. The
latter depend entirely on the direction of the bodies from the
observer ; and two bodies which lie in the same direction will
seem to occupy the same position, no matter how much farther
one may be than the other. Notwithstanding the enormous
differences between the distances of different heavenly bodies,
there is no way of telling even which is farthest and which
nearest by mere inspection, much less can the absolute dis-
tance be determined in this way.
The distances of the heavenly bodies are generally deter-
mined from their Parallax. Parallax may be defined, in the
most general way, as the difference between the
directions of a body as seen from two different
points. Other conditions being equal, the
more distant the body, the less this differ-
ence, or the less the parallax. To show, in
the most elementary way, how difference of
direction depends on distance, suppose an
observer at to see two lights, A and J?, at
night. He cannot tell by mere inspection fo
which is the more distant. But suppose he FIG. 47. Diagram mus-
Walks Over to the point P. Both lights will trating parallax.
then seem to change their direction, moving in the direction
opposite to that in which he goes. But the light A will change
more than the light B, for, being to the right of B when the
166 PRACTICAL ASTRONOMY.
observer was at 0, it is now to the left of it. The observer
can then say with entire certainty that A is nearer than B.
As a steamship crosses the ocean, near objects at rest
change their direction rapidly, and soon flit by, while more
distant ones change very slowly. The stars are not seen to
change at all. If, however, the moon did not move, the pas-
senger would see her to have changed her apparent position
about one and a half times her diameter in consequence of
the journey. If, when the moon is near the meridian, an ob-
server could in a moment jump from New York to Liverpool,
keeping his eye fixed upon her, he would see her apparently
jump in the opposite direction about this amount.
Astronomically, the direction of an object from an observer
is determined by its position on the celestial sphere ; that is,
by its right ascension and declination. In consequence of
parallax, the declination of a body is not the same when seen
from different parts of the earth. As the moon passes the
meridian of the Cape of Good Hope, her measured declina-
tion may be a degree or more farther north than it is when
she passes the meridian of Greenwich. The determination of
the parallax of the moon was one of the objects of the British
Government in establishing an observatory at the Cape, and
so well has this object been attained that the best determina-
tions of the parallax have been made by comparing the Green-
wich and Cape observations of the moon's declination.
The determination of the distance of a celestial object from
the parallax depends on the solution of a triangle. If, in Fig.
48, we suppose the circle to represent the earth, and imagine
an observer at A to view a celes-
tial object, M, he will see it pro-
jected on the infinite celestial
sphere in the direction AM con-
tinued. Another observer at A'
will see it in the direction AM.
The difference of these directions
is the angle at M. Knowing all
FIG. 48. Diagram illustrating parallax, the angles of the quadrilateral
PAEALLAX IN GENERAL. 167
AC AM, and the length of the earth's radius, CA, the dis-
tance of the object from the three points, A, A f , and (7, can
be found by solving a simple problem of trigonometry.
The term parallax is frequently used in a more limited
sense than that in which we have just defined and elucidated
it. Instead of the difference of directions of a celestial body
seen from any two points, the astronomer generally means the
difference between the direction
of the body as it would appear
from the centre of the earth, and
the direction seen by an observer
at the surface. Thus, in Fig. 49,
an observer at the centre of thG
earth, (7, would see the object M f
in the direction CM ', while one
on the surface at P will see it in
the direction PM f . The differ-
ence of these directions 18 the FIG. -ID. Variation of parallax with the
altitude.
angle PM'C. If the observer
should be at the point where the line M f G intersects the sur-
face of the earth, there would be no parallax: in this case,
the object would be in his geocentric zenith. If, on the other
hand, the observer has the object in his horizon, so that the
line PM" is tangent to the surface of the earth, the angle
CM"P is called the horizontal parallax.' The horizontal paral-
lax is equal to the angle which the radius of the earth subtends as
seen from the object When we say that the horizontal parallax
of the moon is 57", and that of the sun 8".85, it is the same
tiling as saying that the diameter of the earth subtends twice
those angles as seen from the moon and sun respectively.
Owing to the ellipticity of the earth, all its diameters will
not subtend the same angle; the polar diameter being the
shortest of all, and the equatorial the longest. The equatorial
diameter is, therefore, adopted by astronomers as the standard
for parallax. The corresponding parallax, that is, the equato-
rial radius of the earth as seen from a celestial body, is called
the Equatorial Horizontal Parallax of that body.
168 PRACTICAL ASTUONOMY.
To measure directly the distance of the moon or any other
heavenly body, the line PC must be replaced by the line join-
ing the positions of the two observers, called the base-line.
Knowing the length and direction of this base-line, and the
difference of directions, or parallax, the distance is at once ob-
tained. If the absolute length of the base-line should not be
known, the astronomer could still determine the proportion
of the distance of the object to the base-line, leaving the final
determination of the absolute distances to be made when the
base-line could be measured.
It is not always necessary for two observers actually to sta-
tion themselves in two distant parts of the earth to determine
a parallax. If the observer 'himself could move along the
base-line, and keep up a series of observations on the object, to
see how it seemed to move in the opposite direction, he would
still be able to determine its distance. Now, every observer is
actually carried along by two such motions, because he is on
the moving earth. He is carried round the sun every year,
and round the axis of the earth every day. We have already
shown how, in consequence of the first motion, all the planets
seem to describe a series of epicycles. This apparent motion
is an effect of parallax, and by means of it the proportions of
the solar system can be determined with extreme accuracy.
The base-line is the diameter of the earth's orbit. But the
parallax in question does not help us to determine this base-
line. To find it, we must first know the distance of the earth
from the sun, and here we have no base-line but the diameter
of the earth itself. Nor can the annual motion of the earth
round the sun enable us to determine the distance of the
moon, because the latter is carried round by the same motion.
The result of the daily revolution of the observer round the
earth's axis is, that the apparent movement of the planet along
its course is not perfectly uniform : when the observer is east,
the planet is a little to the west, and vice versa. By observing
the small inequalities in the motion of the planet correspond-
ing to the rotation of the earth on its axis, we have the means
of observing its distance with the earth's diameter as a base-
PAEALLAX IN GENERAL. 169
line, and this diameter is well known. Unfortunately, how-
ever, the earth is so small compared with the distances of the
planets, that the parallax in question almost eludes measure-
ment, except in the case of those planets which are nearest
the earth, and even then it is so minute that its accurate de-
termination is one of the most difficult problems of modern
astronomy.
The principal difficulty in determining a parallax from the
revolution of the observer around the earth's axis is that the
observations are not to be made in the meridian, but when the
planet is near the horizon in the east and west. Hence the
most accurate and convenient instrument of all, the meridian
circle, cannot be used, and recourse must be had to methods
of observation subject to many sources of error.
In measuring very minute parallaxes, it may be doubtful
whether the position of the body on the celestial sphere can
be determined with the necessary accuracy. In this case re-
sort is sometimes had to relative parallax. By this is meant
the difference between the parallaxes of two bodies lying near-
ly in the same direction. The most notable example of this
is afforded by a transit of Venus over the face of the sun.
To determine the absolute direction of Venus when nearest
the earth with the accuracy required in measurements of par-
allax has not hitherto been found practicable, because the ob-
servation must be made in the daytime, when the atmosphere
is much disturbed by the rays of the sun, and also because
only a small part of the planet can then be seen. But if the
planet is actually between us and the sun, so as to be seen pro-
jected on the sun's face, the apparent distance of the planet
from the centre or from the limb of the sun may be found
with considerable accuracy. Moreover, this distance will be
different as seen from different parts of the earth's surface at
the same moment, owing to the effect of parallax ; that is, dif-
ferent observers will see Venus projected on different parts of
the sun's face. But the change thus observed will be only
that due to the difference of the parallaxes of the two bodies;
while both change their directions, that nearest the observer
170 PRACTICAL ASTRONOMY.
changes the more, and thus seems to move past the other, ex-
actly as in the diagram of the lights.
It may be asked how the parallax of the sun can be found
from observations of the transit of Venus, if such observations
show only the difference between the parallax of Venus and
that of the sun. We reply that the ratio of the parallaxes of
the two bodies is known with great precision from the propor-
tions of the system. We have already shown that these pro-
portions are known with great accuracy from the third law of
Kepler, and from the annual parallax produced by the revolu-
tion of the earth round the sun. It is thus known that at the
time of the transit of Venus, in 1874, the sun was nearly four
times the distance of Venus, or, more exactly, that he was
3.783 times as far as that planet. Consequently, the parallax
of Venus was then 3.783 times that of the sun. The differ-
ence of the parallaxes, that is, the relative parallax, must then
have been 2.783 times the sun's parallax. Consequently, we
have only to divide the relative parallax found from the ob-
servations by 2.783 to have the parallax of the sun itself.
Still another parallax, seldom applied except to the fixed
stars, is the Annual Parallax. This is the parallax already ex-
plained as due to the annual revolution of the earth in its or-
bit. It is equal to the angle subtended by the line joining the
earth and sun, as seen from the star or other body. When we
say that the annual parallax of a star is one second of arc, it is
the same thing as saying that at the star the line joining the
earth and sun would subtend an apparent angle of one sec-
ond, or that the diameter of the earth's orbit would appear un-
der an angle of two seconds.
It will be seen that the measurement of the heavens involves
two separate operations. The one consists in the determina-
tion of the distance between the earth and the sun, which is
made to depend on the solar parallax, or the angle which the
semidiameter of the earth subtends as seen from the sun, and
which is the unit of distance in celestial measurements. The
other consists in the determination of the distances of the stars
and planets in terms of this unit, which gives what we may
MEASURES OF THE DISTANCE OF THE SUN. 171
call the proportions of the universe. Knowing this proportion,
we can determine all the distances of the universe when the
length of our unit or the distance of the sun is known, but not
before. The determination of this distance is, therefore, one
of the capital problems of astronomy, as well as one of the most
difficult, to the solution of which both ancient and modern as-
tronomers have devoted many efforts.
2. Measures of the Distance of the Sun.
We have already shown, in describing the phases of the
moon, how Aristarchus attempted to determine the distance
of the sun by measuring the angle between the sun and the
moon, when the latter appeared half illuminated. From this
measure, the sun was supposed to be twenty times as far as
the moon ; a result which arose solely from the accidental er-
rors of the observations.
Another method of attacking the problem was applied by
Ptolemy, but is probably due to Ilipparchus. It rests on a
very ingenious geometrical construction founded on the prin-
ciple that the more distant the sun, the narrower will be the
shadow of the earth at the distance of the moon. The actual
diameter was determined from an ingenious combination of
two partial eclipses of the moon, in one of which half of the
moon was south of the limit of the shadow, while in the other
three-fourths of her diameter was north of the limit ; that is,
one fourth of the moon's disk was eclipsed. It was thus found
that the moon's apparent diameter was 31-J', and the appar-
ent diameter of the shadow 40f '. The former number was
certainly remarkably near the truth. From this it was con-
cluded tli at the sun's parallax was 3' II", and his distance 1210
radii of the earth. This result was an entire mistake, arising
from the uncertainty of any measure of so small an angle,
lieally, the parallax is so minute as to elude all measurement
with any instrument in which the vision is not assisted by the
use of a telescope. Yet this result continued to figure in as-
tronomy through the fourteen centuries during which the"-4Z-
magest" of Ptolemy was the supreme authority, without, appar-
172 PRACTICAL ASTRONOMY.
ently, any astronomer being bold enough to seriously under-
take its revision.
Kepler and his contemporaries saw clearly that this distance
must be far too small ; but all their estimates fell short of the
truth. Wendell came nearest the truth, as he claimed that
the parallax could not exceed 15". But the best estimate of
the seventeenth century was made by Huyghens,* the reason
why it was the best being that it was not founded on any
attempt to measure the parallax itself, which was then real-
ly incapable of measurement, but on the probable magnitude
of the earth as a planet. The parallax of the sun is, as al-
ready explained, the apparent semidiarneter of the earth as
seen from the sun. If, then, we can find what size the earth
would appear if seen from the sun, the problem would at once
be solved. The apparent magnitudes of the planets, as seen
from the earth, are found by direct measurement with the
telescope. The proportions of the solar system being known,
as already explained, it is very easy to determine the magni-
tudes of all the planets as seen from the sun, the earth alone
exeepted. The idea of Huyghens was that the earth, being a
planet, its magnitude would probably be somewhere near that
of the average of the two planets on each side of it, namely,
Venus and Mars. So, taking the mean of the diameters of
Venus and Mars, and supposing this to represent the diameter
of the earth, he found the angle which the semidiameter of
the supposed earth would subtend from the sun, which would
be the solar parallax.
Although this method may look like a happy mode of
guessing, it was much more reliable than any which had be-
fore been applied, for the reason that, in supposing the mag-
nitude of the earth to be between those of Venus and Mars,
he was likely to be nearer the truth than any measure of an
angle entirely invisible to the naked eye would be. And, by
a lucky accident, Huyghens's estimate was nearer the truth
than any determinations made previous to the transit of Ve-
* At the close of his "Systema Saturnium."
MEASURES OF THE DISTANCE OF THE SUN. 173
nus in 1769, his result for the distance of the sun being 25,086
semidianieters of the earth, or 99 millions of miles. If he
had used the correct diameters of Venus and Mars, he would
have been farther from the truth, because the earth is consid-
erably larger than the mean of Venus and Mars in fact, rath-
er larger than Venus herself. But the imperfect telescopes
used by Huyghens showed the planets larger than they really
were, so that when he took the mean diameter of these planets
as they appeared in his telescopes, he just hit the diameter of
the earth, and reached the true solution of the problem.
We now come to the modern methods of measuring the
parallax of the sun. These consist, not in measuring this par-
allax directly, because this cannot even now be done with any
accuracy, but in measuring the parallax of one of the planets
Venus and Mars when nearest the earth. These planets pass-
ing from time to time much nearer to us than the sun does,
have then a much larger parallax, and one which can easily
be measured. Having the parallax of the planet, that of the
sun is determined from the known proportion between their
respective distances.
The first application of this method was made by the French
astronomers to the planet Mars. In 1671 they sent an ex-
pedition to the colony of Cayenne, in South America, which
made observations of the position of Mars during the opposi-
tion of 1672, while corresponding observations were made at
the Paris Observatory. The difference of the two apparent
positions, reduced to the same moment, gave the parallax of
Mars. From a discussion of these observations, Cassini con-
cluded the parallax of the sun to be 9".5, corresponding to a
distance of the sun equal to 21,600 semidiameters of the earth.
This distance was as much too small as Huyghens's was too
great, so that, as we now know, no real improvement was
made. Still, the data were much more certain than those on
which the estimate of Huyghens was made, and for a hundred
years it was generally considered that the sun's parallax was
about 10", and his distance between 80 and 90 millions of miles.
The method by observations of Mars is still, in some of its
174: PRACTICAL ASTRONOMY.
forms, among the most valuable which have been applied to
the determination of the solar parallax. About once in six-
teen years Mars approaches almost as near the earth as Venus
does at the times of her transits, the favorable times being
those when Mars at opposition is near his perihelion. His
distance outside the earth's orbit is then only 0.373 of the as-
tronomical unit, or 34J millions of miles, while at his aphe-
lion the distance is nearly twice as great. At the nearest op-
positions, his parallax is over 23", an angle which can be meas-
ured with some accuracy. The plan of observation has gen-
erally been to send an observing party to the southern hemi-
sphere in advance, for the purpose of making observations of
the position of Mars on the celestial sphere, or of its distance
from certain selected stars, from night to night, while corre-
sponding observations are made at the fixed observatories of
the northern hemisphere. The displacement of the planet
due to parallax is then found by comparing the results of
these observations.
The last expedition of this sort was that of Captain James
M. Gilliss, late of the United States Navy, who went out to
Chili under the auspices of the American Government in
1849, and remained till 1852, for the purpose of observing
both Venus and Mars during the periods when the parallax
was greatest. Several circumstances conspired to prevent this
enterprise from producing results corresponding to its merits.
The opposition of Mars was a very unfavorable one ; observa-
tions of Venus could not be made with the necessary accu-
racy, and there was a lack of sufficient cooperation on the
part of northern observers. The astronomical results of the
expedition were, nevertheless, important, Captain Gilliss hav-
ing prepared an immense catalogue of the stars of the south-
ern hemisphere, while his instruments became the property of
the Government of Chili, which employed them in fitting up
a*national observatory. Several observatories have since been
founded in the southern hemisphere, so that there is no longer
any need of sending out expeditions to observe the planet
Mars for the purpose in question.
SOLAR PARALLAX FROM TRANSITS OF VENUS.
175
3. Solar Parallax from Transits of Venus.
The most celebrated method of determining the solar paral-
lax has been by transits of Venus over the face of the sun, by
which the difference between the parallax of the planet and
that of the sun can be found, as explained in 1. We know
from our astronomical tables that this phenomenon has recur-
red in a certain regular cycle four times every 9A3 years for
many centuries past. This cycle is made up of four intervals,
the lengths of which are, in regular order, 105 J years, 8 years,
121^ years, 8 years, after which the intervals repeat them-
selves. The dates of occurrence for eight centuries are as
follows :
1518 June2d.
1526 June 1st.
1631.. ...December 7th.
1639 December 4th.
1761 June 5th.
1769 June 3d.
1874 December 9th.
1882 December 6th.
2004 June 8th.
2012 June 6th.
2117 December llth.
2125 December 8th.
2247 June llth.
2255 June 9th.
It has been only in comparatively recent times that this phe-
nomenon could be predicted and observed. In the years 1518
and 1526 the idea of looking for such a thing does not seem
to have occurred to any one. The following century gave
birth to Kepler, who so far improved the planetary tables
as to predict that a transit would occur on December 6th,
1631. But it did not commence until after sunset in Eu-
rope, and was over before sunrise next morning, so that it
passed entirely unobserved. Unfortunately, the tables were
so far from accurate that they failed to indicate the transit
which occurred eight years later, and led Kepler to announce
that the phenomenon would not recur till 1761. The transit
of 1639 would, therefore, like all former ones, have passed
entirely unobserved, had it not been for the talent and enthu-
siasm of a young Englishman. Jeremiah Horrox was then a
young curate of eighteen, residing in the North of England,
who, even at that early age, was a master of the astronomy of
170 PRACTICAL ASTRONOMY.
his times. Comparing different tables with his own observa-
tions of Venus, he found that a transit might be expected to
occur on December 4th, and prepared to observe it, after the
fashion then in vogue, by letting the image of the sun passing
through his telescope fall on a screen behind it. Unfortu-
nately, the day was Sunday, and his clerical duties prevented
his seeing the ingress of the planet upon the solar disk a cir-
cumstance which science has mourned for a century past, and
will have reason to mourn for a century to come. When he
returned from church, he was overjoyed to see the planet upon
the face of the sun, but, after following it half an hour, the ap-
proach of sunset compelled him to suspend his observations.
During the interval between this and the next transit, which
occurred in 1761, exact astronomy made very rapid progress,
through the discovery of the law of gravitation and the ap-
plication of the telescope to celestial measurements. A great
additional interest was lent to the phenomenon by Halley's
discovery that observations of it made from distant points of
the earth could be used to determine the distance of the sun.
The principles by which the parallaxes, and therefore the
distances, of Venus and the sun are determined by Halley's
method arc quite simple. In consequence of the parallax of
Venus, two observers at distant points of the earth's surface,
watching her course over the
solar disk, will see her describe
slightly different paths, as shown
in Fig. 50. It is by the distance
between these paths that the par-
allax has hitherto been deter-
mined.
The essential principle of Hal-
ley's method consists in the mode
FIG. Ba-Apparent paths of Venus'across ^ determining the distance be-
the BUD, as Been from different stations tWCCll these apparent paths. All
during the transit of 18T4. The upper . . * A x
T>ath is that seen from a southern sta- inspection 01 the nglire Will SHOW
tlon; the lower is that seen from a that t]ie pat1l f art hest from the
northern Btation, but the distance be- *
tween the paths is exaggerated. SUIl's centre is shorter than the
SOLAR PARALLAX FROM TRANSITS OF VENUS. 177
other, so that Venus will pass over the sun more quickly when
watched from a southern station than when watched from a
northern one. Halley therefore proposed that the different ob-
servers should, with a telescope and a chronometer, note the
time it took Yenus to pass over the disk, and the difference be-
tween these times, as seen from different stations, would give
the means of determining the difference between the parallaxes
of Yenus and the sun. The ratio between the distances of
the planet and the sun is known with great exactness by Kep-
ler's third law, from which, knowing the differences of paral-
laxes, the distance of each body can be determined.
By this plan of Halley the observer must note with great
exactness the times both of beginning and end of - the transit.
There are two phases which may be observed at the beginning
and two at the end, making four in all.
The first is that when the planet first touches the edge of
the solar disk, and begins to make a notch in it, as at a, Fig. 50.
This is called first external contact.
The second is that when the planet has just entered entirely
upon the sun, as at b. This is called first internal contact.
The third contact is that in which the planet, after crossing
the sun, first reaches the edge of the disk, and begins to go
off, as at c. This is called second internal contact.
The fourth contact is that in which the planet finally disap-
pears from the face of the sun, as at d. This is called second
external contact.
Now, it was the opinion of Halley, and a very plausible one,
too, that the internal contacts could be observed with far great-
er accuracy than the external ones. He founded this opinion
on his own experience in observing a transit of the planet Mer-
cury at St. Helena in 1677. It will be seen by inspecting Fig.
51, which represents the position of the planet just before first
internal contact, that as the planet moves forward on the solar
disk the sharp horns of light on each side of it approach each
other, and that the moment of internal contact is marked by
these horns meeting each other, and forming a thread of light
all the way across the dark space, as in Fig. 52. This thread
13
178 PRACTICAL ASTRONOMY.
of light is indeed simply the extreme edge of the sun's disk
coming into view behind the planet. In observing the tran-
sit of Mercury, Halley felt
sure that he could fix the
moment at which the horns
met, and the edge of the
sun's disk appeared un-
broken, within a single sec-
ond ; and he hence con-
cluded that observers of
the transit of Venus could
observe the time required
FIG. 51. Venus approaching internal contact on f O1 1 VenUS to paSS aCl'OSS
the face of the sun. The planet is supposed t j ie gun w jthin OI1C Or tWO
to be moving upward.
seconds. These times would
differ in different parts of the earth by fifteen or twenty min-
utes, in consequence of parallax. Hence it followed, that if
Halley 's estimate of the de-
gree of accuracy attainable
were correct, the parallax of
Venus and the sun would be
determined by the proposed
system of observations within
the six hundredth of its whole
amount.
When the long-expected 5th
of June, 1761, at length ap-
proached, which was a gener-
ation after Halley's death, ex- FlG> C2.-Internnl contact of the limb of Ve-
. J 7 nus with that of the sun.
peditions were sent to distant
parts of the world by the principal European nations to make
the required observations. The French sent out from among
their astronomers, Le Grentil to Pondicherry ; Pingre to Rod-
riguez Island, in the neighborhood of the Mauritius ; and the
Abbe Chappe^fo Tobolsk, in Siberia. The war with England,
unfortunately, prevented the first two from reaching their sta-
tions in time, but Chappe was successful. From England, Ma-
SOLAE PARALLAX FROM TRANSITS OF FENUS. 179
son he of the celebrated Mason and Dixon's Line was sent
to Sumatra ; but he, too, was stopped by the war : Maskelyne,
the Astronomer Royal, was sent to St. Helena. Denmark,
Sweden, and Russia also sent out expeditions to various points
in Europe and Asia.
With those observers who were favored by fine weather, the
entry of the dark body of Venus upon the limb of the sun
was seen very- well until the critical moment of internal con-
tact approached. Then they were perplexed to find that the
planet, instead of preserving its circular form, appeared to
assume the shape of a pear or a balloon, the elongated portion
being connected with the limb of the sun. We give two fig-
ures, 52 and 53, the first showing how the planet ought to have
looked, the last how it really did look. Now, we can readily
see that the observer, looking
at such an appearance as in
Fig. 53, would be unable to
say whether internal contact
had or had not taken place.
The round part of the planet
is entirely within the sun, so
that if he judged from this
alone, he would say that in-
ternal contact is passed. But
the horns are still separated
by this dark elongation, or K<) _. .. , .
J & ' Fio. 53. The black drop, or ligament.
" black drop,," as it is general-
ly called, so* that, judging from this, internal contact has not
taken place. The result was an uncertainty sometimes amount-
ing to nearly a minute in observations which were expected to
be correct within a single second.
When the parties returned home, and their observations
were computed by various astronomers, the resulting values
of the solar parallax were found to range from 8".5, found by
Short of England, to 10".5, found by Pingr^, of France, so
that there was nearly as much uncertainty as ever in the value
of the element sought. Nothing daunted, however, prepara-
180 PRACTICAL ASTRONOMY.
tions yet more extensive were made to observe the transit of
1769. Among the observers was one whose patience and
whose fortune must excite our warmest sympathies. We have
said that Le Gentil, sent out by the French Academy to ob-
serve the transit of 1761 in the East Indies, was prevented
from reaching his station by the war with England. Finding
the first port he attempted to reach in the possession of the
English, his commander attempted to make another, and,
meeting with unfavorable winds, was still at sea on the day of
the transit. He thereupon formed the resolution of remain-
ing, with his instruments, to observe the transit of 1769. He
was enabled to support himself by some successful mercantile
adventures, and he also industriously devoted himself to scien-
tific observations and inquiries. The long-looked-for morning
of June 4th, 1769, found him thoroughly prepared to make
the observations for which he had waited eight long years.
The sun shone out in a cloudless sky, as it had shone for a
number of days previously. But just as it was time for the
transit to begin, a sudden storm arose, and the sky became
covered with clouds. When they Cleared away the transit
was over. It was two ^weeks before the ill-fated astronomer
could hold the pen which was to tell his friends in Paris the
story of his disappointment.
In this transit the ingress of Venus on the limb of the sun
occurred just before the sun was setting in Western Europe,
which allowed numbers of observations of the first two phases
to be made in England and France. The commencement was
also visible in this country which was then these colonies
under very favorable circumstances, and it was well observed
by the few astronomers we then had. The leader among
these was the talented and enthusiastic Bittenhouse, who was
already well known for his industry as an observer. The ob-
servations were organized under the auspices of the American
Philosophical Society, then in the vigor of its youth, and par-
ties of observers were stationed at Norristown, Philadelphia,
and Cape Henlopen. These observations have every appear-
ance of being among the most accurate made on the transit;
SOLAR PARALLAX FROM TRANSITS OF VENUS. 181
but they have not received the consideration to which they are
entitled, partly, we suppose, because the altitude of the sun
was too great to admit of their being of much value for the
determination of parallax, and partly because they were not
very accordant with the European observations.
The phenomena of the distortion of the planet and the
"black drop," already described, were noticed in this, as in
the preceding transit. It is strongly indicative of the ill
preparation of the observers that it seems to have taken them
all by surprise, except the few who had observed the preced-
ing transit. The cause of the appearance was first pointed
out by Lalande, and is briefly this : when we look at a bright
object on a dark ground, it looks a .little larger than it real-
ly is, owing to the encroachment of the light upon the dark
border. This encroachment, or irradiation, may arise from a
number of causes imperfections of the eye, imperfections of
the lenses of the telescope when an instrument is used, and
the softening effect of the atmosphere when we look at a ce-.
lestial object near the horizon. To understand its effect, we
have only to imagine a false edge painted in white around the
borders of the bright object, the edge becoming narrower and
darker where the bright object is reduced to a very narrow
line. Thus, by painting around the borders of the light por-
tions of Fig. 51, we have formed Fig. 53, and produced an ap-
pearance quite similar to that described by the observers of
the transit. The better the telescope and the steadier the at-
mosphere, the narrower this border will be, and the more the
planet will seem to preserve its true form, as in Fig. 52. In
the observations of the recent transit of Venus with the im-
proved instruments of the present time, very few of the more
experienced observers noticed any distortion at all.
The results of the observations of 1769 were much more
accordant than those of 1761, and seemed to indicate a paral-
lax of about 8".5. Curious as it may seem, more than half a
century elapsed after the transit before its results were com-
pletely worked up from all the observations in an entirely
satisfactory manner. This was at length done by Encke, in
182 PRACTICAL ASTRONOMY.
1824, for both transits, the result giving 8".5776 for the solar
parallax. Some suspicion, however, attached to some of the
observations, which he was not at that time able to remove.
In 1835, having examined the original records of the observa-
tions in question, he corrected his work, and found the follow-
ing separate results from the two transits :
Parallax from the observations of 1761 8",53
Parallax from the observations of 1769 8". 59
Most probable result from both transits 8' / .571
The probable error of the result was estimated at 0".037,
which, though larger than was expected, was much less than
the actual error has since proved to be. The corresponding
distance of the sun is 95,370,000 miles, a classic number
adopted by astronomers everywhere, and familiar to every
one who has read any work on astronomy.
This result of Encke was received without question for
^nore than thirty years. But in 1854 the celebrated Hansen,
completing his investigations of the motions of the moon,
found that her observed positions near her first and last quar-
ters could not be accounted for except by supposing the par-
allax of the sun increased, and therefore his distance dimin-
ished, by about a thirtieth of its entire amount. The exist-
ence of this error has since been amply confirmed in several
ways. The fact is, that although a century ago a transit of
Venus afforded the most accurate way of obtaining the dis-
tance of the sun, yet the great advances made during the
present generation in the art of observing, and the applica-
tion of scientific methods, have led to other means of greater
accuracy than these old observations. It is remarkable that
while nearly every class of observations is now made with
a precision which the astronomers of a century ago never
thought possible, yet this particular observation of the interior
contact of a planet with the limb of the sun has never been
made with any thing like the accuracy which Halley himself
thought he attained in his observation of the transit of Mer-
cury two centuries ago.
SOLAR PARALLAX FROM TRANSITS OF VENUS. 183
The knowledge of this error in the fundamental astronom-
ical unit gave increased interest to the transit of' Venus which
was to occur on December 8th, 1874. The rarity of the phe-
nomenon was an advantage, in that it led to an amount of
public interest being taken in it which could not have been
excited by any other astronomical event, and thus secured
from various governments the grants necessary to fit out the
necessary parties of observation. Plans of observation began
to be worked out very far in advance. In 1857, Professor
Airy sketched a general plan of operations for the observation
of the transits, and indicated the regions of the globe in which
he considered the observations should be made. In 1870, be-
fore any steps whatever were taken in this country, he had ad-
vanced so far in his preparations as to have his observing huts
all ready, and his instruments in process of construction. In
1869, the Prussian Government appointed a commission, con-
sisting of six or eight of its most eminent astronomers, to de-
vise a plan of operations, and report it to the Government
with an estimate of the expenses. About the same time the
Russian Government began making extensive preparations
for observing the transit from a great number of stations in
Siberia.
Active preparations for the observations in question were
commenced by the United States Government in 1871. An
account of the method of observation adopted by the Com-
mission to whom the matter was intrusted may not be devoid
of interest. The observations of the older transits having
failed in giving results of the accuracy now required, it be-
came necessary to improve upon the system then adopted.
In this system, the parallax depended entirely on observations
of contacts, the uncertainty of which we have already shown.
Besides this uncertainty, Halley's method was open to the ob-
jection that, unless both contacts were observed at each sta-
tion, the path of Venus could not be determined, and no re*
suit could be deduced. It was therefore proposed by De
Tlsle early in the last century, that the observers should de*
tennine the longitudes of their stations, in order that, by
184 PRACTICAL ASTRONOMY.
means of it, they could find the actual intervals between the
moments at which any given contact was seen at the different
stations. This method was an improvement on Halley's, in
that it diminished the chances of total failure. Still, it de-
pended entirely upon making an accurate observation of the
moment of contact, and was liable to fail from any accident
which might interfere with such an observation a passing
cloud, or a disarrangement of some of the instruments of ob-
servation. Besides, it was not yet certain whether the obser-
vations could be made with the necessary accuracy. It was,
therefore, desirable that, instead of depending on contacts
alone, some method should be adopted of finding the position
of Venus on the face of the sun as often as possible during
the four hours which she should occupy in passing. The
easiest and most effective way of doing this seemed to be to
take photographs of the sun with Venus on his disk, which
photographs could be brought home, compared, and measured
at leisure.
This mode of astronomical measurement has been brought
to great perfection in this country by Mr. L. M. Rutherfurd
and others, and has been found to give results exceeding in
accuracy any yet attained by ordinary eye observations. The
advantages of the photographic method are so obvious that
there could be no hesitation about employing it, and, so far
as is known, it was applied by every European nation which
sent out parties of observation. But there is a great and
essential difference between the methods of photographing
adopted by the Americans and by most of the Europeans.
The latter seein to have devoted all their attention to the
problem of securing a good sharp photograph, taking it for
granted that when this photograph was measured there would
be no further difficulty. But the measurement at home is
necessarily made in inches and fractions, while the distance
we must know is to be found in minutes and seconds of an-
gular measure. If we have a map by measurements on which
we desire to know the exact distance of two places, we must
first know the exact scale on which the map is laid down,
SOLAR PARALLAX FROM TRANSITS OF VENUS. 185
with a degree of accuracy corresponding to that of our meas-
ures. Just so with our photographs taken at various parts of
the globe. We must know the scale on which the images are
photographed before we can derive any conclusions from our
measures. While the determination of this scale with suffi-
cient precision for ordinary purposes is quite easy, this is by
no means the case with a problem where so much accuracy
was required, so that here lay the greatest difficulty which the
photographic method offered.
In the mode of photographing adopted by the Americans
this difficulty was met by using a telescope of great length
nearly forty feet So long a telescope would be too un-
wieldy to point at the sun ; it was therefore fixed in a hor-
izontal position, the rays of the sun being thrown into it by a
mirror. The scale of the picture was determined by actually
measuring the distance between the object-glass and the pho-
tograph-plate. Each station was supplied with special appa-
ratus by which this measurement could be made within the
hundredth of an inch. Then, knowing the position of the op-
tical centre of the glass, it is easy to calculate exactly how
many inches any given angle will subtend on the photograph-
plate. The following brief description of the apparatus will
be readily understood by reference to the figures :
The object-glass and the support for the mirror are mount-
ed on an iron pier extending four feet into the ground, and
firmly embedded in concrete. The mirror is in a frame at
the end of an inclined cast-iron axis, which is turned with a
very slow motion by a simple and ingenious piece of clock-
work. The inclination of the axis and the rate of motion are
so adjusted that, notwithstanding the diurnal motion of the
sun or, to speak more accurately, of the earth the sun's
rays will always be reflected in the same direction. This re-
sult is not attained with entire exactness, but it is so near that
it will only be necessary for an assistant to touch the screws
of the mirror at intervals of fifteen or twenty minutes during
the critical hours of the transit. The reflector is simply a
piece of finely polished glass, without any silvering whatever,
186
PRACTICAL ASTRONOMY.
It only reflects about a twentieth of the sun's light ; but so in-
tense are his rays that a photograph can be taken in less than
the tenth of a second. The polishing of this mirror was the
most delicate and difficult operation in the construction of
the apparatus, as the slightest deviation from perfect flatness
would be fatal. For instance, if a straight edge laid upon the
glass should touch at the edges, but be the hundred -thou-
sandth of an inch above it at the centre, the reflector would
be useless. It might have seemed hopeless to seek for such a
degree of accuracy, had it not been for the confidence of the
Commission in the mechanical genius of Alvan Clark & Sons,
to whom the manufacture of the apparatus was intrusted.
The mirrors were tested by observing objects through a tele-
scope, first directly, and then by reflection from the mirror.
If they were seen with equally good definition in the two
cases, it would show that there were no irregularities in the
surface of the mirror; while if it were either concave or con-
vex, the focus of the telescope would seem shortened or
lengthened. The first test was sustained perfectly, while the
DISTANOI
AMP A rUUIQM*
PIG. 64 Method of photographing the transit of Venus used by the French and Ameri-
can observers, and by Lord Lindsay.
SOLAR PARALLAX FROM TRANSITS OF VENUS. 187
circles of convexity or concavity indicated by the changes of
focus of the photographic telescope were many miles in di-
ameter.
Immediately in front of the mirror is the object-glass. The
curves of the lenses of which it is formed are so arranged that
it is not perfectly achromatic for the visual rays, but gives the
best photographic image. Thirty -eight feet and a fraction
from the glass is the focus, where an image of the sun about
four arid a quarter inches in diameter is formed. Here an-
other iron pier is firmly embedded in the ground for the sup-
port of the photographic plate -holder. This consists of a
brass frame seven inches square on the inside, revolving on a
vertical rod, which passes through the iron plate on top of the
pier. Into this frame is cemented a square of plate-glass, just
as a pane of glass is puttied in a window. The glass is divided
into small squares by very fine lines about one-five-lmndredth
of an inch thick, which were etched by a process invented and
perfected by Mr. W. A. Rogers, of the Cambridge Observatory.
The sensitive plate goes into the other side of the frame, and
when in position for taking the photograph, there is a space
of about one-eighth of an inch between the ruled lines and
the plate. The former are, therefore, photographed on every
picture of the sun which is taken, and serve to detect any
contraction of the collodion film on the glass plate.
The rod on which the plate-holder turns, and the frame it-
self, are perforated from top to bottom by a vertical opening
one-sixth of an inch in diameter. Through the centre of this
opening, passing between the ruled plate and the photograph
plate, hangs a plumb-line of very fine silver wire. In every
picture of the sun this plumb-line is also photographed, and
this marks a truly vertical line on the plate very near the mid-
dle vertical etched line. A spirit-level is fixed to the top of
the frame, and serves to detect any changes in the inclination
of the ruled lines to the horizon.
One of the most essential features of the arrangement is
that the photographic object-glass and plate-holder are on the
same level, and in the meridian of the transit instrument with
188 PRACTICAL ASTRONOMY.
which the time is determined. The central ruled line on the
plate-holder is thus used as a meridian mark for the transit.
The great advantage of this arrangement is, that it permits
the angle which the line joining the centres of the sun and
Venus makes with the meridian to be determined with the
greatest precision by means of the image of the plumb-line
which is photographed across the picture of the sun.*
Although the contact observations were not wholly relied
on, they were by no means neglected. On the contrary, the
greatest pains were taken to avoid the sources of error which
caused so much trouble in 1769. To learn what these errors
probably were, and to practise the observers in making their
observations so as to avoid them, an artificial planet was con-
structed to move over an artificial representation of a portion
of the solar disk by clock-work. The apparatus was mounted
on the top of a building about 3300 feet distant, in order to
give the effect of atmospheric undulations and softening of
the edges of the planet. The planet was represented by a
black disk one foot in diameter, which made its apparent mag-
nitude the same as that
of Venus in transit. The
sun was represented by
a white screen behind
the artificial Venus, the
portions of the edge of
FIG. 55.-Artificial transit of Venus. tne ^ where VenilS
entered and left being formed by the sloping edges of a black
triangle, as shown in the figure. There was no need of a rep-
resentation of the entire sun. The motion was so regulated
that the time occupied by the disk in passing from external to
* The method of photographing the sun by a fixed horizontal telescope with a
reflector in front of it is believed to have been first proposed in France by Captain
Laussedat. It was independently invented by the late Professor Winlock, who
put it into actual operation at the Harvard College Observatory in 1869, and, so
far as the author is aware, was the first one to do so. It was employed not only
by the American observers, but by the French, and by Lord Lindsay, M.P., of
Scotland. The latter gentleman fitted out a finely equipped expedition at his own
expense to observe the transit of Venus at the Mauritius.
SOLAR PARALLAX FROM TRANSITS OF VENUS. 189
internal contact, and the angle its motion made with the edges
of the triangle, were the same as they would be in the actual
transit as viewed from some point where it occurred near the
zenith. The disk was put at such a height that it was only
about three minutes from internal contact at ingress to inter-
nal contact at egress, instead of four hours.
The observations of this instrument have thrown much light
on the question of the black drop, and the distortion of the
planet seen in former transits of Venus, which have been al-
ready described. What is perhaps yet better, it has enabled
us to account for a number of puzzling and discordant appear-
ances described by the observers. Father Hell's black drop,
seen before the limbs were in contact ; the formation of inter-
nal contact by a fine line of light, though the cusps were blunt,
as seen at Hudson Bay ; Captain Cook's "atmosphere " around
Venus, and his curious black piece cut out of the edge of the
sun, may all be said to have been identified nearly enough to
judge what the appearances really were which werd so vari-
ously described. In looking at the artificial planet near the
moment of internal contact, when the air is not still, the first
thing which the observer sees is . that there is really no con-
stant shape to those parts of Venus and the sun which are ap-
proaching each other ; but that, owing to the undulations of
the air, they assume all sorts of shapes in rapid succession, so
that different observers may give different descriptions of the
appearances presented, though looking at the very same ob-
ject In the varied forms which may be seen, we recognize
all the peculiar appearances described by the observers of the
transit of 1769.
At each American station the scientific corps consisted of
a chief of party, an assistant astronomer, and three photog-
raphers. The instruments at all the stations were precisely
similar, and the operations and observations the same at all.
This system was adopted to secure two great advantages: first,
to run the least risk of entire failure from bad weather ; and,
second, to have all the observations strictly comparable. Much
pains and trouble were devoted to these objects. To appreci-
190 PRACTICAL ASTRONOMY.
ate their importance, we must remember that, in order to de-
duce the parallax from the observations at any two stations,
it is essential that the difference between observations should
be due only to parallax, and that in every other respect they
should be exactly the same ; because, if there are other dif-
ferences which we cannot certainly allow for, our calculation
of the parallax will be wrong. It is also necessary that we
compare the same kind of observations in order to get the
parallax. To show how the chances of failure are lessened,
suppose we have two stations in each hemisphere, in one of
which eye observations are made, while in the other photo-
graphs are taken. Then, if the photographs in one hemi-
sphere and the eye observations in the other are lost by clouds,
or any other cause, everything will be lost, although one sta-
tion in each hemisphere is successful, because the eye obser-
vations in the one hemisphere cannot be compared with the
photographs in the other. It being decided, for these reasons,
to have the same system of observations at all the stations, it
became necessary to confine the choice of stations to points
where the entire transit would be visible.
One of the most important features of the preparations,
which distinguishes them from the preparations to observe
the former transits, was the previous training of the observers.
All the members of the observing parties assembled at Wash-
ington to practise together before leaving to make the obser-
vations. They took all their multitudinous instruments and
apparatus out of their boxes, mounted them, and proceeded to
practise with them in the same way they were to be used at
the stations. Photographs of the sun were taken from day to
day in the same way as on the 8th of December, and each
chief of party was instructed in all the delicate operations
necessary to secure the entire success of his operations.
To know where a party could be sent, it had first to be
known when and where the transit would be visible. We
give a small map of the world showing this at a glance.
Could we have seen the planet Venus from the Eastern States
on the afternoon of December 8th, 1874, we should have seen
SOLAR PARALLAX FROM TRANSITS OF FJENUS. 191
FIG. 56. Map of the earth, showing the areas of visibility of the transit of 1874.
her approaching nearer and nearer the sun as the latter ap-
proached the horizon. In San Francisco, where sunset is three
hours later than here, she would have been so near the sun as
almost to seem to touch it. About an hour later she actual-
ly reached the solar disk. The sun was then shining on the
whole Pacific Ocean, except that portion nearest the Ameri-
can coast, and on Eastern Asia, Australia, and the Indian and
Antarctic oceans to the south pole. Venus was about four
and a half hours passing over the face of the sun, and during
this time the latter had set across the entire northern portion
of the Pacific Ocean, and had risen as far west as Moscow
and Vienna, from which cities the planet might have been
seen to leave the disk just as the sun rose.
In the northern hemisphere suitable stations were easily
found, as we have the whole of China, Japan, and Northern
India. But in the southern hemisphere great difficulties were
encountered, owing to the want of habitable stations in the
regions which were astronomically the most favorable. Ob-
servations cannot be made from the deck of a ship ; astrono-
mers must have solid ground for their instruments. The south
pole would have been the best station of all, if some antarc-
tic Kane or Hall could take a party thither. The antarctic
continent and the neighboring islands were not to be thought
of, because a party could neither be landed nor subsisted there ;
192 PRACTICAL ASTRONOMY.
and if they could, the weather would probably have prevented
any observations from being taken. The chance of having a
clear sky on the eventful 8th of December was, indeed, one
of the most important considerations on which the choice of
a station had to depend. Information from every available
source, official and private, respecting the meteorology of the
various possible stations, was therefore sought. Where there
was any American consul or consular agent, he was applied
to through the State Department to have meteorological ob-
servations made during the months of November and Decem-
ber, 1872 and 1873. A sealing ship belonging to the firm of
Williams, Haven, & Co., of New London, made observations
at Heard's Island, in the Southern Indian Ocean. From all
these reports, as well as from the printed reports issued by
various authorities, it was found that the chances of good
weather were much better in the northern than in the south-
ern hemisphere. In consequence, instead of sending an equal
number of parties north and south, it was determined to send
three to the northern and five to the southern hemisphere.
The stations which the American parties finally occupied,
with the names of the chiefs of party, are as follows :
NORTHERN HEMISPHERE.
Wladiwostok, Siberia Professor ASAPH HALL, U. S.N.
Pekin, China Professor J. C. WATSON.
Nagasaki, Japan ....Professor GEORGE DAVIDSON, U. S. Coast Survey.
SOUTHERN STATIONS.
Kerguelen Island Commander G. P. RYAN, U. S. N.
Hobart-town, Tasmania Professor W. HARKNESS, U. S. N.
Campbelltown, Tasmania* Captain C. W. RAYMOND, Engineer Corps, U. S. A.
Queenstown, New Zealand. ...Professor C. H. F. PETERS.
Chatham Island EDWIN SMITH, Esq., U. S. Coast Survey.
The southern parties were all carried to their respective sta-
tions by the U. S. steamer Swatara, Captain Kalph Chandler,
U. S. N., commanding.
* Captain Raymond's party was designed for the Crozet Islands, but the Swa-
tara failed to effect a landing there.
SOLAR PARALLAX FROM TRANSITS OF VENUS. 193
The only thing which seriously interfered with the observa-
tions was the weather. Some photographs were obtained at
every station, but the full number at none. Altogether, there
were only about half the expected number obtained. No
contacts at all were observed at Hobart-town or Chatham Isl-
and, but one or more were observed at each of the remaining
six stations. Pekin was, however, the only one at which all
four were observed. Among the parties sent out by other
nations, the most fortunate, as regards weather, were the Ger-
mans, who were successful at all six of their stations. The
English, French, and Russians were, on the average, about as
successful as the Americans.
If the observations on the transit of 1874 had been made
in the same way as those of the transit of 1769, they could be
very speedily worked up, and we should soon expect to see
the solar parallax deduced from the combination of them all.
But the investigation and measurement of the photographs is
so laborious an operation that the American results can hard-
ly be published before 1878. The definitive value of the
parallax must then be deduced, not from the observations of
any one nation, but so far as possible from the combination
of those of all nations. We must, therefore, wait for the final
publication and discussion of all the observations before the
definitive value of the parallax can be announced.
Under these circumstances, the question whether it is worth
while to send out parties to observe the transit of 1882 will
soon be a subject of discussion among astronomers, the answer
to which will depend very largely on the success of the efforts
made in 1874. On this success we cannot pronounce a final
judgment until all the observations are worked up. The rea-
son why doubt still remains on this point is that the sun is a
very difficult object either to observe or to photograph with
accuracy, owing to the action of his rays on the atmosphere.
The air near the ground becomes heated, and thus causes the
limb of the sun to undulate to a degree which sometimes ren-
ders its exact definition out of the question, while the outline
of Venus undulates in the same way. Another difficulty is,
14
194 PRACTICAL ASTRONOMY.
that the irregularity in the transparency of the atmosphere,
owing to clouds and vapors, renders the photographic repre-
sentation of the limb of the sun quite uncertain, and thus re-
quires all measures to be made from the sun's centre. Now,
we cannot say how far these difficulties have been surmount-
ed by the methods of observation adopted until we finally
compare all the observations, and see how consistent they are
with each other; and this cannot be done for several years.
The region of visibility of the transit of 1882 will be quite
different from that of 1874, as it will include the whole Amer-
ican continent, except some portions in or near the arctic cir-
cle. The beginning will be visible over a large part of Afri-
ca, and the end over most of the Pacific Ocean. The most
favorable northern stations for its observation are in the East-
ern and Middle States.
4. Other Methods of determining the Sans Distance, and their
Results.
The methods of determining the astronomical unit which
we have described rest entirely upon measures of parallax, an
angle which hardly ever exceeds 20", and which it is there-
fore exceedingly difficult to measure with the necessary ac-
curacy. If there were no other way than this of determining
the sun's distance, we might despair of being sure of it with-
in 200,000 miles. But the refined investigations of modern
science have brought to light other methods, by at least two
of which we may hope, ultimately, to attain a greater degree
of accuracy than we can by measuring parallaxes. Of these
two, one depends on the gravitating force of the sun upon the
moon, and the other upon the velocity of light.
Parallactic Equation of the Moon. The motion of the moon
around the earth is largely affected by the gravitating force
of the sun, or, to speak more exactly, by the difference of the
gravitating force of the sun upon the moon and upon the
earth. A part of this difference depends upon the proportion
between the respective distances of the moon and the sun, so
that when this force is known, the proportion can be deter-
I
METHODS OF DETEEMININ& THE SUN'S DISTANCE. 197
mined. The distance of the moon being known with all nec-
essary precision, we have only to multiply it by the proportion
thus obtained to get the distance of the sun. The force in
question shows itself by producing a certain inequality in the
moon's motion, by which she falls two minutes, behind her
mean place near the first quarter, and is two minutes ahead
near her last quarter. In determining this inequality, we have
to measure an angle about six times as great as the average
of the planetary parallaxes on which the sun's distance de-
pends ; so that, if we could measure both angles with the same
precision, the error, by using the moon, would be only one*
sixth as great as in direct measures of parallax. But it seems
as if nature had determined to allow mankind no royal road
to a knowledge of the sun's distance. It is the position of
the moon's centre which we require for the purpose in ques-
tion, and this can never be directly fixed. We have to make
our observations on the limb or edge of the moon, as illu-
minated by the sun, and must reduce our observations to the
moon's centre, before we can use them. The worst of the
matter is, that one limb is observed at the first quarter, and
another at the third quarter, so that we cannot tell with abso-
lute certainty how much of the observed inequality is real,
and how much is due to the change from one limb to the other.
So great is the uncertainty here that, previous to 1854, it was
supposed that the inequality in question was about 122",
agreeing with the theoretical inequality from Encke's errone-
ous value of the solar parallax. Hansen then found that it
was really about 4" greater, and thus was led to the conclusion
that the parallax of the sun must be increased, and his distance
diminished, by one-thirtieth of the whole amount.
It is quite likely that by adopting improved modes of ob-
servation, it will be found that the sun's distance can be more
accurately measured in this way than through the parallaxes
of the planets. Some pains have already been taken to deter-
mine the exact amount of the inequality from observations,
the result being 125".5. The entire seconds may here be re-
lied on, but the decimal is quite uncertain. We can only say
198 PRACTICAL ASTRONOMY.
that we are pretty surely within three or four tenths of a sec-
ond of the truth. From this value the parallax of the sun is
found to be S".83, with an uncertainty of two or three hun-
dredths of a second.
Sun's Distance from the Velocity of Light. There is an ex-
traordinary beauty in this method of measuring the sun's dis-
tance, arising from the contrast between the simplicity of the
principle and the profoundness of the methods by which alone
the principle can be applied. Suppose we had a messenger
whom we could send to and fro between the sun and the
earth, and who could tell, on his return, exactly how long it
took him to perform his journey; suppose, also, we knew the
exact rate of speed at which he travelled. Then, if we mul-
tiply his speed by the time it took him to go to the sun, we
shall at once have the sun's distance, just as we could deter-
mine the distance of two cities when we knew that a train
running thirty miles an hour required seven hours to pass be-
tween them. Such a messenger is light. It has been found
practicable to determine, experimentally, about how fast light
travels, and to find from astronomical phenomena how long
it takes to come from the sun to the earth. How these de-
terminations are made will be shown in the next chapter;
here we shall stop only to give results. It is found by Fou-
cault's experiment that light travels about 185,200 miles per
second ; and it is known from a study of several astronomical
phenomena that it passes from the sun to the earth in 498 sec-
onds. The product of these numbers gives a distance of
92,230,000 miles, a result, however, which is uncertain by T ^j
of its entire amount, or nearly half a million of miles, owing to
the uncertainty in each of the factors. This result was reached
in 1862, and was one of the first confirmations of the increased
value of .the solar parallax found by Hansen. But since that
time a redetermination of the velocity of light has been made
by Cornu, of Paris, by a method soon to be described, with a
different result. He finds a velocity of 300,400 kilometres or
186,670 miles per second, making the distance of the sun
92,960,000 miles, and its parallax 8".794. This discrepancy
METHODS OF DETERMINING THE SUN'S DISTANCE. 199
is not yet explained, and the truth can be reached only by a
repetition of one or both of the experiments.
These two methods of determining* the distance of the sun
may fairly be regarded as equal in accuracy to that by tran-
sits of Venus when they are employed in the best manner.
There are also two or three minor methods which, though
less accurate, are worthy of mention. One of the most in-
genious of these was first applied by Leverrier. It is known
from the theory of gravitation that the earth, in consequence
of the attraction of the itioon, describes a small monthly orbit
around the common centre of gravity of these two bodies, cor-
responding to the monthly revolution of the moon around the
earth, or, to speak with more precision, around the same com-
mon centre of gravity. If we know the mass (or weight) of
the moon relatively to that of the earth, and her distance, we
can thus calculate the radius of the little orbit referred to.
In round numbers, it is 3000 miles. This monthly oscillation
of the earth will cause a corresponding oscillation in the lon-
gitude of the sun, and by measuring its apparent amount we
can tell how far the sun must be placed to make this amount
correspond to, say 3000 miles. Leverrier found the oscilla-
tions in arc to be 6".50. From this he concluded the solar
parallax to be 8". 95. But Mr. Stone,"* of Greenwich, found
two errors in Leverrier's computation ,f and, when these are
corrected, the result is reduced to 8".85.
Another recondite method has been employed by Leverrier.
It is founded on the principle that when the relative masses
of the sun and earth are known, their distance can be found
by comparing the distance which a heavy body will fall in
one second at the surface of the earth with the fall of the lat-
ter towards the sun in the same time. The mass of the earth
was found by its disturbing action on the planets Venus and
Mars, as explained in the chapter on Gravitation. Leverrier
* Mr. E. J. Stone was then first assistant at the Royal Observatory, Green-
wich, but has been Astronomer Royal at the Cape of Good Hope since 1870.
t <; Monthly Notices of the Royal Astronomical Society," vol. xxvii., p. 241,
and vol. xxviii., pp. 22, 23,
200 PRACTICAL ASTRONOMY.
concluded that tins method gave the value of the solar paral-
lax as S".86. But one of his numbers requires a small correc-
tion, which reduces it to S".83. Another determination of the
mass of the earth relative to that of the sun has recently been
made by Von Asten, of Pnlkowa, from the action of the earth
upon Encke's comet. The solar parallax thence resulting is
9 X/ .009, the largest recent value ; but the anomalies in the ap-
parent motions of this comet are such that very little reliance
can be placed upon this result.
Yet another method of determining the solar parallax has
been proposed and partially carried out by Dr. Galle.* It
consists in measuring the parallax of some of the small plan-
ets between Mars and Jupiter at the times of their nearest
approach to the earth, by observations in the northern and
southern hemispheres. The least distance of the nearest of
these bodies from us is little less than that of the sun, so that
in this respect they are far less favorable than Venus and
Mars. But they have the great advantage of being seen in
the telescope only as points of light, like stars, and, in conse-
quence, of having their position relative to the surrounding
stars determined with greater precision than can be obtained
in the case of disks like those of Venus and Mars. Observa-
tions of Flora were made in this way at a number of observa-
tories in both hemispheres during the opposition of 1874, from
which Dr. Galle has deduced 8 7/ .875 as the value of the solar
parallax.
Most Probable Value of the Surfs Parallax. From the gen-
eral accordance of the various methods we have described, it
would appear that the solar parallax must lie between pretty
narrow limits, probably between 8".82 and 8".86, and that
the distance of the sun in miles probably lies between the
limits 92,200,000 and 92,700,000. Of the distance of the
sun, we may say with a reasonable approach to certainty that
it is 92,000,000 and some fraction of another million ; and
* Dr. J. G. Galle, now director of the observatory at Breslau, Eastern Prussia.
He was formerly assistant at the Observatory of Berlin, where he became cele-
brated as the optical discoverer of the planet Neptune.
STELLAR PARALLAX. 201
if we should guess that fraction to be 400,000, we should
probably be within 200,000 miles of the truth. This is all
we can say of the sun's distance until the results of the tran-
sits of Venus are obtained, when we may hope to find the
uncertainty brought between yet narrower limits.
In many recent works the distance in question will be found
stated at 91,000,000 and some fraction. This arises from the
circumstance that into several of the first determinations by
the new methods small errors and imperfections crept, which,
by a singular coincidence, all tended to make the parallax too
great, and therefore the distance too small. For instance,
Hansen's original computations from the motion of the moon
led him to a parallax of 8".96. Revising his calculations, he
reduced it to 8".917. When his lunar tables, published in
1857, came to be compared with observations, it was found
that his parallactic inequality was undoubtedly too great by
one second or more. When this is corrected, the parallax is
reduced about a tenth of a second more.
The observations of Mars, in 1862, as reduced by Winnecke
and Stone, first led to a parallax of 8".92 to 8".94. But in
these investigations only a small portion of the observations
was used. When the great mass remaining was joined with
them, the result was 8".85.
The early determinations of the time required for light to
come from the sun were founded on the extremely uncertain
observations of eclipses of Jupiter's satellites, and were five to
six seconds too small. The time, 493 seconds, being used in
some computations instead of 498 seconds, the distance of the
sun from the velocity of light was made too small.
In both of Leverrier's methods some small errors of computa-
tion have been found, the effect of all of which is to make his
parallax too great. Correcting these, and making no change in
any of his data, the results are respectively 8".85 and 8".83.
5. Stellar Parallax.
It is probable that no one thing tended more strongly to
impress the minds of thoughtful men in former times with
202 PEACTICAL ASTRONOMY.
the belief that the earth was immovable than did the absence
of stellar parallax. We may call to mind that the annual par-
allax of the fixed stars arises from the change in their direc-
tion produced by the motion of the earth from one side of
its orbit to the other. One of the earliest forms in which we
may suppose this parallax to have been looked for is shown
in Fig. 58. Suppose AB to be the earth's orbit with the sun,
FIG. 58. Effect of stellar parallax.
8, near its centre, and RT two stars so situated as to be direct-
ly opposite each other when the earth is at A ; that is, when
the direction of each star is 90 distant from that of the sun.
Then it is clear that, after six months, when the earth is at /i,
the stars will no longer be opposite each other, the point /,
which is opposite J2, making the angle TBU, with the direc-
tion of T. The stars will all be displaced in the same direc-
tion that the sun is in from the earth. When it was found
that the most careful observations showed no such displace-
ment, the conclusion that the earth did not move seemed in-
evitable. We have seen how Tycho was led in this way to
reject the doctrine of the earth's motion, and favor a system
in which the sun moved around it. In this Tycho was fol-
lowed by the ecclesiastical astronomers who lived during the
seventeenth century, and who, finding no parallax whatever to
auy of the stars, were led to reject the Coperriican system.
The telescope furnishing so powerful an auxiliary in meas-
uring small angles, it was natural that the defenders of the
Copernican system should be anxious to employ it in detect-
ing the annual parallax of the stars. But the earlier observ-
ers had very imperfect notions of the mechanical appliances
necessary to do this with success, and, in consequence, the in-
vention of the telescope did not result in any immediate im-
STELLAR PARALLAX. 203
provement in the methods of celestial measurement. A step
was taken in 1669 by Hooke, of England, who was among the
first to see how the telescope was to be applied in the meas-
urement of the apparent distances of the stars from the ze-
nith. He fixed a telescope thirty-six feet long in his house, in
a vertical position, the object-glass being in an opening in the
roof, while the eye-piece was in one of the lower rooms. A
fine plumb-line hung down from the object-glass to a point
below the eye -piece, which gave a truly vertical line from
which to measure. The star selected for observation \vas y
Draconis, because it was comparatively bright, and passed over
the zenith of London. His mode of observation was to meas-
ure the distance of the image of the star from the plumb-line
from day to day at the moment of its passing the meridian.
He had made but four observations when his object-glass was
accidentally broken, and the attempt ended without leading
to any result whatever.
Between 1701 and 1704, Roomer, then of Copenhagen, at-
tempted to determine the sum of the double parallaxes of
Sirius and a Lyrse by the principle shown in Fig. 58. These
stars lie somewhere near the opposite quarters of the celestial
sphere, and the angle between them will vary from spring to
autumn by nearly double the sum of their parallaxes. The
angle was measured by the transit instrument and the astro-
nomical clock, by noting the time which elapsed between the
transit of Sirius over the meridian, and that of a Lyrae. This
time was found to be, on the average,
Hrs. Min. See.
In February, March , a nd A pri 1 11 54 59.7
In September and October 11 54 55. 4
Difference 4.3
Here was a difference of four seconds of time, or a minute of
angle, which was then very naturally attributed to the motion
of the earth, and which was afterwards printed in a disserta-
tion entitled " Copernicus Triuinphans." It is now known that
there is no such parallax as this to either of these stars, and
204 PRACTICAL ASTRONOMY.
Peters* has shown that the difference which was attributed
to parallax by the enthusiastic Danish astronomers really arose,
in great part, from the diurnal irregularity in the rate of their
clock, caused by the action of the diurnal change of tempera-
ture upon the un compensated pendulums. In the spring the
interval of time measured elapsed during the night, Sirius
passing the meridian in the evening, and a Lyrse in the morn-
ing. The cold of night made the clocks go too fast, and so
the measured interval came out too great. In the autumn
Sirius passed in the morning, and a Lyrse in the evening ; the
clock was going too slow on account of the heat of the day,
and the interval came out too small.
Among the numerous other vain efforts made by the astron-
omers of the last century to detect the stellar parallax, that of
Bradley is worthy of note, owing to the remarkable discovery
of the aberration of light to which it led. The principle of
his instrument was the same as that of Hooke, the zenith dis-
tance of the star y Draconis at the moment of -its passing the
meridian being determined by the inclination of a telescope to
a fine plumb-line. The instrument thus used, which has be-
come so celebrated in the history of astronomy, has since been
known as Bradley's zenith sector. In accuracy it was a long
step in advance of any which preceded it, so that by its means
Bradley was able to announce with certainty that the star in
question had no parallax approaching a single second. But
he found another annual oscillation of a very remarkable
character, arising from the progressive motion of light, which
will be described in the next chapter. It lias frequently hap-
pened in the history of science that an investigation of some
cause has led to discoveries in a different direction of an en-
tirely unexpected character.
It would be tedious to describe in detail all the efforts
made by astronomers, during the last century and the early
part of the present one, to detect the stellar parallax. It will
* C. A. F. Peters, then of the Pulkowa Observatory, and now editor of the As-
tronomische Nachrichten.
STELLAR PARALLAX. 205
be sufficient to say, in a general way, that they depended on
absolute measures; that is, the astronomer endeavored, gen-
erally by a divided circle, to determine from day to day the
zenith distance at which the star passed the meridian. The
position of the zenith was determined in various ways some-
times by a fine plumb-line, sometimes by the level of quick-
silver. What is required is the angle between the plumb-line
and the line of sight from the observer to the star. The same
result can be obtained by observing the angle between a ray
coming directly from a star and the ray which, coming from
the star, strikes the surface of a basin of quicksilver, and is re-
flected upwards. Whatever method is used, a large angle has
to be measured, an operation which is always affected by un-
certainty, owing to the influences of varying temperatures and
many other causes upon the instrument. The general result
of all the efforts made in this way was that while several of
the brighter stars seemed to some astronomers to have paral-
laxes, sometimes amounting to two or three seconds, though
generally not much exceeding a second, yet there was no such
agreement between the various results as was necessary to in-
spire confidence. As a matter of fact, we now know that
these results were entirely illusory, being due, not to parallax,
but to the unavoidable errors of the instruments used.
Struve was the first one to prove conclusively that the par-
allaxes even of the brighter stars were so small as to abso-
lutely elude every mode of measurement before adopted. In
principle his method was that employed by Roemer, the sum
of the parallaxes of stars twelve hours distant in right ascen-
sion being determined by the annual change in the intervals
between their times of transit over the meridian. But he
made the great improvement of selecting stars which could
be observed as they passed the meridian below the pole, as
well as above it, so that a short time before or after observing
the transit of a star he could turn his transit instrument be-
low the. pole, and observe the transit of the opposite star from
west to east. Thus he was not under the necessity of depend-
ing on the rate of his clock for more than an hour or two.
206 PRACTICAL ASTRONOMY.
while Roemer had to depend on it for twelve hours. The re-
sult of Struve was that the average parallax of the twenty-
five brightest stars within 45 of the pole could not much, if
at all, exceed a single tenth of a second.
Such was the general state of things up to the year 1835.
It was then decided by Struve and Bessel, in lieu of attempt-
ing to determine zenith distances, to adopt the method of
relative parallaxes. The idea of this method really dates al-
most from the invention of the telescope. It was considered
by Galileo and Huyghens that where a bright and a faint
star were seen side by side in the field of view of a telescope,
the latter was probably vastly more distant than the former,
and that consequently they would change their relative po-
sition as the earth moved from one side of the sun to the oth-
er. If, for instance, one star was three times the distance of
the other, its apparent motion produced by parallax would be
only a third that of the other, and there would remain a rel-
ative parallax equal to two-thirds that of the brighter star,
which could be detected by measuring the angular distance
of the two stars as seen in the telescope from day to day
throughout the year. The drawback to which this method is
subject is the impossibility of determining how many times
farther the one star is than the other ; in fact, it may be that
the smaller star is really no farther than the large one. No
doubt it was this consideration which deterred the astrono-
mers of the last century from trying this very simple method.
The astronomers of the last generation found cases in
which there could be little doubt that a star was much near-
er to us than the small stars which surrounded it in the field
of the telescope. For instance, the star 61 Cygni, or rather
the pair of stars thus designated, are found not to occupy a
fixed position in the celestial sphere, like the surrounding
small stars, but to be moving forward in a straight line at the
rate of six seconds per year. This amount of proper motion
was so unusual as to make it probable that the star must be
one of the nearest to us, although it was only of the sixth mag-
nitude. It was therefore selected by Bessel for the investi-
STELLAR PARALLAX. ' 207
gation of its parallax relative to two other stars in its neigh-
borhood. The instrument used was the heliometer, an in-
strument which, as now made, admits of great precision, but
which was then liable to small uncertainties from various
causes. His early attempts to detect a parallax failed as
completely as had those of former observers. He recom-
menced them in August, 1837, his first series of measures be-
ing continued until October, 1838. The result of this series
was the detection of a parallax of about three-tenths of a sec-
ond (0".3136). He then took down his instrument, made some
improvements in it, and commenced a second series, which he
continued until July, 1839 ; and his assistant, Schliiter, until
March, 1840. The final value of the parallax deduced by
Bessel from all these observations was 0".35. The reality of
this parallax has been well established by subsequent investi-
gators, only it has been found to be a little larger. From a
combination of all the results, Auwers, of Berlin, finds the
most probable parallax to be 0".51.
The star selected by Struve for the measure of relative par-
allax was the bright one a Lyrse. This has not only a sensible
proper motion, but is of the first magnitude ; so that there is
every reason to believe it to be among those which are nearest
to us. The comparison was made with a single very small
star in the neighborhood, the instrument used being the nine-
inch telescope of the Dorpat Observatory. The observations
extended from November, 1835, to August, 1838. The result
was a relative parallax of a quarter of a second. Subsequent
investigations have reduced this parallax to two-tenths of a
second, so that although a LyrsB is nearly a hundred times as
bright as either of the pair of stars 61 Cygni, it is more than
twice as far from us.
So far as is known, and, beyond all reasonable doubt, in re-
ality, the nearest fixed star is a Centauri, in the southern hem-
isphere. This fact was discovered by Henderson, the English
Astronomer Royal at the Cape of Good Hope, about the same
time that Struve and Bessel were making their first measures
of parallaxes. The observations on which it was founded
208 PRACTICAL ASTRONOMY.
were made with the mural circle of the Cape Observatory,
and were therefore absolute measures of zenith distance, in-
stead of comparisons with surrounding stars, like the measures
of Struve and Bessel. From a discussion of his own obs^rva-
tions, and a very careful series by his successor, Hender-
son found the parallax of the pair of stars which compose
a Centauri to be 0".91.* This parallax corresponds to the
distance of 226,000 astronomical units,f or more than twenty
millions of millions of miles. Yet it is not only the nearest
star, but so far the nearest that no other is known to be with-
in nearly double the distance.
The most elaborate measures of stellar parallax made in
recent times are those by Dr. Briinnow, formerly director of
the observatory at Ann Arbor, Michigan. On Ids appointment
to the post of Astronomer Royal for Ireland, Dr. Briinnow
employed the equatorial telescope of the Dunsink Observa-
tory in such determinations with great success. The results
of his measures, with those of other astronomers, are given in
the Appendix to the present work.
The recent researches of various observers have resulted in
showing that there are about a dozen stars visible in our lati-
tudes of which the parallax ranges from a tenth to half a sec-
ond. Part of these are small stars, supposed to be near us
from their large proper motion, while others are stars of the
far brighter classes. It is, however, remarkable that among the
thirteen stars of the first magnitude visible in our latitudes,
less than half have been found to have any measurable paral-
lax, even when the greatest refinements have been applied in
the observations. For the most part, the stars with a decided
parallax are not of a conspicuous magnitude. The two stars
next in distance to a Centauri are 61 Cygni, of the fifth mag-
nitude, and one in Ursa Major without a name, and too small
* The mean of all the measures of the parallax of this pair of stars hitherto
made, gives 0".93 as their most probable parallax, corresponding to a distance
of 221,000 astronomical units.
t The astronomical unit is the distance of the earth from the sun, about 92
millions of miles.
STELLAR PARALLAX. 209
to be seen without a telescope. The parallax of the latter has
been found by Professor Winnecke* to be 0".501, which is
nearly the same as that of 61 Cygni. The question of the
average distance of the stars of the first magnitude must
therefore be regarded as still unsolved. We can only say
that the parallax of at least half of them is probably less than
the tenth of a second, and, therefore, the distance greater than
two million radii of the earth's orbit, f
In these measurements of the annual parallax of the fixed
stars, it sometimes happens that the astronomer finds his ob-
servations to give a negative parallax. To understand what
this means, we remark that a determination of the distance of
a star is made by determining its directions, as seen from op-
posite points of the earth's orbit. If we draw a line from
each of these points, in the observed direction of the star, the
point in which the lines meet marks the position of the star.
A negative parallax shows that the two lines, instead of con-
verging to a point, actually diverge, so that there is no pos-
sible position of the star to correspond to the observations.
Such a paradoxical result can arise only from errors of obser-
vation.
* Dr. A. Winnecke, formerly assistant at the Pulkowa Observatory, and now
director of the observatory at Strasburg.
t A list of the stars of which the parallaxes have been determined will be found
in the Appendix.
15
210 PRACTICAL ASTRONOMY.
CHAPTEK IV.
THE MOTION OF LIGHT.
INTIMATELY connected with celestial measurements are the
curious phenomena growing out of the progressive move-
ment of light. It is now known that when we look at a star
we do not see the star that now is, but the star that was sev-
eral years ago. Though the star should suddenly be blotted
out of existence, we should still see it shining for a number
of years before it would vanish from our sight. We should
see an event that was long past, perhaps one that was past
before we were born. This non-coincidence of the time of
perception with that of occurrence is owing to the fact that
light requires time to travel. We can see an object only by
light which emanates from it arid reaches our eye, and thus
our sight is behind time by the interval required for the light
to travel over the space which separates us from the object.
It was by observations of the satellites of Jupiter that it
was first found that celestial phenomena were thus seen be-
hind time. These bodies revolve round Jupiter much more
rapidly than our moon does around the earth, the inner satel-
lite making a complete revolution in eighteen hours. Owing
to the great magnitude of Jupiter and his shadow, this satel-
lite, as also the two next outside of it, are eclipsed at every rev-
olution. The accuracy with which the times of disappearance
in the shadow could be observed, and the consequent value of
such observations for the determination of longitudes, led the
astronomers of the 'seventeenth century to make tables of the
times of occurrence of these eclipses. In attempting to im-
prove the tables of his predecessors, it was found by Eoemer
(then of Paris, though a Dane by birth) that the times of the
THE MOTION OF LIGHT. 211
eclipses could not be represented by an equable motion of
the satellites. He could easily represent the times of the
eclipses when Jupiter was in opposition to the sun, and there-
fore the earth nearest to Jupiter. But then, as the earth re-
ceded from Jupiter in its annual course round the sun, the
eclipses were constantly seen later, until, when it was at its
greatest distance from Jupiter, the times appeared to be 22
minutes late. Such an inequality, Koemer concluded, could
not be real ; he therefore attributed it to the fact that it must
take time for light to come from Jupiter to the earth, and
that this time is greater the more distant the earth is from
the planet. He therefore concluded that it took light 22
minutes to cross the orbit of the earth, and, consequently, 11
minutes to come from the sun to the earth.
The next great step in the theory of the progressive motion
of light was made by the celebrated Bradley, afterwards As-
tronomer Koyal of England, to whose observations at Kew on
the star y Draconis with his zenith sector, in order to deter-
mine the parallax of the star, allusion has already been made.
The effect of parallax would have been to make the declina-
tion greatest in June and least in December ; while in March
and September the star would occupy an intermediate or
mean position. But the actual result of the measures was
entirely different, and exhibited phenomena which Bradley
could not at first account for. The declinations of June and
December were the same, showing no effect of parallax. But,
instead of remaining the same the rest of the year, the decli-
nation was some forty seconds greater in September than to
March, when the effect of parallax should be the same. Thus,
the star had a regular annual oscillation ; but instead of its
apparent motion in this little orbit being opposite to that of
the earth in its annual orbit, as required by the laws of rela-
tive motion, it was constantly at right angles to it.
After long consideration, Bradley saw the cause of the
phenomenon in the progressive motion of light combined
with the motion of the earth in its' orbit. In Fig. 59 let S
be a star, and OT a telescope pointed at it. Then, if the
rt
T
212 PRACTICAL ASTRONOMY.
telescope is not in motion, the ray SOT emanating from the
star, and entering the centre of the object-glass,
Will pass down near the right-hand edge of the eye-
piece, and the star will appear in the right of the
field of view. But, instead of being at rest, all our
telescopes are carried along with the earth in its
orbit round the sun at the rate of nearly nineteen
miles a second. Suppose this motion to be in the
direction of the arrow; then, while the ray is pass-
ing down the telescope, the latter moves a short dis-
tance, so that the ray no longer strikes the right-
hand edge of the eye-piece, but some point farther
to the left, as if the star were in the direction /S',
and the ray followed the course of the dotted line.
In order to see the star centrally, the eye end of the
telescope must be dropped a little behind, so that,
Flo> 59 instead of pointing in the direction S, it will really
Aberration be pointing in the direction /S", shown by the dotted
ray. This will then represent the apparent direc-
tion of the star, which will seem displaced in the direction in
which the earth is moving.
The phenomenon is quite similar to that presented by the
apparent direction of the wind on board a steamship in mo-
tion. If the wind is really at right angles to the course of the
ship, it will appear more nearly ahead to those on board ; and
if two ships are passing each other, they will appear to have
the wind in different directions. Indeed, it is said to have
been through noticing this very result of motion on board a
boat on the Thames, that the cause of the phenomenon he
had observed was suggested to Bradley.
The displacement of the stars which we have explained is
called the Aberration of Light. Its amount depends on the ra-
tio of the velocity of the earth in its orbit to the velocity of
light It can be determined by observing the declination of
a star at the proper seasons during a number of years, by
which the annual displacement will be shown. The value
now most generally received is that determined by Struve at
THE MOTION OF LIGHT. 213
the Pulkowa Observatory, and is 20' ; .445. Though this is the
most reliable value yet found, the two last figures are both
uncertain. We can say little more than that the constant
probably lies between 20".4:3 and 20".48, and that, if outside
these limits at all, it is certainly very little outside.
This amount of aberration of each star shows that light
travels 10,089 times as fast as the earth in its orbit. From
this we can determine the time light takes to travel from the
sun to the earth entirely independent of the satellites of Ju-
piter. The earth makes the circuit of its orbit in 365J days.
Then light would make this same circuit in TirTrf^ of a day,
which we find to be 52 minutes 8-| seconds. The diameter
of the earth's orbit is found by dividing its circumference by
3.1416, and the mean distance of the sun is half this diameter.
We thus find from the above amount of aberration that light
passes from the sun to the earth in 8 minutes 18 seconds.
The question now arises, Does the same result follow from
the observations of the satellites of Jupiter? If it does, we
have a striking confirmation of the astronomical theory of the
propagation of light. If it does not, we have a discrepancy,
the cause of which must be investigated. We have said that
the first investigator of the subject found the time required
to be 11 minutes. This determination was, however, uncertain
by several minutes, owing to the very imperfect character
of the early observations on which Roemer had to depend.
Early in the present century, Delambre made a complete in-
vestigation from all the eclipses of the satellites which had
been observed between 1662 and 1802, more than a thousand
in number. His result was 8 minutes 13.2 seconds.
There is a discrepancy of five seconds between this result
of Delambre, obtained some seventy years ago, and the mod-
ern determinations of the aberrations of the fixed stars made
by Struve and others. What is its cause? Probably only the
errors of the observations used by Delambre. In this case,
there would be no real difference. But some physicists and
astronomers have endeavored to show that there is a real
cause for such a difference, which they hold to indicate an er-
214 PRACTICAL ASTRONOMY.
ror in the value of the aberration derived from observation
arising in this way. It is known from experiment that light
passes through glass or any other refracting medium more
slowly than through a void. In observations with a telescope
the light has to pass through the objective, and the time lost
in doing so will make the aberration appear larger than it
really is, and the velocity of light will appear too small. But
the commonly received theory (that of Fresnel) is that this
loss of time is compensated by the objective partially drawing
the ray with it. Desirous of setting the question at rest, Pro-
fessor Airy, a few years ago, constructed a telescope, which
he filled with water, with which he observed the constant of
aberration. The aberration was found to be the same as with
ordinary telescopes, thus proving the theory of Fresnel to be
correct, because on the other theory the aberration ought to
have been much increased by the water.
Hence this explanation of the difference of the two results
fails, and renders it more probable that there is some error in
Delambre's result. A reinvestigation of all the observations
of Jupiter's satellites is very desirable ; but so vast is the labor
that no one since Delambre has undertaken it. Mr. Glasenapp,
a young Kussian astronomer, has, however, recently investi-
gated all the observations of Jupiter's first satellite made dur-
ing the years 1848-1873, and found from these that the time
required for light to pass from the sun to the earth is 8 min-
utes 20 seconds. Instead of being smaller than Struve's re-
sult, this is two seconds larger, and seven seconds larger than
that of Delambre. It is therefore concluded that the differ-
ence between the results of the two methods arises entirely
from the errors of the observations used by Delambre, and
that Struve's time (498 seconds) is not a second in error.
Each of the two methods we have described gives us the
time required for light to pass from the sun to the earth ; but
neither of them gives us any direct information respecting the
velocity of light. Before we can determine the latter from
the former, we must know what the distance of the sun is,
Dividing this distance in miles by 498, we shall have the dis-
THE MOTION OF LIGHT. 215
tance which light travels in a second. Conversely, if we can
find experimentally how far light travels in a second, then by
multiplying this distance by 498 we shall have the distance of
the sun. But we need only reflect that the velocity of light
is about 180,000 miles per second to see that the problem of
determining it experimentally is a most difficult one. It is
seldom that objects on the surface of the earth are distinctly
seen at a greater distance than forty or fifty miles, and over
such a distance light travels in the forty-thousandth part of a
second. As might be expected, the earlier attempts to fix the
time occupied by light in passing over distances so short as
those on the surface of the earth were entire failures. The
first of these is due to Galileo ; and his method is worth men-
tioning, to show the principle on which such a determination
can be made. He stationed two observers a mile or two apart
by night, each having a lantern which he could cover in a
moment. The one observer, A, was to cover his lantern, and
the distant one, B, as soon as he saw the light disappear, cov-
ered his also. In order that A might see the disappearance
of B's lantern, it was necessary that the light should travel
from A to B, and back again. For instance, if it took one
second to travel between the two stations, B would continue
to see A's light an entire second after it was really extinguish-
ed ; and if he then covered his lantern instantly, A would
still see it during another second, making two seconds in all
after he had extinguished his own, besides the time B might
have required to completely perform the movement of cover-.,
ing his.
Of course, by this rough method Galileo found no inter-
val whatever. An occurrence which only required the hun-
dredth part of the thousandth of a second was necessarily in-
stantaneous. But we can readily elaborate his idea into the
more refined methods used in recent times. Its essential feat-
ure is that which must always be employed in making the de-
termination ; that is, it is necessary that the light shall be sent
from one station to another, and then returned to the first
one, where the double interval is timed. There is no possi-
216 PRACTICAL ASTRONOMY.
bility of comparing the times at two distant stations with the
necessary precision. The first improvement we should make
on Galileo's method would be to set up a mirror at the dis-
tant station, and dispense with the second lantern, the ob-
server A seeing his own lantern by reflection in the mirror.
Then, if he screened his lantern, he would continue to see it
by reflection in the mirror during the time the light required
to go and come. But this also would be a total failure, be-
cause the reflection would seem to vanish instantly. Our next
effort would be to try if we could not send out a flash of
light from our lantern, and screen it off before it got back
again. An attempt to screen off a single flash would also be
a failure. We should then try sending a rapid succession of
flashes through openings in a moving screen, and see wheth-
er they could be cut off by the sides of the openings before
their return. This would be
effected by the contrivance
shown in Fig. 60. We have
here a wheel with spokes ex-
^lEii Xi/^ H??l ^nding from its circumfer-
ence, the distance between
them being equal to their
breadth. This wheel is placed
in front of the lantern, L, so
that the light from the latter
FIG. 60. Revolving wheel, for measuring the has to paSS between the Spokes
velocity of light. ^ t j ie w } iee ] j n or( j er t o reach
the distant mirror. In the figure the reader is supposed to be
between the wheel and the reflecting mirror, facing the for-
mer, so that he sees the light of the lantern, and also the eye
of the observer, between the spokes. The latter, looking be-
tween the spokes, will see the light of the lantern reflected
from the mirror. Now, suppose he turns the wheel, still keep-
ing his eye at the same point. Then, each spoke cutting off the
light of the lantern as it passes, there will be a succession of
flashes of light which will pass through between the spokes,
travel to the mirror, and thence be reflected back again to the
THE MOTION OF LIGHT. 217
wheel. Will they reach the eye of the observer behind the
wheel ? Evidently they will, if they return so quickly that a
tooth has not had time to intervene. But suppose the wheel to
turn so rapidly that a tooth just intervenes as the flash gets
back to it. Then the observer will see no light in the mirror,
because each successive flash is caught by the following tooth
just before it reaches the observer's eye. Suppose, next, that
he doubles the speed of his wheel. Then, while the flash is
travelling to the mirror and back, the tooth will have passed
clear across and out of the way of the flash, so that the latter
will now reach the observer's eye through the opening next
following that which it passed through to leave the lantern.
Thus, the observer will see a succession of flashes so rapid
that they will seem entirely continuous to the eye. If the
speed of the wheel be again increased, the return flash will be
caught on the second tooth, and the observer will see no light,
while a still further increase of velocity will enable him to
see the flashes as they return through the second interval be-
tween the spokes, and so on.
In principle, this is Fizeau's method of measuring the ve-
locity of light. In place of spokes, he has exceedingly fine
teeth in a large wheel. He does not look between the teeth
with the naked eye, but employs a telescope so arranged that
the teeth pass exactly through its focus. An arrangement is
made by which the light passes through the same focus with-
out reaching the observer's eye except by reflection from the
distant mirror. The latter is placed in the focus of a second
telescope, so that it can be easily adjusted to send the rays
back in the exact direction from which they come. To find
the time it takes the light to travel, it is necessary to know the
exact velocity of the wheel which will cut off the return light
entirely, and thence the number of teeth which pass in a sec-
ond. Suppose, for instance, that the wheel had a thousand
teeth, and the reflector was nine miles away, so that the light
had to travel eighteen miles to get back to the focus of the
telescope. Then it would be found that with a velocity of
about five turns of the wheel per second, the light would be
218 PRACTICAL ASTRONOMY.
first cut off. Increasing the velocity, it would reappear, and
would grow brighter until the velocity reached ten turns per
second. It would then begin to fade away, and at fifteen
turns per second would be again occulted, and so on. With
the latter velocity, fifteen thousand teeth and fifteen thousand
intervals would pass in a second, while two teeth and one in-
terval passed during the time the light was performing its
journey. The latter would, therefore, be performed in the
ten-thousandth part of a second, showing the actual velocity
to be 180,000 miles per second. The most recent determina-
tion made in this way is by M. Cornu, of Paris, who has made
some improvements in the mode of applying it. His results
will be described presently.
Ingenious and beautiful as this method is, I do not think it
can be so accurate as another employed by Foucault, in which
it is not a toothed wheel which revolves, but a Wheatstone
mirror. To explain the details of the apparatus actually used
would be tedious,
but the principle on
which the method
rests can be seen
quite readily. Sup-
pose AB, Fig. 61, to
\A' represent a flat mir-
ror, seen edgewise,
revolving round an
w' ax i 8 a ^ -^> an d G a
FIG. 61. Illustrating Foucault's method of measuring the fixed COllCave mir-
velocity of light. ^ ^ pkced ^
the centre of its concavity shall fall on X. Let be a lumi-
nous point, from which emanates a single ray of light, OX.
This ray, meeting the mirror at X, is reflected to the concave
mirror, (7, which it meets at a right angle, and is therefore re-
flected directly back on the line from which it came, first to
JT, and then through the point 0, from which it emanated, so
that an eye stationed at E will see it returning exactly through
the point 0. No matter how the observer may turn the mir-
THE MOTION OF LIGHT. 219
ror AB, he cannot make the reflected ray deviate from this
line : he can only make it strike a different point of the mir-
ror 0. If he turns AB so that after the ray is reflected from
it, it -does not strike G at all, then he will see no return ray.
If the ray is reflected back at all, it will pass through 0. This
result is founded on the supposition that the mirror AB re-
mains in the same position during the time the r#y occupies
in passing from X to C and back. But suppose the mirror
AB to be revolving so rapidly that when the ray gets back
to X, the mirror has moved to the position of the dotted line
A'B'. Then it will no longer be reflected back through 0,
but will be sent in the direction J57', the angle EXE' being
double that through which the mirror has moved during the
time the ray was on its passage. Knowing the velocity of
the mirror, and the angle EXE'^ this time is easily found.
Evidently the observer cannot see a continuous light at JE\
because a reflection can be sent back only when the revolving
mirror is in such a position as to send the ray to some point
of the concave mirror, C. What will really be seen, therefore,
is a succession of flashes, each flash appearing as the revolving
mirror is passing through the position AB. But when the
mirror revolves rapidly, these flashes will seem to the eye to
form a continuous light, which, however, will be fainter than
if the mirror were at rest, in the proportion which the arc of
the concave mirror, (7, bears to an entire circle. Beyond the
enfeeblement of the light, this want of continuity is not pro-
ductive of any inconvenience. It was thus found by Fou-
cault that the velocity of light was 185,000 miles per second, a
result which is probably within a thousand miles of the truth.
The preceding explanation shows the principle of the meth-
od, but not the details necessary in applying it. It is not
practicable to isolate a single ray of light in the manner sup-
posed in the figure, and therefore, without other apparatus,
the light from would be spread all over the space around E
and E '. The desired result is obtained by placing a lens be-
tween the luminous point and the revolving mirror in such
a position that all the light falling from upon the lens shall,
220 PRACTICAL ASTRONOMY.
after reflection, be brought to a focus upon the surface of the
concave mirror, C. Then when the mirror A B is made to re-
volve rapidly, the return rays passing back through the lens
on their return journey are brought to a focus at a point
along-side 0, and distant from it by an amount which is pro-
portional to the time the light has required to pass from X to
(7 and back again.
So delicate is this method, that the millionth of a second of
time can be measured by it as accurately as a carpenter can
measure the breadth of a board with his rule. Its perfection
is the result of the combined genius of several men. The first
idea of employing a revolving mirror in the measurement of
a very minute interval of time is due to the late Sir Charles
Wheatstone, who thus measured the duration of the electric
spark. Then Arago showed that it could be applied to de-
termine whether the velocity of light was greater in water
or in air. Fizeau and Foucault improved on Arago's ideas
by the introduction of the concave mirror, having its centre
of curvature in the revolving mirror, and then this wonderful
piece of apparatus was substantially complete. The last de-
termination of the velocity of light with it was made by Fou-
cault, and* communicated to the French Academy of Sciences
in 1862, with the statement that the velocity resulting from
all his experiments was 298,000 kilometres (185,200 miles)
per second.
The problem in question was next taken up by Cornu, of
Paris, whose result has already been alluded to. Notwith-
standing the supposed advantages of the Foucault -Wheat-
stone method, M. Cornu preferred that of Fizeau. His first
results, reached in 1872, accorded quite well with those of
Foucault just cited, indicating a small but somewhat uncer-
tain increase. His experiments were repeated in 1874, and
their results were communicated to the French Academy of
Sciences in December of that year. In this last series of
measurements his station was the observatory, and the distant
mirror was placed on the tower of Montlhdry, at a distance of
about fourteen English miles. The telescope through which
THE MOTION OF LIGHT.
221
the flashes of light were sent and received was twenty-nine
feet long and of fourteen inches aperture. The velocity of
the toothed wheel could be made to exceed 1600 turns a sec-
ond, and by the electro-chronograph, on which the revolutions
were recorded, the time could be determined within the thou-
sandth of a second. At Montlhery, the telescope, in the focus
of which the reflecting mirror was placed, was six inches in
aperture, and was held by a large cast-iron tube set in the
masonry of the tower. At this distance M. Cornu was able,
with the highest velocity of his revolving wheel, to make
twenty of its teeth pass before the flashes of light got back,
and to catch them, on their return, on the twenty-first tooth.
All the determinations, however, were not made with the
wheel going at this rate, but with such different velocities that
the rays were caught sometimes on one tooth and sometimes
on another, from the fourth to the twenty-first. The follow-
ing table shows the velocity of light in kilometres per second
when the ray was caught on the fourth tooth, on the fifth, and
so on to the twenty-first :
Tooth 13 300,340
14 300,350
15 , 300,290
16 300,620
17 .....300,000
18 300,150
19 299,550
20
21 300,060
M. Cornu hence concludes that the velocity of light in air
is 300,330, and in a vacuum 300,400 kilometres per second.
But Helmert, of Aix, has noticed a tendency in M. Cornu's
numbers, as given above, to diminish as the velocity of the
wheel is increased, and concludes that the true velocity to be
derived from the measures is 299,990 kilometres. This re-
sult, though less than that derived by Cornu himself, is still
nearly 2000 kilometres greater than that of Foucault.
Tooth 4 300,130
5 300,530
6 300,750
7 300,820
8 299,940
9 300,550
10 300,640
11 300,350
12 300,500
222 PRACTICAL ASTRONOMY.
CHAPTER V.
THE SPECTROSCOPE.
IN one of Dr. Lardner's popular lectures on astronomy, de-
livered some thirty years ago, he introduced the subject of
weighing the planets as one in which he could with difficulty
expect his statements to be received with credulity. That
men should measure the distances of the planets was a state-
ment he expected his hearers to receive with surprise; but the
step from measuring to weighing was so long a one, that it
seemed to the ordinary mind to extend beyond all the bounds
of possibility.
Had a hearer told the lecturer that men would also be able
to determine the chemical constituents of the sun and stars,
and to tell whether any of them did or did not contain iron,
hydrogen, and other chemical elements, the lecturer would
probably have replied that that statement quite exceeded the
limits of his own credulity ; that, while he himself saw clearly
how the planets were measured and weighed, he looked upon
the idea of determining their chemical constitution as a mere
piece of pleasantry, or the play of an exuberant fancy. And
yet, this very thing has, to a certain extent, been done by the
aid of the spectroscope. The chemical constitution of matter
in the state of gas or vapor can be detected almost as readily
at the distance of the stars as if we had it in our laboratories.
The difficulties which stand in the way do not arise from the
distance, but from the fact that matter in the heavenly bodies
seems to exist in some state which we have not succeeded in
exactly reproducing in our laboratories. Like many other
wonders, spectrum analysis, as it is called, is not at all extraor-
dinary after we see how it is done. Indeed, the only wonder
THE SPECTROSCOPE. 223
now is how the first half of this century could have passed
without physicists discovering it. The essential features of
the method are so simple that only a knowledge of the ele-
ments of natural philosophy is necessary to enable them to be
understood. We shall, therefore, briefly explain them.
It is familiarly known that if we pass the rays of the sun
which enter a room by a small opening through a prism, the
light is separated into a number of bright colors, which are
spread out on a certain scale, the one end being red and the
other violet, while a long range of intermediate colors is found
between them. This shows that common white light is really
a compound of every color of the spectrum. This compound
is not like chemical compounds, made up of two or three or
some limited number of simples, but is composed of an infini-
ty of different kinds of light, all running into each other by
insensible degrees ; the difference, however, being only in col-
or, or in the capacity of being refracted by the prism through
which it passes. This arrangement of colors, spread out to our
sight according to the ref rangibility of the light which forms
them, is called the spectrum. By the spectrum of any object
is meant the combination of colors found in the light which
emanates from that object. For instance, if we pass the light
from a candle through a prism, so as to separate it into its
component colors, and make the light thus separated fall on
a screen, the arrangement of colors on the screen would be
called the spectrum of the candle. If we look at a bright
star through a prism, the combination of colors which we see
is called the spectrum of the star, and so with any other object
we may choose to examine.
As the experiment of forming a spectrum is commonly
made, there is a slight mixing-up of light of the different col-
ors, because light of the same degree of refrangibility will
fall on different parts of the screen according to the part of
the prism it passes through. When the separation of the light
is thus incomplete, the spectrum is said to be impure. In or-
der to make any successful examination of the light which
emanates from an object, our spectrum must be pure ; that is,
224: PRACTICAL ASTRONOMY.
each point of the spectrum must be formed by light of one
degree of refrangibility. To effect this in the most perfect
way, the spectrum is not formed on a screen, but on the retina
of the observer's eye. An instrument by which this is done
is called a spectroscope.
The most essential parts of a spectroscope consist of a small
telescope with ^ prism in front of the object-glass. The ob-
server must adjust his telescope so that, removing the prism,
and looking directly at the object, he shall obtain distinct vis-
ion of it. Then, putting the prism in its place, and turning
the telescope to such an angle that the light which comes from
the object shall, after being refracted by the prism, pass direct-
ly into the telescope, he looks into the latter. When the prop-
er adjustments are made, he will see a pure spectrum of the
object. In order that this experiment may succeed, it is es-
sential that the object, when viewed directly, shall present the
appearance of a point, like a star or planet. If it is an object
which has a measurable surface, like the sun or moon, he will
see either no spectrum at all or only a very impure one.
For this reason, a spectroscope which consists of nothing but
a telescope and prism is not fitted for any purpose but that of
trial and illustration. To fit it for general use, another ob-
ject-glass, with a slit in its focus, is added. Fig. 62 shows the
FIG. 62. Course of rays through a spectroscope.
essential parts of a modern spectroscope. At the farther end
of the second telescope, where the light enters, is a narrow
slit, which can be opened or closed by means of a screw, and
THE SPECTROSCOPE. 225
through which the light from the object is admitted. The
rays of light following the dotted lines are made parallel by
passing through the lens, L. They then fall on the prism, P,
by which they are refracted, and from which they emerge par-
allel, except that the direction of the rays of different colors
is different, owing to the greater or less degree of refraction
produced by the prism. They then pass thr<pgh the object-
glass of the telescope, T^ by which the rays of each color are
brought to a focus at a particular point in the field of view,
the red rays all coming together at the lower point, the violet
ones at the upper point, and those of each intermediate color
at their proper place along the line. The observer, looking
into the telescope, sees the spectrum of whatever object is
throwing its light through the slit.
If the object of which the observer wishes to see the spec-
trum is a flame, he places it immediately in front of the slit ;
and'if it is an object of sensible surface, like the sun or moon,
he points the collirnator, C, 'directly at it, so that the light
which enters the slit shall fall on the lens, A J3ut if it is a
star, he cannot get light enough in this way to see it, and he
must either remove his collimator entirely, or fasten his spec-
troscope to the end of a telescope, so that the slit shall be
exactly in the focus. The latter is the method universally
adopted in examining the spectrum of a star.
If, with this instrument, we examine the light which comes
from a candle, from the fire, or from a piece of white-hot
iron, we shall find it to be continuous ; that is, there is no gap
in the series of colors from one end to the other. But if we
take the light from the sun, or from the moon, a planet, or
..any object illuminated by the sun, we shall find the spectrum
to be crossed by a great number of fine dark lines, showing
that certain kinds of light are wanting. It is now known
that the particular kinds of light which originally belonged
in these dark lines have been culled out by the gases surround-
ing the sun through which the light has passed. This culling-
out is called Selective Absorption. It is found by experiment
that each kind of gas has its own liking for light of peculiar
226 PRACTICAL ASTRONOMY.
degrees of refrangibility, and absorbs the light which belongs
in the corresponding parts of the spectrum, letting all the
other light pass.
Perhaps we may illustrate this process by a similar one
which we might imagine mankind to perform. Suppose Nat-
ure should loan us an immense collection of many millions
of gold piecespout of which we were to select those which
would serve us for money, and return her the remainder.
The English rummage through the pile, and pick out all the
pieces which are of the proper weight for sovereigns and half-
sovereigns ; the French pick out those which will make five,
ten, twenty, or fifty franc pieces ; the Americans the one, five,
ten, and twenty dollar pieces, and so on. After all the suit-
able pieces are thus selected, let the remaining mass be spread
out on the ground according to the respective weights of the
pieces, the smallest pieces being placed in a row, the next in
weight in an adjoining row, and so on. We shall then find a
number of rows missing : one which the French have taken
out for five-franc pieces; close to it another which the Amer-
icans have taken for dollars; afterwards a row which have
gone for half-sovereigns, and so on. By thus arranging the
pieces, one would be able to tell what nations had culled over
the pile, if he only knew of what weight each one made its
coins. The gaps in the places where the sovereigns and half-
sovereigns belonged would indicate the English, that in the
dollars and eagles the Americans, and so on. If, now, we re-
flect how utterly hopeless it would appear, from the mere ex-
amination of the miscellaneous pile of pieces which had been
left, to ascertain what people had been selecting coins from it,
and how easy the problem would appear when once some
genius should make the proposed arrangement of the pieces
in rows, we shall see in what the fundamental idea of spec-
trum analysis consists. The formation of the spectrum is the
separation and arrangement of the light which comes from an
object on the same system by which \ve have supposed the
gold pieces to be arranged. The gaps we see in the spectrum
tell the tale of the atmosphere through which the light has
THK SPECTROSCOPE. 227
passed, as in the case of the coins they would tell what nations
had sorted over the pile.
That the dark lines in the solar spectrum are picked out by
the gases of the sun's atmosphere has long been surmised ; in-
deed, Sir John Herschel seems to have had a clear idea of
the possibility of spectrum analysis half a cenjury ago. The
difficulty was to find what particular lines any particular sub-
stance selects; since, to exert any selective action, a vastly
greater thickness of gas is generally required than it is prac-
ticable to obtain experimentally. This difficulty was sur-
mounted by the capital discovery of Kirchhoff and Bunsen,
that a glowing gas gives out rays of the same degree of refrangibil-
ity tvhich it absorbs when light passes through it. For example,
if we put some salt into the flame of a spirit-lamp, and ex-
amine the spectrum of the light, we shall find a pair of bright-
yellow lines, which correspond most accurately to a pair of
black lines in the solar spectrum. These lines are known to
be due to sodium, a component of common salt, and their ex-
istence in the solar spectrum shows that there is sodium
in the sun's atmosphere. They are therefore called the sodi-
um lines. By vaporizing various substances in sufficiently hot
flames, the spectra of a great number of metals and gases
have been found. Sometimes there are only one or two bright
lines, while with iron the number is counted by hundreds.
The quantity of a substance necessary to form these bright
lines is so minute that the presence of some metals in a com-
pound have been detected with the spectroscope when it was
impossible to find a trace of them in any other way. Indeed,
two or three new metals, the existence of which was before en-
tirely unknown, first told their story through the spectroscope.
The general relations of the spectrum to the state of the
substance from which the light emanated may be condensed
into three rules, or laws, as follows :
1. The light from a glowing solid or liquid forms a contin-
uous spectrum, in which neither bright nor dark lines are
found. The spectrum is of the same nature, no matter how
finely the substance may be divided.
228 PRACTICAL ASTRONOMY.
2. If the light from the glowing solid passes through a gas-
eous atmosphere, the spectrum will be crossed by dark lines
occupying those parts of the spectrum where the light culled
out by the atmosphere belongs.
3. A glowing gas sends out light of the same degrees of
refrangibility as belong to that which it absorbs, so that its
spectrum consists of a system of bright lines occupying the
same position as the dark lines it would produce by absorption.
If, then, on examining the spectrum of a star or other heav-
enly body, we find only bright lines with dark spaces between
them, we may conclude that the body consists of a glowing
gas, and we judge what the gas is by comparing the spectrum
with those of various substances on the earth. If, on the oth-
er hand, the spectrum is a continuous one, except where cross-
ed by fine dark lines, we conclude that it emanates from a
glowing body surrounded by an atmosphere which culls out
some of the rays of light.
It will be seen that the spectroscope gives us no definite in-
formation respecting the nature or composition of bodies in
the solid state. If we heat any sort of metal white-hot, sup-
posing only that it will stand this heat without being vapor-
ized, we shall have a spectrum continuous from end to end, in
which there will be neither bright nor dark lines to give any
indications respecting the substance. In order, therefore, to
detect the presence of any chemical element with this instru-
ment, that element must be in the form of gas or vapor. Here
we have one limitation to the application of the spectroscope
to the celestial bodies. The tendency of bodies in space is to
cool off, and when they have once become so cool as to solidi-
fy, the instrument in question can give us no further definite
information respecting their constitution.
Even if the body be in the gaseous state, we cannot always
rely on the spectroscope informing us with certainty of the
nature of the gas. The light we analyze must either be emit-
ted by the gas, the latter being so hot as to shine by its own
light, or it must be transmitted through it. Thus, the appli-
cation of spectrum analysis is confined to glowing gases arid
THE SPECTROSCOPE. 229
the atmospheres of the stars and planets, the application to the
latter depending on the fact that the sunlight reflected from
the surface of the planet passes twice through its atmosphere.
Even in these cases the interpretation of its results is sometimes
rendered difficult in consequence of the varied spectrum of the
same gas at different temperatures and under different degrees
of pressure. Under some conditions so many new lines are
introduced into the spectrum of hydrogen that it can hardly
be recognized. As a general rule, the greater the pressure, the
greater the number of lines which appear ; indeed, it has been
found by Lockyer and Frankland that as the pressure and den-
sity of a gas are increased, its spectrum tends to become con-
tinuous. We must therefore regard the third of the above
rules respecting spectrum analysis, or, rather, the general rule
that a glowing gas gives a spectrum of bright lines, as not uni-
versally true. If we could, by artificially varying the temper-
ature, pressure, and composition of gases, accurately reproduce
the spectrum of a celestial body, the changes of the spectrum
which we have mentioned would be a positive advantage ;
since they would enable us to determine, not merely the com-
position of a gaseous body, but its temperature and pressure.
This is, however, a field in which success has not yet been
reached.
The reader now understands that when the light from a ce-
lestial object is analyzed by the prism, and the component col-
ors are spread out singly as on a sheet, the dark and bright
lines which we see are the letters of the open book which we
are to interpret so as to learn what they tell us of the body
from which the light came, or the vapors through which it
passed. When we see a line or a set of lines which we rec-
ognize as produced by a known substance, we infer the pres-
ence of that substance. The question may now be asked, How
do we know but that the lines we observe may be produced
by other substances besides those which we find to produce
them in our laboratories ? May not the same lines be pro-
duced by different substances? This question can be an-
swered only by an appeal to probabilities. The evidence iii
230 PRACTICAL ASTRONOMY.
the case is much the same as that by which, recognizing the
picture of a friend, we conclude that it is not the picture of
any one else. For anything we can prove to the contrary,
another person might have exactly the same features, and
might, therefore, make the very same picture. But, as a mat-
ter of fact, we know that practically no two men whom we
have ever seen do look exactly alike, and it is extremely im-
probable that they ever would look so. The case is the same
in spectrum analysis. Among the great number of substances
which have been examined with the spectroscope, no two give
the same lines. It is therefore extremely improbable that a
given system of bright lines could be produced by more than
one substance. At the same time, the evidence of the spec-
troscope is not necessarily conclusive in all cases. Should
only a single line of a substance be found in the spectrum of
a star or nebula, it would hardly be safe to conclude, from that
alone, that the line was really produced by the known sub-
stance. Collateral evidence might, however, come in. If the
same line were found both in the sunlight, and in that of a
great number of stars, we should be justified in concluding
that the lines were all produced by the same substance. All
we can say in doubtful cases is, that our conclusions must be
drawn with care and discrimination, arid must accord with the
probabilities of each special case.
PART III. THE SOLAR SYSTEM.
CHAPTER L
GENERAL STRUCTURE OF THE SOLAR SYSTEM.
HAVING, in the preceding parts, described the general struct-
ure of the universe, and the methods used by astronomers in
measuring the heavens and investigating the celestial motions,
we have next to consider in detail the separate bodies which
compose the universe, and to trace the conclusions respecting
the general order of creation to which this examination may
lead us. Our natural course will be to begin with a general
description of the solar system to which our earth belongs,
considering, first, the great central body of that system, then
the planets in their order, and, lastly, such irregular bodies as
comets and meteors.
We have shown in the first part that the solar system was
found by Copernicus, Kepler, and Newton to consist of the
sun, as the great central body, with a number of planets re-
volving around it in ellipses, having the sun in one of their
foci ; the whole being bound together by the law of universal
gravitation. Modern science has added a great number of
bodies, and shown the system to be a much more complex one
than Newton supposed. As we now know them, the bodies
of the system may be classified as follows :
1. The snn, the great central body ;
2. A group of four inner planets Mercury, Venus, the
Earth, and Mars ;
3. A swarm of small planets or asteroids revolving outside
the orbit of Mars (about 175 of them are now known) ;
232 THE SOLAR SYSTEM.
4. A group of four outer planets Jupiter, Saturn, Uranus,
and Neptune ;
5. A number of satellites of the planets, 18 being now
known, of which all but one belong to the group of outer
planets ;
SUN.
PIG. 63. Relative size of sun and planets.
6. An unknown number of comets and meteors, revolving
in very eccentric orbits.
The eight planets of groups 2 and 4 are called the major
platiets, to distinguish them from all others, which are smaller
or less important.
GENERAL STRUCTURE OF THE SOLAR SYSTEM. 233
The range of size, distance, and mass among the bodies of
the system is enormous. Neptune is eighty times as far from
the sun as Mercury, and Jupiter several thousand times as
heavy. It is, therefore, difficult to lay down a map of the
whole system on the same scale. If the orbit of Mercury were
represented with a diameter of one-fourth of an inch, that of
Neptune would have a diameter of 20 inches.
With the exception of Neptune, the distances of the eight
major planets proceed in a tolerably regular progression, the
group of small planets taking the place of a single planet in
the series. The progression is known as the law of Titius,
from its first proposer, and is as follows : Take the series of
numbers 0, 3, 6, 12, 24, 48, each one after the second being
formed by doubling the one which precedes it. Add 4 to
each of these numbers, and we shall have a series of numbers
giving very nearly the relative distances of the planets from
the sun. The following table shows the series of numbers thus
formed, together with the actual distances of the planets ex-
pressed on the same scale, the distance of the earth being
called 10 :
Planet.
Numbers of Titius.
Actual Distance.
Error.
Mercury
+ 4 = 4
3.9
O.I
Venus
34-4= 7
7.2
0.2
Earth.
C -f 4 = 10
10
0.0
Mars
12 + 4 1G
15.2
0.8
Minor planets
24 + 4 28
20 to 35
Jupiter
48 -f 4 = 52
52.0
0.0
Saturn
06 + 4 = 1 00
95 4
4 G
Uranus
192 -f 4 = 190
191.9
4.1
Neptune
384 + 4 = 388
300.6
87.4
It will be seen that before the discovery of Neptune the
agreement was so close as to suggest the existence of an actual
Jaw of the distances. But the discovery of this planet in 1846
completely disproved the supposed law ; and there is now no
reason to believe that the proportions of the solar system are
the result of any exact and simple law whatever. It is true
that many ingenious people employ themselves from time to
time in working out numerical relations between the distances
of the planets, their masses, their times of rotation, and so on,
234 THE SOLAR SYSTEM.
.and will probably continue to do so ; because the number of
such relations which can be made to come somewhere near to
exact numbers is very great. This, however, does not indicate
any law of nature. If we take forty or fifty numbers of any
kind say the years in which a few persons were born ; their
ages in years, months, and days at some particular event in
their lives ; the numbers of the houses in which they live ; and
so on we should find as many curious relations among the
numbers as have ever been found among those of the planet-
ary system. Indeed, such relations among the years of the lives
of great actors in the world's history will be remembered by
many readers as occurring now and then in the public journals.
Range of Planetary Masses. The great diversity of the size
and mass of the planets is shown by the curious fact, that, con-
sidering the sun and the eight planets, the mass of each of the
nine bodies exceeds the combined mass of all those which are
smaller than itself. This is shown in the following simple cal-
culation. Suppose the sun to be divided into a thousand mill-
ions of equal parts, one of which parts we take as the unit of
weight: then, according to the best determinations yet made,
the mass of each planet will be that used in the following cal-
culation, in which each mass is added to the masses of all the
planets which are smaller than itself, the planets being taken
in the order of their masses, beginning with the smallest :
Mass of Mercury 200
Mass of Mars...'. , 339
Combined mass of Mercury and Mars 539
Mass of Venus 2,353
Combined mass of Mercury, Venus, and Mars 2,892
Mass of the Earth 3,000
Combined mass of the four inner planets 5,952
Mass of Uranus 44,250
Combined muss of five planets 50,202
Mass of Neptune 51,600
Combined mass of six planets 101,802
Mass of Saturn 285,580
Combined mass of seven planets 387,382
Mass of Jupiter 954,305
Combined mass of all the planets 1,341,687
Mass of the sun 1,000,000,000
ASPECTS OF THE PLANETS. 235
It will be seen that the combined mass of all the planets is
less than T -Ju that of the sun ; that Jupiter is between two and
three times as heavy as the other seven planets together; Sat-
urn more than twice as heavy as the other six ; and so on.
Aspects of the Planets. The apparent motions of the plan-
ets are described in the first chapter of this work; and in the
second chapter it is shown how these apparent motions result
from the real motions as laid down by Copernicus. The best
time to see one of the outer planets is when in opposition to
the sun. It then rises at sunset, and passes the meridian at
midnight. Between sunset and midnight it will be seen some-
where between east and south. During the three months fol-
lowing the day of opposition, the planet will rise from three
to six minutes earlier every day. A month after opposition, it
will be two to three hours high soon after sunset, and will pass
the meridian between nine and ten o'clock at night; while
three months after opposition, it will be on the meridian about
six in the evening. Hence, knowing when a planet is in op-
position, a spectator will know pretty nearly where to look for
it. His search will be facilitated by the use of a star map
showing the position of the ecliptic among the stars, because
the planets are always very near the ecliptic. Indeed, if any
bright star is not down on the map, he may feel sure that it is
a planet.
In describing the individual planets, we give the times when
they are in opposition, so that the reader may always be able
to recognize them at favorable seasons, if he wishes to do so.
The arrangement of the planets, with their satellites, is as
follows :
I Mercury.
Venus.
1
Earth, with its moon.
Mars.
The minor planets, or asteroids.
Jupiter, with 4 moons.
OITTKB Gnour OK
GBEAT PLANETS.
Saturn, with rings and 8 moons.
Uranus, with 4 moons.
Neptune, with 1 moon.
236
THE SOLAR SYSTEM.
This arrangement is partly exhibited in the following plan
of the solar system, showing the relations of the planetary or-
bits from the earth outward. The scale is too small to show
the orbits of Mercury and Venus.
FIG. 64. Orbits of the planets from the earth outward, showing their relative distances
from the sun iu the centre. The positions of the planets are near those which they oc-
cupy in 1877.
THE PHOTOSPHERE. 237
CHAPTEE IT.
THE SUN.
THE sun presents to our view the aspect of a brilliant globe
32', or a little more than half a degree, in diameter. To give
precision to our language, the shining surface of this globe,
which we see with the eye or with the telescope, and which
forms the visible sun, is called the photosphere. Its light ex-
ceeds in intensity any that can be produced by artificial
means, the electric light between charcoal points being the
only one which does not look absolutely black against the un-
clouded sun. Our knowledge of the nature of this luminary
commences with the invention of the telescope, since without
this instrument it was impossible to form any conception of
its constitution. The ancients had a vague idea that it was a
globe of fire, and in this they were more nearly right than
some of the moderns ; but there was so entire an absence of
all real foundation for their opinions that the latter are of lit-
tle interest to any one but the historian of philosophy. "We
shall, therefore, commence our description of the sun with a
consideration of the telescopic researches of recent times.
1. The Photosphere.
To the naked eye the photosphere, or shining surface of the
sun, presents an aspect of such entire uniformity that any at-
tempt to gain an insight into its structure seems hopeless.
But when we apply a telescope, we generally find it diversified
with one or more groups of dark-looking spots ; and if the vis-
ion is good, and we look carefully, we shall soon see that the
whole bright surface presents a mottled appearance, looking
like a fluid in which ill-defined rice-grains are suspended. Per-
haps the most familiar idea of this appearance will be pre-
238 THE SOLAR SYSTEM.
sented by saying that the sun looks like a plate of rice soup,
the grains of rice, however, being really hundreds of miles in
length. Some years ago Mr. Nasmyth, of England, examining
the suri with high telescopic powers, announced that this mot-
tled appearance seemed to him to be produced by the inter-
lacing of long, narrow objects shaped like willow leaves, which,
running and crossing in all directions, form a net-work, cover-
ing the entire photosphere. This view, though it has become
celebrated through the very great care which Mr. Nasmyth
devoted to his observations, has not been confirmed by subse-
quent observers.
Among the most careful and laborious telescopic studies of
the sun recently made are those of Professor Laugley.* He
has a fine telescope at his command, in a situation where the
air seems to be less disturbed by the sun's rays than is usual
in other localities. According to his observations, when the
sun is carefully examined, the mottling which we have de-
scribed is seen to be caused by an appearance like fleecy
clouds whose outlines are nearly indistinguishable. We may
also discern numerous faint dots on the white background.
Under high powers, used in favorable moments, the surface
of any one of the fleecy patches is resolved into a congeries
of small, intensely bright bodies, irregularly distributed, which
seem to be suspended in a comparatively dark medium, and
whose definiteness of size and outline, though not absolute, is
yet striking, by contrast with the vagueness of the cloud-like
forms seen before, and which we now perceive to be due to
their aggregation. The "dots" seen before are considerable
openings, caused by the absence of the white nodules at cer-
tain points, and the consequent exposure of the gray medium
which forms the general background. These openings have
been called pores. Their variety of size makes any measure-
ments nearly valueless, though we may estimate in a very
rough way the diameter of the more conspicuous at from 2"
tojt^ ;
* Professor S. P. Langley, Director of the Observatory at Allegheny, Pennsyl-
vania.
THE PHOTOSPHERE. 239
In moments when the definition is very fine, the bright nod-
ules or rice-grains are found to be made up of clusters of mi-
nute points of light or "granules," about one-third of a second
in diameter. These have also been seen around the edges of
the pores by Secchi,who estimated their magnitude as even less
than that assigned by Langley. The fact that these points are
aggregated into little clusters, which ordinarily present the ap-
pearance of rice-grains, gives the latter a certain irregularity of
outline which has been remarked by Mr. Huggins. Thus, there
appear to be three orders of aggregation in the brighter re-
gions of the photosphere : cloud-like forms which can be easi-
ly seen at any time ; rice-grains or nodules, into which these
forms are resolved, and which can always be seen with a fair
telescope under good definition ; and granules which make up
the rice - grains. This structure of the rice - grains has been
seen only by Professor Langley.
If we carefully examine the sun with a very dark smoked
glass, we shall find that the disk is brightest at the centre,
shading off on all sides towards the limb. Careful compari-
sons of the intensity of radiation of different parts of the disk
show that this diminution near the limb is common to all the
rays, whether those of heat, of light, or of chemical action.
The most recent measures of the heat rays were made by
Langley by means of a thermo-electric pile, those of the light
rays by Pickering,* and those of the chemical rays by Vogel.f
The intensities of these several radiations at different distances
from the centre of the disk as thus determined are shown in
the table on the following page. The intensity at the centre
is always supposed 100. The first column gives the distance
from the centre in fractions of the sun's radius, which is sup-
posed unity. Thus, the first line of the table corresponds to
the centre ; the last to the edge. Professor Langley's meas-
ures do not, however, extend to the extreme edge.
* Professor E. C. Pickering, director of the Harvard Observatory, Cambridge,
Massachusetts.
t Dr. Hermann C. Vogel, formerly astronomer at Bothkamp, now of the Solar
Observatory in Potsdam, Prussia.
240
THE SOLAS SYSTEM.
Distance from
Centre of the Sun.
Heat Rays ,
(Langley).
Light
(Pickwing).
Chemical Rays
(Vogel).
.00
100
100
100
.125
99
100
.25
'99
97
98
.375
94
95
.50
95
91
90
.625
86
81
.75
"86
79
66
.85
69
48
.95
...
55
25
.96
62
< . . .
23
.98
50
. ...
18
1.00
....
37
13
It will be seen that near the edge of the disk the chemical
rays fall off most rapidly, the light rays next, and the heat
rays least of all. Koughly speaking, each square minute near
the limb of the sun gives about half as much heat as at the
centre, about one-third as much light, and less than one-seventh
as* many photographic rays. Of the cause of this degradation
of light and heat towards the limb of the sun no doubt has
been entertained since it was first investigated. It is found in
the absorption of the rays by a solar atmosphere. The sun
being a globe surrounded by an atmosphere, the rays which
emanate from the photosphere in a horizontal direction have
a greater thickness of atmosphere to pass through than those
which strike out vertically; while the former are those we
see near the edge of the disk, and the latter near the centre.
The different absorptions of different classes of rays corre-
spond exactly to this supposition, it being known that the
more refrangible or chemical rays are most absorbed by va-
pors, and the heat rays the least.
From this it follows that we get but a fractionperhaps a
small fraction of the light and heat actually emitted by the
sun ; and that if the latter had no atmosphere, it would be
much hotter, much brighter, and bluer in color/ than it actually
is. The total amount of absorption has been very differently
estimated by different authorities, Laplace supposing it might
be as much as eleven - twelfths of the whole amount. The
smaller estimates are, however, more likely to be near the
THE PHOTOSPHERE. 241
truth, there being no good reason for holding that more than
half the rays are absorbed. That is, if the sun had no atmos-
phere, it might be twice as bright and as hot as it actually is,
but would not be likely to be three or four times teo. Profess-
or Langley suggests that the glacial epoch may have been due
to a greater absorption of the sun's heat by its atmosphere in
some past geological age.
A very important physical and astronomical problem is that
of measuring the total amount of heat radiated by the sun to
the earth during any period of time say a day or a year.
The question admits of a perfectly definite answer, but there
are two difficulties in the way of obtaining it; one, to distin-
guish between the heat coming from the sun itself, and that
coming from the atmosphere and surrounding objects; the
other, to allow for the absorption of the solar heat by our at-
mdsphere, which must be done in order to determine the to-
tal quantity emanating from the sun. The most successful
experiments for this purpose are those of Pouillet and of
Sir John Herscliel. The results obtained by the former may
be expressed thus : if the air were out of the way, and a sheet
of ice were so held that the sun's rays should fall upon it per-
pendicularly, and be all absorbed, the ice would melt away at
the rate of 14J inches in 24 hours. Since the sun is part of
the time below the horizon, and is not perpendicular to more
than a single point of the earth's surface when above it, the
average amount of ice which would be melted over the whole
earth is only a fraction of this, namely, 3.62 inches per day,
or something more than 100 feet per year.
Attempts have been made to determine the temperature of
the sun from the amount of heat which it radiates, but the
estimates have varied very widely, owing to the uncertainty
respecting the law of radiation at high temperatures. By sup-
posing the radiation proportional to the temperature, Secchi*
finds the latter to be several million degrees, while, by taking
another law indicated by the experiments of Dulong and
* Father Angelo Secchi, Director of the Observatory at Borne.
17
24:2 THE SOLAR SYSTEM.
Petit, others find a temperature not many times exceeding
that of a reverberatory furnace. For the temperature of the
photosphere, it seems likely that the lower estimates are more
nearly right, being founded on an experimental law ; but the
temperature of the interior must be immensely higher.
2. The Solar Spots and Rotation.
Even the poor telescopes made by the contemporaries of
Galileo could hardly be directed to the sun many times with-
out one or more spots being seen on his surface. Whatever
credit my be due for a discovery which required neither in-
dustry nor skill should, by the rule of modern science already
referred to, be awarded to Fabrititis for the discovery of the
solar spots. This observer, otherwise unknown in astronomy,
made known the existence of the solar spots early in 1611
& year after Galileo began to scan the heavens with his tel-
escope. His discovery was followed up by Galileo and Schei-
ner, by whom the first knowledge of the nature of the spots
was acquired.
The first idea of Scheiner was that the spots were small
planets in the neighborhood of the sun ; but this was speedily
disproved by Galileo, who showed that they rmist be on the
surface of the sun itself. The idea of the sun being affected
with any imperfection so gross as a dark spot was repugnant
to the ecclesiastical philosophy of the times, and it is not Tin-
likely that Schemer's explanation was suggested by the desire
to save the perfection of our central luminary.
A very little observation showed that the spots had a regu
lar motion across the disk of the sun from east to west, occu^
pying about 12 days in the transit. A spot generally appeared
first on or near the east limb, and, after 12 or 14 days, disap-
peared at the west limb. At the end of another 14 days or
more it reappeared at the east limb, unless in the mean time
it had vanished from sight entirely. The spots were found
not to be permanent objects, but to come into existence from
time to time, and, after lasting a few days, weeks, or months,
to disappear. But so long as they lasted, they always ex-
THE SOLAR SPOTS AND ROTATION.
243
liibited the motion just described, and it was thence inferred
that the sun rotated on his axis in about 25 days.
The astronomers of the seventeenth and eighteenth centuries
used a method of observing the sun which will often be found
convenient for seeing the spots when one has not a telescope
supplied with dark glasses at his disposal. Take an ordinary
good spy-glass, or, indeed, a telescope of any size, and point
FIG. 65. Man holding telescope, to show sun on screen.
it at the sun. To save the eyes, the right direction may be
found by holding a piece of paper closely in front of the eye-
piece: when the sun shines through the telescope on this pa-
per, the pointing is nearly right. The telescope should be at-
tached to some movable support, so that its pointing can be
changed to the different directions of the sun, and should pass
through a perforation in some sort of a screen, so that the
sun cannot shinf p front of the telescope except by passing
24:4: THE SOLAR SYSTEM.
through it. An opening in a window-shutter will answer a
good purpose, only the rays must not have to pass through the
glass of the window in order to reach the telescope. Draw
out the eye-piece of the instrument about the eighth of an
inch beyond the proper point for seeing a distant object.
Then, holding a piece of white paper before the eye-piece at
a distance of from 6 to 12 inches, an image of the sun will be
thrown upon it. The distance of the paper must be adjusted
to the distance the eye-piece is drawn out. The farther wo
draw out the eye - piece, the nearer the best image will be
formed. Having adjusted everything so that the edge of the
sun's image shall be sharply defined, one or more spots can
generally be seen. This method, or something similar to it, is
often used in observing eclipses and transits of Mercury, and
is very convenient when it is desired to show an enlarged im-
age of the sun to a number of spectators.
When powerful telescopes were applied to the snn, it was
found that the spots were not merely the dark patches which
they first appeared to be, but that they comprised two well-
m. 60. -Solar s*pot, after Secclri.
marked portions. The central part, called the umbra or nu-
cleus, is the darkest, and is surrounded by a border, interme-
diate in tint between the darkness of the spot and the brill-
THE SOLAE SPOTS AND ROTATION. 245
iancy of the solar surface. This border is termed the penum-
bra. Ordinarily it appears of a uniform gray tint. But when
carefully examined with a good telescope in a very steady at-
mosphere, it is found to be striated, looking, in fact, much like
the bottom of a thatched roof, the separate straws being di-
rected towards the interior of the spot. This appearance is
shown in the figure.
The spots are extremely irregular in form and unequal in
size. They are very generally seen in groups sometimes
two or more combined into a single one ; and it frequently
happens that a large one breaks up into several smaller ones.
Their duration is also extremely variable, ranging from a few
days to periods of several months.
Until about a century ago, it was a question whether the
spots were not dark patches, like scoria, floating on the molten
surface of the photosphere. Wilson, a Scotch observer, how-
ever, found that they appeared like cavities in the photosphere,
the dark part being really lower than the bright surface around
it. As a spot approached the edge of the disk, he found that
the penumbra grew disproportionately narrow on the side
nearest to the sun's centre, showing that this side of it was
seen at a smaller angle than the other. This effect of per-
spective is shown in Fig. 67, where, near the sun's limb, the
side of the penumbra nearest us is hidden by the photosphere.
That the spots are cavities is also shown by the fact that
when a large spot is exactly on the edge of the disk a notch
is sometimes seen there. The shaded penumbra seems to
form the sides of the cavity, while the umbra is the invisible
bottom.
These observations gave rise to the celebrated theory of
Wilson, which is generally connected with the name of Her-
schel, who developed it more fully. The interior of the sun
is, by this theory, a cool, dark body, surrounded by two layers
of clouds. The outer layer is intensely brilliant, and forms
the visible photosphere, while the inner layer is darker, and
forms the umbra around the spots. The latter are simply
openings through these clouds, which form from time to
246
THE SOLAR SYSTEM.
FIG. 67. Changes in the aspect of a solar spot as it crosses the sun's disk, showing it to be
a cavity in the photosphere.
time, and through which we see the dark body in the interior.
Anxious that this body should serve some especial purpose in
the economy of creation, they peopled it with intelligent be-
ings, who were protected from the fierce radiation of the pho-
tosphere by the layer of cool clouds, but were denied every
view of the universe without, except such glimpses as they
might obtain through the occasional openings in the photo-
sphere, which we see as spots.
Leaving out the fancy of living beings, this theory account-
ed very well for appearances. That the photosphere could not
be absolutely and wholly solid, liquid, or gaseous seemed evi-
dent from the nature of the spots. If it were solid, the latter
could not be in such a constant state of change as we see
THE SOLAR SPOTS AND ROTATION. 247
them; while if it were liquid. or. .gaseous, these cavities could
not continue for months, as they were sometimes seen to, be-
cause the liquid or gaseous matter would rush in from all
sides, and fill them up. The only hypothesis that seemed left
open to Herschel was that the photosphere consisted of clouds
floating in an atmosphere. As the sides of the cavities looked
comparatively dark, the conclusion seemed inevitable that the
brilliancy of the photosphere was only on and near the sur-
face; and as the bottom of the cavity looked entirely dark,
the conclusion that the sun had a dark interior seemed una-
voidable.
The discovery of the conservation of force, and of the mut-
ual convertibility of heat and force, was fatal to this theory.
Such a sun as that of Herschel would have cooled off entirely in
a few days, and then we should receive neither light nor heat
from it. A continuous flood of heat such as the sun has been
radiating for thousands of years can be kept up only by a con-
stant expenditure of force in some of its forms ; but, on Her-
schel's theory, the supply necessary to meet this expenditure
was impossible. Even if the heat of the photosphere could
be kept up by any agency, it would be constantly conveyed to
the interior by conduction and radiation ; so that in time the
whole sun would become as hot as the photosphere, and its
inhabitants would be destroyed. In the time of Herschel it
was not deemed necessary that the sun should be a very hot
body, the heat received from his rays being supposed by many
to be generated by their passage through our atmosphere.
The photosphere was, therefore, supposed to Be simply phos-
phorescent, not hot. This idea is still entertained by many
educated men who have not made themselves acquainted with
the laws of heat discovered during the present century. We
may, therefore, remark that it is completely untenable. One
of the best established results of these laws is that the surface
of the sun is intensely hot, probably much hotter than any re-
verberatory furnace. The great question in the present state
of science is, how the supply of heat is maintained against
such immense loss by radiation.
248
THE SOLAR SYSTEM.
3. Periodicity of the Spots.
The careful observations of the solar spots which have been
made during the last century seem to indicate a period of
about eleven years in the spot-producing activity of the sun.
During two or three years the spots are larger and more nu-
merous than on the average; they then begin to diminish,
and reach a minimum five or six years after the maximum.
Another six years brings the return of the maximum. The
intervals are, however, somewhat irregular, and further obser-
vations are required before the law of this period can be fixed
with certainty. An idea of the evidence in favor of the pe-
riod may be formed from some results of the observations of
Schwabe, a German astronomer, who systematically observed
the sun during a large part of a long life. One of his meas-
ures of the spot-producing power was the number of days on
which lie saw the sun without spots in the course of each
year. The following are some of his results :
From 1828 to 1831, sun without spots on only 1 day.
In 1833,
From 1836 to 1840,
In 1843,
From 1847 to 1851,
In 1856,
From 1858 to 1861,
In 1867,
139 days.
3 days.
147 days.
2 days.
193 clays.
no clay.
195 days.
We see that the sun was remarkably free from spots in the
years 1833, 1843, 1856, and 1867, about half the time no con-
siderable spot being visible. This recurrence of the period
has been traced back by Dr. Wolf, of Zurich, to the time of
Galileo, and its average length is about 11 years 1 month.
The years of fewest sun-spots during the present century were
1810, 1823, 1833, 1844, 1856, and 1867. Continuing the
series, we may expect very few spots in 1878, 1889, etc. The
years of greatest production of spots were 1804, 1816, 1829,
1837, 1848, 1860, and 1870, from which we may conclude
that 1882, 1893, etc., will be years of numerous sun-spots.
PERIODICITY OF THE SPOTS. 249
The observations of Schwabe and the researches of Wolf
seem to have placed the existence of this period beyond a
doubt; but no satisfactory explanation of its cause has yet
been given. When first noticed, its near approach to the pe-
riod of revolution of Jupiter naturally led to the belief that
there was a connection between the two, and that the attrac-
tion of the largest planet of the system produced some disturb-
ance in the sun, which was greater in perihelion than in aphe-
lion. But this connection seems to be disproved by the fact
that the sun-spot period is at least six months, and perhaps a
year, shorter than the revolution of Jupiter. It is therefore
probable that the periodicity in question is not due to any ac-
tion outside the sun, but is a result of some law of solar action
of which we are as yet ignorant.
There are certain supposed connections of the sun-spot pe-
riod with terrestrial phenomena which are of interest. Sir
William Herschel collected quite a mass of statistics tending to
show that there was an intimate connection between the num-
ber of sun-spots and the price of corn, the latter being low
when there were few spots, and high when they were more
numerous. His conclusion was that the fewer the spots, the
more favorable the solar rays to the growth of the crops.
This theory has not been confirmed by subsequent observa-
tion. There is, however, some reason to believe, from the
researches of Professors Lovering and Loom is, that the fre-
quency of auroras and of magnetic disturbances is subject to
a period corresponding to that of sun-spots, these occurrences
being most frequent when the spots are most numerous. Pro-
fessor Loomis considers the coincidence to be pretty well
proved, while Professor Lovering is more cautions, and waits
for further research before coming to a positive conclusion.
The occurrence of great auroras in 1859 and 1870-'71 was
strikingly accordant with the theory.
4. Law of dotation of the San.
Between the years 1843 and 1861, a very careful series of
observations of the positions and motions of the solar spots
250 THE SOLAR SYSTEM.
was made by Mr. Carrington, of England, with a view of de-
ducing the exact time in which the sun rotates on his axis.
These observations led to the remarkable result that the time
of rotation shown by the spots was not the same on all parts
of the sun, but that the equatorial regions seemed to perform
a revolution in less time than those nearer the poles. Near
the equator the period was about 25.3 days, while it was a
day longer in 30 latitude. Moreover, the period of rotation
seems to be different at different times, and to vary with the
frequency of the spots. But the laws of these variations are
not yet established. In consequence of their existence, we
cannot fix any definite time of rotation for the sun, as we can
for the earth and for some of the planets. It varies at dif-
ferent times, and under different circumstances, from 25 to
26 days.
The cause of these variations is a subject on which there is
yet no general agreement among those who have most care-
fully investigated the subject. Zollner* and Wolf see in the
general motions of the spots traces of currents moving from
both poles of the sun towards the equator. The latter con-
siders that the eleven -year spot -period is associated with a
flood of liquid or gaseous matter thrown up at the poles of
the sun about once in eleven years, and gradually finding its
way to the equator. Zollner adopts the same theory, and has
submitted it to a mathematical analysis, the basis of which is
that the sun has a solid crust, over which runs the fluid in
which the spots are formed. The current springs up near
the poles, and, starting towards the equator without any rota-
tion, is acted on by the friction of the revolving crust. By
this friction the crust continually tends to carry the fluid with
it. The nearer the current approaches the equator, the more
rapid the rotation of the crust, owing to its greater distance
from the axis. The friction acts so slowly that the current
reaches the equator before it takes up the motion of the crust.
On this hypothesis, the crust of the sun really revolves in
* Dr. J. C. F. Zollner, Professor in the University of Leipsic.
THE SUN'S SURROUNDINGS. 251
about 25 days ; and the reason that the fluid which covers it
revolves more slowly at a distance from the suirs equator is
that it has not yet taken up this normal velocity of rotation.
This explanation of the seeming paradox that the equatorial
regions of the sun perform their revolution in a shorter time
than those parts nearer the poles, cannot be regarded as an es-
tablished scientific theory. It is mentioned as being, so far as
the writer is aware, the most completely elaborated explana-
tion yet offered. It is possible that the spots have a proper
motion of their own on the solar surface, and that this is the
reason of the apparent difference in the time of rotation in
different latitudes. Yet another theory of the subject is that
of Faye,* who maintains that these differences in the rates of
rotation are due to ascending and descending currents, as will
be more fully explained in presenting his views. But we here
touch upon questions which science is as yet far from being
in a condition to answer.
5. The Suris Surroundings,
If the sun had never been examined with any other instru-
ment than the telescope, nor been totally eclipsed by the inter-
vention of the moon, we should not have formed any idea of
the nature of the operations going on at his surface ; but we
might have been better satisfied that we had a complete knowl-
edge of his constitution. Indeed, it is remarkable that mod-
ern science has shown us more mysteries in the sun than it has
explained ; so that we find ourselves farther than before from
a satisfactory explanation of solar phenomena. When the an-
cients supposed the sun to be a globe of molten iron, they had
an explanation which quite satisfied the requirements of the
science of their times. The spots were no mystery to Galileo
and Scheiner, being simply dark places in the photosphere.
Herschel's explanation of them was quite in accord with the
science of his time, and he may be regarded as the latest man
who has held a theory of the physical constitution of the sun
* Mr. H. E. Fflyc, member of the French Academy of Sciences.
252 THE SOLAR SYSTEM.
which was really satisfactory at the time it was propounded.
We have shown how his theory was refuted by the discovery
of the conservation of force ; we have now to see what per-
plexing phenomena have been revealed in recent times.
Phenomena during Total Eclipses. If, during the progress
of a total eclipse, the gradually diminishing crescent of the
sun is watched, nothing remarkable is seen until ^ 7 ery near the
moment of its total disappearance. But, as the last ray of sun-
light vanishes, a scene of unexampled beauty, grandeur, and im-
pressiveness breaks upon the view. The globe of the moon,
black as ink, is seen as if it were hanging in mid-air, surround-
ed by a crown of soft, silvery light, like that which the old
painters used to depict around the heads of saints. Besides
this " corona," tongues of rose-colored flame of the most fan-
tastic forms shoot out from various points around the edge of
the lunar disk. Of these two appearances, the corona was no-
ticed at least as far back as the time of Kepler; indeed, it was
not possible for a total eclipse to happen without the specta-
tors seeing it. But it is only within a century that the at-
tention of astronomers has been directed to the rose-colored
flames, although an observation of them was recorded in the
Philosophical Transactions nearly two centuries ago. They
are known by the several names of " flames," " prominences,"
and " protuberances."
The descriptions which have been given of the corona, al-
though differing in many details, have a general resemblance.
Halley's description of it, as seen during the total eclipse of
1715, is as follows:
"A few seconds before the sun was all hid, there discovered
itself round the moon a luminous ring about 'a digit, or per-
haps a tenth part of the moon's diameter, in breadth. It was
of a pale whiteness, or rather pearl-color, seeming to me a lit-
tle tinged with the colors of the iris, and to be concentric
with the moon."
The more careful and elaborate observations of recent times
show that the corona has not the circular form which was for-
merly ascribed to it, but that it is quite irregular in its out-
THE SUN'S SURROUNDINGS. 253
line. Sometimes its form is more nearly square than round,
the corners of the square being about 45 of solar latitude,
and the sides, therefore, corresponding to the poles and the
equator of the sun. This square appearance does not, how-
ever, arise from any regularity of form, but from the fact that
the corona seems brighter and higher half way between the
poles and the equator of the sun than it does near those points.
FIG. 8. Total eclipse of the sun as seen at Des Moines, Iowa, August 7th, 1869. Drawn
by Professor J. K. Eastman. The letters, a, fc, c, etc., mark the positions of the prom-
inences.
These prominent portions sometimes seem like rays shooting
out from the sun. The corona is always brightest at its base,
gradually shading off toward the outer edge. It is impossi-
ble to say with certainty how far it extends, but there is no
doubt that it has been seen as far as one semidiameter from
the moon's limb.
254 TEE SOLAR SYSTEM.
The corona was formerly supposed to be an atmosphere
either of the moon or of the sun. Thirty or forty years ago,
the most plausible theory was that it was a solar atmosphere,
and that the red protuberances were clouds floating in it.
That the corona could be a lunar atmosphere was completely
disproved by its irregular outline, for the atmosphere of a
body like the moon would necessarily spread itself around in
nearly uniform layers, and could not be piled up in some
quarters, as the matter of the corona is seen to be. We shall
soon see that there is no doubt about the corona being some-
thing surrounding the sun.
The question whether the red protuberances belong to the
moon or the sun was settled during the total eclipse of 1860,
which was observed in Spain. It was then proved by meas-
ures of their height above the limb of the moon that the lat-
ter did not carry them with her, but passed over them. This
proved that they were fixed relatively to the sun.
At the time of this eclipse the spectroscope was in its in-
fancy, and no one thought of applying it to the study of the
corona and protuberances. The next considerable eclipse oc-
curred eight years later, in July, 1868, and was visible in In-
dia and Siam. The spectroscope had, in the mean time, come
into very general use, and expeditions were despatched from
several European countries to India to make an examination
of the spectra of the objects in question. The most success-
ful observer was Janssen, of France, who took an elevated
position in the interior, where the air was remarkably clear.
When, on the eventful day, the last ray of sunlight was cut
off by the advancing moon, an enormous protuberance showed
itself, rising to a height of many thousand miles above the sur-
face of the sun. The spectroscope was promptly turned upon
it, and the practised eye of the observer saw in a moment that
the spectrum consisted of the bright lines due to glowing hy-
drogen. The protuberance, therefore, did not consist of any
substance shining merely by reflected sunlight, but of an im-
mense mass of hydrogen gas, so hot as to shine by its own
light. The theory of the cloud -like nature of the protuber-
ances was overthrown in a moment.
THE SUN'S SUBROUNDINaS. 255
This observation marks the commencement of a new era in
solar physics, which, by a singular coincidence, was inaugu-
rated independently by another observer. As Janssen looked
at the lines which he was the first of men to see, it occurred
to him that they were bright enough to be seen after the total
phase of the eclipse had passed. He therefore determined to
watch them, and find how long he could follow them. He
kept sight of them, not only after the total phase had passed,
but after the eclipse was entirely over. In fact, he found that
with a sufficiently powerful spectroscope, he could see the
spectral lines of the protuberances at any time when the air
was perfectly clear, so that the varying forms of these remark-
able objects which had hitherto been seen only during the
rare moments of a total eclipse could be made a subject of
regular observation.
But this great discovery was made in England, independ-
ently of the eclipse, by Mr. J. Norman Lockyer. This gen-
tleman was an active student of the subject of spectroscopy ;
and it had occurred to him that the matter composing these
protuberances, being so near the surface of the sun, must be
hot enough, not only to shine by its own light, but to be quite
vaporized, and, if so, its spectrum might be seen by means of
the spectroscope. Finding that the instrument he possessed
would show nothing, he ordered a more powerful one. But
its construction was attended with so much delay that it was
not ready till October, 1868. On the 20th of that month, he
pointed it upon the margin of the sun, and found three bright
lines in the spectrum, two of which belonged to hydrogen.
Thus was realized an idea which he had formed two years be-
fore, but which he was prevented from carrying out by the
want of a suitable instrument. His success was immediately
communicated to the French Academy of Sciences, the news
reaching that body on the very day that word was received
from Janssen, in India, that he had also solved the same prob-
lem.
Following up his researches, Mr. Lockyer found that the
protuberances arose from a narrow envelope surrounding the
256
THE SOLAU SYSTEM.
Fio. 69. Specimens of solar protuberances, as drawn by Secchi. The bright base in cncl
figure represents the chromosphere from which the red flames rise.
whole surface of the sun, being, in fact, merely elevated por
tions of this envelope : that is to say, the sun is surroundec
by an atmosphere composed principally of hydrogen gas, por
tions of which are here and there thrown up in the form oi
THE SUN'S SURROUNDINGS. 257
enormous tongues of flame, which, however, can never be seen
except with the spectroscope, or during total eclipses. To this
atmosphere Mr. Lockyer gave the name of the chromosphere.
It had previously been seen and recognized by several observ-
ers during total eclipses, but nothing had been known respect-
ing its nature.
The researches which we have described threw no light on
the question of the corona, an object which seemed to have
been almost lost sight of in the excitement caused by the dis-
covery of the gaseous nature of the protuberances. Happily,
only a year later, on August 7th, 1869, a total eclipse was visi-
ble in the United States. The shadow of the moon passed
down the coast of Alaska, then entered into the interior, pass-
ing over the south-west portion of British America, entered
the United States in the Territory of Nebraska, and passed over
Iowa, Illinois, Kentucky, South - western Virginia, and North
Carolina. This eclipse was observed very extensively by
American astronomers, Professor Harkness, of the Naval Ob-
servatory, and Professor Young, of Dartmouth College, devot-
ing especial attention to the spectroscopic observations. These
observers found that the corona gave a very faint, continuous
spectrum crossed by a single bright-green line, which was also
seen in the spectrum of the protuberances. This solitary line
was again seen during the eclipse of December 21st, 1870,
in the Mediterranean ; but it has not been certainly identified
in the spectrum of any known terrestrial substance. There
are several lines of iron in its neighborhood; but as this line
stands alone, it does not seem likely that it can arise from the
vapor of iron. All we can say is, that the substance which
gives this line, and which seems to be the only gaseous ele-
ment of the corona, is unknown, and may possibly be some gas
much lighter than hydrogen which has not yet been discovered
on the earth.
Continued observations of the spectra of the various gases
surrounding the sun show a much greater number of lines
than have ever been seen during total eclipses. Mr. Lockyer
himself, by diligent observation extending over several years,
18
258 THE SOLAR SYSTEM.
found over a hundred. But the greatest advance in this re-
spect was made by Professor C. A. Young. In 1871 an astro-
nomical expedition was fitted out by the Coast Survey, for the
purpose of learning by actual trial whether any great advan-
tage would be gained by establishing an observatory on the
most elevated point crossed by the Pacific Railway. This
point was Sherman. The spectroscopic part of the expedition
was intrusted to Professor Young. Although there was a
great deal of cloudy weather, yet, when the air was clear, far
less light was reflected from the sky surrounding the sun than
at lower altitudes, which was a great advantage in the study
of the sun's surroundings. Professor Young found no less
than 273 bright lines which he was able to identify with cer-
tainty. The presence of inanj r known substances, especially
iron, magnesium, and titanium, is indicated by these lines
but there are also many lilies which are not known to pertaii
to any terrestrial substance.
6. Physical Constitution of the Sun.
Respecting the physical constitution of the sun, there ar
some points which may be established with more or less ce
tainty, but the subject is, for the most part, involved in doul
and obscurity. Since the properties of matter are the san
everywhere, the problem of the physical constitution of tl
sun is solved only when we are able to explain all solar ph
nornena by laws of physics which we see in operation aroui
us. The fact that the physical laws operative on the sun mi
be at least in agreement with those in operation here, is r
always remembered by those who have speculated on the si
ject. In stating what is probable, and what is possible,
the causes of solar phenomena, we shall begin on the outsi
and go inwards, because there is less doubt about the ope
tions which go on outside the sun than about those on his s
face or in the interior.
As we approach the sun, the first material substance
meet with is the corona, rising to heights of five or ten,
haps even fifteen, minutes above his surface, that is, to a he^
PHYSICAL CONSTITUTION OF THE SUN. 259
of from one to three hundred thousand miles. Of this ap-
pendage we may say with entire confidence that it cannot be
an atmosphere in the sense in which that word is commonly
used, that is, a continuous mass of elastic gas held up by its
own elasticity. Of the two reasons in favor of this denial, one
seems to me almost conclusive, the other entirely so. They
are as follows :
1. Gravitation on the sun is about 27 times as great as on
the earth, and any gas is there 27 times as heavy as here. In
an atmosphere each stratum is compressed by the weight of
all the strata above it. The result is, that as we go down by
successive equal steps, the density of the atmosphere increases
in geometrical progression. An atmosphere of the lightest
known gas hydrogen would double its density every five or
ten miles, though heated to as high a temperature as is likely
to exist at the height of a hundred thousand miles above the
sun's surface. But there is no approximation to such a rapid
increase in the density of the corona as we go downwards. If
we suppose the corona to be such an atmosphere, we must
suppose it to be hundreds of times lighter than hydrogen.
2. The great cornet of 1843 passed within three or four
minutes of the surface of the sun, and therefore directly
through the midst of the corona. At the time of nearest ap-
proach its velocity was 350 miles per second, and it went with
nearly this velocity through at least 300,000 miles of corona,
coming out without having suffered any visible damage or
retardation. To form an idea what would have become of
it had it encountered the rarest conceivable atmosphere, we
have only to reflect that shooting-stars are instantly and com-
pletely vaporized by the heat caused by their encounter with
our atmosphere at heights of from 50 to 100 miles j that is, at
a height where the atmosphere entirely ceases to reflect the
light of the sun. The velocity of shooting-stars is from 20 to
40 miles per second. Remembering, now, that resistance and
heat increase at least as the square of the velocity, what would
be the fate of a body, or a collection of bodies like a comet,
passing through several hundred thousand miles of the rarest
260 THE SOLAR SYSTEM.
atmosphere at a rate of over 300 miles a second ? And how
rare must such an atmosphere be when the comet passes not
only without destruction, but without losing any sensible ve-
locity ! Certainly so rare as to be entirely invisible, and inca-
pable of producing any physical effect.
What, then, is the corona? Probably detached particles
partially or wholly vaporized by the intense heat to which
they are exposed. A mere dust -particle in a cubic mile of
space would shine intensely when exposed to such a flood of
light as the sun pours out on every body in his neighborhood.
The difficult question which we meet is, How are these parti-
cles held up ? To this question only conjectural replies can
be given. That the particles are not permanently held in one
position is shown by the fact that the form of the corona is
subject to great variations. In the eclipse of 1869, Dr. Gould
thought he detected variations during the three minutes the
eclipse lasted. The three conjectures that have been formed
on the subject are :
1. That the matter of the corona is in what we may call a
state of projection, being constantly thrown up by the sun,
while each particle thus projected falls down again according
to the law of gravitation. The difficulty we encounter here is
that we must suppose velocities of projection rising as high as
200 miles per second constantly maintained in every region
of the solar globe.
2. That the particles thrown out by the sun are held up a
greater or less time by electrical repulsion. We know that at-
mospheric electricity plays an active part in terrestrial mete-
orology ; and if electric action at the surface of the sun is pro-
portional to those physical and chemical actions which we
tind to give rise to electrical phenomena here on the earth,
the development of electricity there must be on an enormous
scale.
3. That the corona is due to clouds of minute meteors cir-
culating around the sun in the immediate vicinity of that lu-
minary.
As already intimated, none of these explanations is much
PHYSICAL CONSTITUTION OF THE SUN. 261
better than a conjecture, though it is quite probable that the
facts of the case are divided somewhere among them.
Next inside the corona lies the chromosphere. Here we
reach the true atmosphere of the sun, rising in general a few
seconds above his surface, but now and then projected up-
wards in immense masses which we might call flarne, if the
word were not entirely inadequate to convey any conception
FIG. 70. The sun, with its chromosphere and red flames, on July 23d, 1871, as drawn by
Secchi. The figures mark the flames, 17 in number.
of the enormous scale on which thermal action is there car-
ried on. What we call fire and flame are results of burn-
ing; but the gases at the surface of the sun are already so
hot that burning is not possible. Hydrogen is the principal
material of the upper part of the chromosphere ; but, as we
descend, we find the vapors of a great number of metals, in-
cluding iron and magnesium. At the base, where the metals
are most numerous, and the density the greatest, occurs the
absorption of the solar rays which causes the dark lines in the
262 THE SOLAR SYSTEM.
spectrum already described (p. 225). This seems satisfactori-
ly proved by an observation of Professor Young's during the
eclipse of 1870, in Spain. At the moment of disappearance
of the last rays of sunlight, when he had a glimpse of the
base of the chromosphere, he saw all the spectral lines re-
versed ; that is, they were bright lines on a dark ground. The
vapors which absorb certain rays of the light which passes
through them from the sun then emitted those same rays
when the sunlight was cut off.
The most astonishing phenomena connected with the chro-
mosphere are those outbursts of its matter which form the pro-
tuberances. The latter are of two classes the cloud-like and
the eruptive. The first class presents the appearance of clouds
floating in an atmosphere ; but as no atmosphere dense enough
to sustain anything can possibly exist there, we find the same
difficulty in accounting for them that we do in accounting for
the suspension of the matter of the corona. In fact, of the
three conjectural explanations of the corona, two are inadmis-
sible if applied to the protuberances, since these cloud -like
bodies sometimes remain at rest too long to be supposed mov-
ing under the influence of the sun's gravitation. This leaves
the electrical explanation as the only adequate one yet brought
forward. The eruptive protuberances seem to be due to the
projection of hydrogen and magnesium vapor from the region
of the chromosphere with velocities which sometimes rise to
150 miles a second. The eruption may continue for hours, or
even days, the vapor spreading out into great masses thousands
of miles in extent, and then falling back on the chromosphere.
Is it possible to present in language any adequate idea of
the scale on which natural operations are here carried on ? If
we call the chromosphere an ocean of fire, we must remember
that it is an ocean hotter than the fiercest furnace, and as deep
as the Atlantic is broad. If we call its movements hurricanes,
we must remember that our hurricanes blow only about a hun-
dred miles ah hour, while those of the chromosphere blow as
far in a single second. They are such hurricanes as, " coming
down upon us from the north, would, in thirty seconds after
PHYSICAL CONSTITUTION OF THE SUN. 263
they had crossed the St. Lawrence, be in the Gulf of Mexico,
carrying with them the whole surface of the continent in a
mass, not simply of ruin, but of glowing vapor, in which the
vapors arising from the dissolution of the materials composing
the cities of Boston, New York, and Chicago would be mixed
in a single indistinguishable cloud." When we speak of erup-
tions, we call to mind Vesuvius burying the surrounding cities
in lava ; but the solar eruptions, thrown fifty thousand miles
high, would ingulf the whole earth, and dissolve every organ-
ized being on its surface in a moment. When the mediaeval
poets sung,
" Dies irse, dies ilia
Solvet sseclum in favilla,"
they gave rein to their wildest imagination, without reaching
any conception of the magnitude or fierceness of the flames
around the sun.
Of the corona and chromosphere the telescope ordinarily
shows us nothing. They are visible only during total eclipses,
or by the aid of the spectroscope. All we see with the eye or
the telescope is the shining surface of the sun called the pho-
tosphere, on which the chromosphere rests. It is this which
radiates both the light and the heat which reach us. The
opinions of students respecting the constitution of the photo-
sphere are so different that it is hardly possible to express any
views that will not be challenged in some quarter. Although
a contrary opinion is held by many, we may venture to say
that the rays of light and heat seem to come, not from a
gas, but from solid matter. This is indicated by the fact that
their spectrum is continuous, and also by the intensity of the
light, which far exceeds any that a gas has ever been made
to give forth. It does not follow from this that the photo-
sphere is a continuous solid or crust, since floating particles of
solid matter will shine in the same way. The general opinion
has been that the photosphere is of a cloud-like nature ; that
is, of minute particles floating in an atmosphere of heated gases.
That it is not continuously solid like our earth seemed to be
fully shown by the variations and motions of the spots, which
264: THE SOLAR SYSTEM.
have every appearance of going on in a fluid or gas. Indeed,
of late, some of the most eminent physicists regard it as pure-
ly gaseous, the pressure making it shine like a solid.
But this theory is attended with a difficulty which has not
been sufficiently considered. The photosphere is in striking
contrast to the gaseous chromosphere, in being subject to no
sensible changes of level. If it were gaseous, as supposed,
the solid particles having no connection with each other, we
should expect those violent eruptions which throw up the pro-
tuberances to carry up portions of it, so that it would now and
then present an irregular and jagged outline, as the chromo-
sphere does. But the most refined observations have never
shown it to be subject to the slightest change of level, or devi-
ation from perfect rotundity, except in the region of the spots,
where its continuity seems to be broken by immense chasm-
like openings.
The serene immobility of the photosphere, under such vio-
lent actions around it as we have described, lends some color
to the supposition that it is a solid crust which forms around
the glowing interior of the sun, or, at least, that it is composed
of a comparatively dense fluid resting upon such a crust. The
latter is the view of Zollner, who considers some sort of an
envelope between the exterior and the interior of the sun ab-
solutely necessary to account for the eruptive protuberances.
He places this solid envelope three or four thousand miles be-
low the surface of the photosphere.
Inside the photosphere we have the enormous interior
globe, 860,000 miles in diameter. The best-sustained theory
of the interior is the startling one that it is neither solid nor
liquid, but gaseous; so that our great luminary is nothing
more than an immense bubble. The pressure upon the inte-
rior portions of this mass is such as to reduce it to nearly the
density of a liquid ; while the temperature is so high as to
keep the substances in a state which is between the liquid and
the gaseous, and in which no chemical action is possible. The
strong point in support of this gaseous theory of the sun's in-
terior is, that it is the only one which explains how the sun's
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 265
light and heat are kept up. How it does this will be shown
in treating of the laws which govern the secular changes of
the universe at large.
7. Views of Distinguished Students of the Sun on the Subject of
its Physical Constitution.
The progress of our knowledge of the sun during the past
ten years has been so rapid that only those can completely fol-
low it who make it the principal business of their lives. For
the same reason, the views respecting the sun entertained by
those who are engaged in studying it must be modified and
extended from time to time. The interest which necessarily
attaches to the physical source of all life and motion on our
globe renders the author desirous of presenting these views to
his readers in their latest form ; and, through the kindness of
several of the most eminent investigators of solar physics now
living, he is enabled to gratify that desire. The following
statements are presented in the language of their respective
authors, except that, in the case of Messrs. Secchi and Faye,
they are translated from the French for the convenience of
the English reader. It will be noticed that in some minor
points they differ from each other, as well as from those which
the author has expressed in the preceding section. Such dif-
ferences are unavoidable in the investigation of so difficult a
subject.
Views of the Rev. Father Secchi. " For me, as for every one
else, the sun is an incandescent body, raised to an enormous
temperature, in which the substances known to our chemists
and physicists, as well as several other substances still unknown,
are in a state of vapor, heated to such a degree that its spec-
trum is continuous, either on account of the pressure to which
the vapor is subjected, or of its high temperature. This incan-
descent mass is what constitutes the photosphere. Its limit is
defined, as in the case of incandescent gases in general, by the
temperature to which the exterior layer is reduced by its free
radiation in space, together with the force of gravity exert-
ed by the body. The photosphere presents itself as composed
266 THE SOLAR SYSTEM.
of small, brilliant granulations, separated by a dark net-work.
These granulations are only the summits of the flames which
constitute them, and which rise above the lower absorbing
layer, which forms the net-work, as we shall soon more clearly
see.
"Above the photospheric layer lies an atmosphere of a very
complex nature. At its base are the heavy metallic vapors,
at a temperature which, being less elevated, no longer permits
the emission of light with a continuous spectrum, although it
is sufficient to give direct spectra with brilliant lines, which
may be observed, during total eclipses of the sun, at its limb.
This layer is extremely thin, having a depth of only one or
two seconds of arc. According to the law of absorption laid
down by Kirchhoff, these vapors absorb the rays of the spec-
trum from the light of the photosphere which passes through
them, thus giving rise to the breaks known as the Fraunhofer
dark lines, of the solar spectrum. These vapors are mixed
with an enormous quantity of hydrogen. This gas is present
in such a quantity that it rises considerably above the other
layer, and forms an envelope rising to a height of from ten
to sixteen seconds, or even more, which constitutes what we
call the chromosphere. This hydrogen is always mixed with
another substance, provisionally called helium, which forms the
yellow line D 3 of the spectrum of the protuberances, and with
another still rarer substance, which gives the green line 1474
K. This last substance rises to a much greater elevation than
the hydrogen ; but it is not so easily seen in the full sun as
the latter. Probably there is some other substance not yet
well determined. Thus, the substances which compose this
solar envelope appear to be arranged in the order of their
density; but still without any well-defined separation, the dif-
fusion of the gases producing a constant mixture.
"This atmosphere becomes visible in total eclipses in the
form of the corona. It is very difficult to fix its absolute
height. The eclipses prove that it may reach to a height
equal to the solar diameter in its highest portions.
" No doubt it extends yet farther, and it may well be con-
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 267
nected with the zodiacal light. The visible layer of this at-
mosphere is not spherical ; it is higher in middle latitudes,
near forty-five degrees, than at the equator. It IB still more
depressed at the poles. At the base of the chromosphere,
the hydrogen has the shape of small flames composed of very
thin, close filaments which seem to correspond to the granu-
lations of the photosphere. During periods of tranquillity
the direction of these filaments is perpendicular to the solar
surface ; but during periods of agitation they are generally
more or less inclined, and often directed systematically tow-
ards the poles.
" The body of the sun is never in a state of absolute repose.
The various substances coming together in the interior of the
body tend to combine, in consequence of their affinity, and
necessarily produce agitations and interior movements of every
kind and of great intensity. Hence the numerous crises which
show themselves at the surface through the elevation of the
lower strata of the atmosphere by eruptions, and often by act-
ual explosions. Then the lower metallic vapors are projected
to considerable heights, hydrogen especially, at an elevation
visible in the spectroscope (in full sunlight) of one-fourth the
solar diameter. These masses of hydrogen, leaving the pho-
tosphere at a temperature higher than that of the atmosphere,
rise to the superior regions of the latter, remaining suspend-
ed, diffusing themselves at considerable elevations, and form-
ing what are called the prominences or protuberances. The
structure of the hydrogenous protuberances is entirely simi-
lar to that of fluid veins raising themselves from denser layers,
and diffusing in the more rare ones : but their extreme varia-
bility, even at the base, and the rapid changes of the place of
exit and diffusion, prove that they do not pass through any
orifice in a solid resisting layer.
" These eruptions are often mixed with columns of metallic
vapors of greater density, which do not attain the elevation
of the hydrogen, and of which the nature can be recognized
by the aid of the spectroscope : occasionally we see them fall-
ing back on the sun in the form of parabolic jets. The most
268 THE SOLAR SYSTEM.
common substances are sodium, magnesium, iron, calcium, etc.
indeed, the same substances which are seen to form the low,
absorbing layer of the solar atmosphere, and which by their
absorption produce the Fraunhofer lines. A rigorous and in-
evitable consequence of these conditions is the fact that when
the mass thus elevated is carried by the rotation of the sun
between the photosphere and the eye of the observer, the ab-
sorption becomes very sensible, and produces a dark spot on
the photosphere itself. The metallic absorption lines are
then really wider and more diffused in this region ; and ii
the elevated mass is high and dense enough, we can even see
the re-reversal of the lines already reversed ; that is to say,
we can see the bright lines of the substance itself on the back-
ground of the spot. This often happens for hydrogen, which
rises to a great height, and also with sodium and magnesium,
which metals have the rarest vapors. Here, then, we have the
origin of the solar spots. They are formed by masses of ab-
sorbing vapors which, brought out from the interior of the sun,
and interposed between the photosphere and the eye of the ob-
server, prevent a large part of the light from reaching our eyes.
" But these vapors are heavier than the surrounding mass
into which they have been thrown. They therefore fall by
their own weight, and, tending to sink into the photosphere,
produce in it a sort of cavity or basin filled with a darker and
more absorbing mass. Hence the aspect of a cavity recognized
in the spots. If the eruption is instantaneous, or of very short
duration, this vaporous mass, fallen back on the photosphere,
soon becomes incandescent, reheated, and dissolved, and the
spot rapidly disappears ; but the interior crises of the body of
the sun may be continued a long time; and the eruption may
maintain itself in the same place during two or more rotations
of the sun. Hence the persistence of the spots ; for the cloud
can continue to form so long and so fast as the photosphere
dissolves it, as happens with the jets of vapor from our vol-
canoes. The eruptions, when about to terminate, rp ay be re-
vived and reproduced several times near the same place, and
give rise to spots very variable in form and position.
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 269
" The spots are formed of a central region, called the nu-
cleus, or umbra, and of a surrounding part less dark, called
the penumbra.- The latter is really formed of thin dark veils,
and of filaments or currents of photospheric matter which
tend to encroach upon the dark mass. These currents have
the form of tongues, often composed of globular masses look-
ing like strings of beads or willow leaves, and evidently are
only the grains of the photosphere precipitating themselves
towards the centre of the spot, and sometimes crossing it like
a bridge.
FIG. 71. Illustrating Secchi's theory of solar spots.
" In each spot we must distinguish three periods of exist-
ence : the first, of formation ; the second, of rest ; the third,
of extinction. In the first, the photospheric mass is raised
and distorted by a great agitation, often in the nature of a
vortex, which elevates it all around the flowing streams, and
forms irregular elevations, either without penumbra or with a
very irregular one. These irregular movements defy descrip-
tion : their velocities are enormous, and the agitated region
270 THE SOLAR SYSTEM.
extends itself over several square degrees; but this upturn-
ing soon comes to an end, and the agitation slowly subsides,
and is succeeded by calm. In the second period, the agi-
tated and elevated mass falls back again, and tends to com-
bine in masses more or less circular, and to sink by its weight
into the surface of the photosphere. Hence the depressed
form of the photosphere, resembling a funnel, and the numer-
ous currents which come from each point of the circumference
to rush upon this obscure mass ; but at the same time the con-
trast between it and the substance issuing still persists. The
spot takes a nearly stable and circular form, a contrast which
may last a long time so long, in fact, as the interior actions of
the solar globe furnish new materials. At length, the latter
ceasing, the eruptive action languishes and is exhausted, and
the absorbing mass invaded on all sides by the photosphere is
dissolved and absorbed, and the spot disappears.
" The existence of these three phases is established by the
comparative study of the spots and eruptions. When a spot
is on the sun's border during its first period, although the
dark region is invisible, its position is indicated by eruptions
of metallic vapors, if the spot be considerable. On the dark-
est ones the vapors of sodium, iron, and magnesium are seen
in the greatest quantity, and raised to great heights. A calm
and circular spot is crowned by beautiful faculse and jets of
hydrogen and metallic vapors, very low, though quite brilliant.
A spot which is on the point of closing up has no metallic
jets, and at the utmost only a few small jets of hydrogen, and
a more agitated and elevated chromosphere. Besides, obser-
vation teaches that the eruptions in general accompany the
spots, and that they are deficient at times when the spots are
wanting. Thus the solar activity is measured by the double
activity of eruptions and spots which have a common source,
and the spots are really only a secondary phenomenon, de-
pending upon the eruptions and the more or less absorbing
quality of the materials: if the erupted materials were not
absorbent, we could see no spots at all.
" The eruptions composed simply of hydrogen do not pro-
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 271
duce spots ; thus they are seen on all points of the disk, while
the spots are limited to the tropical zones, where alone the
metallic eruptions appear. The eruptions of simple hydrogen
give rise to the faculse. The greater brilliancy of the faculse
is due to two causes : the first is, the elevation of the photo-
sphere above the absorbing stratum of vapor which is very
thin (only one or two seconds of arc, as we have before said) ;
this elevated region thus escapes the absorption of the lower
stratum, and appears more brilliant. The other cause may be
that the hydrogen, in coming out, displaces the absorbing
stratum, and, taking the place of the metallic vapors, permits
a better view of the light of the photosphere itself.
"Thus, in conclusion, the spots are a secondary phenomenon,
but, nevertheless, inform us of" the violent crises which pre-
vail in the interior of the radiant globe. The frequency of
the spots corresponding to the frequency of eruptions, the two
phenomena, taken in connection, are the mark of solar activ-
ity. The spots occupy the zones on each side of the solar
equator, and rarely pass beyond the parallel of thirty degrees.
One or two seen at forty-five degrees are exceptions. That
parallel is therefore the limit of greatest activity of the body.
It is remarkable that the parallels of thirty degrees divide the
hemispheres into two sectors of equal volume. Beyond these
parallels we see faculse, but not true spots or, at most, only
veiled spots indicative of a very feeble metallic eruption.
" Such a fluid mass, in which the parts are exposed to very
different temperatures, could not subsist without an interior
circulation. We do not yet know its laws; but the following
facts are well enough established : the zones of spots are not
fixed, but have a progressive motion from the equator towards
the poles. The spots, arrived at a certain high latitude, cease
to appear, but after some time reappear at lower latitudes,
and afterwards go on anew. Between these phases of dis-
placement there is commonly a minimum of spots. During
periods of activity the protuberances have a dominant direc-
tion towards the pole, as also the flames of the chromosphere.
272 THE SOLAR SYSTEM.
the equator to the poles. This movement is supported by the
displacement of the zones of eruption and of the protuber-
ances, which always seem to move towards the poles.
" Besides this movement in latitude, the photosphere has
also a movement in longitude, which is greatest at the equa-
tor. Thus the time of rotation of the body is different upon
different parallels, the minimum being at the equator. These
phenomena lead to the conclusion that the entire mass is af-
fected with a vortical motion which sets from the equator
towards the poles, in a direction oblique to the meridians.
The theory of these movements is still to be elaborated, and
is, no doubt, connected with the primitive mode in which the
sun was formed.
" The activity of the body is subject to considerable fluctu-
ations : the best established period is one of eleven and one-
third years, but the activity increases more rapidly than it di-
minishes it increases about four years, and diminishes about
seven. This activity is connected with the phenomena of ter-
restrial magnetism, but we cannot say in what way. We may
suppose a direct electro-magnetic influence of the sun upon
our globe, or an indirect influence due to the thermal action
of the sun, which reacts upon its magnetism. It is, indeed,
very natural to suppose that the ethereal mass which fills the
spaces of our planetary system may be greatly altered and
modified by the activity of the central body. But, whatever
may be the cause of these changes of activity, we are com-
pletely ignorant of them. The action of the planets has been
proposed as plausible, but it is far from being satisfactory.
The true explanation is reserved for the science which shall
reveal the nature of the connection which unites heat to elec-
tricity, to magnetism, and to the cause of gravity.
" Of the interior of the sun we have no certain information.
The superficial temperature is so great, notwithstanding the
continual loss of heat which it suffers, that we cannot suppose
it less in the interior; and, consequently, no solid layer can ex-
ist there, except perhaps at depths where the pressure due to
gravity equals or surpasses the molecular dilatation produced
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 273
by temperature. However it may be, the layer accessible to
the exploration of our instruments is, no doubt, fluid and gase-
ous, and we can thus explain the variations of the solar diam-
eter established by certain astronomers. Notwithstanding these
small fluctuations, the radiation of the body into its planetary
system is nearly constant during widely separated periods, and
especially is it so during the historic period. This constancy
is due to several causes : first, to the enormous mass of the
body, which can be cooled only very slowly, owing to its very
high temperature ; second, to the contraction of the mass,
which accompanies the condensation consequent upon the loss
of heat; third, to the emission of the heat of dissociation due
to the production of chemical actions which may take place
in the total mass.
" The origin of this heat is to be found in the force of grav-
ity ; for it is well proved that the solar mass, by contracting
from the limits of the planetary system to its present volume,
would produce, not only its actual temperature, but one sev-
eral times greater. As to the absolute value of this tempera-
ture, we cannot fix it with certainty. Science not yet having
determined the relation which exists between molecular liv-
ing force (vis viva) and the intensity of radiation to a distance
(which last is the only datum given by observation), we find
ourselves in a state of painful uncertainty. Nevertheless, this
temperature must be several million degrees of our thermom-
eter, and capable of maintaining all known substances in a
state of vapor.
" Rome, February llth, 1877."
Views of M. Faye. " In studying without any prepossession
the movements of the spots, we find, with Mr. Carrington, that
there exists a simple relation between their latitude and their
angular velocity. Nevertheless, this law does not suffice to
represent the observations with the exactitude which they ad-
mit of. It is still necessary to take account by calculation of a
parallax of depth which I estimate at -^-$ of the radius of the
sun, and of certain oscillations of very small extent, and of
long period, which the spots undergo perpendicular to their
19
THE SOLAR SYSTEM.
parallels. Then the observations are represented with great
precision, from which I conclude that we have to deal with a
quite simple mechanical phenomenon. The law in question
can be expressed by the formula,
to ab sin 3 X;
<o being the angular velocity of a spot at the latitude X, and a
and b being constants, having the same value (a=:857'.6 and
1=157'. 3) over the whole surface of the sun. These constants
may vary slowly with the time, but I have not studied their
variations.
"Admitting, as we shall see farther on, that the velocity of
a spot is the same as the mean velocity of that zone of the
photosphere in which it is formed, we see :
" 1. That the contiguous strips of the photosphere are ani-
mated with a velocity of rotation nearly constant for each fila-
ment, at least during a period of several months or years, but
varying with the latitude from one strip to another.
" 2. That these strips move nearly parallel to the equator,
and never give indications of currents constantly directed tow-
ards either pole, as in the upper regions of our atmosphere.
" 3. That the spots are hollow, or at least that the black nu-
cleus is perceptibly depressed in respect to the photosphere.
" The diminution in the rate of superficial rotation, more
and more marked towards the poles, and the absence of all
motion from the equator, can only proceed from the vertical
ascent of materials rising incessantly from a great depth tow-
ards all points of the surface. It is sufficient that this depth
goes on increasing from the equator towards the poles, follow-
ing a law analogous to that of the rotation, in order that it
may produce at the surface a retardation increasing with the
latitude. This retardation is about two days in each rotation
at forty-five degrees of latitude. The mass of the sun, being
formed principally of metallic vapors condensable at a certain
temperature, and that temperature being reached at a certain
level in consequence of the exterior cooling, there ought to be
established a double vertical movement of ascending vapors,
which go to form a cloud of condensed matter susceptible of
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 275
intense radiation, and of condensed products which fall back
in the form of rain into the interior. The latter are stopped
at the depth at which they meet a temperature high enough
to vaporize them anew, and afterwards force them to reascend.
As almost the entire mass of the sun partakes of this double
movement, the heat radiated by the cloud will be borrowed
from this mass, and not from a superficial layer, the tempera-
ture of which would rapidly fall, and which would soon con-
dense into a complete crust. Hence the formation and sup-
port of the photosphere, and the constancy and long duration
of its radiation, which is also partly fed by the slow contrac-
tion of the whole mass of the sun.
" The contiguous bands of the photosphere being animated
with different velocities, there results a multitude of circular
gyratory movements around a vertical axis extending to a
great depth, as in our rivers and in the great upper currents
of our atmosphere. These whirlpools, which tend to equalize
the differences of velocity just spoken of, follow the currents
of the photosphere in the same way that whirlpools, and the
whirlwinds, tornadoes, and cyclones of our atmosphere follow
the upper currents in which they originate. Like these, they
are descending, as I have proved (against the meteorologists)
by a special study of these terrestrial phenomena. They carry
down into the depths of the solar mass the cooler materials of
the upper layers, formed principally of hydrogen, and thus
produce in their centre a decided extinction of light and heat
as long as the gyratory movement continues. Finally, the
hydrogen set free at the base of the whirlpool becomes re-
heated at this great depth, and rises up tumultuously around
the whirlpool, forming irregular jets which appear above the
chromosphere. These jets constitute the protuberances.
" The whirlpools of the sun, like those on the earth, are of
all dimensions, from the scarcely visible pores to the enormous
spots which we see from time to time. They have, like those
of the earth, a marked tendency first to increase, and then to
break up, and thus form a row of spots extending along the
same parallel. The penumbra is due to a portion of the photo-
276 THE SOLAR SYSTEM.
sphere which forms around their conical surface at a lower
level, on account of the lowering of the temperature produced
by the whirlpool. Sometimes in this sort of luminous sheath we
see traces of the whirling movement going on in the interior.
" It is more difficult to account for the periodicity of the
spots. It seems to me that it must depend upon fluctuations in
the form of the interior layer, to which the condensed matter
of the photosphere falls in the form of rain. This flew of
materials from above must alter, little by little, the velocity
of rotation of this layer. If its compression is changed in the
course of time, and if it becomes rounder, the variations in
the superficial velocity of the photosphere, as well as the gyra-
tory movements, will diminish in intensity and frequency.
"A time will at length arrive when the vertical movements
which feed the photosphere will become more and more hin-
dered. The cooling will then be purely superficial, and the
surface of the sun will harden into a continuous crust.
" Paris, February, 1877."
Views of Professor Young. " 1. It seems to me almost dem-
onstrated, as a consequence of the low mean density of the
sun and its great force of gravity, that the central portions of
that body, and, in fact, all but a comparatively thin shell near
the surface, must be in a gaseous condition, and the gases at
so high a temperature as to remain for the most part dissoci-
ated from each other, and incapable of chemical interaction.
Under the influence of the great pressure and high tempera-
ture, however, their density and viscosity are probably such as
to render their mechanical behavior more like that of such
substances as tar or honey than that of air, as we are famil-
iar with it.
" 2. The visible surface of the sun, the photosphere, is com-
posed of clouds formed by the condensation and combination
of such of the solar gases as are cooled sufficiently by their
radiation into space. These clouds are suspended in the mass
of uncondensed gases like the clouds in our own atmosphere,
and probably have, for the most part, the form of approximate-
ly vertical columns, of irregular cross -section, and a length
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 277
many times exceeding their diameter. The liquid and solid
particles of which they are made up descend continually, their
places being constantly supplied by fresh condensation from
the ascending currents which rise between the cloud-columns.
From the uiider-surface of the photosphere there must be an
immense precipitation of what may be called solar * rain and
snow/ which descends into the gaseous core, and by the inter-
nal heat is re-evaporated, decomposed, and restored to its origi-
nal gaseous condition ; the heat lost by the surface radiation
being replaced mainly by the mechanical work due to the
gradual diminution of the sun's bulk, and the thickening of
the photosphere. I do not know any means of determining
the thickness of the photospheric shell, but, from the phenom-
ena of the spots, judge that it can hardly be less than ten
thousand miles, and that it may be much more.
" 3. The weight of the cloud-shell, and the resistance offered
to the descending products of condensation, act to produce on
the enclosed gaseous core a constricting pressure, which forces
the gases upwards through the intervals between the clouds
with great velocity ; so that jets or blasts of heated gas con-
tinually ascend all over the sun's surface, the same material
subsequently redescending in the cloud-columns, partly con-
densed into solid or liquid particles, and partly uncondensed,
but greatly cooled. It seems also not unlikely that in the up-
per part of the channels through which the ascending currents
rush, there may often occur the mixture of different gases
cooled by expansion to temperatures sufficiently below r the
dissociation point to allow of their explosive combination.
" 4. The ' chromosphere' is simply the layer of uncondensed
gases which overlies the photosphere, though separated from
it by no definite surface. The lower portion of the chromo-
sphere is rich in all the vapors and gases which enter into the
sun's composition; but at a comparatively small height the
denser and less permanent gases disappear, leaving in the up-
per regions only hydrogen and some other substances not as
yet identified. The dark lines of the solar spectrum originate
mainly in the absorption produced by the denser gases which
278 THE SOLAR SYSTEM.
bathe the photospheric clouds, and these metallic vapors are
only occasionally carried into the upper regions by ascending
jets of unusual violence. When this occurs, it is almost in-
variably in connection with a solar spot. The prominences
are merely heated masses of the hydrogen and other chromo-
spheric gases, carried to a considerable height by the ascend-
ing currents, and apparently floating in the ' coronal atmos-
phere,' which interpenetrates and overtops the chromosphere.
" 5. I do not know what to make of the corona. Its spec-
trum proves that, a considerable portion of its light comes
from some exceedingly rare form of gaseous matter, which
cannot be identified with anything known to terrestrial chem-
istry ; and this gas, whatever it may be, exists at a height of
not less than a million of miles above the solar surface, con-
stituting the * coronal atmosphere.' Another portion of its
light appears to be simply reflected sunshine. But by what
forces the peculiar radiated structure of the corona is deter-
mined, I have no definite idea. The analogies of comets' tails
and auroral streamers both appear suggestive ; but, on the other
hand, the spectra of the corona, the aurora borealis, the com-
ets, and the nebulae are all different no two in the least alike.
" 6. As to sun-spots, there can be no longer any doubt, I
think, that they are cavities in the upper surface of the photo-
sphere, and that their darkness is due simply to the absorbing
action of the gases and vapors which fill them. It is also cer-
tain that very commonly, if not invariably, there is a violent
uprush of hydrogen and metallic vapors' all around the outer
edge of the penumbra, and a considerable depression of the
chromosphere over the centre of the spot ; probably, also, there
is a descending current through its centre. As to the cause
of the spots, and the interpretation of their telescopic details,
I am unsatisfied. The theory of Faye appears to me, on the
whole, the most reasonable of all that have yet been proposed ;
but I cannot reconcile it with the want of systematic rotation
in the spots, or their peculiar forms. Still, it undoubtedly has
important elements of truth, and may perhaps be modified so
as to meet these difficulties. As to the periodicity of the spots,
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 279
I am unable to think it due in any way to planetary action;
at least, the evidence appears to me wholly insufficient as yet;
but I have no hypothesis to offer. Nor have I any theory to
propose to account for the certain connection between disturb-
ances of the solar surface and of terrestrial magnetism.
" 7. As to the temperature of the sun's surface, I have no
settled opinion, except that I think it must be much higher
than that of the carbon points in the electric light. The esti-
mates of those who base their calculations on Newton's law of
cooling, which is confessedly a mere approximation, seem to
me manifestly wrong and exaggerated ; on the other hand, the
very low estimates of the French physicists, who base their
calculations on the equation of Dulong and Petit, seem to rne
hardly more trustworthy, since their whole result depends
upon the accuracy of a numerical exponent determined by ex-
periment at low temperatures and under circumstances differ-
ing widely from those of the sun's surface. The process is an
unsafe extrapolation. The sensible constancy of the solar
radiation seems to be fairly accounted for on the hypothesis
of slow contraction of the sun's diameter.
" 8. I look upon the accelerated motion of the sun's equator
as the most important of the unexplained facts in solar phys-
ics, and am persuaded that its satisfactory elucidation will carry
with it the solution of most of the other problems still pending.
" Such, in brief, are my * opinions ;' but many of them I
hold with little confidence and tenacity, and anxiously await
more light, especially as regards the theory of the sun's rota-
tion, the cause and constitution of the spots, and the nature of
the corona. The only peculiarity in my views lies, I think,
in the importance I assign to the effects of the descending
products of condensation, which I conceive to form virtually
a sort of constricting skin, producing pressure upon the gas-
eous mass beneath, something as the film of a bubble com-
presses the enclosed air. To the pressure thus produced I
ascribe mainly the eruptive phenomena of the chromosphere
and prominences.
" Dartmouth College, March, 1877."
280 THE SOLAR SYSTEM.
Views of Professor Langley. "It seems to me that we have
now evidence on which to pass final adverse judgment on
views which regard the photosphere as an incandescent liquid,
or the spots as analogous either to scoriae matter, on the one
hand, or to clouds above the luminous surface, on the other.
According to direct telescopic evidence, the photosphere is
purely vaporous, and I consider these upper vapors to be
lighter than the thinnest cirri of our own sky. The obser-
vation of f aculiB allies them and the whole ' granular ' cloud
structure of the surface most intimately with chromospheric
forms, seen by the spectroscope, and associates both with the
idea of an everywhere-acting system of currents which trans-
mit the internal heat, generated by condensation, to the sur-
face, and take back the cold, absorbent matter. This vertical
circulation goes to a depth, I think, sensible even by compari-
son with the solar diameter* It coexists with approximately
horizontal movements observed in what may be called the
successive upper photospheric strata in the vicinity of spots.
The spots give evidence of cyclonic action such as could only
occur in a fluid. Their darkness is due to the presence, in
unusual depth, of the same obscuring atmosphere which forms
the gray medium in which the luminous photospheric forms
seem suspended, and which we here look through, where it
fills openings in the photospheric stratum, down to regions
of the solar interior made visible by the dim light of clouds
of luminous vapor, precipitated in lower strata where the dew-
point lias been altered by changed conditions of temperature
and pressure. All observation and all legitimate inference
go to show that the sun is gaseous throughout its mass, though
by this it is not meant to deny the probable precipitation of
cooling photospheric vapors in something analogous to rain ;
a condition perhaps necessary to the maintenance of the equi-
librium of the interchange of cold and heated matter between
exterior and interior; nor is it meant that the conditions of a
perfect fluid are to be expected, where these are essentially
modified (if by no other cause) by the viscosity due to extreme
heat. The temperature of the sun is, in my view, necessarily
VIEWS ON THE PHYSICAL CONSTITUTION OF TILE SUN. 281
much greater than that assigned by the numerous physicists,
who maintain it to be comparable with that obtainable in the
laboratory furnace ; but we cannot confidently assign any up-
per limit to it until physics has advanced beyond its present
merely empirical rules connecting emission and temperature ;
for this, and not the lack of accurate data from physical
astronomy, is the source of nearly all the obscurity now at>
FIG. 7'2. Solar spot, after Langley,
tending this important question. No theory of the solar con-
stitution which is free from some objection has yet been pro-
posed ; but if the master-key to the diverse problems it pre-
sents has not been found, it is still true, I think, that the one
which unlocks most is that of M. Faye.
" Of the potential energy of the sun, we may say that we
believe it to be sufficient for a supply of the present heat dur-
ing periods to be counted by millions of years. But what im-
282 THE SOLAR SYSTEM.
mediately concerns us is the constancy of the rate of conver-
sion of this potential into actual radiant energy, as we receive
it, for on this depends the uniformity of the conditions under
which we exist. Now, this uniformity in turn depends on
the equality of the above-mentioned interchanges between the
solar surface and the interior, an equality of whose constancy
we know nothing save by limited experience. The most im-
portant statement with reference to the sun, perhaps, which
we can make with certainty is even a negative one. It is
that we have no other than empirical grounds, in the present
state of knowledge, for believing in the uniformity of the
solar radiation in prehistoric periods and in the future.
" The above remarks, limited as they are, appear to me to
coyer nearly all the points as to the sun's physical constitu-
tion (outside of the positive testimony of the spectroscope) on
which we are entitled to speak with confidence, even at the
present time."
THE PLANET MERCUHY.
283
Its mean distance from
CHAPTER IEL
THE INNER GROUP OF PLANETS.
1. The Planet Mercury.
MERCURY is the nearest known planet to the sun, and the
smallest of the eight large planets,
the sun is 40 millions of
miles, and its diameter about
one-third that of the earth.
It was well known to the an-
cients, being visible to the
naked eye at favorable times,
if the observer is not in too
high a latitude. The central
and northern regions of Eu-
rope are so unfavorably sit-
uated for seeing it that it is
said Copernicus died without
ever having been able to ob-
tain a view of it. The diffi-
culty of seeing it arises from
its proximity to the sun, as it seldom sets more than an hour
and a half after the sun, or rises more than that length of
time before it. Plence, when the evening is sufficiently ad-
vanced to allow it to be seen, it is commonly so near the hori-
zon as to be lost in the vapors which are seen in that direction.
Still, by watching for favorable moments, it can be seen sev-
eral times in the course of the year in any part of the United
States. The following are favorable times for seeing it after
sunset :
1877 May 3d, August 26th, December 25th.
1878 ,. .April Hth, August 9th, December Oth.
1879 March 28th, July 23d, November 21st.
FIG. 73. Orbits of the four inner planets, il-
lustrating the eccentricity of those of Mercu-
ry and Mars.
284: THE SOLAR SYSTEM.
The corresponding times in subsequent years may be found
by subtracting 18 days from the dates for each year; that is,
they will occur 18 days earlier in 1879 than in 1878 ; 18 days
earlier in 1880 than in 1879, and so on. It is not necessary
to look on the exact days we have given, as the planet is gen-
erally visible for fifteen or twenty days at a time. Each date
given is about the middle of the period of visibility, which ex-
tends a week or ten days on each side. The best time for look-
ing is in the evening twilight, about three-quarters of an hour
after sunset, the spring is in this respect much more favorable
than autumn.
Aspect of Mercury. Mercury shines with a brilliant white
light, brighter than that of any fixed star, except, perhaps,
Sirius. It does not seem so bright as Sirius, because it can
never be seen at night except very near the horizon. Owing
to the great eccentricity of its orbit and the great variations of
its distance from the earth, its brilliancy varies considerably ;
but the favorable times we have indicated are near those of
greatest brightness.
Viewed with a telescope under favorable conditions, Mer-
cury is seen to have phases like the moon. When beyond the
sun, it seems round and small, being only about 5" in diame-
ter. When seen to one side of the sun, near its greatest ap-
parent angular distance, it appears like a half-moon. When
nearly between the sun and earth, its diameter is between 10"
and 12", but only a thin crescent is visible. The manner in
which these various phases are connected with the position of
the planet relative to the earth and sun is the same as in the
case of Venus, and will be shown in the next section.
Rotation, Figure, Atmosphere, etc. About the beginning of
the present century Schroter, the celebrated astronomer of
Lilienthal, who made the telescopic study of the planets a
speciality, thought that at times, when Mercury presented the
aspect of a crescent, the south horn of this crescent seemed
blunted at certain intervals. He attributed this appearance to
the shadow of a lofty mountain, and by observing the times
of its return was led to the conclusion that the planet revolved
TRANSITS OF -MERCURY. 285
on its axis in 24 hours 5 minutes. He also estimated the
height of the mountain at twelve miles. But the more power*
fill instruments of modern times have not confirmed these
conclusions, and they are now considered as quite doubtful, if
not entirely void of foundation. That is, we must regard the
time of rotation of Mercury on its axis, and, of course, the
position of that axis, as not known with certainty, but as per-
haps very nearly 24 hours.
The supposed atmosphere of Mercury, the deviation of its
body from a spherical form, and many other phenomena
which observers have described, must be received with the
same scepticism. No deviation from a spherical form can be
considered as proved, the discordance of the measures showing
that the supposed deviations are really due to errors of obser-
vation. So, also, the appearances which many observers have
attributed to an atmosphere are all to be regarded as optical
illusions, or as due to the imperfections of the telescope made
use of. From measures of its light at various phases Zollner
has been led to the conclusion that Mercury, like our moon,
is devoid of any atmosphere sufficiently dense to reflect the
light of the sun. If this doubt and uncertainty seems surpris-
ing, it must be remembered that the nearness of this planet to
the sun renders it a very difficult object to observe with accu-
racy. We must look at it either in the daytime, when the air
is disturbed by the sun's rays, or in the early evening, when the
planet is very near the horizon, and therefore in an unfavorable
situation.
Transits of Mercury. Transits of this planet across the face
of the sun are much more frequent than those of Venus, the
average interval between successive transits being less than ten
years, and the longest interval thirteen years. These transits
are always looked upon with great interest by astronomers, on
account of the questions to which they have given rise. From
the earliest ages in which it was known that Mercury moved
around the sun, it was evident that it must sometimes pass be-
tween the earth and the sun ; but its diameter is too small to
admit of its being seen in this position with the naked eye;
286
THE SOLAR SYSTEM.
The first actual observation of Mercury projected on the face
of the sun was made by Gassendi, on November 7th, 1631.
His mode of observation was that already described for viewing
the solar spots, the image of the sun being thrown on a screen
by means of a small telescope. He came near missing his ob-
servation, owing to his having expected that the planet would
look much larger than it did. The imperfect telescopes of
that time surrounded every brilliant object with a band of
diffused light which greatly increased its apparent magni-
tude, so that Gassendi had no idea how small the planet really
was.
Gassendi's observation was hardly accurate enough to be of
any scientific value at the present time. It was riot till 1677
that a really good observation was made. Halley, of England,
in that year was on the island of St. Helena, and, being pro-
vided with superior instruments, was fortunate enough to make
a complete observation of a transit of Mercury over the sun
which occurred on November 7th. We have already men-
tioned the great accuracy which he attributed to his observa-
tion, and the phenomenon of the black drop which he was the
first to see.
The following are the dates at which it has been calculated
that transits of Mercury will occur during the remainder of
the present century. The first transit will be visible over the
whole United States, and the second on the Pacific coast.
1878 May 6th.
1881 November 7th.
1891 May 9th.
1894 November 10th.
1901 November 4th.
2. The Supposed Intra-Mercurial Planets.
At the present time the greatest interest which attaches to
transits of Mercury arises from the conclusion which Lever-
rier has drawn from a profound comparison of transits ob-
served before 1848 with the motion of Mercury as determined
from the theory of gravitation. This comparison indicates,
according to Leverrier, that the perihelion of Mercury moves
more rapidly by 40" a century than it ought to from the grav-
THE SUPPOSED INTRA- MERCURIAL PLANETS. 287
itation of all the known planets of the system. He accounted
for this motion by supposing a group of small planets between
Mercury and the sun, and the question whether such planets
exist, therefore, becomes important.
Apparent support to Leverrier's theory is given by the fact
that various observers have within the past century recorded
the passage over the disk of the sun of dark bodies which had
the appearance o planets, and which went over too rapidly or
disappeared too suddenly to be spots. But when we examine
these observations, we find that they are not entitled to the
slightest confidence. There is a large class of recorded as-
tronomical phenomena which are seen only by unskilful ob-
servers, with imperfect instruments, or under unfavorable cir-
cumstances. The fact that they are not seen by practised ob-
servers with good instruments is sufficient proof that there is
something wrong about them. Now, the observations of in-
tra-Mercurial planets belong to this class. Wolf has collected
nineteen observations of unusual appearances on the sun, ex-
tending from 1761 to 1865, but, with two or three exceptions,
the observers are almost unknown as astronomers. In at least
one of these cases the observer did not profess to have seen
anything like a planet, but only a cloud-like appearance. On
the other hand, for fifty years past the sun has been constant-
ly and assiduously observed by such men as Schwabe, Carring-
ton, Secchi, and Spoerer, none of whom have ever recorded
anything of the sort. That planets in such numbers should
pass over the solar disk, and be seen by amateur observers,
and yet escape all these skilled astronomers, is beyond all
moral probability.
In estimating this probability we must remember that a
real planet appearing on the sun would be far more likely to
be recognized by a practised than by an unpractised observer,
much as a new species of plant or animal is more likely to be
recognized by a naturalist than by one who is not such. One
not accustomed to the close study of the solar spots might
have some difficulty in distinguishing an unusually round spot
from a planet. He is also liable to be deceived in various
288 THE SOLAR SYSTEM.
Ways.* For instance, the sun, by his apparent diurnal motion,
presents different parts of the edge of his disk to the hori-
zon in the course of a day ; he seems, in fact, in the north-
ern hemisphere to turn round in the same direction with the
hands of a watch. Hence, if a spot is seen near the edge of
his disk it will seem to be in motion, though really at rest.
On the other hand, should an experienced observer see a planet
projected on the sun's face, he could hardly fail to recognize it
iri a moment ; and should any possible doubt exist, it would be
removed by a very brief scrutiny,
The strongest argument against these appearances being
planets is, that the transit of a planet in such a position could
not be a rare phenomenon, but would necessarily repeat itself
at certain intervals, depending on its distance from the sun
and the inclination of its orbit. For instance, supposing an
inclination of 10, which is greater than that of any of the
principal planets, and a distance from the sun one-half that
of Mercury, the planet would pass over the face of the sun,
on the average, about once a year, and its successive transits
would occur either very near the same day of the year, or on
a certain day of the opposite season. The supposed transits
to which we have referred occur at all seasons, and if we sup-
pose them real, we must suppose, as a logical consequence,
that the transits of these several planets are repeated many
times a year, and yet constantly elude the scrutiny of all good
observers, though occasionally seen by unskilled ones. This is
a sufficient reductio ad absurdum of the theory of their reality.
It is very certain, then, that if the motion of the perihelion
of Mercury is due to a group of planets, they are each so
small as to be invisible in transits across the sun. They must
* Some readers may recall Butler's sarcastic poem of the "Elephant in the
Moon, " as illustrative of the possibility of an observer being deceived by some pe-
culiarity of his telescope. In one instance, about thirty years since, a telescopic
observation of something which we now know must have been flights of distant
birds over the disk of the sun was recorded, and published in one of the leading
astronomical journals, as a wonderful transit of meteors. 'The publication was
probably not seriously intended, the description being a close parallel to that of
the satirical poet. See Astronomische Nachrichten, No. 549.
THE PLANET VENUS. 289
also be so small as to be invisible during total eclipses of the
sun, because they have always failed to show themselves then.
But to produce the observed effect on Mercury, their total
mass must be three or four times that of Mercury. Being so
small individually, and so large in the aggregate, their num-
ber must be counted by thousands ; and if seen at all, they
will be seen only as a cloud-like mass. Now, in the zodiacal
light we have such a mass, and the question arises whether the
matter which reflects this light can be that which 'affects the
motions of Mercury. Although the affirmative of this ques-
tion involves nothing intrinsically improbable, it cannot be
accepted without further investigation. The delicate point
involved is, that unless we suppose the hypothetical group of
planetoids to move nearly in the plane of the orbit of Mercury,
they must change the node of that planet as well as its peri-
helion. Now, the observations discussed by Leverrier do not
show any motion of the node above that due to the action of
the known planets. We thus reach the enforced conclusion
that if the motion of the perihelion is due to the cause as-
signed by Leverrier, the planetoids which cause it must, in the
mean, move in nearly the same plane with Mercury. But it
has not yet been shown that the axis of the zodiacal light de-
viates from the ecliptic by so great an angle as the orbit of
Mercury, namely 7. A great deal of research more, in fact,
than is likely to be applied to the subject during the present
generation will be required before the question can be settled.
3. The Planet Venus.
The planet Venus moves around the sun about half - way
between the orbits of Mercury and the earth, its mean distance
from the sun being 67 millions of miles. Its orbit is more
nearly circular than that of any of the other principal planets.
It is very nearly the size of the earth, its diameter being little,
if any, more than four per cent, less than that of our globe.
Next to the sun and moon, it is the most brilliant object in
the heavens, sometimes casting a very distinct shadow. It
never recedes more than about 45 from the sun, and is,there-
20
290 THE SOLAR SYSTEM.
fore, seen by night only in the western sky in the evening, or
the eastern sky in the morning, according as it is east or west
of the sun. There is, therefore, seldom any difficulty in rec-
ognizing it. When at its greatest brilliancy, it can be clearly
seen by the naked eye in the daytime, provided that one knows
exactly where to look for it. It was known to the ancients by
the names of Hesperus and Phosphorus, or the evening and
the morning star, the former name being given when the
planet, being east of the sun, was seen in the evening after
sunset, and the latter w r hen, being to the west of the sun, it
was seen in the east before sunrise. It is said that before the
birth of exact astronomy Hesperus and Phosphorus were sup-
posed to be two different bodies, and that it was not until
their motions were studied, and the one was seen to emerge
from the sun's rays soon after the other was lost in them, that
their identity was established.
Aspect of Venus. To the unaided eye Venus presents the
appearance of a mere star, distinguishable from other stars
only by its intense brilliancy. But when Galileo examined
this planet with his telescope, he found it to exhibit phases
like those of the moon. Desiring to take time to assure him-
self of the reality of his discovery, without danger of losing
his claim to priority through some one else in the mean time
making it independently, he published the following anagram,
in which it was concealed:
" Hoec immatura a me jam frustra legimtur o. y."
(These unripe things are now vainly gathered by me).
By transposing the letters of this sentence he afterwards
showed that they could be made into the sentence,
U 0ynthise figuras semnlatur mater amorum "
'* (The mother of the loves imitates the phases of Cynthia).
That the disk of Venus was not round was first noticed by
Galileo in September, 1610. A computation .of its position
at that time show r s that it must have been a little gibbous,
more than half of its face being illuminated ; but after a
THE PLANET VENUS. 291
few months it changed into a crescent. Therefore Galileo
conld not have found it necessary to wait long before explain-
ing his anagram.
The variations of the aspect and apparent magnitude of
Venus are very great. When beyond the sun, it is at a dis*
tance of 160 millions of miles, and presents the appearance
of a small round disk 10" in diameter. When nearest the
earth, it is only 25 millions of miles distant ; and if its whole
face were visible, it would be more than 60" in diameter.
O
.11 3
FIG. 74. rhases of Venus, showing apparent figure and magnitude of the bright and dark
portions of the planet in various points of its orbit.
But, being then on the same side of the sun with us, its dark
hemisphere is turned towards us, except, perhaps, an extreme-
ly thin crescent of the illuminated hemisphere. Between
these two positions it goes through all the intermediate
phases, the universal rule of which is that the nearer it is
to the earth, the smaller the proportion of its apparent disk
which is illuminated ; but the larger that disk would appear
could the whole of it be seen. Its greatest brilliancy occurs
between the time of its greatest elongation from the sun and
its inferior conjunction.
Supposed Rotation of Venus. The earlier telescopists natu-
rally scrutinized the planets very carefully, with a view of find-
ing whether there were any inequalities or markings on their
surfaces from which the time of rotation on their axes could
be determined. In April, 1667, Oassini saw, or thought he
saw, a bright spot on Venus, by tracing which for several suc-
cessive evenings he found that the planet revolved in between
23 and 24 hours. Sixty years later Blanchini, an Italian as-
THE SOLAR SYSTEM.
tronomer, whose telescope is shown on page 112, supposed that
he found seven spots on the planet, which lie considered to be
seas. By watching them from night to night, he concluded
that it required more than 24: days for Venus to revolve on
its axis. This extraordinary result was criticised by the sec-
ond Cassini, who showed that Blanchini, only seeing the plan-
et a short time each evening, and finding the spots night after
night in nearly the same position, concluded that it had moved
very little from night to night ; whereas, in fact, it had made
a complete revolution, and a little more. At the end of 24
days it would be seen in its original position, but would have
made 25 revolutions in the mean time, instead of one only, as
Blanchini supposed. This would make the time of rotation
23 hours 2-J minutes, while Cassini found 23 hours 15 minutes
from his father's observations.
Between 1788 and 1793 Schroter applied to Venus a mode
of observation similar to that he used to find the rotation of
Mercury. Watching the sharp horns when the planet appear-
ed as a crescent, he thought that one of them was blunted at
certain intervals. Attributing this appearance to a high moun-
tain, as in the- case of Mercury, he found a time of rotation
of 23 hours 21 minutes.
On the other hand, Herschel was never able to see any per-
manent markings on Venus. He thought he saw occasional
spots, but they varied so much and disappeared so rapidly that
he could not gather any evidence of the rotation of the plan-
et. He therefore supposed that Venus was surrounded by an
atmosphere, and that whatever markings might be occasional-
ly seen were due to clouds or other varying atmospheric phe-
nomena.
In 1842, De Vico, of Rome, came to the rescue of the older
astronomers by publishing a series of observations tending to
show that he had rediscovered the markings found by Blan-
chini more than a century before. He deduced for the time
of rotation of the planet 23 hours 21 minutes 22 seconds.
The best-informed astronomers of the present day look with
suspicion on nearly all these observations, being disposed to
THE PLANET VENUS. 293
sustain the view of Herschel, though on grounds entirely dif-
ferent from those on which he founded it. It is certain that
there are plenty of observers of the present day, with instru-
ments much better than those of their predecessors, who have
never been able to see any permanent spots. The close agree-
ment between the times of rotation found by the older ob-
servers is indeed striking, and might seem to render it certain
that they must have seen spots which lasted several days. It
must also be admitted in favor of these observers that a fine
steady atmosphere is as necessary for such observations as a
fine telescope, and it is possible that in this respect the Italian
astronomers may be better situated than those farther north.
But the circumstance that the deduced times of rotation in
the cases both of Mercury and Venus differ so little from that
of the earth is somewhat suspicious, because if the appearance
were due to any optical illusion, or imperfection of the tele-
scope, it might repeat itself several days in succession, and
thus give rise to the belief that the time of rotation was near-
ly one day. The case is one on which it is not at present pos-
sible to pronounce an authoritative decision ; but the balance
of probabilities is largely in favor of the view that the rota-
tation of Venus on its axis has never been seen or determined
by any of the astronomers who have made this planet an ob-
ject of study. *
Atmosphere of Venus. The appearance of Venus when near-
ly between us s,nd the sun affords very strong evidence of the
existence of an atmosphere. The limb of the planet farthest
from the sun is then seen to be illuminated, so that it appears
as a complete circle of light. If only half the globe of the
planet were illuminated by the sun, this appearance could
never present itself, as it is impossible for an observer to see
more than half of a large sphere at one view. There is no
* The latest physical observations on Venus with which I am acquainted are
those of Dr. Vogei at Bothkamp, in Part II. of the "Bothkamp Observations"
(Leipzig, Engelraann, 1873). The result to which these observations point is that
the atmosphere of Venus is filled with clouds so dense that the solid body of the
planet can not be seen, and no time of rotation can be determined.
294 THE SOLAR SYSTEM.
known way in which the sun can illuminate so much more
than the half of Venus as to permit a complete circle of light
to be seen except by the refraction of an atmosphere.
The appearance to which we allude was first noticed by
David Kittenhouse, of Philadelphia, while observing the tran-
sit of Venus on June 3d, 1769. When Venus had entered
about half-way upon the sun's disk, so as to cut out a notch of
the form of a half-circle, that part of the edge of the planet
which was off the disk appeared illuminated so that the out-
line of the entire planet could be seen. As this appearance
was not confirmed by other observers, it seems to have excit-
ed no attention. But it was found by Madler in 1849 that
when Venus was near inferior conjunction, the visible crescent
extended through more than a half-circle. This showed that
more than half the globe of Venus was illuminated by the
sun, and Madler, computing the refractive power of the atmos-
phere which would be necessary to produce this effect, found
that it would exceed that of our own atmosphere ; the hori-
zontal refraction being 44', whereas on the earth it is only
34'. He therefore concluded that Venus was surrounded by
an atmosphere a little more dense than that of the earth.
. The next important observation of the kind was made by
Professor C. S. Lyman, of Yale College. In December, 1866,
Venus was very near her node at inferior conjunction, and
passed unusually near the line drawn from the earth to the
sun. Examining the minute crescent of the planet with a
moderate-sized telescope, he found that he could see the entire
circle of the planet's disk, an exceedingly thin thread of light
being stretched round the side farthest from the sun. So far
as known, this was the first time that the whole circle of Venus
had been seen in this way since the time of Eittenhouse. It
is remarkable that both observations should have been made
by isolated observers in America.
Notwithstanding the concurrent testimony of Eitterihouse,
Madler, and Lyman, the bearing of their observations on what
was to be expected during the transit of Venus in December,
1874, was entirely overlooked. Accordingly, many of the ob*
THE PLANET VENUS. 295
servers were quite taken by surprise to find that when Venus
was partly on and partly off the sun, the outline of that part
of her disk outside the sun could be distinguished by a deli-
cate line of light extending around it. In some cases the
time of internal contact at egress of the planet was missed,
through the observer mistaking this line of light for the limb
of the sun.
That no one but Kittenhouse saw this line of light during
the transit of 1769 is to be attributed to the low altitude of
the planet at most of the stations, and to the imperfect char-
acter of many of the instruments used. It is also to be re-
marked that the observers of that time had an erroneous no-
tion of the appearance which would be presented by an atmos-
phere of Venus. It was supposed that the atmosphere would
give the planet a nebulous border when on the sun, caused by
the partial absorption of the light in passing through it. Cap-
tain Cook, at Otaheite, made separate observations of the
contacts of the supposed atmosphere and of the planet with
the limb of the sun. In fact, however, it would not be possi-
ble to see any indications of an atmosphere under such cir-
cumstances, for the reason that the light passing through its
denser portions would be refracted entirely out of its course,
so as not to reach an observer on t}ie earth at all.
The spectroscope shows no indication that the atmosphere
of Venus exerts any considerable selective absorption upon
the light which passes through it. No new and well-marked
spectral lines are found in the light reflected from the planet,
nor has the spectrum been certainly found to differ from the
regular solar spectrum, except, perhaps, that some of the lines
are a little stronger. This would indicate that the atmosphere
in* question does not differ in any remarkable degree from our
own, or, at least, does not contain gases which exert a power-
ful selective absorption on light.
Supposed Visibility of the Dark Hemisphere of Venus. Many
astronomers of high repute have seen the dark atmosphere of
Venus slightly illuminated, the planet presenting the appear-
ance known as " the old moon in the new moon's arms," which
296 THE SOLAR SYSTEM.
may be seen on any clear evening three or four days after the
change of the moon. It is well known that in the case of
the moon her dark hemisphere is thus rendered visible by the
light reflected from the earth. But in the case of Venus,
there is no earth or other body large enough to shed so much
Ifght on the dark hemisphere as to make it visible. There
being no sufficient external source of light, it has been attrib-
uted to a phosphorescence of the surface of the planet. If
the phosphorescence were always visible under favorable cir-
cumstances, there would be no serious difficulty in accepting
this explanation. But, being only rarely seen, it is hard to
conceive how any merely occasional cause could act all at
once over the surface of a planet the size of our globe, so as
to make it shine. Indeed, one circumstance makes it ex-
tremely difficult to avoid the conclusion that the whole ap-
pearance is due to some unexplained optical illusion. The
appearance is nearly always seen in the daytime or during
bright twilight rarely or never after dark. But such an il-
lumination would be far more easily seen by night than by
day, because during the day an appearance easily seen at
night might be effaced by the light of the sky. If, then, the
phenomenon is real, why is it not seen when the circumstances
are such that it should be .most conspicuously visible? This
is a question to which no satisfactory answer has been given,
and until it is answered we are justified in considering the ap-
pearance to be purely optical.
Supposed Satellite of Venus. No better illustration of the er-
rors to which observations with imperfect instruments are lia-
ble can be given than the supposed observations of a satellite
of Venus, made when the telescope was still in its infancy.
In 1672, and again in 1686, Cassini saw a faint object near
Venus which exhibited a phase similar to that of the planet.
But he never saw it except on these two occasions. A similar
object was reported by Short, of England, as seen by him on
October 23d, 1740. The diameter of the object was a third
of that, of Venus, and it exhibited a similar phase. Several
other observers saw the same thing between 1760 and 1764.
THE PLANET VENUS. 297
One astronomer went so far as to compute an orbit from all
the observations ; but it was an orbit in which no satellite of
Venus could possibly revolve unless the mass of the planet were
ten times as great as it really is. A century has now elapsed
without the satellite having been seen, and the fact that dur-
ing this century the planet has been scrutinized with better
telescopes than any which were used in the observations re-
ferred to affords abundant proof that the object was entirely
mythical.
How the observers who thought they saw the object could
have been so deceived it is impossible, at this distance of
time, to say with certainty. Had they been inexperienced,
we could say with some confidence that they were misled by
the false images produced to some extent in every telescope
by the light reflected from the cornea of the eye against the
nearest surface of the eye-piece, and thence back again into
the eye. Similar images are sometimes produced by the re-
flection of light between the surfaces of the various lenses of
the eye - piece. They are well known to astronomers under
the name of " ghosts ;" and one of the first things a young ob-
server must learn is to distinguish them from real objects.
They may also arise from a slight maladjustment of the lenses
of the eye-piece, and if, proceeding from this cause, they are
produced only when the actual object is in the centre of the
field, they may, for the moment, deceive the most experienced
observer.* If, in an ordinary achromatic telescope, in which
the interior curvatures of the lenses are the same, the latter
are not exactly at the same distance all the way round, a ghost
will be seen along-side of every bright object in all positions.
It is probable that all the .observations alluded to were the re-
sults of some sort of derangements in the telescope, producing
false images by reflection from the glasses.
* One of the eye-pieces of the great Washington telescope shows a beautiful
little satellite along -side the planet Uranus or Neptune when the image of the
planet is brought exactly in the centre of the field of view, but it disappears as
soon as the telescope is moved. The writer was deceived by this appearance on
two occasions while scrutinizing these planets for close satellites.
298 THE SOLAR SYSTEM.
4. The Earth.
Our earth is the third planet in the order of distance from
the sun, and slightly the largest of the inner group of four.
Its mean distance from the sun is about 92 millions of miles ;
but it is a million and a half less than this mean on January
1st of every year, and as much greater on July 1st. That
is, its actual distance varies from 91 to 94 millions of miles.
As already remarked, these numbers are uncertain by several
hundred thousand miles.
Much of what we may call the astronomy of the earth
such as its figure and mass, the length of the year, the obliq-
uity of the ecliptic, the causes of the changes in the seasons
and in the length of the days has already been treated in
the chapter on gravitation, so that we have little of a purely
astronomical character to add here. The features of its sur-
face and the phenomena of its atmosphere belong rather to
geography and meteorology than to astronomy. But its consti-
tution gives rise to several questions in the treatment of which
astronomical considerations come into play. Prominent among
these is that of the state of the great interior mass of our
globe, whether solid or liquid. It is well known that wher-
ever we descend into the solid portions of the earth, we find a
rise in temperature, going on uniformly with the depth, at a
rate which nowhere differs greatly from 1 Fahrenheit in 50
feet. This rise of temperature has no connection with the
sea-level, but is found at all points of the surface, no matter
how elevated they may be. Wherever a difference of temper-
ature like this exists, there is necessarily a constant transfer of
heat from the warmer to the cooler strata by conduction. In
this way, the inequality would soon disappear by the warmer
strata cooling off, if there were not a constant supply of heat
inside the earth. The rise of temperature, therefore, cannot
be something merely superficial, but must continue to a great
depth. If we trace to past times the conditions which must
have existed in order that the increase might show itself at the
present time, we shall find it almost certain that, a thousand
THE EARTH. 299
years ago, the whole earth was red-hot at a distance of ten or
fifteen miles below its surface ; because otherwise its interior
could not have furnished the supply of heat which now causes
the observed increase. This being the case, it is probably red-
hot still, since it would be absurd to expect a state of things
like this to be merely temporary. In a word, we have every
reason to believe that the increase of say 100 a mile contin-
ues many miles into the interior of the earth. Then we shall
have a red heat at a distance of 12 miles, while, at the
depth of 100 miles, the temperature will be so high as to
melt most of the materials which form the solid crust of the
globe.
We are thus led to the theory, very generally received by
geologists, that the earth is really a sphere of molten matter
surrounded by a comparatively thin solid crust, on which we
live. This crust floats, as it were, on the molten interior. It
must be confessed that geological facts are, on the whole, fa-
vorable to this view. Observations on the pendulum have
been supposed to show that the specific
gravity of the earth under the great
mountain chains is generally less than in
the adjoining plains, which is exactly the
result that would flow from the theory.
The heavier masses, pressing upon the in-
terior fluid, would tend to elevate the sur-
rounding lighter masses, and when the two FIG. 75. showing thickness
were in equilibrium, the latter would be ?'&
the higher, as a floating block of pine ry of a molten interior.
j -n i i . n 4.1 . The circle is thicker in
wood will rise higher out of the water proportion than the solid
than a block of oak. Boiling springs in crust -
many parts of the globe show that there are numerous hot re-
gions in the earth's interior, and this heat cannot be merely
local, because then it would soon be dissipated. But the geol-
ogist finds the strongest proof of the theory in volcanoes and
earthquakes. The torrents of lava which have been thrown
out of the former through thousands of years show that there
are great volumes of molten matter in the earth's interior,
300 THE SOLAll SYSTEM.
while the latter show this interior to be subject to violent
changes which a solid could not exhibit.
But mathematicians have never been able entirely to rec-
oncile the theory in question with the observed phenomena of
precession, nutation, and tides. To all appearance, the earth
resists the tide-producing action of the sun and moon exactly
as if it were solid from centre to circumference. Sir William
Thomson has shown that if the earth were less rigid than steel,
it would yield so much to this action that the tides would be
much smaller than on a perfectly rigid earth; that is, the at-
traction of the bodies in question would draw the earth itself
out into an ellipsoidal form, instead of drawing merely the
waters of the ocean. Earth and ocean moving together, we
could see no tides at all. If the earth were only a thin shell
floating on a liquid interior, the tides would be produced in
the latter ; the thin shell would bend in such a way that the
tides in the ocean would be nearly neutralized. Again, the
question has arisen whether the liquid interior would be af-
fected by precession ; whether, in fact, the crust would not slip
over it, so that in time the liquid would rotate in one direc-
tion, and the crust in another. Altogether, the doctrine of the
earth's fluidity is so fraught with difficulty that, notwithstand-
ing the seeming strength of the evidence in its favor, it must
be regarded as at least very doubtful. It may be added that
no one denies that the interior of our planet is intensely hot
hot enough, in fact, to melt the rocks at its surface but it
is supposed that the enormous pressure of the outer portions
tends to keep the inner part from melting. Nor is it ques-
tioned by Sir William Thomson that there are great volumes
of melted matter in the earth's interior from which volcanoes
are fed; but he maintains that, after all, these volumes are
small compared with that of the whole earth.
Refraction of the Atmosphere. If a ray of light pass through
our atmosphere in any other than a vertical direction, it is
constantly curved downwards by the refractive power of that
medium. The more nearly horizontal the course -of the ray,
the greater the curvature. In consequence of this, all the
THE EARTH. 301
heavenly bodies appear a little nearer the zenith, or a little
higher above the horizon, than they actually are. The dis-
placement is too small to be seen by the naked eye except
quite near the horizon, where it increases rapidly, amounting
to more than half a degree at the horizon itself. Consequent-
ly, at any point where we have a clear horizon, as on a prairie,
or the sea-shore, the whole disk of the sun will be seen above
the horizon when the true direction is below it. A slight in-
crease is thus given to the length of the day. The sun in our
latitudes always rises three or four minutes sooner, and sets
three or four minutes later, than he would if there were no
atmosphere. At the time of the equinoxes, if we suppose the
day to begin and end when the centre of the sun is on the
horizon, it is not of the same length with the night, but is six
or eight minutes longer. If we suppose the day to begin with
the rising of the sun's upper limb, and not to end till the same
limb has set, then we must add some three minutes more to
its length.
If, standing on a hill, we watch the sun rise or set over the
ocean, one effect of refraction will be quite clearly visible.
When his lower limb almost seems to touch the water, it will
be seen that the form of his disk is no longer round, but ellip-
tical, the horizontal diameter being greater than the vertical.
The reason of this is that the lower limb is more elevated by
refraction than the upper one, and thus the vertical diameter
is diminished.
In practical astronomy, all observations of the altitude of
the heavenly bodies above the horizon must be corrected for
refraction, the true altitude being always less than that ob-
served. Very near the zenith the refraction is about 1" for
every degree, or -5-^$ part the distance from the zenith. But
it increases at first in the proportion of the tangent of the ze-
nith distance, so that at 45, or half-way between the zenith
and the horizon, it amounts to 60"; at the horizon it is 34/.
The Aurora Borealis. This phenomenon, though so well
known, is one of which great difficulty has been found in giv-
ing a satisfactory explanation. That it is in some way con-
302
THE SOLAR SYSTEM.
FIQ. 70. Distribution of auroras, after Loomis. The darker the color, the more frequently
auroras are seen.
iiected with the pole of the earth is shown by the fact that
its frequency depends on the latitude. In the equatorial re-
gions of our globe it is quite rare, and increases in frequency
as we go north. But the region of greatest frequency seems
THE EARTH. 303
to be, not the poles, bnt the neighborhood of the Arctic Cir-
cle, from which it diminishes towards both the north and the
south. This is shown more exactly in Professor Loomis's
auroral map, of which we give a copy on the preceding page.
A close study of the aurora indicates that its connection is
not with the geographical, but with the magnetic pole. Two
distinct kinds of light are seen in the aurora; or we might
say that the light assumes two distinct forms, of which some-
times the one and sometimes the other preponderates. They
are as follows :
1. The cloud-like form. This consists of a large irregular
patch of light, frequently of a red or purple tinge. It is seen
in every direction, but more frequently in or near the northern
horizon, where it assumes the form of an arch or crown of
light. The two ends of the arch rest on the horizon, one on
each side of the north point. The middle of the arch rises a
few degrees above the horizon.
FIG. 77. View of aurora.
2. The streamer or pillar form. This form consists of long
streamers or pillars, which extend in the direction of the dip-
ping magnetic needle. They look curved or arched, like the
celestial sphere on which they are projected, but they are re-
ally straight. They are in a state of constant motion. Some-
304 THE SOLAR SYSTEM.
times they are spread out in the fofm of an immense flag
with numerous folds, dancing, quivering, and undulating, as
if moved by the wind.
Electri$ Nature of the Aurora. There is abundant evidence
that the aurora is intimately connected with the electricity
and magnetism of the earth. During a brilliant aurora such
strong and irregular currents of electricity pass through the
telegraph wires that it is difficult to send a despatch. Some-
times the current runs with such force that a message may
be sent without a battery. The magnetic needle is also in a
state of great agitation. Before the spectroscope came into
use, these electric phenomena gave rise to the opinion that
the aurora was due entirely to currents of electricity passing
through the upper regions of the atmosphere from one pole to
the other. But recent researches seem to show that, though
this view may be partly true, it is far from the whole truth,
and does not afford a complete explanation. The great height
of the aurora and the nature of its spectrum both militate
against it.
Height of the Aurora. Several attempts have been made in
recent times to determine the height of the aurora above the
surface of the earth, by simultaneous observations of some
prominent streamer or patch of light from several far-distant
stations. The general result is that it efteuds to the height of
from 400 to 600 miles. But the evidence of shooting- stars
and meteors seems to indicate that the limit of the atmosphere
is between 100 and 110 miles in height If it extends above
this, it must be too rare to conduct electricity long before it
reaches the greatest height of the aurora ; indeed, it is doubt-
ful whether it does not attain this rarity at a height of 40 or
50 miles. If, then, the aurora really extends to the great
height we have mentioned, and still exists in a gaseous medi-
um, it seems difficult to avoid the conclusion that this medium
is something far more ethereal than the gases which form our
atmosphere. It would, however, be iinphilosopliical to assume
the existence of such a medium without some other evidence
in its favor than that afforded by the aurora. We must in-
THE EARTH.
305
elude the aurora among those things in which modern ob-
servations have opened up more difficulties than modern theo-
ries have explained.
Spectrum oftiie Aurora. rThe spectrum of the aurora is so
far from uniform as to be quite puzzling. There is one char-
acteristic bright line in the green part of the spectrum, known
as Angstrom's line, from its first discoverer. This was the
only line Angstrom could see: he therefore pronounced the
light of the aurora to be entirely of one color. Subsequent
observers, however, saw many additional lines, but they were
different in different auroras. Among those who have made
careful studies of the aurora with the spectroscope are the
late Professor Winlock, of Harvard University; Professor
Barker, of Philadelphia ; and Dr. H. C. Vogel, formerly of
Bothkamp.
D E A F
FIG. 78. Spectrum of two of the great auroras of 1871, after Dr. H. C. Vogel.
Fig. 78 shows the spectra of two auroras, as drawn by Dr.
Vogel. It will be seen that there is one fine bright line be-
tween D and E, which would fall in the yellowish-green part
of the spectrum, while the others are all broad, ill -defined
bands. Dr. Vogel notices a remarkable connection between
these lines and several groups of lines produced by the vapor
of iron, and inquires whether this vapor can possibly exist in
the upper regions of our atmosphere. A more complete study
of the spectra of vapors at different pressures and tempera-
tures is necessary before we can form a decided opinion as to
what the aurora really is.
21
'306 THE SOLAR SYSTEM.
Of the supposed periodicity of the aurora, and its connection
with sun-spots, we have already spoken. Granting the reality
of this connection, we may expect that auroras will be very
frequent between the years 1880 and 1884 ; and if this ex-
pectation is realized, little doubt of the connection will remain.
. 5. The Moon.
The moon is much the nearest to us of all the heavenly
bodies ; no other, except possibly a comet, ever coining nearer
than a hundred times her distance. Her mean distance is, in
round numbers, 240,000 miles. Owing to the ellipticity of her
orbit and the attractive force of the sun, it varies from ten to
twenty thotisand miles on each side of this mean in the course
of each monthly revolution. The least possible distance is
221,000 miles ; the greatest is 259,600 miles. It very rarely
approaches either of these limits, the usual oscillation being
about 13,000 miles on each side of the mean distance of
240,300. The diameter of the moon is 2160 miles, or some-
what less than two-sevenths that of the earth. HeV volume is
about one-fiftieth that of the earth, and if she were as dense
as the latter, her mass would be in the same proportion.
Fia. 79. Relative size of earth and moon.
Bnif her actual mass is only about one-eightieth that of the
earth^ Showing that her density, or the specific gravity of the
material of which she is composed, is little more than half that
THE MOON. 307
of our globe. Her weight is, in fact, about 3J times that of
her bulk of water.
The most remarkable feature of the motion of the moon is,
that she makes one revolution on her axis in the same time
that she revolves around the earth, and so always presents the
same face to us. In consequence, the other side of the moon
must remain forever invisible to human eyes. The reason of
this peculiarity is to be found in the ellipticity of her globe.
That she should originally have been set in revolution on her
axis with precisely the same velocity with which she revolved
around the earth, so that not the slightest variation in the re-
lation of the two motions should ever occur in the course of
ages, is highly improbable. If such had been the state of
things, the correspondence of the two motions could not have
been kept up withput her axial rotation varying; because,
owing to the secular acceleration already described, the moon,
in the course of ages, varies her time of revolution, and so
the two motions would cease to correspond. But the effect of
the attraction of the earth upon the slightly elongated lunar
globe is such that if the two motions are, in the beginning,
very near together, n<5t only will thejaxial rotation accommo-
date itself to the orbital revolution around the earth, but as
the latter varies, the former will vaiy with it, and thus the
correspondence will be kept up.
Figure, Hotation, and Libration of the Moon. Supposing the
shape of the moon to be the same as if it were a fluid mass,
or covered by an ocean, it will be an ellipsoid with three un-
equal axes. The shortest axis will be that around which it
revolves, which is not very far from being perpendicular to
the ecliptic. The next longest is that which lies in the direc-
tion in which the moon moves ; while the longest of all is
that which points towards the earth. The reason that the
polar axis is the shortest is the same which makes the polar
axis of the earth the shortest, that is, the centrifugal f$rce
generated by the revolution round that axis. If we consid-
ered only the action of this force, we should conclude that the
moon, like the earth, was an oblate spheroid, the equator be-
308 THE SOLAR SYSTEM.
ing a perfect circle. But the attraction of the earth upon the
moon tends to elongate it in the direction of the line joining
the two bodies, in the same way that the attraction of the moon
upon the earth generates a tide-producing force which we have
already explained. At the centre of the moon the attraction
of the earth and the centrifugal force of the moon in its or-
bit exactly balance each other. But if we go to the farther
side of the moon, the centrifugal force will be greater, owing
to the larger orbit which that part of the moon has to de-
scribe, while the attraction of the earth will be less owing to
the greater distance of the particles it attracts. Hence, that
part of the moon tends to fly off from the centre and from the
earth. On this side of the moon the case is reversed, the at-
tractive force of the earth exceeding the centrifugal force of
those parts of the moon, whence those parts are impelled by a
force tending to draw them to the earth. The effect would
be much the same as if a rope were fastened to this side of
the moon, and constantly pulled towards the earth, while an-
other were fastened to the opposite side, and as constantly
pulled from the earth. Supposing the moon to be a liquid,
so as to yield freely, it is clear that the effect of these forces
would be to elongate her in the direction of the earth.
The deviations from a spherical form produced by these
causes are very minute. Taking the results of Lagrange and
Newton, the mean axis would be 46J feet longer than the
shortest one, and the longest 186 feet longer than the mean
one, or 232^ feet longer than the shortest one.* These differ-
ences are so much smaller than the average height of the
lunar mountains that the irregularities produced by the latter
might entirely overpower them ; but the correspondence be-
tween the motions of rotation and revolution of the moon
shows that there must be, on the average, a real elongation in
* These numbers are, perhaps, not strictly correct. The extension of 186 feet
was deduced by Newton from a comparison of the distorting powers of the centrif-
ugal force of the earth with that of the force we have just described. He seems
to have overlooked the fact that the small density of the moon will cause the
elongation to be greater.
THE MOON. 309
the direction of the earth. This correspondence is kept up by
the slight additional attraction of the earth upon this extension
of the moon towards the earth, combined with the additional
centrifugal force of the extension on the other side. Although
these forces are not by any means the same as the distorting
forces already described, they may be represented in the same
way by two ropes, one of which pulls the protuberance on this
side towards the earth, while the other pulls the protuberance
on the other side from it. If the two protuberances do not
point exactly towards the earth, the effect of these two minute
forces will be to draw them very slowly into line. Conse-
quently, notwithstanding the slow variations to which the mo-
tion of the moon around the earth is subject in the course
of ages, the attraction of the earth will always keep this pro-
tuberant face turned towards us. Human eyes will never be-
hold the other side of the moon, unless some external force
acts upon her so as to overcome the slight balancing force
just described, and set her in more or less rapid motion on
her axis. If it is disappointing to reflect that we are for-
ever deprived of the view of the other side of our satellite, we
may console ourselves with the reflection that there is not the
slightest reason to believe that it differs in any respect from
this side. The atmosphere with which it has been covered,
and the inhabitants with which it has been peopled, are no
better than the products of a poetic imagination.
The forces we have just described as tending to keep the
same face of the moon pointed towards us would not produce
this effect unless the adjustment of the two motions that
around the earth, and that on her axis were almost perfect
in the beginning. If her axial rotation were accelerated by so
small an amount as one revolution in two or three years, there
is every reason to believe that she would keep on revolving at
the new rate, notwithstanding the force in question. The case
is much like that of a very easy-turning fly-wheel, which is
slightly weighted on one side. If we give the wheel a gentle
motion in one direction or another, the weight will cause the
wheel to turn till the heavy side is the lowest, and the wheel
310 THE SOLAR SYSTEM.
will then vibrate very slowly on one side and the other of this
point. But if we give the wheel a motion rapid enough to
carry its heavy side over the highest point, then the weight
will accelerate the wheel while it is falling as much as it will
retard it while rising ; and if there were no friction, the wheel
would keep on turning indefinitely. The question now arises,
How does it happen that these two motions are so exactly ad-
justed to each other that not only is the longer axis of the
moon pointed exactly towards the earth, but not the slightest
swing on one side or the other can be detected ? That this
adjustment should be a mere matter of chance, without any
physical cause to produce it, is almost infinitely improbable,
while to suppose it to result from the mere arbitrary will of
the Creator is contrary to all scientific philosophy. But if the
moon were once in a partially fluid state, and rotated on her
axis in a period different from her present one, then the enor-
mous tides produced by the attraction of the earth, combined
with the centrifugal force, would be accompanied by a fric-
tion which would gradually retard the rate of rotation, until
it was reduced to the point of exact coincidence with the rate
of revolution round the earth, as we now find it. We there-
fore see in the present state of things a certain amount of
probable evidence that the moon was once in a state of par-
tial fluidity.
The force we have just described as drawing the protuber-
ant portion of the moon towards the earth is so excessively
minute that it takes it a long time to produce any sensible ef-
fect ; consequently, although the moon moves more rapidly in
some points of her orbit than in others, the force in question
produces no corresponding change in the moon's rotation.
The protuberance does not, therefore, always point exactly at
the earth, but sometimes a little one side, and sometimes a lit-
tle the other, according as the moon is ahead of or behind her
mean place in the orbit. The result is, that the face which
the moon presents to us is not always exactly the same, there
being a slight apparent (not real) oscillation, due to the real
inequality in her orbital motion. This apparent swaying is
THE MOON. 311
called libration, and in consequence of it there is nearly six-
tenths of the lunar surface which may, at one time or another,
corne into view from the earth.
The Lunar Day. In consequence of the peculiarity in the
moon's rotation which we have described, the lunar day is 29
times as long as the terrestrial day. Near the moon's equator
the sun shines without intermission nearly fifteen of our days,
and is absent for the same length of time. In consequence,
the vicissitudes of temperature to which the surface is exposed
must be very great. During the long lunar night the temper-
ature of a body on the moon's surface would probably fall
below any degree of cold that we ever experience on the earth,
while during the day it must become hotter than anywhere
on our globe.
Astronomical phenomena, to an observer on the moon, would
exhibit some peculiarities. The earth would be an immense
moon, going through the same phases that the moon does to
us ; but instead of rising and setting, it would only oscillate
back and forth through a few degrees. On the other side of
the moon it would never be seen at all. The diurnal motion
of the stars would take place in twenty -seven of our days,
much as they do here every day, while, as we have said, the
sun would rise and set in 29 of our days.
Geography of the Moon.- With the naked eye it is quite
readily seen that the brilliancy of the moon is far from uni-
form, her disk being variegated with irregular dark patches,
which have been supposed to bear a rude resemblance to a
human face. It is said to have been a fancy of some of the
ancient philosophers that the light and dark portions were
caused by the reflection of the seas and continents of the ter-
restrial globe, though it is hard to conceive of such an opin-
ion being seriously entertained. The first rude idea of the
real nature of the lunar surface was gained by Galileo with
his telescope. He saw that the brighter portions of the disk
were broken up with inequalities of the nature of mountains
and craters, while the dark parts were, for the most part,
smooth and uniform. Here he saw a striking resemblance to.
312 THE SOLAR SYSTEM.
the geographical features of our globe, and is said to have sug-
gested that the brighter and rougher portions might be conti-
nents, and the dark, smooth portions oceans. This view of the
resemblance to terrestrial scenery is commemorated in Mil-
ton's description of Satan's shield :
*' Like the moon, whose orh
Through optic glass the Tuscan artist views
At evening, from the top of Fesole,
Or in Valdarno, to descry new lands,
Rivers, or mountains in her spotty globe. "
The opinion that the dark portions of the lunar disk were
seas was shared by Kepler, Hevelius, and Ricciolus. The last
two made maps of the moon in which they gave names to the
supposed seas, which names the regions still bear, though they
are strikingly fanciful. Among them are Oceanus Procella-
rum (the Ocean of Storms), Mare Tranqaillitatis (Sea of Tran-
quillity), Mare Imbrium (Ilainy Sea), etc. The names of great
philosophers and astronomers were given to prominent feat-
ures, craters, etc.
If this resemblance between the earth and moon had been
established ; if it had been found that our satellite really had
seas and atmosphere, and was fitted for the support of or-
ganic life; still more, if any evidence of the existence of in-
telligent beings had been found,- our interest in lunar geogra-
phy would have been immensely heightened. But the more
the telescope was improved, the more clearly it was seen that
there was no similarity between lunar and terrestrial scenery.
A very slight increase of telescopic power showed that there
was no more real smoothness in the regions of the supposed
seas than elsewhere. The inequalities were smaller and hard-
er to see on account of the darkness of color ; but that was
all. The sun would have been brilliantly imaged back from
the surfaces of the oceans in certain positions of the moon ;
but nothing of the kind was ever seen. The polariscope
showed that the sun's rays did not pass through any liquid at
the moon's surface. Positive evidence of an atmosphere was
sought in vain. Supposed volcanoes were traced to bright
THE MOON. 313
spots, illuminated by light from the earth. Inequalities of
surface there were ; but in form they were wholly different
from the mountains of the earth. So the beautiful fancies of
FIG. 80. View of moon near the third quarter. From a photograph by Professor Henry
Draper.
the earlier astronomers all faded away, leaving our satellite as
lifeless as an arid rock.
As the moon is now seen and mapped, the difference be-
tween the light and dark portions is due merely to a differ-
ence in the color of the material, much of which seems to be
314 THE SOLAR SYSTEM.
darker than the average of terrestrial objects. The mountains
consist, for the most part, of round saucer-shaped elevations,
the interior being flat, with small conical mounds rising here
and there. Sometimes there is a single mound in the centre.
It is very curious that the figures of these inequalities in the
lunar surface can be closely imitated by throwing pebbles
upon the surface of some smooth plastic mass, as mud or
mortar. They may be well seen during an eclipse of the sun,
when the contrast between the smoothness of the sun's limb
and the roughness of that of the moon cannot escape notice.
Their appearance is most striking when the eclipse is annular
or total. In the latter case, as the last streak of sunlight is
disappearing, it is broken up into a number of points, which
have been known as " Baily's beads," from the observer who
first described them, and which are caused by the sun shining
through the depressions between the lunar mountains.
To give the reader an idea what the formation of the lunar
surface is, we present a view of the spot or crater " Coper-
nicus," by Secchi, taken from the " Memoirs of the Royal As-
tronomical Society," vol. xxxii. The diameter of the central
portion, so much like a fort, is about 45 or 50 miles.
Among the most curious and inexplicable features of the
moon's surface are the long narrow streaks of white material
which radiate from certain points, especially from the great
crater Tycho. Some of these can be traced more than a
thousand miles. The only way in which their formation has
been accounted for is by supposing that in some former age
immense fissures were formed in the lunar surface which were
subsequently filled by an eruption of this white matter which
forms the streaks.
Has the Moon an Atmosphere? This question may be an-
swered by saying that no evidence of a lunar atmosphere
entitled to any weight has ever been gathered, and that if
there is such an atmosphere, it is certainly not ^ part the
density of the earth's atmosphere. The most delicate known
test of an atmosphere is afforded by the behavior of a star
when in apparent contact with the limb of the moon. In this
THE MOON.
315
FIG. 81. Luiiar crater "Copernicus," after Secchi.
position the rays of light coming from the star would pass
through the lunar atmosphere, and be refracted by twice the
horizontal refraction of that atmosphere. The star would
then be apparently thrown out of its true position in the di-
rection from the moon's centre by the amount of this double
refraction. But observations of stars in this position, at the
moment when the limb of the moon passes over them, have
never indicated the slightest displacement. It is certain that,
had the displacement been decidedly in excess of half a sec-
ond, it would have been detected ; therefore, the double hori-
zontal refraction of the lunar atmosphere, if any exist, must
be as small as half a second.* The corresponding refraction
of the earth's atmosphere is 4000 seconds. Therefore, the re-
* A similar test is afforded by the occultation of a planet, especially Saturn or
Venus, the limb of which would be a little flattened as it touched the moon. The
writer looked very carefully for this appearance during an unusually favorable oc-
cultation of Saturn which occurred on Aug. 6th, 1876, without seeing a trace of it.
316 THE SOLAR SYSTEM.
fractive power of the lunar atmosphere cannot be much in ex-
cess of -grnnr that of the earth's, and certainly falls below -s^nnr-
Without an atmosphere no water or other volatile fluid can
exist on the moon, because it would gradually evaporate and
form an atmosphere of its own vapor. The evaporation would
not cease till the pressure of the vapor became equal to its
elastic force at the mean temperature of the moon. If this
temperature were as low as the freezing-point, the pressure of
an atmosphere of water vapor would be T ^ that of our at-
mosphere. So dense an envelope could not fail of detection
with our present means of observation.
The question whether any change is taking place on the
surface of the moon is one of interest. Hitherto, the pre-
ponderance of evidence has been against the idea of any
change. It is true that a few years ago there was a great
discussion in the astronomical world about a supposed change
in the aspect of the spot Linnaeus, which was found not to
present the same appearance as on Beer and Madler's map.
But careful scrutiny showed that, owing to some peculiarity
of its surface, this spot varied its aspect according to the
manner in which it was illuminated by the sun, and these
variations appear to be sufficient to account for the supposed
change. To whatever geological convulsions the moon may
have been subjected in ages past, it seems as if she had now
reached a state in which no further change was to take place,
unless by the action of some new cause. This will not seem
surprising if we reflect what an important part the atmosphere
plays in the changes which are going on on the surface of the
earth. The growth of forests, the formation of deltas, the
washing-away of mountains, the disintegration and blacken-
ing of rocks, and the decay of buildings, are all due to the
action of air and water, the latter acting in the form of rain.
Changes of temperature powerfully re-enforce the action of
these causes, but are not of themselves sufficient to produce
any effect. Now, on the moon, there being neither air, wa-
ter, rain, frost, nor organic matter, the causes of disintegra-
tion and decay are all absent. A marble building erected
THE MOON. 317
upon the surface of the moon would remain century after
century just as it was left. It is true that there might be
bodies so friable that the expansions and contractions due to
the great changes of temperature to which the surface of the
moon is exposed would cause them to crumble. But whatev-
er crumbling might thus be caused would soon be done with,
and then no further change would occur.
Light and Pleat of the Moon. That the sun is many times
brighter than the moon is evident to the eye ; but no one
judging by the unaided eye would suppose the disparity to be
BO great as it really is. It is found by actual trial that the
light of the sun must be diminished several hundred thousand
times before it becomes as faint as the full moon. The results
of various experiments range between 300,000 and 800,000.
Professor G. B. Bond, of Cambridge, found the ratio to be
470,000. The most careful determination yet made is by
Zollner, who flnds the sun to give 619,000 times as much
light as the full moon. This result is probably quite near
the truth.
The moon does not shine by sunlight alone. Whenever
the narrow crescent of the new moon is seen through a clear
atmosphere, her whole surface may be plainly seen faintly il-
luminated. This appearance is known as " the old moon in
the new moon's arms." The faint light thus shed upon the
dark parts of the moon is reflected from the earth. An ob-
server on the moon would see the earth in his sky as a large
moon, much larger than the moon is seen by us. When it is
new moon with us, it would be full earth, if we may be allowed
the term, to an observer on this side of the moon. Hence,
under those circumstances, most of the lunar hemisphere hid-
den by the sun is illuminated by earth-light, or by sunlight re-
flected by the earth, and is thus rendered visible. The case
is the same as if an observer on the moon should see the dark
hemisphere of the earth by the light of the full moon.
As the moon reflects the light of the sun, so also must she
reflect his heat. Besides, she must radiate off whatever heat
she absorbs from the sun". Hence, we must receive some heat
318 THE SOLAR SYSTEM.
from the moon, though calculation will, show the quantity to
be so small as to defy detection with the most delicate ther-
mometer, the average quantity being only -ysTnnnr P art of that
received from the sun. As the direct rays of the sun will not
raise the black-bulb thermometer more than 50 or 60 degrees
above the temperature of the air, those of the moon cannot
raise it more than -^THF ^ a degree. By concentrating the
rays in the focus of a telescope of large aperture and compar-
atively short focal length, the temperature might be increased
a hundred times or more ; but even then we should only have
an increase of -^V of a degree. Even this increase might be
unattainable, for the reason that the heat radiated by the
moon would not pass through glass. It is, therefore, only
since the discovery of thermo-electricity and the invention of
the thermo-electric pile that the detection of the heat from
the moon has been possible. The detection is facilitated by
using a reflecting telescope to concentrate the lunar rays,
because the moon is not hot enough to radiate such heat as
will penetrate glass. Lord Eosse and M. Marie - Davy, of
Paris, have thus succeeded in measuring the heat emanating
from the moon. The former sought not merely to determine
the total amount of heat, but how much it varied from one
phase of the moon to the other, and what portion of it was
the reflected heat of the sun, and what portion was radiated
by the moon herself, as if she were a hot body. He found
that from new to full moon, and thence round to new moon
again, the quantity of heat received varied in the same way
with the quantity of light ; that is, there was most at full-
moon, and scarcely any when the moon was a thin crescent.
That only a small proportion of the total heat emitted was the
reflected heat of the sun, was shown by the fact that while 86
per cent, of solar heat passes through glass, only 12 per cent,
of lunar heat does so. This absorption by glass is well known
to be a property of the heat radiated by a body which is not
itself at a high temperature. The same result was indicated
in another way, namely, that while the sun is found by Zoll-
ner to give 618,000 times as much light as the moon, it only
THE MOON. 319
gives 82,600 times as much heat. Thus both the ratio of solar
to lunar heat, and the proportion of the latter which is ab-
sorbed by glass, agree in indicating that about six-sevenths of
the heat received from the moon is radiated by the latter,
owing. to the temperature of her surface produced by the ab-
sorption of the sun's rays.
Lord Rosse was thus enabled to estimate the change of
temperature of the moon's surface according as it was turned
towards or from the sun, and found it to be more than 500
Fahrenheit. But there was no way of determining the tem-
peratures themselves with exactness. Probably when the sun
does not shine the temperature is two or three hundred de-
grees below zero, and therefore below any ever known on the
earth; while under the vertical sun it is as much above zero,
and therefore hotter than boiling water.
Effect of the Moon on the Earth. We have already explained,
in treating of gravitation, how the attraction of the moon
causes tides in the ocean. This is one of the best-known ef-
fects of lunar attraction. It is known from theory that a sim-
ilar tide is produced in the air, affecting the height of the ba-
rometer ; but it is so minute as to be entirely masked by the
changes constantly going on in the atmospheric pressure from
other causes. There is also reason to believe that the occur-
rence of earthquakes may be affected by the attraction of the
moon ; but this is a subject which needs further investiga-
tion before we can pronounce with certainty on a law of con-
nection.
Thus far there is no evidence that the moon directly affects
the earth or its inhabitants in any other way than by her at-
traction, which is so minute as to be entirely insensible except
in the ways we have described. A striking illustration of the
fallibility of the human judgment when not disciplined by sci-
entific training is afforded by the opinions which have at vari-
ous times obtained currency respecting a supposed influence
of the moon on the weather. Neither in the reason of the
case nor in observations do we find any real support for such
a theory. It must, however, be admitted that opinions of this
320 THE SOLAR SYSTEM.
character are not confined to the uneducated. In scientific
literature several papers are found in which long series of me-
teorological observations are collated, which indicate that the
mean temperature or the amount of rain had been subject to
a slight variation depending on the age of the moon. But
there was no reason to believe that these changes arose from
any other cause than the accidental vicissitudes to which the
weather is at all times subject. There is, perhaps, higher au-
thority for the opinion that the rays of the full moon clear
away clouds ; but if we reflect that the effect of the sun it-
self in this respect is not very noticeable, and that the full
moon gives only -g- 1 of the heat of the sun, this opinion
will appear extremely improbable.
6. The Planet Mars.
The fourth planet in the order of distance from the sun,
and the next one outside the orbit of the earth, is Mars. Its
mean distance from the sun is about 141 millions of miles.
The eccentricity of its orbit is such that at perihelion it is only
128 millions of miles from the sun, while in aphelion it is 154
millions distant. It is, next to Mercury, the smallest of the
primary planets, its diameter being little more than 4000
miles. It makes one revolution in its orbit in less than two
years (more nearly in 687 days, or 43J days short of two Ju-
lian years). If the period were exactly two years, it would
make one revolution while the earth made two, and the oppo-
sitions would occur at intervals of two years. But, going a
little faster than this, it takes the earth, on the average, fifty
days over the two years to catch up to it. The times of oppo-
sition are shown in the following table :
1373 April 27th.
1875 June 20th.
1877 September 5th.
1879 November 12th.
The times of several subsequent oppositions may be found
with sufficient exactness for the identification of the planet by
adding two years and two months for every opposition, except
during the spring months, when only one month is to be
THE PLANET MARS. 321
added. Oppositions will occur in January, 1882, and Febru-
ary, 1884. At the times of opposition Mars rises when the
sun sets, and may be seen during the entire night.
Aspect of Mars. Mars is easily recognized with the naked
eye when near its opposition by its fiery-red light. It is much
more brilliant at some oppositions than at others, but always
exceeds an ordinary star of the first magnitude. The varia-
tions of its brilliancy arise from the eccentricity of its orbit,
and the consequent variations of its distance from the earth
and the sun. The perihelion of Mars is in the same longitude
in which the earth is on August 27th; and when an opposition
occurs near that date, the planet is only 35 millions of miles
from the earth. This is about the closest approach which the
two planets can ever make. When an opposition occurs in
February or March the planet is near its aphelion 154 mill-
ions of miles from the sun and 62 millions from the earth.
The result of these variations of distance is that Mars is more
than four times brighter when an opposition occurs in August
or September than when it occurs in February or March. The
opposition of 1877 (September 5th) is quite remarkable in this
respect, as it occurs only nine days after the planet has passed
its perihelion. At that time Mars will form a conspicuous
object in the south-eastern sky during the early evening.
Mars has been an interesting object of telescopic research
from the fact that it is the planet which exhibits the greatest
analogy with our earth. The equatorial regions, even with a
small telescope, can be distinctly seen to be divided into light
and dark portions, which some observers suppose to be conti-
nents and oceans. Around each pole is a region of brilliant
white, which the same class of astronomers suppose to be due
to a deposit of snow. The outlines of the dark and light por-
tions are sometimes so hard to trace as to give rise to the sus-
picion of clouds in a Martial atmosphere. At the same time,
a single look at Mars through a large telescope would convince
most observers that these resemblances to our earth have a
very small foundation in observation, the evidence being neg-
ative rather than positive. It must be said in their favor that
22
322
THE SOLAR SYSTEM.
if our earth were viewed at the distance at which we view
Mars, and with the same optical power, it would present a
similar telescopic aspect. But it is also possible that if the
optical power of our tele-
scopes were so increased
that we could see Mars as
from a distance of a thou-
sand miles, the resemblances
would all vanish as com-
pletely as they did in the
case of the moon.
So many drawings of
Mars in various positions
have been made by the nu-
merous observers who have
studied it, that it has be-
FIG. 82 The planet Mars on June 23d, 1875, at 10
hours 45 minutes, as seen by Professor Holden COine pOSSlble to CODStrilCt
with the great Washington telescope. tolerably accurate maps of
the surface of the planet. We give a copy of one of these
sets of maps by Kaiser, the late Leyden astronomer. Kaiser
does not pretend to call the different regions continents and
oceans, but merely designates them as light and dark portions.
PIG. 83. Map of Mars, after Kaiser, on Mercntor's projection.
Rotation of Mars. Mars is the only planet besides the earth
of which we can be sure that the time of axial rotation ad-
mits of being determined with entire precision. Drawings by
Hooke, two centuries ago, exhibit markings which can still be
recognized, and from a comparison of them with recent ones
Mr. Proctor has found for the period of rotation 24 hours 37
THE SMALL PLANETS.
323
minutes 22.73 seconds, which he considers correct within three
or four huudredths of a second. The equator of Mars is in-
clined to the plane of its orbit about 27,so that the vicissitudes
of the seasons are greater on Mars than on the earth in the pro-
portion of 27 to 23. Owing to this great obliquity, we can
sometimes see one pole of the planet, and sometimes the other,
from the earth. When in longitude 350, that is, in the same
FIG. 84. Northern hemisphere of Mars. FLO. 85.Sonthern hemisphere of Mars.
direction from the sun in which the earth is situated on Sep-
tember 10th, the south pole of the planet is inclined towards
the sun ; and if the planet is then in opposition, it will be in-
clined towards the earth also, so that we can see the region of
the planet to a distance of 27 beyond the pole. At an op-
position in March the north pole of the planet is inclined tow-
ards the sun, and towards the earth also. We have just seen
that Mars is much farther at the latter oppositions than at the
former, so that we can get much better views of the south pole
of the planet than of the north pole.
7. The Small Planets.
It was impossible to study the solar system, as it was known
to modern astronomy before the beginning of the present cent-
ury, without being struck by the great gap which existed be-
tween Mars and Jupiter. Except this gap, all the planets then
known succeeded each other according to a tolerably regular
324 THE SOLAR SYSTEM.
law, and by interpolating a single planet at nearly double the
distance of Mars the order of distances would be complete.
The idea that an unknown planet might really exist in this
region was entertained from the time of Kepler. So sure
were some astronomers of this that, in 1800, an association of
twenty-four observers was formed, having for its object a sys-
tematic search for the planet. The zodiac was divided into
twenty-four parts, one of which was to be searched through
by each observer. But by one of those curious coincidences
which have so frequently occurred in the history of science,
the planet was accidentally discovered by an outside astrono-
mer before the society could get fairly to work On January
1st, 1801, Piazzi, of Palermo, found a star in the constellation
Taurus which did not belong there, and on observing it the
night after, he found that it had changed its position among
the surrounding stars, and must, therefore, be a planet. He
followed it for a period of about six weeks, after which it was
lost in the rays of the sun without any one else seeing it.
When it was time to emerge again in the following autumn,
its rediscovery became a difficult problem. But the skill of the
great mathematician Gauss came to the rescue with a method
by which the orbit of any planetary body could be complete-
ly and easily determined from three or four observations. He
was thus able to tell observers where their telescopes must be
pointed to rediscover the planet, and it was found without dif-
ficulty before the end of the year. Piazzi gave it the name
Ceres. The orbit found by Gauss showed it to revolve between
Mars and Jupiter at a little less than double the distance of
the former, and therefore to be the long -thought -of planet.
But the discovery had a sequel which no one anticipated, and
of which we have not yet seen the end. In March, 1802, Ol-
bers discovered a second planet, which was also found to be
revolving between Mars and Jupiter, and to which he gave
the name Pallas. The most extraordinary feature of its orbit
was its great inclination, which exceeded 34. Olbers there-
upon suggested his celebrated hypothesis that the two bodies
might be fragments of a single planet which had been shat-
THE SMALL PLANETS. 325
tered by some explosion. If such were the case, the orbits of
all the fragments would at first intersect each other at the
point where the explosion occurred, lie therefore thought it
likely that other fragments would be found, especially if a
search were kept up near the point of intersection of the orbits
of Ceres and Pallas. Acting on this idea, Harding, of Lilien-
thal, found a third planet in 1804, while Olbers found a
fourth one in 1807. These were called Juno and Vesta. The
former came quite near to Olbers's theory that the orbits
should all pass near the same point, but the latter did not.
Olbers continued a search for additional planets of this group
for a number of years, but at length gave it up, and died
without the knowledge of any but these four.
In December, 1845, thirty-eight years after the discovery of
Vesta, Hencke, of Driesen, being engaged in the preparation
of star-charts, found a fifth planet of the group, and thus re-
commenced a series of discoveries which have continued till
the present time. No less than three were discovered in 1847,
and at least one has been found every year since. To show
the rate at which discovery has gone on, we divide the time
since 1845 into periods of five years each, and give the num-
ber found during each period :
In 1846-50 8 were discovered.
" 1851-55 24 " "
" 1856-60 25 " "
In 1 86 1-65 23 were discovered?
" 1866-70 27 " "
" 1871-75 45 " "
In 1876, 12 were discovered, and three additional ones have been found during
the first five months of 1877, making a total of 172 known at the present time
(May, 1877).
It will be seen that the rate of discovery has been pretty
steadily increasing during thirty years. This is not because
the number of those visible, but not yet found, is so great that
it is as easy as ever to find one, but because they are now
sought after with more skill and more system than formerly.*
* In illustration of this the writer has been informed by Professor Peters that
in searching for these bodies he falls upon several already known for every new one
that he finds. Consequently, were they all lost, he alone could now rediscover
them at a more rapid rate than they actually have been discovered by the efforts
of all the observers engaged in the search.
326 THE SOLAR SYSTEM.
Of those discovered during the last ten years, nearly half
have been found by two American observers, Professors Pe-
ters and Watson. American discoveries of these bodies were
commenced by Mr. James Ferguson, who discovered Euphros-
yne at Washington on September 1st, 1854.
All the planets of this group are remarkable for their mi-
nuteness. The disks are all so small as to defy exact meas-
urement, presenting the appearance of mere stars. A rough
estimate of their diameters can, however, be made from the
amount of light which they reflect ; and although, in the ab-
sence of exact knowledge of their reflecting power, the results
of this method are not very certain, they are the best we can
obtain. It is thus found that Ceres and Vesta are the largest
of the group, their diameters lying somewhere between 200
and 400 miles ; while, if we omit some very lately discovered,
the smallest are Atalanta, Maja, and Sappho, of which the di-
ameters may be between 20 and 40 miles. We may safely
say that it would take several thousand of the largest of these
small planets to make one as large as the earth.
It has sometimes been said that some of these bodies are of
irregular shape, and thus favor Olbers's hypothesis that they
are fragments of an exploded planet. But this opinion has
no other foundation than a suspected variability of their light,
which may be an illusion, and which, if it exists, might result
from one side of the planet being darker in color than the
other. The latter supposition is not at all improbable, as many
of the satellites are known to be variable from this or some
analogous cause. As the supposed irregularities of form have
never been seen, and are not necessary to account for the va-
riations of brilliancy, there is no sufficient reason for believing
in their existence.
Olberds Hypothesis. The question whether these bodies
could ever have formed a single one has now become one of
cosmogony rather than of astronomy. If a planet were shat-
tered, the orbit of each fragment would, at first, pass through
the point at which the explosion occurred, however widely
they might be separated through the rest of their course. But
THE SMALL PLANETS. 32?
owing to the secular changes produced by the attractions of
the other planets, this coincidence would not continue. The
orbits would slowly move away, and after the lapse of a few
thousand years no trace of a common intersection would be
seen. It is, therefore, curious that Gibers and his contempora-
ries should have expected to find such a region of intersection,
as it implied that the explosion had occurred within a few
thousand years. The fact that the required conditions were
not fulfilled was no argument against the hypothesis, because
the explosion might have occurred millions of years ago, and
in the mean time the perihelion and node of each orbit
would have made many entire revolutions ; so that the orbits
would have been completely mixed up.
Desirous of seeing whether the orbits passed nearer a com-
mon point of intersection in times past than at present, En eke
computed their secular variations. The result seemed to be
adverse to Olbers's hypothesis, as it showed that the orbits
were farther from having a common point in ages past than
at present. But this result was not conclusive either, because
he only determined the rates at which the orbits are now
changing, whereas, as previously explained, the orbits of all
the planets really go through periodic oscillations ; and it is
only by calculating these oscillations that their positions can
be determined for very remote epochs. They have since
been determined for some of the planets in question, and the
result seems to show that the orbits could never have intersect-
ed unless some of them have, in the mean time, been altered
by the attraction of the small planets on each other. Such an
action is not impossible; but it is impossible to determine it,
owing to the great number of these bodies, and our ignorance
of their masses. We can, however, say that if the explosion
ever did occur, an immense interval, probably millions of
years, must have elapsed in the mean time. A different ex-
planation of the group is given by the nebular hypothesis, of
which we shall hereafter speak, so that Olbers's hypothesis is
no longer considered by astronomers.
The planets in question are distinguished from the others,
328 THE SOLAR SYSTEM.
not only by their small" size, but by the great eccentricities
and inclinations of their orbits. If we except Mercury, none
of the larger planets has an eccentricity amounting to one-
tenth the diameter of its orbit, nor is any orbit inclined more
than two or three degrees to the ecliptic. But the inclina-
tions of many of the small planets exceed ten degrees, and
the eccentricities frequently amount to a fourth of the radii
of their orbits. The result is that the same small planet is at
very different distances from the sun in various points of its
orbit. Add to this the fact that the mean distances of these
bodies from the sun have a pretty wide range, and we shall
find that they extend through a quite broad zone. The inside
edge of this zone seems pretty well marked, its distance being
about 180 millions of miles from the sun, or between 30 and
40 millions beyond the orbit of Mars. On the outside, it ter-
minates more gradually, but nowhere extends within 50 mill-
ions of miles of the orbit of Jupiter. If any of the small
planets ever ranged outside of certain limits, the attraction of
Mars or Jupiter was so great as to completely derange their
orbits, so that we have a physical law which sets a limit to the
zone ; but whether the limit thus set would coincide with the
actual limit we cannot at present say.
There are also within the limits of the group certain posi-
tions, in which, if the orbits were placed, they would be greatly
changed by the action of Jupiter. These positions are those
in which the time of revolution would be some simple exact
fraction of that of Jupiter, as -J, , f , , etc. Professor Daniel
Kirkwood has pointed out the curious fact that there are gaps
in the series of small planets corresponding to these periodic
times. Whether these gaps are really due to the relations of
the periodic times, or are simply the result of chance, cannot
yet be settled. The fact that quite a number of the small
planets have a period very nearly three-eighths that of Jupiter,
may lead us to wait for further evidence before concluding
that we have to deal with a real law of nature in the cases
pointed out by Professor Kirkwood.
Number and Total Mass of the Small Planets. At present it
THE SMALL PLANETS. 329
is not possible to set any certain limits to the probable number
of the small planets. Although a hundred and seventy-two
are now known, there is as yet no sensible diminution in the
rate at which they are being discovered. The question of
their total number depends very largely on whether there is
any limit to their minuteness. If there is no such limit, then
there may be an indefinite number of them, too small to be
found with the telescopes now engaged in searching for them;
and the larger the telescopes engaged in the search, the more
will be found. On the other hand, if they stop at a certain
limit say twenty miles in diameter we may say with con-
siderable confidence that their total number is also limited,
and that by far the largest part of them will be discovered
by the present generation of astronomers.
So far as we can now see, the preponderance of evidence is
on the side of the number and magnitude being limited. The
indications in this direction are that the newly discovered ones
are not generally the smallest objects which could be seen
with the telescopes which have made the discovery, and do
not seem, on the average, to be materially smaller than those
which were discovered ten years ago. It is not likely that the
number of this average magnitude which still remain undis-
covered can be very great, and new ones will probably be
found to grow decidedly rare before another hundred are dis-
covered. Then it will be necessary to employ greater optical
power in the search. If this results in finding a number of
new ones too small to be found with the former telescopes, we
shall have to regard the group as unlimited in number. But
if no such new ones are thus found, it will show that the end
has been nearly reached.
In gravitational astronomy, the question of the total mass
of the small planets is more important than that of their total
number, because on this mass depends their effect in altering
the motions of the large planets. Any individual small planet
is so minute that its attraction on the other planets is entirely
insensible. But it is not impossible that the whole group
might, by their combined action, produce a secular variation
330 THE SOLAR SYSTEM.
in the form of the orbits of Mars and Jupiter which, in the
course of years, will be clearly shown by the observations.
But, although accurate observations of these planets have been
made for more than a century, no such effect has yet been no-
ticed. The sum total of their masses must, therefore, be much
less than that of an average planet, though we cannot say pre-
cisely what the limit is. The apparent magnitude of those
which have been discovered is entirely accordant with the
opinion that the mass of the entire group is so small that it
cannot make itself felt by its attraction on the other planets
for many years to come. In fact, if their diameters be esti-
mated from their brightness, in the manner already indicated,
we shall find that if all that are yet known were made into a
single planet the diameter would be less than 400 miles ; and
if a thousand more, of the average size of those discovered
since 1850 should exist, their addition to the consolidated
planet would not increase its diameter to 500 miles. Such a
planet would be only TF \nr of the bulk of the earth, and, un-
less we supposed it to possess an extraordinary specific gravity,
could not much exceed ^oinr of the mass of the earth, or -^V of
the mass of Mercury. We may fairly conclude that unless
the group of small planets actually consists of tens of thou-
sands of minute bodies, of which only a few of the brightest
have yet been discovered, their total volume and mass are far
less than those of any one of the major planets.
The number of these bodies now known is so great that the
mere labor of keeping the run of their motions, so that they
shall not be lost, is out of proportion to the value of its results.
It is mainly through the assiduity oLGerman students that
most of them are kept from being lost. Should many more
be found, it may be necessary to adopt the suggestion of an
eminent German astronomer, and let such of them as seem
unimportant go again, and pursue their orbit undisturbed by
telescope or computer.
THE PLANET JUP1TE1L
331
CIIAPTEE IV.
THE OUTER GROUP OF PLANETS.
1. The Planet Jupiter.
JUPITER is the " giant planet " of our system, his mass large-
ly exceeding that of all the other planets combined. His
mean diameter is about 85,000 miles ; but owing to his rapid
rotation on his axis, his equatorial exceeds his polar diameter
Fio. 86. Jupiter as seen with the great Washington telescope, March 21st, 1876, 15 hours
38 minutes mean time. Drawn by Professor Holden.
by 5000 miles. In volume he exceeds our earth about 1300
times, while in mass he exceeds it about 213 times. His spe-
cific gravity is, therefore, far less than that of the earth, and
even less than that of water. His mean distance from the
sun is 480 millions of miles, but, owing to the eccentricity of
his orbit, his actual distance ranges between 457 arid 503 mill-
ions. His time of revolution is fifty days less than twelve
years.
332 THE SOLAR SYSTEM.
Jupiter is easily recognized by his brilliant white light, with
which he outshines every other planet except Venus. To fa-
cilitate his recognition, we give the dates of opposition dur-
ing a few years.
1877 June 19th.
1878 July 25th.
1879 August 31st.
1880 October 7th.
During the four years following 1880 he will be in opposition,
on the average, about a month and seven days later each year.;
namely, in the middle of November, 1881 ; towards the latter
part of December, 1882, and so on. A month or two before
opposition he can be seen rising late in the evening, while
during the three months following opposition he will always
be seen in the early evening somewhere between south-east
and south-west.
The Surface of Jupiter. Except the sun and moon, there is
no object of our system which has during the last few years
been the subject of more careful examination than this planet.
Unlike Mars, there are no really permanent markings on his
surface, and a map of Jupiter is therefore impossible. But
this surface always presents a very diversified appearance.
The earlier telescopic observers described light and dark belts
as extending across it. Until a quite recent period, it has
been customary to describe these belts as two in number, one
north of the equator, and the other south of it. Commonly,
they are seen as dark bands on the bright disk of the planet ;
but it is curious that Huyghens represents them as brighter
than the rest of the surface. As telescopic power was in-
creased, it was seen that these so-called bands were of a far
more complex structure than had been supposed, and consisted
of great numbers of stratified, cloud-like appearances of the
most variegated forms. These forms change so rapidly that
the face of the planet hardly ever presents the same appear-
ance on two successive nights. They are most strongly
marked at some distance on each side of the Jovian equator,
and thus give rise to the appearance of two belts when a very
small or imperfect telescope is used.
THE PLANET JUPITER. 333
Both the outlines 'of these belts and the color of some parts
of the planet, seem subject to considerable changes. The
equatorial regions, and indeed the spaces between the belts
generally, are often of a rosy tinge. This coloring is some-
times so strongly marked as to be evident to the most super-
ficial observer, while at other times hardly a trace of it can be
seen.
Spots which are much more permanent than the ordinary
markings on the belt are sometimes visible. By watching
these spots from day to day, and measuring their distance
from the apparent disk, the time of rotation of Jupiter on his
axis has been determined. Commonly the spots are dark;
but on some rather rare occasions the planet is seen with a
number of small, round, bright spots like satellites. Of these
bright spots no explanation has been given.
FIG. 87.View of Jupiter, as seen in Lord Rosse's great telescope on February 27th,
1861, at 12 hours 30 minutes.
From the changeability of the belts, and indeed of nearly all
the visible features on the surface of Jupiter, it is clear that
what we see on that planet is not the surface of a solid nu-
cleus, but vaporous or cloud-like formations which cover the
entire surface and extend to a great depth below. To all ap-
pearance, the planet is covered with a deep and dense atmos-
334 THE SOLAR SYSTEM.
phere, through which light cannot penetrate on account of
thick masses of clouds and vapor. In the arrangements of
these clouds in streaks parallel to the equator, and in the
change of their forms with the latitude, there may be some-
thing analogous to the zones of clouds and rain on the earth.
But of late years it has been noticed that the physical consti-
tution of Jupiter seems to offer more analogies to that of the
sun than to that of the earth. Like the sun, he is brighter in
the centre than near the edges. This is shown in the most
striking manner in the transits of his satellites over his disk.
When the satellite first enters on the disk, it commonly seems
like a bright spot on a dark background ; but as it approaches
the centre, it appears like a dark spot on the bright back-
ground of the planet. The brightness of the centre is prob-
ably two or three times greater than that of the limb. This
diminution of light towards the edge may arise, as in the case
of the sun, from the light near the edge passing through a
greater depth of atmosphere, and thus becoming fainter by
absorption.
A still more remarkable resemblance to the sun has some-
times been suspected nothing less, in fact, than that Jupiter
shines partly by his own light. It was at one time supposed
that he actually emitted more light than fell upon him from
the sun ; and if this were proved, it would show conclusive-
ly that he was self-luminous. If all the light which the sun
shed upon the planet were equally reflected in every direction,
we might speak with some certainty on this question ; but in
the actual state of our knowledge we cannot. Zollner has
found that the brightness of Jupiter may be accounted for by
supposing him to reflect 62 per cent, of the sunlight which he
receives. But if this is his average reflecting power, the re-
flecting power of his brighter portions must be much greater;
in fact, they are so bright that they must shine partly by their
own light, unless they reflect a disproportionate share of the
sunlight back in the direction of the earth and sun. Clouds
would not be likely to do this. On the other hand, if we as-
sume that the planet emits any great amount of light, we are
THE PLANET JUPITER. 335
met by the fact that, if this were the case, the satellites would
shine by this light when they were in the shadow of the
planet. As these bodies totally disappear in this position, the
quantity of light emitted by Jupiter must be quite small. On
the whole, there is a small probability that the brighter spots
of this planet are from time to time slightly self-luminous.
Again, the interior of Jupiter seems to be the seat of an
activity so enormous that we can attribute it only to a very
high temperature, like that of the sun. This is shown by the
rapid movements always going on in his visible surface, which
frequently changes its aspect in a few hours. Such a power-
ful effect could hardly be produced by the rays of the sun,
because, owing to the great distance of the planet, he receives
only between one-twenty-fifth and one-thirtieth of the light
and heat which we do. It is therefore probable that Jupiter
is not yet covered by a solid crust, as our earth is, but that
his white-hot interior, whether liquid or gaseous, has nothing
to cover it but the dense vapors to which that heat gives rise.
In this case the vapors may be self-luminous when they have
freshly arisen from the interior, and may rapidly cool off after
reaching the upper limit to which they ascend.
Rotation of Jupiter. Owing to the physical condition of Ju-
piter, no precisely determinate time of rotation can be assign-
ed him, as in the case of Mars. Without a solid crust which
we can see from time to time, the observed times of rota-
tion will be those of liquid or vaporous formations, which may
have a proper motion of their own. A spot has, however, on
some occasions been observed for several months, and it has
thus been pretty certainly determined that the time of rota-
tion is about 9 hours 55^ minutes. The first observation of a
spot of this kind was made by Cassini, who found the time of
rotation to be 9 hours 55 minutes 58 seconds. No further
exact observations were made until the time of Schroter, who
observed a number of transient spots during 1785 and 1786.
The times of rotation varied from 9 hours 55 minutes to 9
hours 56 minutes, from which he concluded that heavy storms
raged on the surface of the planet, and gave the cloudy masses
33f> THE SOLAR SYSTEM.
which iormed the spots a motion of their own. In Novem-
ber, 1834, a remarkable spot was observed by Madler, of Dor-
pat, which lasted until the following April, from which the
time of rotation carne out 9 hours 55 minutes 30 seconds; but
the observations showed that the spot did not move uniformly.
Professor Airy, who observed the same spot at Cambridge,
found the period to be 9 hours 55 minutes 21.3 seconds.
Recent observations and researches indicate that the equa-
torial regions of Jupiter rotate in less time, and with more ir-
regularity, than the others, thus showing still another analogy
between that planet and the sun. Thus, in 1871, Dr. Lohse,
of Bothkainp, observed a spot near Jupiter's equator, which
during several days performed its revolution in a period of
9 hours 51 minutes 47 seconds. Other equatorial spots had a
very irregular motion, but their period was generally less than
that found by Madler and Airy.
2. T/ie Satellites of Jupiter.
One of the earliest telescopic discoveries by Galileo was
that Jupiter was accompanied by four satellites, which re-
volved round him as a centre, thus forming a miniature copy
of the solar system. As in the case of spots on the sun, Gal-
ileo's announcement of this discovery was received with in-
credulity by those philosophers of the day who believed that
everything in nature was described in the writings of Aris-
totle. One eminent astronomer Clavius said that to see
the satellites one must have a telescope which would produce
them ; but he changed his mind as soon as he saw them him-
self. Another philosopher, more prudent, refused to put his
eye to the telescope lest he should see them and be con-
vinced. He died shortly afterwards. " I hope," said the caus-
tic Galileo, " that he saw them while on his way to heaven."
A very small telescope, or even a good opera-glass, is suf-
ficient to show these bodies. Indeed, very strong evidence is
on record that they have been seen with the naked eye. That
they could be seen by any good eye, if the planet were out of
the way, there is no doubt, the difficulty in seeing them ari$-
THE SATELLITES OF JUPITER. 337
ing from the glare of the planet on the eye. If the lenses of
the eye are so transparent and pure that there is no such
glare, it is quite possible that the two outer satellites might
be seen, especially if they should happen to be close to-
gether.
According to the best determinations, which are, however,
by no means certain, the diameters of the satellites of Jupiter
range between 2200 and 3700 miles, the third from the planet
being the largest, and the second the smallest. The volume of
the smallest is, therefore, very near that of our moon.
The light of these satellites varies to an extent which it
is difficult to account for, except by supposing very violent
changes constantly going on on their surfaces. It has some-
times been supposed that some of them, like our moon, always
present the same face to Jupiter, and that the changes in their
brilliancy are due to differences in the color of the parts of
the satellites which are successively turned towards us during
one revolution round the planet. But the careful measures
of their light made by Auwers, of Berlin, and Engelmann, of
Leipsic, show that this hypothesis does not account for the
changes of brilliancy, which are sometimes sudden in a sur-
prising degree. The satellites are so distant as to elude tele-
scopic examination of their surfaces. We cannot, therefore,
hope to give any certain explanation of these changes.
The satellites of Jupiter offer problems of great difficulty
to the mathematician who attempts to calculate the eifect of
their mutual attractions. The secular variations of their or-
bits are so rapid that the methods applied in the case of the
planets cannot be applied here without material alterations.
The most curious and interesting effect of their mutual at-
traction is that there is a connection between the motions of
the three inner satellites such as exists nowhere else in the
solar system. The connection is shown by these two laws :
1. That the mean motion of the first satellite added to twice the
mean motion of the third is exactly equal to three times the mean
motion of the second.
2. That if to the mean longitude of the first satellite ive add
23
338 TEE SOLAR SYSTEM.
twice the mean longitude of the third, and subtract three times the
mean longitude of the second, the difference is always 180.
The first of these relations is shown in the following table
of the mean daily motions of the satellites :
Satellite I. in one day moves 203. 4890
II. " " 101.3748
" " III. " " 50.3177
" IV. " " 2l.571l
Motion of Satellite 1 203.48 ( JO
Twice that of Satellite III 100.G354
Sum 304.1244
Three times motion of Satellite II 304. 1244
It was first found from observations that the three satellites
moved together so nearly according to this law that no certain
deviation could be detected. But it was not known whether
this was a mere chance coincidence, or an actual law of nat-
ure, till Laplace showed that, if they moved so nearly in this
way as observations had shown them to, there would be an ex-
tremely minute force arising from their mutual gravitation,
sufficient to keep them in this relative position forever. There
is, in this case, some analogy to the rotation of the moon,
which, being once started presenting the same face to the
earth, is always held in that position by a minute residual of
the earth's attraction.
We have already spoken of the discovery of the progressive
motion of light from the eclipses of these satellites, and of
the uses of these eclipses for the rough determination of
longitudes. Both the eclipses, and the transits of their bodies
over the face of Jupiter afford interesting subjects of obser-
vation with a telescope of sufficient power, say four inches ap-
erture or upwards. To facilitate such observations the times
of these phenomena are predicted in both the American and
British Nautical Almanacs.
3. Saturn and its System, Physical Aspect, Belts, Rotation.
Saturn is the sixth of the major planets in the order of dis-
tance from the sun, around which it revolves in 29 years at
SATURN AND HIS , SYSTEM. 339
a mean distance of about 880 millions of miles. In mass and
size it stands next to Jupiter. To show the disparity in the
masses of the planets we may refer to the table already given,
showing that although Saturn is not one -third the mass of
Jupiter, it has about three times the mass of the six planets,
which are smaller than itself put together. Its surroundings
are such as to make it the most magnificent object in the solar
system. While no other planet is known to have more than
FIG. 88. View of Saturn and his rings.
four satellites, Saturn has 110 less than eight. It is also sur-
rounded by a pair of rings, the interior diameter of which is
about 100,000 miles. The aspect of these rings is subject to
great variations, for reasons which will soon appear. The
great distance of the planet renders the study of its details
difficult unless the highest telescopic power is applied. The
whole combination of Saturn, his rings, and his satellites is
often called the Saturnian System.
The planet Saturn generally shines with the brilliancy of a
340 THE SOLAR SYSTEM.
moderate first-magnitude star, and with a dingy, reddish light,
as if seen through a smoky atmosphere. Its apparent bright-
ness is, however, different at different times : during the years
1876-1879 it is fainter than the average, owing to its ring be-
ing seen nearly edgewise. From 1878 till 1885 it will con-
stantly grow brighter, on account both of the opening out of
the ring and the approach of the planet to its perihelion.
The times of opposition are as follow :
1877 September 9th.
1878 September 22d.
1879 October 5th.
1880 October 18th.
In subsequent years opposition will occur about thirteen days
later every year, so that by adding this amount to the date for
each -year the oppositions can be found until the end of the
century without an error of more than a few days.
The physical constitution of Saturn seems to bear a great
resemblance to that of Jupiter ; but, being twice as far away,
it cannot be so well studied. The farther an object is from
the sun, the less brightly it is illuminated ; and the farther
from the earth, the smaller it looks, so that there is a double
difficulty in getting the finest views of the more distant plan-
ets. When examined under favorable circumstances, the sur :
face of Saturn is seen to be diversified with very faint mark-
ings; and if high telescopic powers are used, two or more
very faint streaks or belts may be seen parallel to its equator,
the strongest ones lying on, or very near, the equator. As in
the case of Jupiter, these belts change their aspect from time
to time, but they are so faint that the changes cannot be
easily followed. It is therefore, in general, difficult to say
with certainty whether we do or do not see the same face of
Saturn on different nights ; and, consequently, it is only on
extraordinary occasions that the time of rotation can be de-
termined.
The first occasion on which a well-defined spot was known
to remain long enough on Saturn to determine the period of
its rotation was in the time of Sir W. Herschel, who, from
observations extending over several weeks, found the time of
THE KINGS OF SATURN. 341
rotation to be 10 hours 16 " minutes.* No further opportu-
nity for determining this period seems to have offered itself
until 1876, when an appearanqe altogether new suddenly
show r ed itself on the globe of this planet. On the evening of
December 7th, 1876,- Professor Hall, who had been engaged
in measures of the satellites of Saturn with the great Wash-
ington telescope, saw a brilliant white spot near the equator
of the planet. It seemed as if an immense eruption of white-
hot matter had suddenly burst up from the interior. The
spot gradually spread itself out in the direction which would
be east on the planet, so as to assume the form of a long light
streak, of which the brightest point was near the following
end. It continued visible until January, when it became faint
and ill-defined, and the planet was lost in the rays of the sun.
Immediately upon the discovery of this remarkable phenom-
enon, messages were sent to other observers in various parts of
the country, and on the 10th it was seen by several observers,
who noted the time at which it crossed the centre of the disk
in consequence of the rotation of the planet. From all the
observations of this kind, Professor Hall found the period of
Saturn to be 10 hours 14 minutes, taking the brightest part
of the streak, which, as we have said, was near one end.
Had the middle of the streak been taken, the time would have
been less, because the bright matter seemed to be carried
along in the direction of the planet's rotation. Attributing
.this to a wind, the velocity of the latter would have been be-
tween 50 and 100 miles an hour.
4. The Rings of Saturn.
The most extraordinary feature of Saturn is the magnificent
system of rings by which he is surrounded. To the early
telescopists, who could not command sufficient optical power
to see exactly what it was, this feature was a source of great
* It is very curious that nearly all modern writers give about 10 hours 29 min-
utes as the time of rotation of Saturn which Herschel finally deduced. I can
find no such result in Herschel's papers. A suspicious coincidence is that this
period agrees with that assigned for the time of rotation of the ring.
34:2 THE SOLAR SYSTEM.
perplexity and difference of opinion. To Galileo it made the
planet appear triform a large globe with two small ones af-
fixed to it, one on each side. After he had observed it for a
year or two, he was greatly perplexed to find that the append-
ages had entirely disappeared, leaving Saturn a single round
globe, like the other planets. His chagrin was heightened by
the fear, not unnatural under the circumstances, that the curi-
ous form he had before seen might be due to some optical il-
lusion connected with his telescope. It is said (I do not know
on what authority) that his annoyance at the supposed decep-
tion into which he had fallen wa^ so great that he never again
looked at Saturn.
A very few years sufficed to show other observers, who had
command of more powerful telescopes, that the singularity of
form was no illusion, but that it varied from time to time.
We give several pictures from Huyghens's Systema Saturniurrij
showing how it was represented by various observers during
the first forty years of the telescope. If the reader will com-
pare these with the picture of Saturn and his rings as they
actually are, he will see how near many of the observers came
to a representation of the proper apparent form, though none
divined to what sort of an appendage the appearance was
due.
The man who at last solved the riddle was Huyghens, of
whose long telescopes we have already spoken. Examining
Saturn in March and April, 1655, he saw that instead of the
appendages presenting the appearance of curved handles, as
in previous years, a long narrow arm extended straight out on
each side of the planet. The spring following, this arm had
disappeared, and the planet appeared perfectly round as Gal-
ileo had seen it in 1612. In October, 1655, the handles had
reappeared, much as he had seen them a year and a half be-
fore. To his remarkably acute mathematical and mechanical
mind this mode of disappearance of the handles sufficed to
suggest the cause which led to their apparent form. Waiting
for entire confirmation by future observations, he communica-
ted his theory to his fellow-astronomers in the following com-
THE RINGS OF SATURN.
343
Pio. 89. Specimens of drawings of Saturn by various observers before the rings were
recognized as such: I. Form as given by Galileo in 1610 ; II. Drawing by Scheinev, in
1614, "showing ears to Saturn;" III. Drawing by Ricciolus, in 1640 and 1643; IV.,V.,
VI., and VII. are by Hevelius, and show the changes due to the different angles under
which the rings were seen ; VIII. and IX. are by Ricciolus, between 1648 and 1650,
when the ring was seen at the greatest angle ; X. is by a Jesuit who passed under
the pseudonym of EustacMus cfe Divinis; XI. is by Fontana; XII. by Gaesendi and
Blaucauus, and XIII. by Ricciolus.
bination of letters, printed without explanation at the end of a
little pamphlet on his discovery of the satellite of Saturn :
aaaaaaa ccccc d eeeee g h iiiiiii llll mm nnnnnnnnn oooo pp q rr s ttttt uuuuu,
which, properly arranged, read
** Annulo cingitur, tenui, piano, nusquam cokcerente, ad eclipticam inclinato"
(It is girdled by a thin plane ring, nowhere touching, inclined to the ecliptic).
This description is remarkably complete and accurate ; and
enabled Hnyghens to give a satisfactory explanation of the
34:4: THE SOLAR SYSTEM.
various phases which the ring had assumed as seen from the
earth. Owing to the extreme thinness and flatness of the ob-
ject, it was completely invisible in the telescopes of that time
when its edge was presented towards the observer or towards
the sun. This happens twice in each revolution of Saturn, in
much the same way that the earth's equator is twice directed
towards the sun in the course of the year. The ring is in-
clined to the plane of the planet's orbit by 27, corresponding
to the angle of 23J between the earth's equator and the
ecliptic. The general aspect from the earth is very near the
same as from the sun. As the planet revolves around the
sun, the axis and plane of the ring preserve the same absolute
direction in space, just as the axis of the earth and the plane
of the equator do.
When the planet is in one part of its orbit, an observer at
the sun or on the earth will see the upper or northern side of
the ring at an inclination of 27. This is the greatest angle
at which the ring can ever be seen, the position occurring
when the planet is in 262 of longitude, in the constellation
Sagittarius. When the planet has moved through a quarter
of a revolution, the edge of the ring is turned towards the sun,
and, owing to its extreme thinness, it is visible only in the
most powerful telescopes as an exceedingly fine line of light,
stretching out on each side of the planet. In this position the
planet is in longitude 352, in the constellation Pisces. When
the planet has moved 90 farther, an observer on the sun or
earth again sees the ring at an angle of 27 ; but now it is the
lower or southern side which is visible. The planet is now in
longitude 82, between the constellations Taurus and Gemini.
When it has moved 90 farther, to longitude 172, in the con-
stellation Leo, the edge of the ring is again turned towards
the earth and sun.
Thus there are a pair of opposite points of the orbit of Sat-
urn in which the rings are turned edgewise to us, and another
pair half-way between the first in which the ring is seen at
its maximum inclination of about 27. Since the planet per-
forms a revolution in 29 years, these phases occur at average
THE RINGS OF SATUEN. 345
intervals of about seven years and four months. The follow-
ing are some of the times of their occurrence :
1870. The planet being between Scorpio and Sagittarius,
the ring was seen open to its greatest breadth, the north side
being visible. The same phase recurs at the end of 1899.
1878 (February 7th). The edge of the ring is turned tow-
ards the sun, so that only a thin line of light will be visible.
The planet is then between Aquarius and Pisces.
1885. The planet being in Taurus (the Bull) the south side
of the rings will be seen at the greatest elevation.
1892. The edge of the ring is again turned towards the sun,
the planet being in Leo (the Lion).
Owing to the motion of the earth, the times when the edge
of the ring is turned towards it do not accurately correspond
to those when it is turned towards the sun, and the points of
Saturn's orbit in which this may occur range over a space of
several degrees. The most interesting times for viewing the
rings with powerful telescopes are on those rare occasions
when the sun shines on one side of the ring, while the dark
side is directed towards the earth. On these occasions the
plane of the ring, if extended out far enough, would pass be-
tween the sun and the earth. This will be the case between
February 9th and March 1st, 1878 ; but, unfortunately, at that
time the earth and Saturn are on opposite sides of the sun, so
that the planet is nearly lost in the sun's rays, and can be ob-
served only low down in the west just after sunset. In 1891
the position of Saturn will be almost equally unfavorable for
the observation in question, as it can be made only in the early
mornings of the latter part of October of that year, just after
Saturn has risen. In fact, a good opportunity will not occur
till 1907. In northern latitudes the finest telescopic views of
Saturn and his ring may be obtained between 1881 and 1889,
because during that interval Saturn passes his perihelion, and
also the point of greatest northern declination, while the ring
is opened out to its widest extent. In fact, these three most
favorable conditions all fall nearly together during the years
1881-'S5.
346 THE SOLAR SYSTEM.
After Huyghens, the next step forward in discoveries on
Saturn's ring was made by an English observer, named Ball,
otherwise unknown in astronomy, who found that there were
really two rings, divided by a narrow dark line. The breadth
of the rings is very unequal, the inner ring being several times
broader than the outer one. A moderate - sized telescope is
sufficient to show this division near the extreme points of the
ring if the atmosphere is steady ; but it requires both a large
telescope and tine seeing to trace it all the way across that
part of the ring which is between the observer and the ball of
the planet. Other divisions, especially in the outer ring, have
at times been suspected by various observers, but if they real-
ly existed, they must have been only temporary, forming and
closing up again.
In December, 1850, the astronomical world was surprised
by the announcement that Professor Bond, of Cambridge, had
discovered a third ring to Saturn. It lay between the rings
already known and the planet, being joined to the inner edge
of the inner ring. It had the appearance of a ring of crape,
being so dark and obscure that it might easily have been
overlooked in smaller telescopes. It was seen in England by
Messrs. Lassell and Dawes before it was formally announced
by the Bonds. Something of the kind had been seen by Dr.
Galle, at Berlin, as far back as 1838 ; but the paper on the
subject by Encke, the director of the observatory, did not de-
scribe the appearance very clearly. Indeed, on examining the
descriptions of observers in the early part of the eighteenth
century, some reason is found for suspecting that they saw
this dusky ring ; but none of the descriptions are sufficiently
definite to establish the fact, though it is strange if an object
so plain as this ring now is should have been overlooked by
all the older observers.
The question whether changes of various sorts are going qn
in the rings of Saturn is one which is still unsettled. There
is some reason to believe that the supposed additional divis-
ions noticed in the rings from time to time are only errors of
vision, due partly to the shading which is known to exist on
THE RINGS OF SATURN. 347
various parts of the ring. By reference to the diagram of
Saturn, it will be seen that the outer ring has a shaded line
extending around it about two-thirds of the way from its in-
ner to its outer edge. This line, however, is not fine and
sharp, like the known division, but seems to shade off gradual-
ly towards each edge. As observers who have supposed them-
selves to see a division in this ring saw it where this shaded
line is, and do not speak of the latter as anything distinct
from the former, there is reason to believe that they mistook
this permanent shading for a new division. The inner ring is
brightest near its outer edge, and shades off gradually towards
its inner edge. Here the dusky ring joins itself to it, and ex-
tends about half-way in to the planet.
As seen with the great Washington equatorial in the au-
tumn of 1874, there was no great or sudden contrast be-
tween the inner or dark edge of the bright ring and the out-
er edge of the dusky ring. There was some suspicion that
the one shaded into the other by insensible gradations. No
one could for a moment suppose, as some observers have, that
there was a separation between these two rings. All these
considerations give rise to the question whether the dusky
ring may not be growing at the expense of the inner bright
ring.
A most startling theory of changes in the rings of Saturn
was propounded by Struve, in 1851. This was nothing less
than that the inner edge of the ring was gradually approach-
ing the planet in consequence of the whole ring spreading in-
wards, and the central opening thus becoming smaller. The
data on which this theory was founded were the descriptions
and drawings of the rings by the astronomers of the seven-
teenth century, especially Iluyghens, and the measures ex-
ecuted by later astronomers up to the time at which Struve
wrote. The rate at which the space between the ring and the
planet was diminishing seemed to be about 1".3 per century.
The following are the numbers used by Struve, which are de-
duced from the descriptions by the ancient observers, and the
measures by the modern ones :
348
THE SOLAR SYSTEM.
Year.
Distance between
Ring and Planet.
Brnmlth of
1 i .}?.
Huyghens
1657
6.5
4.6
Huyghens and Cassini
1695
6.0
5.1
Bradley.
1719
5.4
5.7
Herschel
1799
5.12
5.98
W. Struve
1826
4.36
6 74
1838
4.04
7.06
1851
3 67
7.43
If these estimates and measures were certainly accurate,
they would place the fact of a progressive approach of the
rings to the ball beyond doubt, an approach which, if it con-
tinued at the same rate, would bring the inner edge of the
ring into contact with the planet about the year 2150. But
in measuring such an object as the inner edge of the ring of
Saturn, which, as we have just said, seems to fade gradually
into the obscure ring, different observers will always obtain
different results, and the differences among the four observ-
ers commencing with W. Struve are no greater than are often
seen in measuring an object of such uncertain outline. Hence,
considering the great improbability of so stupendous a cosmi-
cal change going on with so much rapidity, Struve's theory has
always been viewed with doubt by other astronomers.
At the same time, it is impossible to reconcile the descrip-
tions by the early observers with the obvious aspect of the
ring as seen now without supposing some change of the kind.
The most casual observer who now looks at Saturn will see
that the breadth of the two bright rings together is at least
half as great again, if not twice as great, as that of the dark
space between the inner edge of the bright ring and the plan-
et. But Huyghens describes the dark space as about equal
to the breadth of the ring, or a little greater. Supposing the
ring the same then as now, could this error have arisen from
the imperfection of his telescope ? No ; because the effect of
the imperfection would have been directly the opposite. The
old telescopes all represented planets and other bright objects
too large, and therefore would show dark spaces too small,
owing .to the irradiation produced by their imperfect glasses,
A strong confirmation of Struve's view is found in the old
CONSTITUTION OF THE RING. 349
pictures given in Fig. 89 by those observers who could not
clearly make out the ring. In nearly all cases the dark spaces
were more conspicuous than the edges of the ring. But if
we now look at Saturn through a very bad atmosphere, though
the elliptical outline of the ring may be clearly made out,
the dark space will be almost obliterated by the encroachment
of the light of the planet and ring upon it* The question is,
therefore, one of those the complete solution of which must
be left to future observers.
5. Constitution of the Ring.
The difficulties which investigators have met with in ac-
counting for the rings of Saturn are of the same nature as
those we have described as arising from spectroscopic discov-
eries respecting the envelopes of the sun. They illustrate the
philosophic maxim that surprise in which term we may in-
clude all difficulty and perplexity which men meet with in
seeking to account for the phenomena of nature is a result
of partial knowledge, and cannot exist either with entire ig-
norance or complete knowledge. Those who are perfectly
ignorant are surprised at nothing, because they expect noth-
ing, while perfect knowledge of what is to happen also pre-
cludes the same feeling. The astronomers of two centuries
ago saw nothing surprising in the fact of a pair of rings sur-
rounding a planet, and accompanying it in its orbit, because
they were not acquainted with the effects of gravitation on
such bodies as the rings seemed to be. But when Laplace in-
vestigated the subject, he found that a homogeneous and
uniform ring surrounding a planet could not be in a state
of stable equilibrium. Let it be balanced ever so nicely, the
slightest external force, the attraction of a satellite or of a
distant planet, would destroy the equilibrium, and the ring
would soon be precipitated upon the planet. He therefore
remarked that the rings must have irregularities in their
form, such as Herschel supposed he had seen; but he did
not investigate the question whether with those irregularities
the equilibrium would really be stable.
350 THE SOLAR SYSTEM.
The question was next taken up in this country by Profess-
ors Peirce and Bond. The latter started from the supposed
result of observations that new divisions show themselves
from time to time in the ring, and then close up again. lie
thence inferred that the rings must be fluid, and, to confirm
this view, he showed the impossibility of even an irregular
solid pair of rings fulfilling all the necessary conditions of
stability and freedom of motion. Professor Peirce, taking up
the same subject from a mathematical point of view, found
that no conceivable form of irregular solid ring would be in a
state of stable equilibrium; he therefore adopted Bond's view
that the rings were fluid. Following up the investigation,
he found that even a fluid ring would not be entirely stable
without some external support, and he attributed that support
to the attractions of the satellites. But as Laplace did not
demonstrate that irregularities would make the ring stable, so
Peirce merely fell back upon the attraction of the satellites as
a sort of forlorn hope, but did not demonstrate that the fluid
ring would really be stable under the influence of their attrac-
tion. Indeed, it now seems very doubtful whether this at-
traction would have the effect supposed by Peirce.
The next, and, we may say, the last, important step was
taken by Professor J. Clerk Maxwell, of England, in the
Adams prize essay for 1856. lie brought forward objections
which seem unanswerable against both the solid and the fluid
ring, and revived a theory propounded by Cassini about the
beginning of the last century.* This astronomer considered
the ring to be formed by a cloud of satellites, too small to
be separately seen in the telescope, and too close together to
admit of the intervals between them being visible. This is
the view of the constitution of the rings of Saturn now most
generally adopted. The reason why the ring looks solid and
continuous is that the satellites are too small and too numerous
to be seen singly. They are like the separate little drops of
* See Memoirs of the French Academy of Sciences for 1715, p. 47; or Cas-
sini's "iSlemens d'Astronomie,"p. 338, Paris, 1740.
THE SATELLITES OF SATURN. 351
water of which clouds and fog are composed, which, to our
eyes, seem like solid masses. In the dusky ring the particles
may be so scattered that we can see through the cloud, the
reason that it looks dusky being simply the comparatively
small number of the particles, so that to the distant eye they
appear like the faint stippling of an engraving.
The question arises whether the comparative darkness of
some portions of the bright ring may not be due to the paucity
of the particles, which allows the dark background of the sky
to be seen through. This question cannot be positively an-
swered until further observations are made ; but the prepon-
derance of evidence favors the view that the entire bright
ring is opaque, and that the dark shading is due entirely to a
darker color of that part of the ring. Indeed, for anything
we certainly know, the whole ring may be continuous and
opaque, the darker shade of some parts arising solely from the
particles being there black in color. The only way to settle
conclusively the questions whether these parts of the ring look
black, owing to the sky beyond showing through openings, as
it were, or from a black color of the ring, is to find whether a
star or other object can be seen through the dark spaces. But
an opportunity for seeing a bright star through the ring has
never yet presented itself. The most obvious way of settling
the question in respect to the dusky ring is to notice whether
the planet itself can be seen through it ; but this is much more
difficult than might be supposed, owing to the ill -defined as-
pect of the ring. The testimony of both Lassell and Trouve-
lot is in favor of the view that this ring is partially transpar-
ent ; but their observations will need to be repeated when the
ring is opened out to our sight after 1882.
6. The Satellites of Saturn.
When Huyghens commenced his observations of Saturn in
1655, he saw a star near the planet which a few days' observa-
tion enabled him to recognize as a satellite revolving round it
in about fifteen days. In his " Systema Salurnium," he vent-
ured to express the opinion that this discovery completed the
352
THE SOLAR SYSTEM.
solar system, which now comprised six planets (Saturn being
then the outermost known planet) and six satellites (one of
the earth, four of Jupiter, and this one of Saturn), making
the perfect number of twelve. He was, therefore, confident
that no more satellites were left to discover, and through fail-
ing to search for others, he probably lost the honor of addi-
tional discoveries.
Twelve years after this prediction, Cassini discovered a sec-
ond satellite outside that found by Huyghens, and within a
few years more he found three others inside of it. The dis-
covery of four satellites by one astronomer was so brilliant a
result of French science that the Government of France
struck a medal in commemoration of it, bearing the inscrip-
tion Saturni Satellites primum cogniti. These five satellites
completed the number known for more than a century. In
1789 Herschel discovered two new ones still nearer the ring
than those found by Oassini. The space between the ring and
the inner one is so small that the satellite is generally invisible,
even in the most powerful telescopes. Finally, in September,
1848, the Messrs. Bond, at the Observatory of Harvard Col-
lege, found an eighth satellite, while examining the ring of
Saturn. By a singular coincidence, this satellite was found by
Mr. Lassellj of England, only a couple of nights after it was
detected by the Bonds. The names which have been given to
these bodies are shown in the following list, in which the sat-
ellites are arranged in the order of their distance from the
planet. The distances are given in semidiameters of Saturn.
More exact elements will be found in the Appendix to this
volume.
No.
Name.
Distance from
Planet.
Discoverer.
Date.
1
Mimas.. ..
3.3
Herschel.
1789, September 17th.
2
Enceladus
4.3
Herschel.
1789, August 28th.
3
Tethys. . . .
5.3
Cassini . .
1684, March.
4
Dione
6.8
Cassini . .
1684, March.
5
Rhea
9.5
Cassini . .
1672, December 23d.
6
Titan
20.7
Huyghens
1655, March 5th.
7
Hyperion .
26.8
Bond.....
1848, September 16th.
8
Japetus....
64.4
Cassini . .
1671, October.
URANUS ANP ITS SATELLITES, 353
The brightness, or rather, thq visibility, of these satellites
follows the same order as their discovery. The smallest tel-
escope will show Titan, and one of very moderate size will
show Japetus in the western part of its orbit. Four or five
inches aperture will show Rhea, and perhaps Tethys and Di-
one, while seven or eight inches are required for Enceladus,
and even with that aperture it will probably be seen only near
its greatest elongation from the planet. Mimas can be seen
only near the same position, unless the ring is seen edgewise,
and will then require a large telescope, probably twelve inches
or upwards. Finally, Hyperion can be reQognized only with
the most powerful telescopes, not only on account of its faint-
ness, but of the difficulty of distinguishing it from minute stars.
All these satellites, except Japetus, revolve very nearly in
the plane of the ring. Consequently, when the edge of the
ring is turned towards the earth, the satellites seem to swing-
from one side of the planet to the other in a straight line, run-
ning along the thin edge of the ring, like beads on a string.
This phase affords the best opportunity of seeing the inner
satellites Mimas and Enceladus, because they are no longer
obscured by the brilliancy of the ring.
Japetus, the outer satellite of all, exhibits this remarkable
peculiarity, that while in one part of its orbit it is the bright-
est of the satellites, except Titan, in the opposite part it is al-
most as faint as Hyperion, and can be seen only in large
telescopes. When west of the planet, it is bright ; when east
of it, faint. This peculiarity has been accounted for only by
supposing that the satellite, like our moon, always presents
the same face to the planet, and that one side of it is white
and the other intensely black. The only difficulty in the way
of this explanation is that it is doubtful whether any known
substance is so black as one side of the satellite must be to
account for such great changes of brilliancy.
7. Uranus and its Satellites.
Uranus, the next planet beyond Saturn, is at a mean dis-
tance from the sun of about 1770 millions of miles, and per-
9A
354 THE SOLAR SYSTEM.
forms a revolution in 84 years. It shines as a star of the sixth
magnitude, and can therefore be seen with the naked eye, if
one knows exactly where to look for it. It was in opposition
February llth, 1877, and the time of opposition during the
remainder of the present century may be found by adding 4J
days for every year subsequent to 1877. To find it readily,
either with a telescope or the naked eye, recourse must be had
to the Nautical Almanac, where the position (right ascension
and declination) is given for each day in the year.
Of course the smallest telescopes will show this planet as a
star, but to recognize its disk a magnifying power of at least
100 should be used, and 200 will be necessary to any one who
is not a practised observer. As seen in a large telescope, the
planet has a decided sea-green color. No markings have ever
been certainly seen on the disk, and therefore no changes
which could be due to an axial rotation have ever been estab-
lished ; but it may be regarded as certain that it does rotate
in the same plane in which the satellites revolve around it.
Discovery of Uranus. This planet was discovered by Sir
William Herschel, in March, 1781. Perceiving by its disk
that it was not a star, and by its motion that it was not a neb-
ula, he took it for a comet. The possibility of its being a new
planet did not at first occur to him ; and he therefore com-
municated his discovery to the Royal Society as being one of
a new cornet. Various computing astronomers thereupon at-
tempted to find the orbit of the supposed comet, from the ob-
servations of Herschel and others, assuming it to move in a
parabola, like other comets. But the actual motion of the
body constantly deviated from the orbits thus computed to
such an extent that new calculations had to be repeatedly
made. After a few weeks it was found that if it moved in a
parabola, the nearest distance to the sun must be at least four-
teen times that of the earth from the sun, a perihelion distance
many times greater than that of any known comet. This an-
nouncement gave the hint that some other hypothesis must be
resorted to, and it was then found that all the observations
could be well represented by a circular orbit, with a radius
UEANUS AND ITS SATELLITES. 355
nineteen times that of the earth's orbit. The object was, there-
fore, a planet moving at double the distance of Saturn.
With a commendable feeling of gratitude towards the royal
patron who had afforded him the means of making his dis-
co veries, Herschel proposed to call the new planet Georgium
Sidus (the Star of the Georges). This name, contracted to " the
Georgian," was employed in England until 1850, but never
came into use on the Continent. Lalande thought the most
appropriate name of the planet was that of its discoverer, and
therefore proposed to call it Herschel, But this name met
with no more favor than the other. Several other names were
proposed, but that of Uranus at length met with universal
adoption. It was proposed by Bode as the most appropriate,
on the ground that the most distant body of our system might
be properly named after the oldest of the gods.
After the elliptic orbit of the planet had been accurately
computed, and its path mapped out in the heavens, it was
found that it had been seen a surprising number of times as a
star without the observers having entertained any suspicion of
its planetary nature. It had passed through the field of their"
telescopes, and they had noted the time of its transit, or its
declination, or both, but had entered it in their journals simply
as an unnamed star of the constellation in which it happened
to be at the time. It had been thus seen five times by Flam-
steed, the first observation being in 1690, nearly a century be-
fore the discovery by Herschel. What is most extraordina-
ry, it had been observed eight times in rapid succession by
Le Monnier, of Paris, in December, 1768, and January, 1769.
Had that astronomer merely taken the trouble to reduce and
compare his observations, he would have anticipated Herschel
by twelve years. Indeed, considering how easily the planet
can be seen with the naked eye, it is illustrative of the small
amount of care devoted to cataloguing the stars that it was
not discovered without a telescope.
Satellites of Uranus. In January and February, 1787,
Herschel found that Uranus was accompanied by two satel-
lites, of which the inner performed a revolution in a little less
356 THE SOLAR SYSTEM.
than nine days, and the outer in thirteen days and a half.
The existence of these two satellites was well authenticated
by his observations, and they have been frequently observed
in recent times. They can be seen with a telescope of one-
foot aperture or upwards. Afterwards Herschel made a very
assiduous search for other satellites. He encountered many
difficulties, not only from the extreme faintness of the objects,
but from the difficulty of deciding whether any object he
might see was a satellite, or a small star which happened to
be in the neighborhood. He at length announced the probable
existence of four additional satellites, the orbit of one being
inside of those of the two certain ones, one between them, and
two outside them. This made an entire, number of .six; and
though the evidence adduced by Herschel in favor of the ex-
istence of the four additional ones was entirely insufficient,
and their existence has been completely disproved, they figure
in some of our books on astronomy to this day.
For half a century no telescope more powerful than that of
Herschel was turned upon Uranus, and no additional light was
thrown upon the question of the existence or non-existence of
the questionable objects. At length, about 1846, Mr. William
Lassell, of England, constructed a reflector of two feet aper-
ture, of which we have already spoken, and of very excellent
definition, which in optical power exceeded any of the older
instruments. With this he succeeded in discovering two new
satellites inside the orbits of the two brighter ones,* but found
no trace of any of the additional satellites of Herschel. In the
climate of England, he could make only very imperfect obser-
vations of these bodies; but in 1852 he moved his telescope
temporarily to Malta, to take advantage of the purer sky of
that latitude, and there he succeeded in determining their or-
bits with considerable accuracy. Their times of revolution
are about 2 and 4 days respectively. They may fairly be
* These difficult objects were also sought for by Otto Struve with the fifteen-
inch telescope of the Pulkowa Observatory, and occasional glimpses of them were,
he believed, attained before they were certainly found by Mr. Lassell, but he was
not able to follow them so continuously as to fix upon their times of revolution.
URANUS AND ITS SATELLITES. 357
regarded as the most difficult known objects in the planetary
system; indeed, it is only with a few of the most powerful
telescopes in existence that they have certainly been seen.
The non-existence of Herschel's suspected satellites is proved
by the fact that they have been sought for in vain, both with
Mr. Lassell's great reflectors and with the Washington twen-
ty-six-inch refractor, all of which are optically more powerful
than the telescopes of Herschel. There may be additional
satellites which have not yet been discovered ; but if so, they
must be too faint to have been recognized by Herschel. Pro-
fessor Holden, of the Naval Observatory, has sought to show
that some of Herschel's observations of his supposed inner sat-
ellites were really glimpses of the objects afterwards discov-
ered by Mr. Lassell. This he has done by calculating the po-
sitions of these inner satellites from tables for the date of
each of Herschel's observations, and comparing them with the
position of the object noted by Herschel. In four cases, the
agreement is sufficiently close to warrant the belief that Her-
schel actually saw the real satellites ; but Mr. Lassell attributes
these coincidences to chance, and contests Professor Holden's
views.
The most remarkable peculiarity of the satellites of Uranus
is the great inclination of their orbits to the ecliptic. Instead
of being inclined to it at small angles, like the orbits of all
the other planets and satellites, they are nearly perpendicular
to it ; indeed, in a geometrical sense, they are more than per-
pendicular, because the direction of the motion of the satel-
lites in their orbits is retrograde. To change the position of
the orbit of an ordinary satellite into that of the orbits of
these satellites, it would have to be tipped over 100 ; so that,
supposing the orbit a horizontal plane, the point correspond-
ing to the zenith would be 10 below the horizon, and the up-
per surface would be inclined beyond the perpendicular, so as
to be the lower of the two surfaces.
Observations of the satellites afford the only accurate way
of determining the mass of Uranus ; because, of the adjoining'
planets, Saturn and Neptune, tHe observations of the first are
358 THE SOLAR SYSTEM.
too uncertain and those of the last too recent to give any cer-
tain result Measures made with the great Washington tele-
scope show this mass to be -^linr > a result which is probably
correct within -ZVIT P ar ^ f ^ s whole amount.*
8. Neptune and its Satellite.
The discovery of this planet is due to one of the boldest and
most brilliant conceptions of modern astronomy. The planet
was felt, as it were, by its attraction upon Uranus; and its di-
rection was thus calculated by the theory of gravitation before
it had been recognized by the telescope. An observer was
told that if he pointed his telescope towards a certain point in
the heavens, he would see a new planet. He looked, and there
was the planet, within a degree of the calculated place. It is
difficult to imagine a more striking illustration of the certain-
ty of that branch of astronomy which treats of the motions of
the heavenly bodies and is founded on the theory of gravi-
tation.
To describe the researches which led to this result, we shall
have to go back to 1820. In that year, Bouvard, of Paris,
prepared improved tables of Jupiter, Saturn, and Uranus,
which, although now very imperfect, have formed the basis of
most of the calculations since made on the motions of those
bodies. lie found that while the motions of Jupiter and Sat-
urn were fairly in accord with the theory of gravitation, it
was not so with those of Uranus. After allowing for the per-
turbations produced by the known planets, it was impossible
to find any orbit which would satisfy both the ancient and the
recent observations of Uranus. By the ancient observations
we mean those accidental ones made by Flamsteed, Le Mon-
nier, and 'others, before the planetary character of the object
was suspected ; and by the recent ones, those made after the
discovery of the planet by Herschel, in 1781. Bouvard, there-
fore, rejected the older observations, founding his tables on the
modern ones alone ; and leaving to future investigators the
* Washington Observations for 1873 : Appendix.
NEPTUNE AND ITS SATELLITE. 359
question whether the difficulty of reconciling the two systems
arose from the inaccuracy of the ancient observations, or from
the action of some extraneous influence upon the planet
Only a few years elapsed, when the planet began to deviate
from the tables of Bouvard. In 1830 the error amounted to
20"; in 1840, to 90"; in 1844, to 2', From a non- astro-
nomical point of view, these deviations were very minute.
Had two stars moved in the heavens, the one in the place
of the real planet, the other in that of the calculated planet,
it would have been an eye of wonderful keenness which
could have distinguished the two from a single star, even in
1844. But, magnified by the telescope, it is a large and
easily measurable quantity, not for a moment to be neglect-
ed. The probable cause of the deviation was sometimes a
subject of discussion among astronomers, but no very definite
views respecting it seem to have been entertained, nor did
any one express the decided opinion that it was to be attrib-
uted to a trans-Uranian planet, natural as it seems to us such
an opinion would have been.
In 1845, Arago advised his then young and unknown friend
Leverrier, whom he knew to be an able mathematician and
an expert computer, to investigate the subject of the motions
of Uranus. Leverrier at once set about the task in the most
systematic manner. The first step was to make sure that the
deviations did not arise from errors in Bouvard's theory and
tables ; he therefore commenced with a careful recomputation
of the perturbations of Uranus produced by Jupiter and Sat-
urn, and a critical examination of the tables. The result was
the discovery of many small errors in the tables, which, how-
ever, were not of a character to give rise to the observed de-
viations.
The next question was whether any orbit could be assigned
which, after making allowance for the action of Jupiter and
Saturn, would represent the modern observations. The an-
swer was in the negative, the best orbit deviating, first on one
side and then on the other, by amounts too great to be attrib-
uted to errors of observation. Supposing the deviations to be
360 THE SOLAR SYSTEM.
due to the attraction of some unknown planet, Leverrier next
inquired where this planet must be situated. Its orbit could
not lie between those of Saturn and Uranus, because then it
would disturb the motions of Saturn as well as those of Uranus.
Outside of Uranus, therefore, the planet must be looked for,
and probably at not far from double the distance of that
body; this being the distance indicated by the law of Titius.
Complete elements of the orbit of the unseen planet were
finally deduced, making its longitude 325 as seen from the
earth at the beginning of 1847. This conclusion was reached
in the summer of 1846.
Leverrier was not alone in reaching this result. In 1843,
Mr. John C. Adams, then a student at Cambridge University,
England, having learned of the discordances in the theory of
Uranus from a report of Professor Airy, attacked the same
problem which Leverrier took hold of two years later. In
October, 1845, he communicated to Professor Airy elements
of the planet so near the truth that, if a search had been made
with a large telescope in the direction indicated, the planet
could hardly have failed to be found. The Astronomer Royal
was, however, somewhat incredulous, and deferred his search
for further explanations from Mr. Adams, which, from some
unexplained cause, he did not receive. Meanwhile the planet,
which had been in opposition about the middle of August,
was lost in the rays of the sun, and could not be seen before
the following summer. A most extraordinary circumstance
was that nothing was immediately published on the subject of
Mr. Adams's labors, and no effort made to secure his right to
priority, although in reality his researches preceded those of
Leverrier by nearly a year.
In the summer of 1846, M. Leverrier's elements appeared,
and the coincidence of his results with those of Mr. Adams
was so striking, that Professor Challis, of the Cambridge Ob-
servatory, commenced a vigorous search for the planet. Un-
fortunately, he adopted a mode of search which, although it
made the discovery of the planet certain, was extremely la-
borious. Instead of endeavoring to recognize it by its disk,
NEPTUNE AND ITS SATELLITE. 361
he sought to detect it by its motion among the stars a
course which required all the stars in the neighborhood to
have their positions repeatedly determined, so as to find
which of' them had changed its position. Observations of
the planet as a star were actually made on August 4th, 1846,
and again oil August 12th ; but these observations, owing to
Mr. Challis's other engagements, were not reduced, and so the
fact that the planet was observed did not appear. His mode
of proceeding was much like that of a man who, knowing that
a diamond had dropped near a certain spot on the sea-beach,
should remove all the sand in the neighborhood to a conven-
ient place for the purpose of sifting it at his leisure, and
should thus have the diamond actually in his possession with-
out being able to recognize it.
Early in September, 1846, while Professor Challis was still
working away at his observations, entirely unconscious that
the great object of search was securely imprisoned in the pen-
cilled figures of his note-book, Leverrier wrote to Dr. Galle, at
Berlin, suggesting that he should try to find the planet. It
happened that a map of the stars in the region occupied by
the planet was just completed, and on pointing the telescope
of the Berlin Observatory, Galle soon found an object which
had a planetary disk, and was not on the star map. Its posi-
tion was carefully determined, and on the night following it
was re-examined, and found to have changed its place among
the stars. No further doubt could exist that the long-sought-
for planet was found. The date of the optical discovery was
September 23d, 1846. The news reached Professor Challis
October 1st, and, looking into his note-book, he found his own
observations of the planet, made nearly two months before.
As between Leverrier and Adams, the technical right of
priority in this wonderful investigation lay with Leverrier, al-
though Adams had preceded him by nearly a year, for the
double reason that the latter did not publish his results before
the discovery of the planet, and that it was by the directions
of Leverrier to Dr. Galle that the actual discovery was made.
But this does not diminish the credit due to Mr. Adams for
362 THE SOLAR SYSTEM.
his boldness in attacking, and Ins skill in successfully solving,
so noble a problem. The spirit of true science is advancing
to a stage in which contests about priority are looked upon as
below its dignity. Discoveries are made for the benefit of
mankind ; and if made independently by several persons, it is
fitting that each should receive all the credit due to success in
making it. We should consider Mr. Adams as entitled to the
same unqualified admiration which is due to a sole discoverer;
and whatever claims to priority he may have lost by the more
fortunate Leverrier will be compensated by the sympathy
which must ever be felt towards the talented young student
in his failure to secure for his work that immediate publicity
which was due to its interest and importance.
The discovery of Neptune gave rise to a series of research-
es, in which American astronomers took a distinguished part.
One of the first questions to be considered was whether the
planet had, like Uranus, been observed as a star by some pre-
vious astronomer. This question was taken up by Mr. Sears (X
Walker, of the Naval Observatory. A few months' observa-
tion sufficed to show that the distance of the planet from the
sun was not far from 30 (the distance of the earth being, as
usual, unity), and, assuming a circular orbit, he computed the
approximate place of the planet in past years. He traced its
course back from year to year in order to find whether at any
time it passed through a region which was at the same time
being swept by the telescopes of observers engaged in prepar-
ing catalogues of stars. He was not successful till he reached
the year 1795. On the 8th and 10th of May of that year,
Lalande, of Paris, had swept over the place of the planet. It
must now be decided whether any of the stars observed on
those nights could have been Neptune. Although the exact
place of the planet could not yet be fixed for an epoch so
remote, it was easy to mark out the apparent position of its
orbit as a line among the stars, arid it must then have been
somewhere on that line. After taking out the stars which
were too far from the line, and those which had been seen by
subsequent observers, there remained one, observed on May
NEPTUNE AND ITS SATELLITE. 863
10th, which was very near the computed orbit. Walker at
once ventured on the bold prediction that if this region of
the heavens were examined with a telescope, that star would
be found missing. He communicated this opinion officially
to Lieutenant Manry and other scientific men in Washington,
and asked that the search might be made. On the first clear
evening the examination was made by Professor Hubbard,
arid, surely enough, the star was not there.
There was, however, one weak point in the conclusion that
this was really the planet Neptune. Lalande had marked his
observation of the missing star with a colon, to indicate that
there was a doubt of its accuracy : therefore it was possible
that the record of the supposed star might have been the sim-
ple result of some error of observation. Happily, the original
manuscripts of Lalande were carefully preserved at the Paris
Observatory ; and as soon as the news of Walker's researches
reached that city an examination of the observations of May
8th and 10th, 1795, was entered upon. The extraordinary dis-
covery was made that there was no mark of uncertainty in the
original record, but that Lalande had observed the planet both
on the 8th and 10th of May. The object having moved slight-
ly during the two days' interval, the observations did not
agree ; and Lalande supposed that one of them must be wrong,
entirely unconscious that in that little discrepancy lay a dis-
covery which would have made his name immortal. Without
further examination, he had rejected the first observation, and
copied the second as doubtful on account of the discrepancy,
and thus the pearl of great price was dropped, not to be
found again till a half-century had elapsed.
For several years the investigation of the motion of the new
planet was left in the hands of Mr. Walker and Professor
Peirce. The latter was the first one to compute the perturba-
tions of Neptune produced by the action of the other planets.
The results of these computations, together with Mr. Walk-
er's elements, are given in the Proceedings of the American
Academy of Arts and Sciences.
Physical Aspect of Neptune. On the physical appearance of
364 THE SOLAR SYSTEM.
this planet very little can be said. In the largest telescopes
and through the finest atmosphere, it presents the appearance
of a perfectly round disk about 3" in diameter, of a pale-blue
color. No markings have been seen upon it. When first
seen by Mr. Lassell, he suspected a ring, or some such append-
age; but future observations under more favorable circuit
stances showed this suspicion to be without foundation. To
recognize the disk of Neptune with ease, a magnifying power
of 300 or upwards must be employed.
Satellite of Neptune. Soon after the discovery of Neptune,
Mr. Lassell, scrutinizing it with his two-foot reflector, saw on
various occasions a point of light in the neighborhood. Dur-
ing the following year it proved to be a satellite, having a pe-
riod of revolution of about 5 days 21 hours. During 1847
and 1848 the satellite was observed, both at Cambridge by the
Messrs. Bond, and at Pulkowa by Strove. These observations
showed that its orbit was inclined about 30 to the ecliptic,
but it was impossible to decide in which direction it was mov-
ing, since there were two positions of the orbit, and two di-
rections of motion, in which the apparent motion, as seen from
the earth, would be the same. After a few years the change
in the direction of the planet enabled this question to be de-
cided, and showed that the motion was retrograde. The case
was more extraordinary than that of the satellites of TJranus>
since, to represent both the position of the orbit and the di-
rection of motion in the usual way, the orbit would have to be
tipped over 150 ; it is, in fact, nearly upside down. The de-
terminations of the elements of the satellite have been ex-
tremely discordant, a circumstance which we must attribute
to its extreme faintness. It is a minute object, even in the
most powerful telescopes.
Measures of the distance of the satellite from the planet,
made with the great Washington telescope, show the mass of
Neptune to be Trsw The mass deduced from the perturba-
tions of Uranus is -nr^, an agreement as good as could be
expected in a quantity so difficult to determine.
ASPECTS AND POEMS OF COMETS, 365
CHAPTER V.
COMETS AND METEORS.
1. Aspects and Forms of Comets.
THE celestial motions which we have hitherto described
take place with a majestic uniformity which has always im-
pressed the minds of men with a sense of the unchangeable-
ness of the heavens. But this uniformity is on some occasions
broken by the apparition of objects of an extraordinary as-
pect, which hover in the heavens for a few days or weeks, like
some supernatural visitor, and then disappear. We refer to
comets, bodies which have been known from the earliest timeSj
but of which the nature is not yet deprived of mystery.
Comets bright enough to be noticed with the naked eye
consist of three parts, which, however, are not completely dis-
tinct, but run into each other by insensible degrees. These
are the nucleus , the coma, and the tail.
The nucleus is the bright centre which to the eye presents
the appearance of an ordinary star or planet It would hard-
ly excite remark but for the coma and tail by which it is ac-
companied.
: The coma (which is Latin for hair) is a mass of cloudy or
vaporous appearance, which surrounds the nucleus on all sides.
Next to the nucleus, it is so bright as to be hardly distinguish-
able from it, but it gradually shades off in every direction.
Nucleus and coma combined present the appearance of a star,
more or less bright, shining through a small patch of fog, and
are together called the head of the comet.
The tail is a continuation of the coma, and consists of a
stream of milky light, growing wider and fainter as it recedes
from the comet, until the eye can no longer trace it. A curi-
ASPECTS AND FORMS OF COMETS.
367
FIG. 90. Views of Encke's comet in 1871, by Dr. Vogel.
alike when they first come within reach of the telescope, the
subsequent diversities arising from the different developments
of corresponding parts. The first appearance is that of a lit-
tle foggy patch without any tail, and very often without any
visible nucleus. Thus, in the case of Donati's cornet of 1858,
one of the most splendid on record, it was more than two
months after the first discovery before there was any appear-
368 THE SOLAR SYSTEM.
ance of a tail. To enable the reader to see the relation of
this to a very diffused telescopic comet, we present a telescopic
view of the head of this great comet when near its brightest,
and three drawings of Encke's cornet, made by Dr. Vogel, in
November and December, 1871.
When the nucleus of a telescopic comet begins to show it-
self, it is commonly on the side farthest from the sun. Sev-
eral little brandies will then be seen stretched out in the di-
rection of the sun, so that it will appear as if the comet had
a small fan-shaped tail directed towards the* sun, instead of
from it, as is usual. Thus, in the pictures of Encke's comet
in Figs. 1 and 2, the sun is towards the left, and we see what
FIG. 91. Head of Doiiati's great comet of!858, after Bond.
looks like three little tails, the middle one pointed towards the
sun. But if we look at the view of Donati's comet, Fig. 91,
we see several little lines branching upwards from the centre
of the head, and it is to these, and not to the tail, that the lit-
tle tails in the figures of Encke's comet correspond. In fact,
the general rule is that the heads of comets have a fan-shaped
structure, the handle of the fan being in the nucleus, and the
middle arm pointing towards the sun ; and it is this append-
age which first shows itself.
In the larger comets, this fan is surrounded fcy one or more
MOTIONS, OEiaiN, AND NUMBER OF COMETS. 369
semicircular arches, or envelopes, the inner one forming its
curved border; but this arch does not show itself in very faint
comets. The true tail of the comet, when it appears, is always
directed from the sun, and therefore away from the fan. In
Fig. 90, No. 3, a very faint true tail will be seen extending
out towards the lower right-hand corner of the picture, which
was opposite to the direction of the sun. On the other hand,
though the branches turned towards the sun have disappeared,
the fan-like form can still be traced in the head. In Fig. 91,
the true tail is turned downwards : owing to the large scale of
the picture, only the commencement of it can be seen. The
central line of the tail, it will be remarked, is comparatively
dark. This is very generally the case with bright comets.
2. Motions , Origin, and Number of Ccmets.
When it was found by Kepler that all the planets moved
around the sun in conic sections, and when Newton showed
that this motion was the necessary result of the gravitation of
the planets towards the sun, the question naturally arose wheth-
er comets moved according to the same law. It was found by
Newton that the comet of 1680 actually did move in such an
orbit, but instead of being, like the planetary orbits, nearly
circular, it was very eccentric, being to all appearance a pa-
rabola.
A parabola being one of the orbits which gravitation would
cause to be described, it was thus made certain that comets
gravitated towards the sun, like planets. It was, however, im-
possible to say whether the orbit was really a parabola or a
very elongated ellipse. The reason of this difficulty is that
comets are visible in only a very small portion of their orbits,
quite close to the sun, and in this portion the forms of a pa-
rabola and of a very eccentric ellipse are so nearly the same,
that they cannot always be distinguished.
There is this very important difference between an elliptical
and a parabolic orbit that the former is closed up, and a
comet moving in it must come back some time, whereas the
two branches of the latter extend out into infinite space with-
25
370
THE SOLAR SYSTEM.
out ever meeting. A comet moving in a parabolic orbit will,
therefore, never return, but, after once sweeping past the sun,
will continue to recede into infinite space forever. The same
thing will happen if the cornet moves in an hyperbola, which is
Parabolic orbit. Eccentric ellipse.
FIG. 92. Parabolic ami elliptic orbit of a comet. The comet is invisible in the dotted part
of the orbits, and the forms of the visible parts, a, 6, cannot be distinguished in the
two orbits. But the ellipse forms a closed curve, while the two branches of the pa-
rabola continue forever without meeting.
the third class of orbit that may be described under the influ-
ence of gravitation. In a parabola, the slightest retardation
of a comet would change the orbit into an ellipse, the velocity
being barely sufficient to carry the comet off forever, whereas
in an hyperbola there is more or less velocity to spare. Thus
the parabola is a sort of dividing curve between the hyperbola
and the ellipse.
The astronomer, knowing the position of an orbit, can tell
exactly what velocity is necessary at any point of it in order
that a body moving in it may go off, never to return. A body
thrown from the earth's surface with a velocity of seven miles
MOTIONS, ORIGIN, AND NUMBER OF COMETS. 371
a second, and not retarded by the atmosphere, would never
return to the earth, but would describe some sort of an orbit
round the sun. It would, in fact, be a little planet. If the
earth were out of the way, a body moving past the earth's
orbit at the rate of twenty-six miles a second would have just
the velocity necessary to describe a parabola. If the velocity
of a comet exceeds this limit at that point of its orbit which
is 92^ millions of miles from the sun, then the comet must
go off into infinite space, never to return to our system. But
with a less velocity the comet must be brought back by the
sun's attraction at some future time, the time being longer the
more nearly the velocity reaches twenty-six miles per second.
It is by the velocity that the astronomer must, in general, de-
termine the form of the orbit. If it corresponds exactly to
the calculated limit, the orbit is a parabola ; if it exceeds this
limit, it is an hyperbola ; if it falls short of it, it is an ellipse.
Now, in the large majority of comets the velocity is so near
the parabolic limit that it is not possible to decide, from ob-
servations, whether it falls short of it or exceeds it. In the
case of a few comets the observations indicate an excess of
velocity, but an excess is so minute that its reality cannot be
confidently asserted. It cannot, therefore, be said with cer-
tainty that any known comet revolves in a hyperbolic orbit,
and thus it is possible that all comets belong to our system,
and will ultimately return to it. It is, however, certain that
in the majority of cases the return will be delayed many cen-
turies, nay, perhaps many thousand years. There are quite a
number of comets which are known to be periodic, returning
to the sun at regular intervals in elliptic orbits. Some of
these have been observed at several returns, so that their exact
period has been determined with great certainty : in the case
of others, the periodicity has been inferred only from the fact
that the velocity fell so far short of the parabolic limit that
there could be no doubt of the fact that the comet moved in
an ellipse.
In this question of cometary orbits is involved the very in-
teresting one, whether comets should be considered as belong-
372 THE SOLAR SYSTEM.
ing to our system, or as mere visitors from the stellar spaces.
We may conceive of them as stray fragments of original neb-
ulous matter scattered through the great wilderness of space
around us, drawn towards our sun one by one as the long ages
elapse. If no planets surrounded the sun, or if, surrounding
it, they were immovable, a comet thus drawn in would whirl
around the sun in a parabolic orbit, and leave it again, not to
return until millions of years had elapsed, because the veloci-
ty it would acquire by falling towards the sun would be just
sufficient to carry it back into the infinite void from which it
came. I3ut owing to the motions of the several planets in
their orbits, the comet would have its velocity changed in
passing each of them, the change being an acceleration or a
retardation, according to the way in which it passed. If the
total accelerations produced by all the planets exceeded the
retardations, the comet would leave our system with more
than the parabolic velocity, and would certainly never return.
If the retarding forces chanced to be in excess, the orbit
would be changed into an ellipse more or less elongated, ac-
cording to the amount of this excess. In the large majority
of cases, the retardation would be so slight that the most del-
icate observations could not show it, and it could be known
only by calculation, or by the return of the comet after tens
or hundreds of thousands of years. But should the comet
chance to pass very near a planet, especially a large planet
like Jupiter, the retardation might be so great as to make the
comet revolve in an orbit of quite short period, and thus be-
come a seemingly permanent member of our system. So near
an approach of a comet to a planet would not be likely to oc-
cur more than once in a number of centuries, but every time
it did occur there would be an even chance for an additional
comet of short period, the orbit of which would, at first, al-
most intersect that of the planet which had deranged it. It
might not, however, be a known comet, because the orbit
might be wholly beyond the reach of our vision.
It is impossible, in the present state of science, to say with
certainty whether the periodic comets were thus brought into
MOTIONS, OEIGIN, AND NUMBER OF COMETS. 373
our system ; but it seems probable that they were, from the
fact that many, if not all, of the orbits of these comets pass
near the orbits of some of the planets. That the planetary
and cometary orbits in such a case should intersect now is not
to be expected, because both would change by the secular
variations resulting from the action of the planets. Future
research will probably throw more light on this question.
Number of Comets. It was the opinion of Kepler that the
celestial spaces were as full of comets as the sea of fish, only
a small proportion of them coming within the range of our
telescopes. That only an insignificant fraction of all existing
comets have ever been observed, we may regard as certain.
Owing to their extremely elongated orbits, they can be seen
only when near their perihelion, and as it is probable that the
period of revolution of the large majority of those which have
been observed is counted by thousands of years if, indeed,
they ever return at all our observations must be continued
for many thousand years before we have seen all which come
within range of our telescopes. It is also probable that all
which can ever be seen will be but a small fraction of the
number which exist, because a comet can seldom be seen un-
less its perihelion is either inside the orbit of the earth, or but
little outside of it. There are a few exceptions to the rule
that only such comets are seen, the most notable one being
that of the comet of 1729, which, at perihelion, was more than
four times the earth's distance from the sun. This comet must
have been one of extraordinary magnitude, as almost every
other known comet would have disappeared entirely from the
most powerful telescopes of that time, if placed at the dis-
tance at which it was observed.
The actual number of comets recorded as visible to the
naked eye since the Christian era is given in the table on the
following page.*
* This table is taken at second-hand, principally from Arago ("Astronomic
Populaire," Hvre xvii., chap. xv.). Arago mentions but eight as vjsible during
the eighteenth century. I have considered the number thirty-six, gi\*en by Klein,
as more probable.
374
TUB SOLAR SYSTEM.
Years of our Era.
Number
of Comets.
Years of our Era.
Number
of Comets.
Frc
)in t
101
201
301
401
501
601
701
801
901
o 100
22
23
44
27
16
25
22
16
42
26
Frc
>m 1001 t
1101
1201
1301
140 L
1501
1601
1701
1801
o 1100
36
26
26
29
27
31
12
36
16
200
1200
300
1300
400
1 400 .
500
1500
600
1(JOO
700
1700
800
1800 . .
900
1875
1 000 .
In round numbers, about five hundred comets visible to the
naked eye have been recorded since our era, making a general
average of one every four years. Besides these, nearly two
hundred telescopic comets have been observed since the in-
vention of the telescope ; so that the total number of these
bodies observed during the period in question does not fall
far short of 'seven hundred. Several new telescopic comets
are now discovered nearly every year, the number sometimes
ranging up to six or eight. It is probable that the annual
number of this class discovered depends very largely on the
skill, assiduity, and good - fortune of the astronomers who
chance to be engaged in searching for them.
3. Remarkable Comets.
In unenlightened ages comets were looked on with terror,
as portending pestilence, war, the death of kings, or other
calamitous or remarkable events. Hence it happens that in
the earlier descriptions of these bodies, they are generally
associated with some contemporaneous event. The descrip-
tions of the comets themselves are, however, so vague and
indefinite as to be entirely devoid of either instruction or in-
terest, as it often happens that not even their course in the
heavens is stated.
The great comet of 1680 is, as already said, remarkable for
being not only a brilliant comet, but the one by which New-
ton proved that comets move under the influence of the gravi-
tation of the sun. It first appeared in the autumn of 1680,
and continued visible most of the time till the following spring.
EEMAEKABLE COMETS. 875
It fell down almost in a direct line to the sun, passing nearer
to that luminary than any comet before known. It passed its
perihelion on December 18th, and, sweeping round a large
arc, went back in a direction not very different from that from
which it came. The observations have been calculated and
the orbit investigated by many astronomers, beginning with
Newton ; but the results show no certain deviation from a
parabolic orbit. Hence, if the comet ever returns, it is only
at very long intervals. Halley, however, suspected, with some
plausibility, that the period might be 575 years, from the fact
that great comets had been recorded as appearing at that in-
terval. The first of these appearances was in the month of
September, after Julius Caesar was killed ; the second, in the
year 531 ; the third, in February, 1106 ; while that of 1680
made the fourth. If, as seems not impossible, these were four
returns of one and the same comet, a fifth return will be seen
by our posterity about the year 2255. Until that time the
exact period must remain doubtful, because observations made
two centuries ago do not possess the exactitude which will
decide so delicate a point.
Halley 's Comet. Two years after the comet last described,
one appeared which has since become the most celebrated of
modern times. It was first seen on August 19th, 1682, and
observed about a month, when it disappeared. Halley com-
puted the position of the orbit, and, comparing it with previ-
ous orbits, found that it coincided so exactly with that of a
comet observed by Kepler in 1607, that there could be no
doubt of the identity of the two orbits. So close were they
together that, if drawn on the heavens, the naked eye would
almost see them joined into a single line. The chances against
two separate comets moving in the same orbit were so great
that Halley could not doubt that the comet of 1682 was the
same that had appeared in 1607, and that it therefore revolved
in a very elliptic orbit, returning about every seventy-five years.
His conclusion was confirmed by the fact that a comet was
observed in 1531, which moved in apparently the same orbit.
Again subtracting the period of seventy -five years, it was
376 THE SOLAR SYSTEM.
found that the comet had appeared in 1456, when it spread
such terror throughout Christendom that Pope Calixtus or-
dered prayers to be offered for protection against the Turks
and the comet. This is supposed to be the circumstance which
gave rise to the popular myth of the Pope's Bull against the
Comet
Tins is the earliest occasion on which observations of the
course of the comet were made with such accuracy that its
orbit could be determined. If we keep subtracting 75J years,
we shall find that we sometimes fall on dates when the appa-
rition of a comet was recorded ; but without any knowledge
of the orbits of these bodies, it cannot be said with certainty
that they are identical. However, in the returns of 1456,
1531, 1607, and 1682, at nearly equal intervals, Halley had
good reason for predicting that the comet would return again
about 1758. This gave the mathematicians time to investi-
gate its motions ; and the establishment, in the mean time, of
the theory of gravitation showed them how to set about the
work. It was necessary to calculate the effect of the attrac-
tion of the planets on the motion of the comet during the en-
tire seventy-six years. This immense labor was performed by
Clairaut, who found that, in consequence of the attractions of
Jupiter and Saturn, the return of the comet would be delayed
618 days, so that it would not reach its -perihelion until the
middle of April, 1759. Not having time to finish his calcula-
tions in the best way, he considered that this result was uncer-
tain by one month. The comet actually did pass its perihelion
at midnight on March 12th, 1759.
Seventy-six years more were to elapse, and the comet would
again appear about 1835. Meanwhile, great improvements
were made in the methods of computing the effects of planet-
ary attraction on the motions of a comet, so that mathemati-
cians, without expending more labor than Clairaut did, were
enabled to obtain much more accurate results. The French
were still the leading nation of the world in this sort of inves-
tigation, and the computation of the return of the comet was
undertaken independently by two of their leading astronomers,
REMARKABLE COMETS.
377
De Damoiseau and De Pontecoulant. Of these, the first an-
nounced that it would reach its perihelion on November 4th,
1835 ; while De Pontecoulant, after revising his computations
with more exact determinations of the masses of the planets,
assigned November 13th, at 2 A.M., as the date. The expected
comet was, of course, looked for with the greatest assiduity,
and was first seen on August 5th. Approaching the sun, it
passed its perihelion on November 16th, at eleven o'clock in
the morning, only three days after the time predicted by De
Pontecoulant.
This was the last return of the celebrated comet of Halley.
It was followed until May 17th, 1836, when it disappeared
from the sight of the most powerful telescopes of the time,
and has not been seen since. But the astronomer can follow
it with the eye of science with almost as much certainty as if
he had it in the field of view of his telescope. We cannot yet
fix the time of its return with certainty ; but we know that it
reached the farthest limit
of its course, which ex-
tends some distance be-
yond the orbit of Nep-
tune, about 1873, and
that it is now on its re-
turn journey. We pre-
sent a diagram of its or-
bit, showing its position
in 1874. Its velocity
will constantly increase
from year to year, and
*M 'A. 4. FIG. 93. Orbit of Halley's comet.
we may expect it to
reach perihelion about the year 1911. The exact date cannot
be fixed until the effect of the action of all the planets is com-
puted, and this will be a greater labor than before, not only
because greater accuracy will be aimed at, but because the
action of more planets must be taken into account. When
Olairaut computed the return of 1759. Saturn was the outer-
most known planet. When the return of 1835 was computed,
378 THE SOLAR SYSTEM.
Uranus had been added to the list, and its action had to be
taken into account. Since that time Neptune has been dis-
covered ; and the astronomer who computes the return of 1911
must add its action to that of the other planets. By doing so,
we may hope that the time of reaching perihelion will be pre-
dicted within one or two days.
The Lost Bields Comet. Nothing could more strikingly il-
lustrate the difference between comets and other heavenly
bodies than the fact of the total dissolution of one of the for-
mer. In 1826, a comet was discovered by an Austrian named
Biela, which was found to be periodic, and to have been ob-
served in 1772, and again in 1805. The time of revolution
was found to be six years and eight months. In the next two
returns, the earth was not in the right part of its orbit to ad-
mit of observing the cornet ; the latter was therefore not seen
again till 1845. In November and December of that year
it was observed as usual, without anything remarkable being
noticed. But in January following, the astronomers of the
Naval Observatory found it to have suffered an accident nev-
er before known to happen to a heavenly body, and of which
no explanation has ever been given. The comet had sepa-
rated into two distinct parts, of quite unequal brightness, so
that there were two apparently complete comets, instead of
one. During the month following, the lesser of the two con-
tinually increased, until it became equal to its companion.
Then it grew smaller, and in March vanished entirely, though
its companion was still plainly seen for a month longer. The
distance apart of the two portions, according to the computa-
tions of Professor Hubbard, was about 200,000 miles.
The next return of the comet took place in 1852, and was,
of course, looked for with great interest. It was found still
divided, and the two parts were far more widely separated
than in 1846, their distance having increased to about a mill-
ion and a half of miles. Sometimes one part was the bright-
er, and sometimes the other, so that it was impossible to de-
cide which ought to be regarded as representing the principal
comet. The pair passed out of view about the end of Sep-
REMARKABLE COMETS. 379
tember, 1852, and have not been seen since. They would,
since then, have made three complete revolutions, returning in
1859, 1865, and 1872. x\t the first of these returns, the rela-
tive positions of the comet and the earth were so unfavorable
that there was no hope of seeing the former. In 1865, it
could not be found ; but it was thought that this might be due
to the great distance of the comet from us. In 1872, the rela-
tive positions were extremely favorable, yet not a trace of the
object could be seen.* It had seemingly vanished, not into
thin air, but into something of a tenuity compared with which
the thinnest air was as a solid millstone. Some invisible frag-
ments were, however, passing along the comet's orbit, and pro-
duced a small meteoric shower, as will be explained in a later
section.
The Great Comet of 1843. This remarkable comet burst
suddenly into view in the neighborhood of the sun about the
end of February, 1843. It was visible in full daylight, so that
some observers actually measured the angular distance be-
tween the comet and the sun. It was followed until the mid-
dle of April. The most remarkable feature of the orbit of
this comet has been already mentioned : it passed nearer the
sun than any other known body so near it, in fact, that,
with a very slight change in the direction of its original mo-
tion, it would actually have struck it. Its orbit did not cer-
tainly deviate from a parabola. The most careful investigation
of it that of Professor Ilubbard, of Washington indicated
a period of 530 years ; but the velocity which would produce
this period is so near the parabolic limit that the difference
does not exceed the uncertainty of the observations.
Donates Comet of 1858. This great comet, one of the most
magnificent of modern times, which hung in the western sky
during the autumn of 1858, will be well remembered by all
who were then old enough to notice it. It was first seen at
* Just after the meteoric shower, Mr. Pogson, of Madras, obtained observa-
tions of an object which, it was supposed, might have been a fragment of this
comet. But the object was some two months behind the computed position of
the comet, so that the identity of the two has never been accepted by astronomers.
380 THE SOLAR SYSTEM,
Florence, on June 2d, 1858, by Donati, who described it as a
very faint nebulosity, about 3' in diameter. About the end
of the month it was discovered independently by three Amer-
ican observers : H. P. Tuttle, at Cambridge ; II. M. Parkhurst,
at Perth Amboy, New Jersey ; and Miss Maria Mitchel, at
Nantucket. During the first three months of its visibility it
gave no indications of its future grandeur. No tail was no-
ticed until the middle of August, and at the end of that
month it was only half a degree in length, while the comet
itself was barely visible to the naked eye. It continued to
approach the sun till the end of September, and during this
FIG. 94. Great comet of 1858.
month developed with great rapidity, attaining its greatest
brilliancy about the first half of October. Its tail was then
40 in length, and 10 in breadth at its outer end, and of a
curious feather-like form. About October 20th it passed so
far south as to be no longer visible in northern latitudes ; but
it was followed in the southern hemisphere until March fol-
lowing.
Observations of the position of this comet soon showed its
orbit to be decidedly elliptic, with a period of about 2000
years or less. A careful investigation of all the observations
was made by Mr. G. W. Hill, who found a period of 1950
ENCKE'S COMET, AND THE RESISTING MEDIUM. 381
years. If this period is correct, the comet must have appeared
about ninety-two years before our era, and must appear again
about the year 3808 ; but the uncertainty arising from the im-
perfections of the observations may amount to fifty years.
4. Enckds Comet, and the Resisting Medium.
The comet which in recent times has most excited the atten-
tion of astronomers is that known as Encke's, from the astron-
omer who first carefully investigated its motion. It was first
seen in January, 1786, but the observations only continued
through two days, and were insufficient to determine the orbit.
In 1795, a comet was found by Miss Caroline Herschel, on
which observations were continued about three weeks ; but no
very accurate orbit was derived from these observations. In
1805, the same comet returned again to perihelion, but its iden-
tity again failed to be recognized. As in the previous returns,
the observations continued through less than a month. It was
found, for the fourth time, by Pons, of Marseilles, in 1818.
When its orbit was calculated, it was seen to coincide so
closely with that of the comet of 1805 as to leave no doubt
that the two were really the same body. But the first astron-
omers who noticed this were unable to decide whether this
was its first return since 1805, or whether it had in the mean
time made several revolutions.
The motions of the comet were now taken up by Encke, of
Berlin, and investigated with a thoroughness before unknown.
He found the period to be about 1200 days, four complete
revolutions having been made between 1805 and 1818. Know-
ing this, there was no longer any difficulty in identifying the
comet of 1795 as also being the same, three complete revolu-
tions having been made between that date and 1805. In the
o
intermediate returns to perihelion, its position had been so
unfavorable that it had not been observed at all. This result
was received by astronomers with the greatest interest, because
it was the first known case of a comet of short period. Its re-
turn in 1822 was duly predicted, but it was found that when
near its greatest brilliancy it would be visible only in the
382 THE SOLAR SYSTEM.
southern hemisphere. Happily, Sir Thomas Brisbane had an
observatory at Paramatta, New South Wales, and his assistant,
Kurnker, was so fortunate as to find the comet. It was so
near the position predicted by Encke that, by constantly point-
ing the telescope in the direction predicted by that astronomer,
the comet was in the field of view during its whole course.
Encke continued to investigate the course of the comet dur-
ing each revolution up to the time of his death, in 1865. At
some returns it could not be seen, owing to its distance from
the earth, or the otherwise unfavorable position of our planet;
but generally very accurate observations of its course were
made. By a comparison of its motions with those which
would result from the gravitation of the sun and planets, he
found that the periodic time was constantly diminishing, and
was thus led to adopt the famous hypothesis of Gibers, that
the comet met with a resisting medium in space. The dimi-
nution of the period was about two hours and a half in each
revolution. The conclusion of Encke and Olbers was that the
planetary spaces are filled with a very rare medium so rare
that it does not produce the slightest effect on the motion of
such massive bodies as the planets. The comet being a body
of extreme tenuity, probably far lighter than air, it might be
affected by such a medium. The existence of this medium
cannot, however, be considered as established by Encke's re-
searches. In the first place, if we grant the fact that the
time of revolution is continually diminishing, as maintained
by the great German astronomer, it does not follow that a re-
sisting medium is the only cause to which we can attribute it.
But the main point is, that the computations on which Encke
founded his hypothesis are of such intricacy as to be always
liable to small errors, and their results cannot be received
with entire confidence until some one else has examined the
subject by new and improved methods.
Such an examination is now being made by Dr. Von Asten,
of Pulkowa ; and, although it is still unfinished, it seems like-
ly, in the end, to confirm Encke's results, at least in part. Dr.
Von Asten commenced by calculating the motion of the comet
ENCKE' S COMET, AND THE RESISTING MEDIUM. 383
from the theory of gravitation during the period from 1865
to 1871, within which the comet made two entire revolutions,
and was surprised to find that during this time jthere was no
deviation from the computed positions which could be attrib-
uted to the action of a resisting medium. But on carrying
the calculation back to 1861, he found that between that epoch
and 1865 there must have been a retarding action like that
supposed by Encke. Carrying his work forward to 1875, he
found that between 1871 and 1875 there was once more evi-
dence of a retardation about two-thirds as great as that found
by Encke. The absence of such an action between 1865 and
1871, therefore, seems quite exceptional, and difficult of ex-
planation.
To judge whether the deviations in the motion of Encke's
comet are really due to a resisting medium, we should know
whether the motions of other comets exhibit similar anom-
alies. So far as is yet known, no other one does. There is
at least one which has returned a sufficient number of times,
and of which the motions have been computed with sufficient
care, to lead to an entirely definite conclusion on this point,
namely, the periodic comet of Faye, which has been investi-
gated by Moller.* This comet was discovered in 1843 by the
astronomer whose name it bears, and was soon found to move
in an elliptic orbit, with a period of a little more than seven
years. As it has been observed at several returns since, Moller
investigated its motions with a view of finding whether its
period was affected by any resisting medium. At first he
thought there was such an effect, his general result being of
the same nature with that reached by Encke. But on repeat-
ing his calculations with the improved data afforded by a first
calculation, he found that the result arose from the imperfec-
tion of the latter, and that the comet really showed no sign of
a change in its mean motion. It therefore seems certain that,
if there is a resisting medium, it does not extend out far
enough from the sun to meet the orbit of Faye's comet. But
* Professor Axel Moller, director of the observatory at Lund. Sweden.
384 THE SQLAE SYSTEM.
this orbit lies wholly outside the orbit of Mars ; so that if the
sun were surrounded by an atmosphere extending out to Mars,
and no farther, the comet would never enter it. On the other
hand, Encke's comet, when in perihelion, is nearer the sun
than Mercury is, and might there meet a resisting medium
which did not extend so far out as the orbit of Mars. We
must therefore adopt one of two conclusions : either the cause
which is supposed to affect the motion of Encke's comet is
not a resisting medium, or, if it is such, it is confined to the
neighborhood of the sun. Considering the improbability of
the sun having any atmosphere which can extend to such a
distance, the former should be deemed the more probable
alternative. We can accept it the more readily, from the
fact that comets in general exhibit deviations from their cal-
culated orbits many times larger than those of the planets, so
that an exact agreement between theory and observations can
never be expected in the case of those bodies.
The next subject to which we would ask the attention of
the reader is that of the physical constitution of comets. But
this subject can be discussed only in connection with another,
to which, at first sight, it seems to have no relation, though
so curious a relation has really been discovered as greatly to
modify our views of what a comet probably is. We refer to
the phenomena of meteors, meteoric showers, and shooting-
stars, which next claim our attention.
5. Meteors and Shooting-stars.
If we carefully watch the heavens on a cloudless night, we
shall frequently see an appearance as of a star rapidly shoot-
ing through a short space in the sky, and then suddenly dis-
appearing. Three or four such shooting-stars may generally
be seen in the course of an hour. Generally they are visible
only for a second or two, but sometimes move slowly, and are
seen much longer. Occasionally they are so brilliant as to
illuminate the whole heavens, and they are then known as
meteors a term which is equally applicable to the ordinary
shooting-stars. In general, they are seen only one at a time,
METEORS AND SHOOTING-STARS. 385
and are so minute as hardly to attract attention. But they
have on some occasions shown themselves in such numbers as
to fill the beholders with terror, lest the end of the world had
come. The Chinese, Arabian, and other historians have hand-
ed down to us many accounts of such showers of meteors,
which have been brought to light by the researches of Ed-
ward Biot, Quetelet, Professor II. A. Newton, and others. As
an example of these accounts, we give one from an Arabian
writer :
" In the year 599, on the last day of Moharrem, stars shot
hither and thither, and flew against each other like a swarm
of locusts ; this phenomenon lasted until daybreak ; people
were thrown into consternation, and made supplication to the
Most High : there was never the like seen except on the com-
ing of the messenger of God, on whom be benediction and
peace."
In 1799, on the night of November 12th, a remarkable
shoWer was seen by Humboldt and Bonpland, who were then
on the Andes. Humboldt described the shower as commen-
cing a little before two o'clock, and the meteors as rising above
the horizon between east and north-east, and moving over tow-
ards the south. From not continuing his observations long
enough, or from some other cause, he failed to notice that the
lines in which the meteors moved all seemed to converge tow-
ards the same point of the heavens, and thus missed the dis-
covery of the real cause of the phenomenon.
The next great shower was seen in this country in 1833.
All through the Southern States, the negroes, like the Arabs of
a previous century, thought the end of the world had come at
last. The phenomenon was observed very carefully at New
Haven by Professor Olmsted, who worked out a theory of its
cause. Although his ideas are in many respects erroneous,
they were the means of suggesting the true theory to others.
The recurrence of the shower at this time suggested. to the
astronomer Olbers the idea of a thirty-four-year period, and
led him to predict a return of the shower in 1867. A few
years before the expected time, the subject was taken up by
26
386 THE SOLAR SYSTEM.
Professor Newton, of Yale College, to whose researches our
knowledge of the true cause of the phenomenon is very large-
ly due.
The phenomena of shooting-stars branch out in yet another
direction. As we have described them, they are seen only in
the higher and rarer regions of the atmosphere, far above the
clouds : no sound is heard from them, nor does anything reach
the surface of the earth from which the nature of the object
can be inferred. But on rare occasions meteors of extreme
brilliancy are followed by a loud sound, like the discharge of
heavy artillery ; while on yet rarer occasions large masses of
metallic or stony substances fall to the earth. These aerolites
were the puzzle of philosophers. Sometimes there was much
scepticism as to the reality of the phenomenon itself, it ap-
pearing to the doubters more likely that those who described
such things \vere mistaken than that heavy metallic masses
should fall from the air. When their reality was placed be-
yond doubt, many theories were propounded to account for
them, the most noteworthy of which was that they were
thrown from volcanoes in the moon. The problem of the
motion of a body projected from the moon was investigated
by several great mathematicians, the result being that such a
body conld not reach the earth unless projected with a veloci-
ty far exceeding anything seen oil our planet.
When aerolites were examined by chemists and mineralo-
gists, it was found that although they contained no new chem-
ical elements, yet the combinations of these elements were
quite unlike any found on the earth, so that they must have
originated outside the earth. Moreover, these combinations
exhibited certain characteristics peculiar to aerolites, so that
the mineralogist, from a simple examination and analysis of
a substance, could detect it as part of such a body, though
it had not been seen to fall. Great masses of matter thus
known to be of meteoric origin have been found in various
parts of the earth, especially in Northern Mexico, where, at
some unknown period, an immense shower of these bodies
seems to have fallen.
METEORS AND SHOOTING-STARS. 387
Cause of Shooting-stars. It is now universally conceded that
the celestial spaces are crowded with innumerable minute
bodies moving around the sun in every possible kind of orbit.
When we say crowded, we use the word in a relative sense ;
they may not average more than one in a million of cubic
miles, and yet their total number exceeds all calculation. Of
the nature of the minuter bodies of this class nothing is cer-
tainly known. But whatever they may be, the earth is con-
stantly encountering them in its motion around the sun. They
are burned by passing through the upper regions of our at-
mosphere, and the shooting -star is simply the light of that
burning. We shall follow Professor Newton in calling these
invisible bodies meteoroids.
The question which may be asked at this stage is, Why are
these bodies burned ? Especially, how can they burn so sud-
denly, and with so intense a light, as to be visible hundreds
of miles away ? These questions were the stumbling-block of
investigators until they were answered, clearly and conclusive-
ly, by the discovery of the mechanical theory of heat. It is
now established that heat is only a certain form of motion ;
that hot air differs from cold air only in a more rapid vibra-
tion of its molecules, and that it communicates its heat to
other bodies simply by striking them with its molecules, and
thus setting their molecules in vibration. Consequently, if a
body moves rapidly through the air, the impact of the air
upon it ought to heat it just as warm air would, even though
the air itself were cold. This result of theory has been ex-
perimentally proved by Sir William Thomson, who found that
a thermometer placed in front of a rapidly moving body rose
one degree when the body moved through the air at the rate
of 125 feet per second. With higher velocities, the increase
of temperature was proportional to the square of the velocity,
being 4 degrees with a velocity of 250 feet, 16 degrees with
one of 500 feet per second, and so on. This result is in exact
accordance with the mechanical theory of heat. To find the
effective temperature to which a meteoroid is exposed in mov-
ing through our atmosphere, we divide its velocity in feet per
388 THE SOLAR SYSTEM.
second by 125 ; the square of the quotient will give the tem-
perature in degrees.
Let us apply this principle to the case of the meteoroids.
The earth moves in its orbit at the rate of 98,000 feet per
second ; arid if it met a meteoroid at rest, our atmosphere
would strike it with this velocity. By the rule we have given
for the rise of temperature (98,000 -4- 125)':=: 7S4 a = 600,000
degrees, nearly. This is many times any temperature ever
produced by artificial means. If, as will commonly be the
case, the meteoroid is moving to meet the earth, the velocity,
and therefore the potential temperature, will be higher. We
know that the meteoroids which produce the November show-
ers already described move in a direction nearly opposite that
of the earth with a velocity of 26 miles per second, so that the
relative velocity with which the meteoroids meet our atmos-
phere is 44 miles per second. By the rule we have given,
this velocity corresponds to a temperature of between three
and four million degrees. We do not mean that the meteor-
oids are actually heated up to this temperature, but that the
air acts upon them as if it were heated up to the point men-
tioned ; that is, it burns or volatilizes them in less than a sec-
ond with an enormous evolution of light and heat, just as a
furnace would if heated to a temperature of three million de-
grees. It is not at all necessary that the body should be com-
bustible ; the light and heat of ordinary burning are nothing
at all compared with the deflagration which such a tempera-
ture would cause by acting on the hardest known body. A
few grains of platinum or iron striking the atmosphere with
the velocity of the celestial motions might evolve as much light
and heat as are emitted by the burning of a pint of coal-oil or
several pounds of gunpowder ; and as the whole operation is
over in a second, we may imagine how intense the light must be.
The varied phenomena of aerolites, meteors, shooting-stars,
and meteoric showers depend solely on the number and nat-
ure of the meteoroids which give rise to them. If one of
these bodies is so large and firm as to pass through the atmos-
phere and reach the earth without being destroyed by the po-
METEORS AND SHOOTING -STAES. 389
tential heat, we have an aerolite. As this passage only occu-
pies a few seconds, the heat has not time to penetrate far into
the interior of the body, but expends itself in melting and vol-
atilizing the outer portions. When the body first strikes the
denser portion of the atmosphere, the resistance becomes so
enormous that the aerolite is frequently broken to pieces with
such violence that it seems to explode. Further color is given
to the idea of an explosion by the loud detonation which fol-
lows, so that the explosion is frequently spoken of as a fact,
and as the cause of the detonation. Really, there is good rea-
son to believe that both of these phenomena are due to the
body striking the air with a velocity of ten, twenty, or thirty
miles a second.
If, on the other hand, the meteoroid is so small or so fusible
as to be dissipated in the upper regions of the atmosphere, we
have a common shooting-star, or a meteor of greater or less
brilliancy. Very careful observations have been made from
time to time, with a view of finding the height of these bodies
above the earth at their appearance and disappearance. An
attempt of this kind was made by the Naval Observatory on
the occasion of the meteoric shower of November 13th, 1867,
when Professor Harkness was sent to Richmond to map the
paths of the brighter meteors as seen from that point. By
comparing these paths with those mapped at Washington, the
parallaxes, and thence the altitudes, of these bodies were de-
termined. The lightning-like rapidity with which the mete-
ors darted through their course rendered it impossible to ob-
serve them with astronomical precision ; but the general re-
sult was that they were first seen at an average height of 75
miles, and disappeared at a height of 55 miles. There was
no positive evidence that any meteor commenced at a height
much greater than 100 miles. It is remarkable that this cor-
responds very nearly to the greatest height at which the most
brilliant meteors are ever certainly seen. These phenomena
seem to indicate that our atmosphere, instead of terminating
at a height of 45 miles, as was formerly supposed, really ex-
tends to a height of between 100 and 110 miles.
390 THE SOLAU SYSTEM.
The ordinary meteors, which we may see on every clear
evening, move in every direction, thus showing that their or-
bits lie in all possible positions, and are seemingly scattered
entirely at random. But the case is quite different with those
meteoroids which give rise to meteoric showers. Here we
have a swarm of these bodies, all moving in the same direc-
tion in parallel lines. If we mark, on a celestial globe, the
FIG. 95. Meteor paths, illustrating the radiant point.
apparent paths of the meteors which fall during a shower, or
if we suppose them marked on the celestial sphere, and then
continue them backwards, we shall find them all to meet in
the same point of the heavens. This is called the radiant
point. It always appears in the same position, wherever the
observer is situated, and does not partake of the diurnal ino-
RELATIONS OF COMETS AND METEOROWS. 391
tion of the earth ; that is, as the stars seem to move towards
the west in their diurnal course, the radiant point moves with
them. The point in question is purely an effect of perspec-
tive, being the " vanishing point " of the parallel lines in
which the meteors really move. These lines do not appear
in their real direction in space, but are seen as projected on
the celestial sphere. A good visible illustration of the effect
in question may be afforded by looking upwards and watch-
ing falling snow during a calm. The flakes which are fall-
ing directly towards the observer do not seem to move at all,
while the surrounding flakes seem to separate from them on
all sides. So with the meteoric showers. A meteor coming
directly towards the observer does not seem to move at all,
and marks the radiant point from which all the others seem
to diverge. The great importance of the determination of
the radiant point arises from the fact that it marks the direc-
tion in which the meteors are moving relatively to the earth,
and thus affords some data for determining their orbits.
6. Relations of Comets and Meteoroids.
We have now to mention a series of investigations which
led to the discovery of a curious connection between meteor-
oids and comets. These investigations were commenced by
Professor Newton on the November meteoric showers. Tra-
cing back the historical accounts of these showers to which
we have already alluded, he found that the thirty-three-year
period, which had been suspected by Olbers, was confirmed by
records reaching back a thousand years. Moreover, the show-
ers in question occurred only at a certain time of the year : in
1799 and 1833, it was on November 12th or November 13th.
In other words, the shower occurred only as the earth passed
a certain point of its orbit But this point was found not to
be always the same, the showers being found to occur about
a couple of days earlier every century as they were traced
back. The principal conclusions to which these facts led
were as follows :
1. That the swarm of meteoroids which cause the Novem-
392 THE SOLAR SYSTEM.
ber showers revolve around the sun in a definite orbit, which
intersects the orbit of the earth at the point which the latter
now passes on November 13th.
2. The point of intersection of the two orbits moves for-
wards about 52" per annum, or nearly a degree and a half a
century, owing to a change in the position of the meteoric
orbit.
v 3. The swarm of meteoroids is noc equally scattered all
around their orbit, but the thickest portion extends along
about one-fifteenth of the orbit.
4. The earth meets this swarm, on the average, once in
33.25 years. At other times the swarm has not arrived at
the point of crossing, or has already passed it, and a meteoric
shower cannot occur unless the earth and the swarm cross at
the same time.
Professor Newton did not definitely determine the time of
revolution of the meteors in their orbit, but showed that it
must have one of five values. The greatest of these values,
and the one which it seems most natural to select, is that of
the mean interval between the showers, or 33 J years. Adopt-
ing this period, it would follow that between 1799, when
llumboldt saw the meteoric shower, and 1833, when it was
seen throughout the United States, the swarm of meteoroids
had been flying out as far as the planet Uranus in a very el-
liptical orbit, and returning again. But the periodic time
might also be one year and about eleven days. Then the
group which Humboldt saw on November 12th, 1799, would
not reach the same point of its orbit until November 23d,
1800, when the earth would have passed by. Passing 11 days
later every year, it would make about 33 revolutions in 34
years, and thus would pass about the middle of November
once more, and another shower would occur. In a word, giv-
ing exact numbers, we might suppose that in the period of
33J years the meteoroids made one revolution, or 32, 34J,
65J, or 67 revolutions, and the conditions of the problem
would be equally satisfied.
At the same time, Professor Newton gave a test by which
RELATIONS OF COMETS AND METEOEO1DS. 393
the true time could be determined. As we have said, he
showed that the node of the orbit changed its position 52" a
century, and there could be no doubt that this change was
due to the attraction of the planets. If, then, the effect of
this attraction was calculated for each of the five orbits, it
would be seen which of them would give the required change.
This was done by Professor Adams, of England, and the result
was that the thirty-three-year period, and that alone, was ad-
missible.
These researches of Professor Newton were published in
1864, and ended with a prediction of the return of the shower
on November 13th of one or more of the three following
years probably 1866. This prediction was verified by a re-
markable meteoric shower seen in Europe on that very day,
which, however, was nearly over before it could become visi-
ble in this country. On the same date of the year following,
a shower was visible in this country, and excited great public
interest. From the data derived from the first of these show-
ers, Schiaparelli, an Italian astronomer, was led to the discovery
of a remarkable relation between meteoric and cometary orbits.
Assuming the period of the November meteoroids to be 33J
years, he computed the elements of their orbit from the ob-
served position of the radiant point. A similar computation
was made by Leverrier, and the results were presented to the
French Academy of Sciences on January 21st, 1867.
The exact orbit which these bodies followed through space,
crossing the earth's orbit at one point, and extending out
beyond the planet Uranus at another, was thus ascertained.
But, as these bodies were absolutely invisible, no great inter-
est seemed to attach to their orbit until it was found that a
comet was moving in that very orbit. This was a faint tele-
scopic comet discovered by Tempel, at Marseilles, in Decem-
ber, 1865. It was afterwards independently discovered by
Mr. II. P. Tuttle, at the Naval Observatory, Washington. It
passed its perihelion in January, and, receding from the sun,
vanished from sight in March. It was soon found to move
in an elliptic orbit, but, owing to the uncertainty of observa-
394
THE SOLAR SYSTEM.
tions on such a body,
there was at first some
disagreement as to the
exact periodic time.
The subject was taken
up by Dr. Oppolzer, of
Vienna, who, in Janu-
ary, 1867, was able to
present a definitive or-
bit of the comet, which
was published in the As-
tronomische. Nachriditen
on the 28th of that
month. We now pre-
sent the orbit of the
comet, as found by Op-
polzer, and that of the
meteors, as found by
Leverrier, premising
that these orbits were
computed and publish-
ed within a few days
FIG. 96. Orbit of November meteors and the comet * each other, Without
ofl861 - any knowledge on the
part of either astronomer of the results obtained by the other :
The Comet.
Meteoroids.
Period of revolution
33.18 yrs.
33.25 yrs.
Eccentricity
0.9054
0.9044
Perihelion distance
0.9765
0.9890
Inclination of orbit
162 42'
165 19'
Longitude of the node
51 26'
51 18'
Longitude of perihelion
42 24'
Near node.
The similarity of these orbits is too striking to be the result
of chance. The only element of which the values differ ma-
terially is the inclination, and this difference proceeds from
Leverrier not having used a very exact position of the radiant
point in making his computations. Professor Adams found
by a similar calculation that the inclination of the orbit of the
RELATIONS OF COMETS AND METEOR01DS.
395
tneteoroids was 163 14', only half a degree different from that
of the orbit of Tempel's comet. The result of these investiga-
tions was as follows :
The November meteoric showers arise from the earth encountering
a swarm of particles following
Tempers comet in its orbiL
When this fact came out,
Schiaparelli had been working
on the same subject, and had
come to a similar conclusion
with regard to another group
of meteors. It had long been
known that about August 9th
of every year an unusual num-
ber of meteors shoot forth from
the constellation Perseus. At
times these showers have been
inferior only to those of No-
vember. Thus, on August 9th,
1798, they succeeded each oth-
er so rapidly as to keep the
eye of the observer almost con-
stantly engaged, and several
hundred may nearly always be
counted on the nights of the
9th, 10th, and llth. These
August meteors are remarka-
ble in that they leave trails of
luminous vapor which often
last several seconds. Assum-
ing the orbit of this group to
be a parabola, it was calculated
by Schiaparelli, and is substan-
tially the same with that of a
comet observed in 1862. The
following are the elements of
the OrbitS Of the tWO bodies : FIG. 97.-Orbit of the third comet of 1862.
396 THE SOLAE SYSTEM.
Comet II.,
1862.
August
Meteomids.
Perihelion distance
0.9626
0.9643
Inclination of orbit
113 35'
115 57'
Longitude of the node
137 27'
138 1C'
Longitude of the perihelion
344 41'
343 28'
It appears that the August meteors are caused by a long
stream of bodies following the second comet of 1862 in its
orbit, or, rather, moving in the same orbit with it. The orbit
of this comet is decidedly elliptic; the difference from the
parabola is, however, too small to be determined with great
precision. According to Oppolzer, the period derived from
the observations would be 124 years, which, however, may be
ten years or more in error.
A third striking case of the connection between comets and
meteors which we are showing is afforded by the actual pre-
diction of a meteoric shower on the night of November 27th,
1872. I have already described Biela's comet as first break-
ing into two pieces and then entirely disappearing, as though
its parts had become completely scattered. This is one of
the few cornets which may come very near the earth, the lat-
ter passing the orbit of the comet on November 27th of each
year. By calculation, the comet should have passed the point
of crossing early in September, 1872, while the earth reached
the same point between two and three months later. Judg-
ing from analogy, there was every reason to believe that the
earth would encounter a stream of meteoroids consisting of the
remains of the lost comet, and that a small meteoric shower
would be the result. Moreover, it was shown that the mete-
ors would all diverge from a certain point in the constellation
Andromeda, as the radiant point, because that would be the di-
rection from which a body moving in the orbit of the comet
would seem to come. The prediction was fully verified in
every respect. The meteors did not compare, either in num-
bers or brilliancy, with the great displays of November ; but,
though faint, they succeeded each other so rapidly that the
most casual observer could not fail to notice them, and they
all moved in the predicted direction.
RELATIONS OF COMETS AND METEOEOIDS. 397
That the meteoroids in these cases originally belonged to
the comet, few will dispute. Accepting this, the phenomena of
the November showers lead to the conclusion that the comet
of 1866, with which they are associated, was not an original
member of our system, but has been added to it within a
time which, astronomically speaking, is still recent. The sep-
arate meteoroids which form the stream will necessarily have
slightly different periodic times. Such being the case, they
will, in the course of many re volutions, gradually scatter them-
selves around their entire orbit; and then we shall have an
equal meteoric shower on every 13th of November. This
complete scattering seems to have actually taken place in the
ease of the August meteoroids, since we have nearly the same
sort of shower on every 9th or 10th of August. But in the
case of the November meteors, the stream is not yet scattered
over one-tenth of the orbit. If we suppose that the motions
of the slowest and the swiftest bodies of the stream only dif-
fer by a thousandth part of their whole amount which is not
an unreasonable supposition it would follow that the stream
had only made about 100 revolutions around the sun, and had
therefore been revolving only about 3300 years. Though this
number is purely hypothetical, we may say with confidence
that the stream has not been in existence many thousand
years.
This opinion is strongly supported by the fact that the orbit
of this meteoric comet passes very near that of Ilranus as well
as that of the earth, so that there is reason to believe that it
was introduced into our system by the attraction of one of
these planets, probably of Uranus. If the comet is seen on its
next return, in 1899, we may hope that its periodic time will
be determined with sufficient accuracy to enable us to fix with
some probability the exact date at which Uranus brought it
into our system. Indeed, Leverrier has attempted to do this
already, having fixed upon the year 126 of our era as the
probable date of this event ; but, unfortunately, neither the
position of the orbit nor the time of revolution is yet known
with such accuracy as to inspire confidence in this result.
398 THE SOLAR SYSTEM.
The idea that this November group is something compara-
tively new is strengthened by a comparison with that which
produces the August meteors, where we find a decided mark
of antiquity. Here the swiftest of the group has, in the course
of numerous revolutions, overtaken the slowest, so that the
group is now spread almost equally around the entire orbit.
The time of revolution being, in this case, more than a cen-
tury, this equal distribution would take a much longer time
than in the other case, where the period is only thirty-three
years ; so that we can say, with considerable probability, that
the August group has been in our system at least twenty
times as long as the November group.
7. The Physical Constitution of Comets.
A theory of the physical constitution of comets, to be both
complete and satisfactory, must be founded on the properties
of matter as made known to us here at the surface of the
earth. That is, we must show what forms and what combina-
tions of known substances would, if projected into the celes-
tial spaces, present the appearance of a comet. Now, this has
never yet been completely done. Theories without number
have been propounded, but they fail to explain some of the
phenomena, or explain them in a manner not consistent with
the known laws of matter or force. We cannot stop even to
mention most of these theories, and shall therefore confine our
attention to those propositions which are to some extent sus-
tained by facts, and which, on the whole, seem to have most
probability in their favor.
The simplest form of these bodies is seen in the telescopic
comets, which consist of minute particles of a cloudy or vapor-
ous appearance. Now, we know that masses which present
this appearance at the surface of the earth, where we can ex-
amine them, are composed of detached particles of solid or
liquid matter. Clouds and vapor, for instance, are composed
of minute drops of water, and smoke of very minute particles
of carbon. Analogy would lead us to suppose that the tele-
scopic cornets are of the same constitution. They are gener-
THE PHYSICAL CONSTITUTION OF COMETS. 399
ally tens of thousands of miles in diameter, and yet of such
tenuity that the smallest stars are seen through them. The
strongest evidence of this constitution is, however, afforded by
the phenomena of meteoric showers described in the last sec-
tion. We have seen that these are caused by our atmosphere
encountering the debris of comets, and this debris presents it-
self in the form of detached meteoroids, of very small magni-
tude, but hundreds of miles apart.
The only alternative to this theory is that the comet is a
mass of true gas, continuous throughout its whole extent.
This gaseous theory derives its main support from the spec-
troscope, which shows the spectrum of the telescopic comets
to consist of bright bands, the mark of an incandescent gas.
Moreover, the resemblance of these bands to those produced
by the vapor of carbon is so striking that it is quite common
among spectroscopists to speak of a comet as consisting of
the gas of some of the compounds of carbon. But there are
several difficulties which look insuperable in the way of the
theory that a comet is nothing but a mass of gas. In the
first place, the elastic force of such a mass would cause it
to expand beyond all limits when placed in a position where
there is absolutely no pressure to confine it, as in the. celestial
spaces. Again, a gas cannot, so far as experiment has ever
gone, shine by its own light until it is heated to a high tem-
perature, far above any that can possibly exist at distances
from the sun so great as those at which comets have been
situated when under examination with the spectroscope. Fi-
nally, in the event of a purely gaseous comet being broken
up and dissipated, as in the case of Biela's comet, it is hardly
possible to suppose that it would separate into innumerable
widely detached pieces, as this comet did. The gaseous the-
ory can, therefore, not be regarded as satisfactory. It may be
that comets will hereafter be found to consist of some combi-
nation of solid and gaseous matter, the exact nature of which
is not yet determined ; or it may be that this matter is of a
nature or in a form wholly unlike anything that we are ac-
quainted with or can produce here on the earth. As the case
400 THE SOLAli SYSTEM.
now stands, we must regard the spectrum of a comet as some-
thing not yet satisfactorily accounted for.
When we turn from telescopic comets to those brilliant
ones which exhibit a nucleus and a tail, we can trace certain
operations which are not seen in the case of the others. What
the nucleus is whether it is a solid body several hundred miles
in diameter, or a dense mass of the same materials which com-
pose a telescopic comet we are quite unable to say. But
there can hardly be any reasonable doubt that it is composed
of some substance which is vaporized by the heat of the solar
rays. The head of such a comet, when carefully examined
with the telescope, is found to be composed of successive en-
velopes or layers of vapor; and when these envelopes are
watched from night to night, they are found to be gradually
rising upwards, growing fainter and more indistinct in out-
line as they attain a greater elevation, until they are lost in
the outlying parts of the coma. These rising masses form the
fan-shaped appendage described in a preceding section.
The strongest proof that some evaporating process is going
on from the nucleus of the comet is afforded by the move-
ments of the tail. It has long been evident that the tail could
not be an appendage which the comet carried along with it,
and this for two reasons: first, it is impossible that there could
be any cohesion in a mass of matter of such tenuity that the
smallest stars could be seen through a million of miles of it,
and which, besides, constantly changes its form ; secondly, as
a comet flies around the sun in its immediate neighborhood,
the tail appears to move from one side of the sun to another
with a rapidity which would tear it to pieces, and send the
separate parts flying off in hyperbolic orbits, if the movement
were real. The inevitable conclusion is that the tail is not a
fixed appendage of the comet, which the latter carries with it,
but a stream of vapor rising from it, like smoke from a chim-
ney. As the line of smoke which we now see coming from
the chimney is not the same which we saw a minute ago, be-
cause the latter has been blown away and dissipated, so we do
not see the same tail of a comet all the time, because the mat-
THE PHYSICAL CONSTITUTION OF COMETS. 401
ter which makes up the tail is constantly streaming outwards,
and constantly being replaced by new vapor rising from the
nucleus. The evaporation is, no doubt, due to the heat of the
sun, for there can be no evaporation without heat, and the
tails of comets increase enormously as they approach the sun.
Altogether, a good idea of the operations going on in a comet
will be obtained if we conceive the nucleus to be composed of
water or other volatile fluid which is boiling away under the
heat of the sun, while the tail is a column of steam rising
from it.
We now meet a question to which science has not yet been
able to return a conclusive answer. Why does this mass of
vapor always fly away from the sun ? That the matter of the
comet should be vaporized by the sun's rays, and that the nu-
cleus should thus be enveloped in a cloud of vapor, is perfect-
ly natural, and entirely in accord with the properties of mat-
ter which we observe around us. But, according to all known
laws of matter, this vapor should remain around the liead, ex-
cept that the outer portions would be gradually detached and
thrown off into separate orbits. There is no known tendency
of vapor, as seen on the earth, to recede from the sun, and no
known reason why it should so recede in the celestial spaces.
Various theories have been propounded to account for it ; but
as they do not rest on causes which we have verified in other
cases, they 'must be regarded as purely hypothetical.
The first of these explanations, in the order of time, is due
to Kepler, who conceived the matter of the tail to be driven
off by the impulsion of the solar rays, which thus bleached
the comet as they bleach cloths here. If light were an emis-
sion of material particles, as Newton supposed it to be, this
view would have some plausibility. But light is now con-
ceived to consist of vibrations in an ethereal medium ; and
there is no known way in which they could exert any propel-
ling force on matter. Two or three years ago, it was for
a while supposed that the " radiometer " of Mr. Crookes might
really indicate such an action of the solar rays upon matter
in a vacuum, but it is now found that the action exhibited is
27
402 THE SOLAR SYSTEM.
really due to a minute quantity of air left in the instrument
Had Mr. Crookes shown that the motion of his radiometer
was really due to the impulsion of the solar rays, we might
be led to the remarkable conclusion that Kepler's theory,
though rejected for more than two centuries, was, after all,
quite near the truth.
Sir Isaac Newton, being the author of the emission theory
of light, could not dispute the possibility of Kepler's views
being correct, but nevertheless gave the preference to anoth-
er hypothesis. He conceived the celestial spaces to be filled
with a very rare medium, through which the sun's rays passed
without heating it, as they pass through cold air. But the
comet being warmed up by the rays, the medium surrounding
it is warmed up by contact, and thus a warm current is sent
out from the comet, just as a current of warm air rises from
a heated body on the surface of the earth. This current car-
ries the vapor of the comet with it, and thus gives rise to the
tail in the same way that the current of warm air rising from
a chimney carries up a column of smoke. It has long been
established that there is no medium in the planetary spaces
in which such an effect as this is possible : Newton's theory
is, therefore, no longer considered.
In recent times, Zollner has endeavored to account for the
tail of the comet by an electrical action between the sun and
the vapor rising from the nucleus of the cornet. The various
papers in which he has elaborated his views of the constitu-
tion of comets are marked by profound research ; and we
must regard his theories as those which, on the whole, most
completely explain all the phenomena. But they still lack
the one thing needful to secure their reception : there is no
evidence that the sun acts as an electrified body; and until
such evidence is adduced by experiment, or by observation on
other bodies than comets, the electric theory of the comet's
tail can only be regarded as a more or less probable hypothe-
sis. Indeed, some physicists claim that any such electric ac-
tion in the planetary spaces is impossible. Before any theory
can be definitely settled upon, accurate observations must be
- PHYSICAL CONSTITUTION OF COMETS. 403
made upon the tails of comets with a view of learning the
law according to which the vapor is repelled from the sun.
Such observations were made by Bessel on Halley's comet in
1835, and by various observers on the great comet of 1858.
The former were investigated by Bessel himself, and the lat-
ter by several mathematicians, among them Professor Peirce,
whose results are found hi a paper communicated to the
American Academy in 1859. He found the repulsive force
of the sun upon the particles which form the front edge of
the tail to be 1 times its attractive force upon ordinary
bodies at the same distance. It seemed constantly to diminish
as the back edge of the tail was approached ; but, owing to
the poor definition of this edge, and the uncertainty whether it
was composed of a continuous stream of particles, the amount
of the diminution could not be accurately fixed. The suc-
cessive envelopes were found to ascend uniformly towards
the sun at the rate of about thirty-five miles an hour. Bond,
from a careful examination of all the observations, was led to
the result that the rate of ascent diminished as the height
became greater.
An apparently necessary conclusion from this constant evap-
oration and expulsion of vapor from comets with tails is, that
such bodies are constantly wasting away when in the neigh-
borhood of the sun. This conclusion is strengthened by the
fact that not a single comet of very short period has a consid-
erable tail, the probability being that all the volatile matter
which once went to form the tail has been evaporated. In-
deed, from the descriptions of the old chroniclers, it has been
supposed that Halley's comet had a much more conspicuous
tail at the time of its earliest recorded apparitions than it has
exhibited at its last few returns. There is, however, no neces-
sity for supposing the diminution so rapid as this, for the
amount of matter really necessary to make the most splendid
tail is so extremely small that a comet might lose it a hundred
times over without becoming perceptibly smaller. This con-
stant loss of matter through the tail affords an additional
ground for the view that cornets in general are visitors intro-
404: THE SOLAH SYSTEM.
duced into our system by the action of the planets. If, for
instance, such a comet as Halley's had been a member of our
system for millions of years, and had returned to perihelion a
hundred thousand times, all its volatile matter must long ago
have evaporated.
The question of the mass and density of comets is also one
of those on which it is difficult to reach satisfactory conclu-
sions. We cannot certainly decide from mere telescopic ob-
servation whether the nucleus is a single large body, like a
planet or satellite, or whether it is merely the densest part of
an immense cloud of meteoroids. The mass of nebulous mat-
ter which surrounds the nucleus increases so gradually as we
approach the central parts, that it is hardly possible to decide
where the nucleus begins : the more powerful the telescope,
the smaller the nucleus generally appears. Moreover, in the
same comet, the apparent magnitude of the nucleus is subject
to immense variations, thus showing that it cannot be a solid
body out to its apparent limits. If we considered only this
circumstance, and the general analogy with telescopic comets,
we should say that even the densest part of the comet was
nothing but a cloud of solid or liquid particles so thick that it
looked solid, as a cloud does in our sky. But if this was the
case, as Professor Peirce showed in his investigations of the
comet of 1858, the comets of 1680 and of 1843 must have
been completely pulled apart by the enormous tidal forces
generated by their near approach to the sun. In the opinion
of this investigator, the fact that they went through such an
ordeal shows them to be of metallic density.
The question is frequently asked, What would be the effect
if a comet should strike the earth ? This would depend upon
what sort of a comet it was, and what part of the comet came
in contact with our planet. The latter might pass through
the tail of the largest comet without the slightest effect being
produced, the tail being so thin arid airy that a million miles
thickness of it looks only like gauze in the sunlight. It is
not at all unlikely that such a thing may have happened with-
out ever being noticed. A passage through a telescopic comet
THE ZODIACAL LIGHT. 405
would be accompanied by a brilliant meteoric shower, prob-
ably a far more brilliant one than has ever been - recorded.
No more serious danger would be encountered than that aris-
ing from a possible fall of meteorites. But a collision between
the nucleus of a large comet and the earth might be a serious
matter. If, as Professor Peirce supposes, the nucleus is a solid
body of metallic density, many miles in diameter, the effect
where the comet struck would be terrific beyond conception.
At the first contact in the upper regions of the atmosphere,
the whole heavens would be illuminated with a resplendence
beyond that of a thousand suns, the sky radiating a light which
would blind every eye that beheld it, and a heat which would
melt the hardest rocks. A few seconds of this, while the huge
body was passing through the atmosphere, and the collision at
the earth's surface would in an instant reduce everything there
existing to fiery vapor, and bury it miles deep in the solid
earth. Happily, the chances of such a calamity are so minute
that they need not cause the slightest uneasiness. There is
hardly a possible form of death which is not a thousand times
more probable than this. So small is the earth in comparison
with the celestial spaces, that if one should shut his eyes and
fire a gun at random in the air, the chance of bringing down
a bird would be better than that of a comet of any kind strik-
ing the earth.
8. The Zodiacal Light
This object consists of a very soft, faint column of light,
which may be seen rising from the western horizon after twi-
light on any clear winter or spring evening: it may also be
seen rising from the eastern horizon just before daybreak in
the summer or autumn. It really extends out on each side
of the sun, and lies nearly in the plane of the ecliptic. The
reason it cannot be well seen in the summer and autumn
evenings is, that in our latitudes the course of the ecliptic in
the south-west is, during those seasons, so near the horizon that
the light in question is extinguished by the great thickness of
atmosphere through which it has to pass. Near the equator,
406 THE SOLAR SYSTEM.
where the ecliptic always rises high above the horizon, the
light can be seen about equally well all the year round. It
grows fainter the farther it is from the sun, and can gener-
ally be traced to about 90 from that luminary, when it grad-
ually fades away. But in a very clear atmosphere, between
the tropics, it has been traced all the way across the heavens,
from east to west, thus forming a complete ring.
Such is the zodiacal light as it appears to the eye. Put-
ting its appearances all together, we may see that it is due to
a lens -shaped appendage of some sort surrounding the sun,
and extending out a little beyond the earth's orbit. It lies
very nearly in the plane of the ecliptic, but its exact position
is difficult to determine, not only owing to its indistinct out-
line, but because in northern latitudes the southern edge will
be dimmed by the greater thickness of atmosphere through
which it is seen, and thus the light will look farther north
than it really is. The nature of the substance from which
this light emanates is entirely unknown. Its spectrum has
been examined by several observers, some of whom have re-
ported it as consisting of a single yellow line, and therefore
arising from an incandescent gas. This would indicate a len-
ticular-shaped atmosphere of inconceivable rarity surrounding
the sun, and extending out near the plane of the ecliptic be-
yond the orbit of the earth. But Professor Wright, of Yale
College, who has made the most careful observations of this
spectrum, finds it to be continuous. For several reasons, too
minute to enter into now, this observation seems to the writer
more likely to be correct. Accepting it, we should be led to
the conclusion that the phenomenon in question is due to re-
flected sunlight, probably from an immense cloud of meteor-
oids filling up the space between the earth arid sun. But fur-
ther researches must be made before a conclusive result can
be reached.
PART IV. THE STELLAR UNIVERSE.
INTRODUCTORY REMARKS.
HITHERTO our attention has been principally occupied with
the bodies which surround our sun and make up the solar sys-
tem. Notwithstanding the immense distances at which these
bodies are found, we may regard them, in comparison with the
fixed stars, as an isolated family immediately surrounding us,
since a sphere as large as the whole solar system would only
appear as a point to the vision if viewed from the nearest
star. The space which separates the orbit of Neptune from
the fixed stars and the fixed stars from each other is, so far as
we can learn, entirely void of all visible matter, except occa-
sional waste nebulous fragments of a meteoric or cometary
nature which are now and then drawn in by the attraction of
our sun.
The widest question which the study of the stars presents
to us may be approached in this way : We have seen, in our
system of sun, planets, and satellites, a very orderly and
beautiful structure, every body being kept in its own orbit
through endless revolutions by a constant balancing of gravi-
tating and centrifugal forces. Do the millions of suns and
clusters scattered through space, and brought into view by the
telescope, constitute a greater system of equally orderly struct-
ure ? and, if so, what is that structure ? If we measure the
importance of a question, not by its relations to our interests
jand our welfare, but by the intrinsic greatness of the subject
to which it relates, then we must regard this question as one
of the noblest with which the human mind has ever been
408 THE STELLAR UNIVERSE.
occupied. In piercing the mystery of the solar system, and
showing that the earth on which we dwell w T as only one of
the smaller of eight planets which move around the sun, we
made a great step in the w r ay of enlarging our ideas of the
immensity of creation and of the comparative insignificance
of our sublunary interests. But when, on extending our view,
we find our sun to be but one out of unnumbered millions, we
see that our whole system is but an insignificant part of crea-
tion, and that we have an immensely greater fabric to study.
When we have bound all the stars, nebulae, and clusters which
our telescopes reveal into a single system, and shown in what
manner each stands related to all the others, we shall have
solved the problem of the material universe, considered, not in
its details, but in its widest scope.
From the time that Copernicus showed the stars to be self-
luminous bodies, situated far outside of our solar system, the
question thus presented has occupied the attention of the phil-
osophical class of astronomers. The original view, which has
been the starting-point of all speculation on the subject, we
have described in the Introduction as that of a spherical uni-
verse. The apparent sphericity of the vault of heaven, the
uniformity of the diurnal revolution, and the invariability of
the relative positions of the stars, all combined to strengthen
the idea that the latter were set on the interior surface of a
hollow sphere, having the earth or the sun in its centre. This
sphere constituted the firmament of the ancients, outside of
which was situated the empyrean, or kingdom of fire. Coper-
nicus made no advance whatever on this idea. Galileo and
Kepler seem to have made the first real advance the former
by resolving the Milky Way into stars with his telescope, the
latter by suggesting that our sun might be simply one of nu-
merous stars scattered through space, looking so bright only
on account of our proximity to it. In the problem of the
stellar system this conception held the same important place
which that of the earth as a planet did in the problem of the
solar system. But Kepler was less fortunate than Copernicus
in that he failed to commend his idea, even to his own judg-
INTRODUCTORY EEMARKS. 409
ment. It was by affording a starting-point for the researches
of Kant and Herschel that Kepler's suggestion really bore
fruit.
Notwithstanding the amount of careful research which
Herschel and his successors have devoted to it, we are still
very far from having reached even an approximate solution
of the problem of which we speak. In whatever direction we
pursue it, we soon find ourselves brought face to face with the
infinite in space and time. Especially is this the case when
we seek to know, not simply what the universe is to-day, but
what causes are modifying it from age to age. All the knowl-
edge that man has yet gathered is then found to amount to
nothing but some faint glimmers of light shining here and
there through the seemingly boundless darkness. The glim-
mer is a little brighter for each successive generation, but
many centuries must elapse before we can do much more
than tell how the nearer stars are situated in. space. Indeed,
we see as yet but little hope that an inhabitant of this planet
will ever, from his own observations and those of his prede-
cessors, be able to completely penetrate the mystery in which
the structure and destiny of the cosmos are now enshrouded.
However this may be in the future, all we can do at present
is to form more or less probable conjectures, founded on all
we know of the general character of natural law. In a strictly
scientific treatise, such conjectures would find no place ; and
if we had to grope in absolute darkness, they would be en-
tirely inappropriate in any but a poetical or religious produc-
tion. But the subject is too fascinating to permit us to neg-
lect the faintest light by the aid of which we may penetrate
the mystery; we shall therefore briefly set forth both what
men of the past have thought on the subject, what the science
of to day enables us to assert with some degree of probability,
and what knowledge it wholly denies us. To proceed in sci-
entific order, we must commence by laying a wide foundation
of facts. Our first step will therefore be to describe the heav-
ens as they appear to the naked eye, and as they are seen in
the telescope.
410 TEE STELLAR UNIVERSE.
CHAPTER I.
THE STARS AS THEY ARE SEEN.
1. Number and Orders of Stars and Nebulce.
THE total number of stars in the celestial sphere visible
with the average naked eye may be estimated, in round num-
bers, as 5000. The number varies so much with the perfec-
tion and training of the eye, and with the atmospheric condi-
tions, that it cannot be stated very definitely. When the tele-
scope is pointed at the heavens, it is found that for every star
visible to the naked eye there are hundreds, or even thousands,
too minute to be seen without artificial aid. From the counts
of stars made by Herschel, Struve has estimated that the total
number of stars visible with Herschel's twenty-foot telescope
was about 20,000,000. The great telescopes of modern times
would, no doubt, show a yet larger number ; but a reliable
estimate has not been made. The number is probably some-
where between 30,000,000 and 50,000,000.
At a very early age, the stars were classified according to
their apparent brightness or magnitude. The fifteen brightest
ones were said to be of the first magnitude ; the fifty next in
order were termed of the second magnitude, and so on to the
sixth, which comprised the faintest stars visible to the naked
eye. The number of stars of each order of magnitude be-
tween the north pole and the circle 35 south of the equator
is about as follows :
Of magnitude 1 there are about 14 stars.
2 " 48
3 " 152
4 313
5 <c 854
6 " 2010
Total visible to naked eye , 3391
NUMBER AND ORDERS OF STARS AND NEBULA. 411
This limit includes all the stars which, in the Middle States,
culminate at a greater altitude than 15. The number of the
sixth magnitude which can be seen depends very much upon
the eye of the observer and the state of the sky. The forego-
ing list includes all that can be seen by an ordinary good eye
in a clear sky when there is no moonlight ; but the German
astronomer Heis, from whom these numbers are taken, gives a
list of 1964 more which he believes he can see without a glass.
The system of expressing the brightness of the stars by a
series of numbers is continued to the telescopic stars. The
smallest star visible with a six-inch telescope under ordinary
circumstances is commonly rated as of the thirteenth magni-
tude. On the same scale, the smallest stars visible with the
largest telescopes of the world would be of about the six-
teenth magnitude, but no exact scale for these very faint stars
has been arranged.
Measures of the relative brilliancy of the stars indicate
that, as we descend in the scale of magnitude, the quantity
of light emitted diminishes in a geometrical ratio, the stars
of each order being, in general, between two-fifths and one-
third as bright as those of the order next above them. This
order of diminution is not, however, exact, because the arrange-
ment of magnitudes has been made by mere estimation of in-
dividual observers who may have hit on different and varying
ratios ; but it is a sufficient approach to the truth for common
purposes. From the second to the fifth magnitude the dimi-
nution is probably one -third in each magnitude, after that
about two-fifths. Supposing the ratio two-fifths to be exact,
we find that it would take about
2 stars of the second magnitude to make one of the first.
6
third
16
fourth
40
fifth
100
sixth
10,000
1,000,000
eleventh
sixteenth
The number of stars of the several scales of magnitude
vary in a ratio not far different from the inverse of that of
412 THE STELLAR UNIVERSE.
their brightness, the ratio being a little greater in the case of
the higher magnitudes, and probably a little less in the case
of the lower ones. Thus, we see that there are about three
times as many stars of the second magnitude as of the first,
three times as many of the third as of the second, and after
that something less than three times as many of each magni-
tude as of the magnitude next above. Comparing this with
the table of relative brightness just given, we may conclude
that if all the stars of each magnitude were condensed into a
single one, the brightness of the combined stars thus formed
would not vary extravagantly from one to another until we
had passed beyond the ninth or tenth magnitude. But it is
certain that the brightness would ultimately diminish, because
otherwise there would be no limit to the total amount of light
given by the stars, and the whole heavens would shine like
the sun.
The reader will, of course, understand that this arrange-
ment by magnitude is purely artificial. Really the stars are
of every order of brightness, varying by gradations which are
entirely insensible, so that it is impossible to distinguish be-
tween the brightest star of one magnitude and the faintest of
the magnitude next above it. Hence, those astronomers who
wish to express magnitudes with the greatest exactness, divide
them into thirds or even tenths ; so that, for instance, stars be-
tween the sixth and seventh magnitudes are called 6.1, 6.2,
6.3, and so on to 6.9, according to their brilliancy. Various
attempts have been made to place the problem of the relative
amounts of light emitted by the stars upon a more exact basis
than this old one of magnitudes, but this is a very difficult
thing to do, because there is no way of measuring light except
by estimation with the eye. In order to measure the relative
intensity of two lights, it is necessary to have some instrument
by which the intensity of one or both the lights may be varied
until the two appear to be equal. Instruments for this pur-
pose are known as photometers, and are of various construc-
tions. For comparing the light of different stars, the photom-
eter most used at the present time is that of Zollner. By
NUMBER AND ORDERS OF STARS AND NEBULJE. 413
this instrument the light of the stars, as seen through a small
telescope, is compared both in color and intensity with that of
an artificial star, the light of which can be varied at pleasure.
A complete set of measures with this instrument, including
most of the brighter stars, is one of the wants of astronomy
which we may soon hope to see supplied. The most extended
recent series of photometric estimates with which the writer
is acquainted is that of Professor Seidel, of Munich, which in-
cludes 209 stars, the smallest of which are of the fifth magni-
tude. An interesting result of these estimates is that Sirius
gives us four times as much light as any other star visible in
our latitude.
Catalogues of Stars. In nearly every age in which astron-
omy has flourished catalogues of stars have been made, giving
their positions in the heavens, and the magnitude of each.
The earliest catalogue which has come to us is found in the
"Almagest" of Ptolemy, and is supposed to be that of Hippar-
chus, who flourished 150 years before the Christian era. It
is said, but not on the best authority, that he constructed it in
order that future generations might find whether any change
had in the mean time taken place in the starry heavens. An
examination of the catalogue shows that the constellations pre-
sented much the same aspect two thousand years ago that they
do now. There are two or three stars of his catalogue which
cannot now be certainly identified ; but it is probable that the
difficulty arises from the imperfection of the catalogue, and
from the errors which may have crept into the numerous
transcriptions of it during the sixteen centuries which elapsed
before the art of printing was discovered. The catalogue of
Hipparchus contains only about 1080 stars, so that he could
not have given all that he was able to see. He probably omit-
ted many stars of the smaller magnitudes. The actual num-
ber given in the "Almagest" is still less, being only 1030.
The next catalogue in the order of time is that of Ulugh
Beigh, a son of the Tartar monarch Tamerlane, which dates
from the fifteenth century. For the most part, the stars are
the same as in the catalogue of Ptolemy, only the places were
414 THE STELLAR UNIVERSE.
redetermined from the observations at Samarcand. It con-
tains 1019 stars, eleven less than Ptolemy gives. Tycho Brahe,
having made so great an improvement in the art of observa-
tion, very naturally recatalogued the stars, determining their
positions with yet greater accuracy than his predecessors. His
catalogue is the third and last important one formed before
the invention of the telescope. It contains 1005 stars.
Our modern catalogues may be divided into two classes:
those in which the position of each star in the celestial sphere
(right ascension and declination) is given with all attainable
precision, and those in which it is only given approximately,
so as to identify the star, or distinguish it from others in its
neighborhood. The catalogues of the former class are very
numerous, but the more accurate ones are necessarily incom-
plete, owing to the great labor of making the most exact de-
termination of the position of a star. There are, perhaps,
between ten or twenty thousand stars the positions of which
are catalogued with astronomical precision, and a hundred
thousand more in which, though entire precision is aimed at,
it is not attained. Of the merely approximate catalogues, the
greatest one is the " Sternverzeichniss " of Argelander, which
enumerates all the stars down to the ninth magnitude between
the pole and two degrees south of the equator. The work
fills three thin quarto volumes, and the entire number of stars
catalogued in it exceeds three hundred thousand. This " star
census" is being continued to the south pole at the observa-
tory of Cordoba, South America, by Dr. Gould. Of the mill-
ions of stars of the tenth magnitude and upwards, hardly one
in a thousand is, or can be, individually known or catalogued.
Except as one or another may exhibit some remarkable pecu-
liarity, they must pass unnoticed in the crowd.
Division into Constellations. A single glance at the heavens
shows that the stars are not equally scattered over the sky, but
that great numbers of them, especially of the brighter ones,
are collected into extremely irregular groups, known as con-
stellations. At a very early age the heavens were represented
as painted over with figures of men and animals, so arranged
NUMBER AND ORDERS OF STARS AND NEBULAE. 415
as to include the principal stars of each constellation. There
is no historic record of the time when this was done, nor of the
principles by which those who did it carried out their work;
but many of the names indicate that it was during the heroic
age. Some have sought to connect it with the Argonautic ex-
pedition, from the fact that several heroes of that expedition
were among those thus translated to the heavens ; but this is
little more than conjecture. So little pains was taken to fit
the figures to the constellations that we can hardly suppose
them to have all been executed at one time, or on any well-
defined plan. Quite likely, in the case of names of heroes,
the original object was rather to do honor to the man than to
serve any useful purpose in astronomy. Whatever their ori-
gin, these names have been retained to the present day, al-
though the figures which they originally represented no longer
serve any astronomical purpose. The constellation Hercules,
for instance, still exists ; but it no longer represents the figure
of a man among the stars, but a somewhat irregular portion
of the heavens, including the space in which the ancients
placed that figure. In star-maps, designed for school instruc-
tion and for common use, it is still customary to give these
figures, but they ai*e not generally found on maps designed
for the use of astronomers.
Naming the Stars. The question how to name the individ-
ual stars in each constellation, so as to readily distinguish
them, has always involved some difficulty. In the ancient
catalogues they were distinguished by the part of the figure
representing the constellation in which they were found ; as,
the eye of the Bull, the tail of the Great Bear, the right shoul-
der of Orion, and so on. The Arabs adopted the plan of giv-
ing special names to each of the brighter stars, or adopting
such names from the Greeks. Thus, we have the well-known
stars Sirius, Arcturus, Procyon, Aldebaran, and so on. Most
of these names have dropped entirely out of astronomical use,
though still found on some school maps of the stars. The
system now most in use for the brighter stars was designed by
Bayer, of Augsburg, Germany, about 1610. He published a
416 THE STELLAR UNIVERSE.
set of star-maps, in which the individual stars of each constel-
lation were designated by the letters of the Greek alphabet
a, /3, y, etc. The first letters were given to the brightest stars,
the next ones to the next brightest, and so on. After the
Greek letter is given the Latin name of the constellation in
the genitive case. Thus, Alpha (a) Scorpii, or Alpha of the
Scorpion, is the name of Arcturus, the brightest star in Scor-
pins ; a Lyrse, of the brightest star in the Lyre ; and so on.
We have here a resemblance to our system of naming men,
the Greek letter corresponding to the Christian name, and the
constellation to the surname. When the Greek alphabet was
exhausted, without including all the conspicuous stars, the
Latin alphabet w r as drawn upon.
The Bayer system is still applied to all the stars named by
him. Most of the other stars down to the fifth magnitude are
designated by a system of numbers assigned by Flamsteed in
his catalogue. Yet other stars are distinguished by their num-
bers in some well-known catalogue. When this method fails,
owing to the star not being catalogued, the position in the
heavens must be given.
The Milky Way, or Galaxy. To the naked eye so much of^
the Galaxy as can be seen at one time presents the appearance
of a white, cloud-like arch, resting on two opposite points of
the horizon, and rising to a greater or less altitude, according
to the position of the celestial sphere relative to the observer.
Only half of the entire arch can be seen above the horizon at
once, the other half being below it, and directly opposite the
visible half. Indeed, there is a portion of it which can never
be seen in our latitude, being so near the south pole that it
is always below our horizon. If the earth were removed, or
made transparent, so that we could see the whole celestial
sphere at once, the Galaxy would appear as a complete belt
extending around it. The telescope shows that the Galaxy
arises from the light of countless stars, too minute to be sep-
arately visible with the naked eye. We find, then, that the
telescopic stars, instead of being divided up into a limited
number of constellations, are mostly condensed in the region
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 417
of the Galaxy. They are least numerous in the regions most
distant from the galactic belt, and grow thicker as we ap-
proach it. The more powerful the telescope, the more marked
the condensation is. With the naked eye, the condensation is
hardly noticeable, unless by actual count: a very small tele-
scope will show a decided thickening of the stars in and near
the Galaxy ; while, if we employ the most powerful telescopes,
a large majority of the stars they show are found to lie act-
ually in the Galaxy. In other words, if we should blot out
all the stars visible with a twelve-inch telescope, we should
find that the greater part of the remaining stars were in the
Galaxy. The structure of the universe which this fact seems
to indicate will be explained in a subsequent section.
Clusters. Besides this gradual and regular condensation
towards the galactic belt, occasional condensations of stars
into clusters may be seen. Indeed, some of these clusters are
visible to the naked eye, sometimes as separate stars, like the
Pleiades, but more commonly as milky patches of light, be-
cause the stars are too small to be seen separately. The num-
ber visible in powerful telescopes is, however, much greater.
Sometimes there are hundreds, or even thousands, of stars visi-
ble in the field of the telescope at once ; and sometimes the
number is so great, and the individual stars so small, that they
cannot be counted even in the most powerful telescopes ever
made.
Nebulce. Another class of objects which are found in the
celestial spaces are irregular masses of soft, cloudy light,
which are hence termed nebulae. Many objects which look
like nebulse in small telescopes are found by more powerful
ones to be really star clusters. But, as we shall hereafter
show, many of these objects are not composed of stars at all,
but of immense masses of gaseous matter.
2. Description of the Principal Constellations.
For the benefit of the reader who wishes to make himself
acquainted with the constellations in detail, or to identify any
bright star or constellation which he may see, we present a
4:18 THE STELLAR UNIVERSE.
brief description of the principal objects which may be seen
in the heavens at different seasons, illustrated by five maps,
showing the stars to the fifth magnitude inclusive. The
reader who does not wish to enter into these details can pass
to the next section without any break of the continuity of
thought.
For the purpose of learning the constellations, the star-
maps will be a valuable auxiliary. It will be better to begin
with the northern, or circumpolar, constellations, because these
are nearly always visible in our latitude. The first one to be
looked for is Ursa Major (the Great Bear, or the Dipper), from
which the pole star can always be found by means of the
pointers, as shown in Fig. 2, page 10. Supposing the observer
to look for it at nine o'clock in the evening, he will see it in
various positions, depending on the time of year, namely, in
April and May north of the zenith.
July and August to the west of north, the pointers lowest.
October and November close to the north horizon.
January and February .*.... to the east of north, the pointers highest.
These successive positions are in the same order with those
which the constellation occupies in consequence of its diurnal
motion around the pole. The pointers are in the body of the
bear, while the row of stars on the other end of the constella-
tion forms his tail.
Ursa Minor, or the Little Dipper, is the constellation to
which the pole star belongs. It includes, besides the pole
star, another star of the second magnitude, which lies nearly
in the direction of the tail of Ursa Major.
Cassiopeia, or the Lady in the Chair, is on the opposite side
of the pole from Ursa Major, at nearly the same distance.
The constellation can be readily recognized from its three or
four bright stars, disposed in a line broken into pieces at right
angles to each other. In the ancient mythology, Cassiopeia is
the queen of Cepheus ; and in the constellation she is repre-
sented as seated in a large chair or throne, from which she is
issuing her edicts.
Perseus is quite a brilliant constellation, situated in the
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 419
Milky Way, east* of Cassiopeia, and a little farther from the
pole. It may be recognized by a row of conspicuous stars
extending along the Milky Way, which passes directly through
this constellation.
Other circumpolar constellations are Cepheus, the Camelo-
pard, the Lynx, the Dragon (Draco), and the Lizard ; but they
do not contain any stars so bright as to attract especial atten-
tion. The reader who wishes to learn them can easily find
them by comparing the star-maps with the heavens.
Owing to the annual motion of the sun among the stars, the
constellations which are more distant from the pole cannot be
seen at all times, but must be looked for at certain seasons,
unless inconvenient hours of the night be chosen. We shall
describe the more remarkable constellations as they are seen
by an ' observer in middle north latitudes in four different
positions of the starry sphere. The sphere takes all four of
these positions every day, by its diurnal motion ; but some of
these positions will occur in the daytime, and others late at
night or early in the morning.
First Position, Orion on the Meridian. The constellations
south of the zenith are those shown on Maps II. and III., the
former being west of the meridian, the latter east. This posi-
tion occurs on
December 21st at midnight.
January 21st at 10 o'clock p. M.
February 20th at 8 o'clock P.M.
March 21st at 6 o'clock P.M.
And so on through the year. In this position, Cassiopeia and
Ursa Major are near the same altitude, the former high up in
* In the celestial sphere the points of the compass have, of necessity, a mean-
ing which may seem different from that which we attribute to them on the earth.
North always means towards the north pole ; south, from it ; west, in the direc-
tion of the diurnal motion ; east, in the opposite direction. In Fig. 2, the arrows
all point west, and by examining the figure it will be seen that below the pole
north is upwards, and east is towards the west horizon. Really, these definitions
hold equally true for the earth, the same differences being found between the
points of the compass at different places on the earth here and in China, for in-
stancethat we see on the celestial sphere.
420 THE STELLAR UNIVERSE.
the north-west, the latter in the north-east. The Milky Way
spans the heavens like an arch, resting on the horizon in the
north-north-west and south-south-east. We shall first describe
the constellations in its course.
CygnuSj the Swan, is sinking below the horizon, where the
Milky Way rests upon it in the north-north-west, and only a
few stars of it are visible. It will be better seen at another
season.
Next in order come Cepheus, Cassiopeia, and Perseus, which
we have already described as circumpolar constellations.
Above Perseus lies Auriga, the Charioteer, which may be
readily recognized by a bright star of the first magnitude,
called Capella, the Goat, now a few degrees north-west of the
zenith. Auriga is represented as holding a goat in his arm,
in the body of which this star is situated. About ten degrees
east of Capella is the star /3 Aurigse of the second magnitude ;
while still farther to the east is a group of small stars which
also belongs to the same constellation. The latter extends
some distance south of the zenith.
The Milky Way next passes between Taurus and Gemini,
which we will describe presently, and then crosses the equator
east of Orion, the most brilliant constellation in the heavens,
having two stars of the first magnitude and four of the second.
The former are Betelguese, or a Orionis, which is highest up,
arid may be recognized by its reddish color, and Rigel, or j3
Orionis, a sparkling white star, lower down, and a little to the
west. The former is in the shoulder of the figure, the latter
in the foot. Between the two, three stars of the second mag-
nitude, in a row, form the belt of the warrior.
Canis Minor, the Little Dog, lies just across the Milky Way
from Orion, and may be recognized by the bright star Pro-
cyon, of the first magnitude, due east from Betelguese.
Canis Major, the Great Dog, lies south-east of Orion, and is
easily recognized by Sirius, the brightest fixed star in the heav-
ens. A number of bright stars south and south-east of Sirius
belong to this constellation, making it one of great brilliancy.
As the Milky Way approaches the south horizon, it passes
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 421
through Argo Navis, the Ship Argo, which is partly below the
horizon. It contains Canopus, the next brightest star to Siri-
us ; but this object is below the horizon, unless the observer is
as far south as 35 of north latitude.
We can next trace such of the zodiacal constellations as are
high enough above the horizon. In the west, one-third of the
way from the horizon to the zenith, will be seen Aries, the
Earn, which may be recognized by three stars of the second,
third, and fourth magnitudes, respectively, forming an obtuse-
angled triangle, the brightest star being the highest. The
arrangement of these stars, and of some others of the fifth
magnitude, may be seen by Map II.
Taurus, the Bull, is next above Aries, and may be recog-
nized by the Pleiades, or "seven stars," as the group is com-
monly called. Really there are only six stars in the group
clearly visible to ordinary eyes, and an eye which is good
enough to see seven will be likely to see four others, or eleven
in all. A telescopic view of this group will be given in con-
nection with the subject of clusters of stars. Another group
in this constellation is the Ilyades, the principal stars of which
are arranged in the form of the letter V, one extremity of the
V being formed by Aldebaran, a red star ranked as of the
first magnitude, but not so bright as a Orionis.
Gemini, the Twins, lies east of the Milky Way, and may be
found on the left side of Map II. and the right of Map III.
The brightest stars of this constellation are Castor and Pollux,
or a and ]3, which lie twenty or thirty degrees south-east or
east of the zenith, about one-fourth or one-third of the way
to the horizon. They are almost due north from Procyon;
that is, a line drawn from Procyon to the pole star passes be-
tween them. The constellation extends from Castor and Pol-
lux some distance south and west to the borders of Orion.
Cancer, the Crab, lies east of Gemini, but contains no bright
star. The most noteworthy object within its borders is Prse-
sepe, a group of stars too small to be seen singly, which ap-
pears as a spot of milky light. To see it well, the night must
be perfectly clear, and the moon not in the neighborhood.
422 THE STELLAR UNIVERSE.
Leo, the Lion, contains the bright star Regulus, about two
hours above the eastern horizon. This star, with five or six
smaller ones, forms a sickle, Regulus being the handle. The
sickle is represented as in the breast, neck, and head of the
lion, his tail extending- nearly to the horizon, where it ends at
the star Denebola, now just risen.
Such are the principal constellations visible in the supposed
position of the celestial sphere. If the hour of observation is
different from that supposed, the positions of the constellations
will be different by the amount of diurnal rotation during the
interval. For instance, if, in the middle of March, we study
;he heavens at eight o'clock instead of six, the western stars
kvill be nearer the horizon, the southern ones farther west, and
iie eastern ones higher up than we have described them.
Second Position of the Celestial Sphere. The meridian in
;welve hours of right ascension, near the left-hand edge of
Vlap III., and the right-hand edge of Map IV. The stars on
Vlap III. are west of the meridian, those of Map IV. east of it.
This position occurs on
March 21st at midnight.
April 20th at 10 o'clock.
May 21st at 8 o'clock.
In this position Ursa Major is near the zenith, and Cassiopeia
n the north horizon. The Milky Way is too near the horizon
o be visible ; Orion has set in the west ; and there are no very
conspicuous constellations in the south. Castor and Pollux are
risible in the north-west, at a considerable altitude, and Pro-
yon in the west, about an hour and a half above the horizon,
^eo is west of the meridian, extending nearly to it, while three
tew zodiacal constellations have come into sight in the east.
Virgo, the Virgin, has a single bright star Spica about
he brilliancy of Regulus, now about one hour east of the me-
idian, and a little more than half-way from the zenith to the
:orizon.
Libra, the Balance, has no stars which will attract attention,
lie constellation may be recognized by its position between
r irgo and Scorpius.
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 423
Scorpius, the Scorpion, is just rising in the south-east, and is
not yet high enough to be well seen.
Among the constellations north of the zodiac we have :
Coma Berenices, the Hair of Berenice, now exactly 011 the
meridian, and about ten degrees south of the zenith. It is a
close, irregular group of very small stars, quite different from
anything else in the heavens. In the ancient mythology, Ber-
enice had vowed her hair to the goddess Vemis ; but Jupiter
carried it away from the temple in which it was deposited,
and made it into a constellation.
Bootes, the Bear-keeper, is a large constellation east of Coma.
It is marked by Arcturus, a very bright but somewhat red
star, an hour and a half east of Coma Berenices.
Canes Venatid, the Hunting Dogs, are north of Coma. They
are held in a leash by Bootes, and are chasing Ursa Major
round the pole.
Corona Borealis, the Northern Crown, lies next east of Bootes
in the north-east. It is principally composed of a pretty semi-
circle of stars, supposed to form a chaplet, or crown.
Third Position of the Sphere. The southern constellations
are those shown on Maps IV. and V., those of Map IV. being
west of the meridian, and those of Map V. east of it. This
position occurs on
June 2 1 st at midnight.
July 21st at 10 o'clock.
August 21st at 8 o'clock.
etc etc.
In this position the Milky Way is once more in sight, and
seems to span the heavens, but we do not see the same part
of it which was visible in the first position. Cassiopeia is
now in the north-east, and Ursa Major has passed over to the
north-west. Arcturus is two or three hours high in the west,
and Corona is above it, two or three hours west of the zenith.
Commencing, as in the first position, with the constellations
which lie along the Milky Way, we start upwards from Cas-
siopeia, pass Cepheus and Lacerta, neither of which contains
any striking stars, and then reach
424 THE STELLAR UNIVERSE.
Cygnus, the Swan, now north-east from the zenith, which
may be recognized by four or five stars forming a cross, di-
rectly in the Milky Way. The brightest of these stars some-
what exceeds the brightest ones of Cassiopeia.
Lyra, the Harp, is west and south-west of Cygnns, and near
the zenith. It contains the bright star Vega, or a Lyrse, of
the first magnitude, of a brilliant white color with a tinge of
blue.
Passing south, over Vulpecula, the Little Fox, and Sagitta,
the Arrow, the next striking constellation we reach is
Aquila, the Eagle, now midway between the zenith and the
horizon, and two hours east of the meridian. It contains a
bright star Altair, or a Aquilse situated between two
smaller ones, the row of three stars running nearly north and
south.
We next pass west of the Milky Way, and direct our atten-
tion to a point two hours west of the meridian, and some dis-
tance towards the south horizon. Here we find
Scorpius, the Scorpion, a zodiacal constellation and a quite
brilliant one, containing Antares, or a Scorpii, a reddish star
of nearly the first magnitude, with a smaller star on each side
of it, and a long curved row of stars to the west.
Sagittarius, the Archer, comprises a large collection of sec-
ond-magnitude stars east of Scorpius, and in and east of the
Milky Way, and now extending from the meridian to a point
two hours east of it.
Capricornus, the Goat, another zodiacal constellation, is now
in the south-east, but contains no striking stars. The same
remark applies to Aquarius, the Water-bearer, which has just
risen, and Pisces, the Fishes, partly below the eastern horizon.
Leaving the zodiac again, we find, north of Scorpius and
west of the Milky Way, a very large pair of constellations,
called Ophiuchus, the Serpent-bearer, and Serpens, the Serpent.
Ophiuchus stands with one foot on Scorpius, while his head is
marked by a star of the second magnitude twelve degrees
north of the equator, and now on the meridian. It is, there-
fore, one-third or one-fourth of the way from the zenith to the
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 4:25
horizon. The Serpent, which he holds in his hands, lies with
its tail in an opening of the Milky Way, south-west of Aquila,
while its neck and head are formed by a collection of stars of
the second, third, and fourth magnitudes some distance north
of Scorpius, and extending up to the borders of Bootes.
Hercules is a very large constellation, bounded by Corona
on the west, Lyra on the east, Ophiuchus on the south, and
Draco on the north. It is now in the zenith, but contains no
striking stars.
Draco, the Dragon, lies with his head just north of Hercules,
while his body is marked by a long curved row of stars ex-
tending round the pole between the Great and the Little Bear.
His head is readily recognized by a collection of stars of the
second and third magnitudes which might well suggest such
an object.
Fourth Position of the Sphere. The southern constellations
are now found on Maps V. and II. those of Map V. west of
the meridian, those of Map II. east of it. The times are ;
September 21st at midnight.
October 21st at 10 o'clock.
November 20th at 8 o'clock.
December 21st at G o'clock.
In this position Cassiopeia is just north of the zenith, while
Ursa Major is glimmering in the north horizon. Following
the Milky Way from Cassiopeia towards the west, we shall
cross Cepheus, Cygnus, Lyra, and Aquila, while towards the
east we pass Perseus and Auriga, all of which have been de-
scribed.
In the south, the principal constellation is Pegasus , the Fly-
ing Horse, distinguished by four stars of the second magni-
tude, which form a large square, each side of which is about
fourteen degrees.
Andromeda, her hands in chains, is readily found by a row
of three bright stars extending north-east from the north-east
corner of Pegasus in the direction of Perseus.
Cdus, the Whale, is a large constellation in the south, ex-
tending from the meridian to a point three hours east of it.
426 THE STELLA K VNIVERSE.
Its brightest stars are j3 Ceti, now near the meridian, at an al-
titude of 20, which stands by itself, and a Ceti, about 20 be-
low Aries, which is now about 30 south-east from the zenith.
The reader who wishes to consult the constellations in
greater detail can readily do so by means of the star-maps.
3. New and Variable Stars.
The large majority of stars always appear to be of the same
brightness, though it is quite possible that, if the quantity of
light emitted by a star could be measured with entire preci-
sion, it would be found in all cases to vary slightly, from time
to time. There are, however, quite a number of stars in which
the variation is so decided that it has been detected by com-
paring their apparent brightness with that of other stars at dif-
ferent times. More than a hundred such stars are now known ;
but in a large majority of cases the variation is so slight that
only careful observation with a practised eye can perceive it.
There are, however, two stars in which it is so decided that
the most casual observer has only to look at the proper times,
in order to see it. These are /3 Persei and o Ceti, or Algol
and Mira, to which we might add i) Argus, a star of the south-
ern hemisphere, which exhibits variations of a very striking
character.
Variations of Algol. This star, marked /3 in the constel-
lation Perseus, may be readily found on Maps I. and II., in
right ascension 3 hours and declination 40 23'. When once
found, it is readily recognized by its position nearly in a line
between two smaller stars. The most favorable seasons for
seeing it in the early evening are the autumn, winter, and
spring. In autumn it will, after sunset, generally be low
down in the north-east; in winter, high up in the north, not
far from the zenith; and in spring, low down in the north-
west. Usually it shines as a faint second-magnitude star: on
an accurate scale the magnitude is about 2. But at inter-
vals of a little less than three days, it fades out to the fourth
magnitude for a few hours, and then resumes its usual splen-
dor once more. These changes were first noticed about two
NEW AND VARIABLE STARS. 427
centuries ago, but it was not till 1782 that they were accu-
rately observed. The period is now known to be 2 days, 20
hours, 49 minutes that is, 3 hours 11 minutes less than three
days. It takes about four hours and a half to fade away to
its least brilliancy, and four hours more are spent in recover-
ing its light ; so that there are nine and a half hours during
each period in which its light is below the average. But near
the beginning and end of the variations, the change is very
slow, so that there are not more than five or six hours during
which the ordinary eye would see that the star was any smaller
than usual.
The apparent regularity of this variation of light at first
suggested, as an explanation of its cause, that a large dark
planet was revolving round Algol, and passed over its face
at every revolution, thus cutting off a portion of its light.
This theory accounts very well for the salient features of
the variation. But when the latter came to be studied more
closely and carefully, it was found that there were small irreg-
ularities in the variation which the theory would not well ac-
count for. The period of the variation was found to change a
little at different times, while the star does not lose and recover
its light in the same time as it would if the passage of a dark
body caused the changes.
Another remarkable variable star, but of an entirely differ-
ent type, is o Ceti, or Mira (the Wonderful). It may be found
on Map II., in right ascension 2 hours 12 minutes, declination
3 39 f south. During most of the time this star is entirely
invisible to the naked eye, but at intervals of about eleven
months it shines forth with the brilliancy of a star of the sec-
ond or third magnitude. It is, on the average, about forty
days from the time it first becomes visible until it attains its
greatest brightness, and it then requires about two months to
become invisible ; so that it comes into sight more rapidly
than it fades away. It is expected to attain its greatest brill-
iancy in November, 1877 ; in October, 1878, and so on, about
a month earlier each year; but the period is quite irregular,
ranging from ten to twelve months, so that the times of its
428 THE STELLAR UNIVERSE.
appearance cannot be predicted with certainty. Its maximum
brilliancy is also variable, being sometimes of the second mag-
nitude, and at others only of the third or fourth.
y Argus. Perhaps the most extraordinary known variable
star in the heavens is rj Argus, of the southern hemisphere, of
which the position is, right ascension, 10 hours 40 minutes ;
declination, 59 1' south. Being so far south of the equator,
it cannot be seen in our latitudes, and the discovery and ob-
servations of the variations of its light have been generally
made by astronomers who have visited the southern hemi-
sphere. In 1677, Halley, while at St. Helena, found it to be
of the fourth magnitude. In 1751, Lacaille found that it had
increased to the second magnitude. From 1828 to 1838 it
ranged between the first and second magnitudes. The first
careful observations of its variability were made by Sir John
Herschel while at the Cape of Good Hope. He says: "It
was on the 16th December, 1837, that, resuming the photo-
metrical comparisons, my astonishment was excited by the ap-
pearance of a new candidate for distinction among the very
brightest stars of the first magnitude in a part of the heav-
ens with which, being perfectly familiar, I was certain that no
such brilliant object had before been seen. After a momen-
tary hesitation, the natural consequence of a phenomenon so
utterly unexpected, and referring to a map for its configura-
tion with other conspicuous stars in the neighborhood, I be-
came satisfied of its identity with my old acquaintance, r? Ar-
gus. Its light, was, however, nearly tripled. While yet low,
it equalled Rigel, and, when it attained some altitude, was
decidedly greater."* Sir John states that it continued to in-
crease until January 2d, 1838, when it was nearly matched
with a Centauri. It then faded a little till the close of his
observations in April following, but was still as bright as Al-
debaran. But in 1842 and 1843 it blazed up brighter than
ever, and in March of the latter year was second only to
Sirius. During the twenty-five years following, it slowly but
* ''Astronomical Observations at the Cape of Good Hope," p. 33.
NEW AND VARIABLE STARS. 429
steadily diminished : in 1867 it was barely visible to the naked
eye, and the year following it vanished entirely from the un-
assisted view, arid has not yet begun to recover its brightness.
When we speak of this star as the most remarkable of the
well-known variables, we refer, not to the mere range of its
variations, but to its brilliancy when at its maximum. Sev-
eral cases of equally great variation are known ; but the stars
are not so bright, and therefore would not excite so much no-
tice. Thus, the star R Andromedse varies from the sixth to
the thirteenth magnitude in a pretty regular period of 405
days. When at its brightest, it is just visible to the naked
eye, while only a large telescope will show it when at its min-
imum. A number of others range through five or six orders
of magnitude, but o Ceti is the only one of these which ever
becomes as bright as the second magnitude.
The foregoing stars are the only ones the variations of
which would strike the ordinary observer. Among the hun-
dred remaining ones which astronomers have noticed, j3 Lyrse
is remarkable for having two maxima and two minima of un-
equal brilliancy. If we take it when at its greatest minimum,
we find its magnitude to be 4J. In the course of three days,
it will rise to magnitude 3J. In the course of the week fol-
lowing, it will first fall to the fourth magnitude, and increase
again to magnitude 3J. In three days more it will drop
again to its minimum of magnitude 4 ; the period in which
it goes through all its changes being thirteen days. This pe-
riod is constantly increasing. The changes of this star can
best be seen by comparing it with its neighbor, j Lyras. Soiue-
times it will appear equally bright with the latter, and at other
times a magnitude smaller.*
* In 187f>, Professor Schonfeld, now director of the observatory at Bonn, pub-
lished a complete catalogue of known variable stars, the total number being 143.
The following are the more remarkable ones of his list. The positions are re-
ferred to the ecliptic and equinox of 1875 :
T Cassiopeia) : right ascension, hours 16 minutes 29 seconds; declination, ,55
6'.0 N. This is a case in which a star, having once been observed, was after-
wards found to be missing. Examination showed that it had so far diminished
as to be no longer visible without a larger telescope, and continued observations
430 THE STELLAR UNIVERSE.
New Stars. It was once supposed to be no uncommon occur-
rence for new stars to come into existence and old ones to dis-
appear, the former being looked upon as new creations, and
the disappearances as due to the destruction or annihilation
of those stars which had f ultilled their end in the economy of
nature. The supposed disappearances of stars are, however,
found to have no certain foundation in fact, probably owing
their origin to errors in recording the position of stars actu-
ally existing. It was explained, in treating of Practical As-
tronomy, that the astronomer determines the position of a
body in the celestial vault by observing the clock- time at which
it passes the meridian, and the position of the circle of his in-
showed it to range from the seventh to the eleventh magnitude with a regular
period of 436 days.
B Cassiopeia : right ascension, hours 17 minutes 52 seconds ; declination,
63 27'. N. This is supposed to be the celebrated star which blazed out in
November, 1572, and was so fully described by Tycho Brahe. But the proof of
identity can hardly be considered conclusive, especially as no variation has, of re-
cent years, been noticed in the star.
o Ceti: right ascension, 2 hours 13 minutes 1 second; declination, 3 32'. 7
S. We have already described the variations of this star.
ft Persei, or Algol: right ascension, 3 hours minutes 2 seconds; declina-
tion, 40 28'. 4 N. The variations of this star, which is the most regular one
known, have just been described.
B Aurigae : right ascension, 5 hours 7 minutes 12 seconds; declination, 53
26'.6 N, This star is one of very wide and complex variation, changing from the
sixth to the thirteenth magnitude in a period of about 465 days.
RGeminorum: right ascension, 6 hours 59 minutes 49 seconds; declination,
22 53'. 8 N. This star was discovered by Mr. Hind, of England, and ranges be-
tween the seventh and the twelfth magnitude in a period of 371 days.
U Geminorum : right ascension, 7 hours 47 minutes 41 seconds ; declination,
22 19'. 7 N. An irregular variable, never visible to the naked eye, remarkable
for the rapidity with which it sometimes changes. Schonfeld says that in Feb-
ruary, 1869, it increased three entire magnitudes in 24 hours. The periods of its
greatest brightness have ranged from 75 to 617 days.
q Argus : right ascension, 10 hours 40 minutes 13 seconds ; declination, 59
r.6 S. This remarkable object has already been described.
R Hydrse: right ascension, 13 hours 22 minutes 53 seconds; declination, 22
38'.0 S. The variability of this star was recognized by Maraldi, in 1704. It is
generally invisible to the naked eye, but rises to about the fifth magnitude at
intervals of about 437 days. Its period seems to be diminishing, having been
about 500 days when first discovered.
NEW AND VARIABLE STARS. 431
strument when his telescope is pointed at the object. If he
happens to make a mistake in writing down any of these
numbers if, for example, he gets his clock-time one minute
or five minutes wrong, or puts down a wrong number of de-
grees for the position of his circle he will write down the
position of the star where none really exists. Then, some sub-
sequent astronomer, looking in this place and seeing no star,
may think the star has disappeared, when, in reality, there was
never any star there. Where thousands of numbers have to be
written down, such mistakes will sometimes occur ; and it is to
them that some cases of supposed disappearance of stars are to
be attributed. There have, however, been several cases of ap-
parently new stars coming suddenly into view, of which we
shall describe some of the most remarkable.
T Coronas: right ascension, 15 hours 51 minutes 16 seconds; declination, 26
1C'. 5 N. This is the "new star" which blazed out in the Northern Crown in
I860, as hereafter described. Of late years it has remained between the ninth
and tenth magnitudes without exhibiting any remarkable variations.
T Scorpii : right ascension, 16 hours 9 minutes 36 seconds ; declination, 22
40'. S. This star was discovered by Auwers, in 1860, in the midst of a well-
known cluster. It gradually diminished during the following months, and finally
disappeared entirely among the stars by which it is surrounded.
Serpentarii : right ascension, 17 hours 23 minutes 9 seconds ; declination,
21 22'. 4 S. This is supposed to be the celebrated "new star" seen and de-
scribed by Kepler in 1604, soon to be described.
X Cygni: right ascension, 19 hours 45 minutes 46 seconds ; declination, 32 36'.
N. This star becomes visible to the naked eye at intervals of about 406 days, and
then sinks to the twelfth or thirteenth magnitude, so that only large telescopes will
show it. Its greatest brightness ranges from the fourth to the sixth magnitude.
rj Aquila; : right ascension, 19 hours 46 minutes 6 seconds ; declination,
41'. 2 N. This star varies from magnitude 3^ to 4f, and is therefore one of
those which can readily be observed with the naked eye. Its period is 7 days 4
hours 1 4 minutes 4 seconds.
P Cygni: right ascension, 20 hours 13 minutes 11 seconds; declination, 37
38'. 7 N. This was supposed to be a new star in 1600, when it was first seen
by Janson. During the remainder of the century it varied from the third to the
sixth magnitude; but during two centuries which have since elapsed no further
variations have been noticed, the star being constantly of the fifth magnitude.
/iCephei: right ascension, 21 hours 39 minutes 41 seconds; declination, 58
TJ'.4 N. One of the reddest stars visible to the naked eye in the northern hemi-
sphere. Its magnitude is found to vary from the fourth to the fifth in a very ir-
regular manner.
4:32 THE STELLAR UNIVERSE.
In 1572 an apparently new star showed itself in Cassiopeia.
It was first seen by Tycho Brahe on November llth, when
it had attained the first magnitude. It increased rapidly in
brilliancy, soon becoming equal to Venus, so that good eyes
could discern it in full daylight. In December it began to
grow smaller, and continued gradually to fade away until the
following May, when it disappeared entirely. This was forty
years before the invention of the telescope. Tycho has left us
an extended treatise on this most remarkable star.
In 1604 a similar phenomenon was seen in the constella-
tion Ophiuchus. The star was first noticed in October of that
year, when it had attained the first magnitude. In the follow-
ing winter it began to wane, but remained visible during the
whole year 1605. Early in 1606 it faded away entirely, hav-
ing been visible for more than a year. A very full history of
this star has been left to us by Kepler.
The most striking recent case of this kind was in May,
1866, when a star of the second magnitude suddenly appeared
in Corona Borealis. On the llth and 12th of that month it
was remarked independently by at least five observers in Eu-
rope and America, one of the first being Mr. Farquhar, of the
United States Patent-office. Whether it really blazed out as
suddenly as this would indicate has not been definitively set-
tled. If, as would seem most probable, it was several days
attaining its greatest brilliancy, then the only person known
to have seen it was Mr. Benjamin Hallowell, a well-known
teacher near Washington, whose testimony is of such a nature
that it is hard to doubt that the star was visible several days
before it was generally known. On the other hand, Schmidt,
of Athens, asserts in the most positive manner that the star
was not there on May 10th, because he was then scanning
that part of the heavens, and would certainly have noticed it.
However the fact may have been in this particular case, it is
noteworthy that none of the new stars we have described were
noticed until they had nearly or quite attained their greatest
brilliancy, a fact which gives color to the view that they have
all blazed up with great rapidity.
NEW AND VARIABLE STAltS. 433
In November, 1876, a new star of the third magnitude was
noticed by Schmidt, of Athens, in the constellation Cygnus.
It soon began to fade away, and disappeared from the unaided
vision in a few weeks. The position of the constellation Cyg-
nus becomes so unfavorable for observation in November that
very few people got a sight of this object.
The view that these bodies may be new creations, designed
to rank permanently among their fellow-stars, is completely
refuted by their transient character, if by nothing else. Their
apparently ephemeral existence is in striking contrast to the
permanency of the stars in general, which endure from age to
age without any change whatever. They are now classified
by astronomers among the variable stars, their changes being
of a very irregular and fitful character. There is no serious
doubt that they were all in the heavens as very small stars
before they blazed forth in this extraordinary manner, and
that they are in the same place yet. The position of the star
of 1572 was carefully determined by Tycho Brahe; and a
small telescopic star now exists within V of the place com-
puted from his observations, and is probably the same. The
star of 1866 was found to have been recorded as one of the
ninth magnitude in Argelander's great catalogue of the stars
of the northern hemisphere, completed several years before.
After blazing up in the way we have described, it gradually
faded away to its former insignificance, and has shown no
further signs of breaking forth again. There is a wide differ-
ence between these irregular variations, or break! ng-f or th of
light, on a single occasion in the course of centuries, and the
regular changes of Algol and ]3 Lyras. But the careful obser-
vations of the industrious astronomers who have devoted them-
selves to this subject have resulted in the discovery of stars
of nearly every degree of irregularity between these extremes.
Some of them change gradually from one magnitude to another,
in the course of years, without seeming to follow any law what-
ever, while in others some tendency to regularity can be faintly
traced. The best connecting link between new and variable stars
is, perhaps, afforded by ?j Argus, which we have just described.
^
434 THE STELLAR UNIVERSE.
It is probable that the variations of light of which we have
spoken are the result of operations going on in the star itself,
which, it must be remembered, is a body of the same order of
magnitude and brilliancy with our sun, and that these opera-
tions are analogous to those which produce the solar spots. It
was shown in the chapter on the sun that the frequency of
solar spots shows a period of eleven years, during one portion
of which there are frequently no spots at all to be seen, while
during another portion they are very numerous. Hence, if
an observer so far away in the stellar places as to see our sun
like a star, could, from time to time, make exact measures of
the amount of light it emitted, he would find it to be a vari-
able star, with a period of eleven years, the amount of light
being least when we see most spots, and greatest when there
are few spots. The variation would, indeed, be so slight that
we could not perceive it with any photometric means which
we possess, but it would exist nevertheless. Now, the general
analogies of the universe, as well as the testimony of the spec-
troscope, lead us to believe that the physical constitution of
the sun and the stars is of the same general nature. We may
therefore expect that, as we see spots on the sun which vary
in form, size, and number from day to day, so, if we could
take a sufficiently close view of the faces of the stars, we
should, at least in some of them, see similar spots. It is also
likely that, owing to the varying physical constitution of these
bodies, the number and extent of the spots might be found to
be very different in different stars. In the cases in which the
spots covered the larger portion of the surface, their variations
in .number and extent would alone cause the star to vary in
light, from time to time. Finally, we have only to suppose
the same kind of regularity which we see in the eleven-year
cycle of the solar spots, to have a variation in the brightness
of a star going through a regular cycle, as in the case of Algol
and Mira Oeti.
The occasional outbursts of stars which we have described,
in which their light is rapidly increased a hundred-fold, would
seem not to be accounted for on the spot theory, without car-
NEW AND VARIABLE STARS. 435
rying this theory to an extreme. It would, in fact, if not
modified, imply that ninety-nine parts of the surface out of a
hundred were ordinarily covered with spots, and that on rare .
occasions these spots all disappeared. But the spectroscopic
observations of the star of 1866 showed an analogy of a little
different character with operations going on in our sun. Mr.
Huggins found the spectrum of this star to be a continuous
one, crossed by bright lines, the position of which indicated
that they proceeded partly or wholly from glowing hydrogen.
The continuous spectrum was also crossed by dark absorption
lines, indicating that the light had passed through an atmos-
phere of comparatively cool gas. Mr. Hnggins's interpreta-
tion of this is that there was a sudden and extraordinary out-
burst of hydrogen gas from the star which, by its own light,
as well as by heating up the whole surface of the star, caused
the immense accession of brilliancy. Now, we have shown
that the red flames seen around the sun during a total eclipse
are caused by eruptions of hydrogen from his interior ; more-
over, these eruptions are generally connected with faculse, or
portions of the sun's disk several times more brilliant than the
rest of the photosphere. Hence, it is not unlikely that the
blazing-forth of this star arose from an action similar to that
which produces the solar flames, only on an immensely larger
scale.
We have thus in the spots, faculae, and protuberances of
the sun a few suggestions as to what is probably going on in
those stars which exhibit the extraordinary changes of light
which we have described. Is there any possibility that our
sun may be subject to such outbursts of light and heat as
those we have described in the cases of apparently new and
temporary stars ? We may almost say that the continued ex-
istence of the human race is involved in this question ; for if
the heat of the sun should, even for a few days only, be in-
creased a hundred-fold, the higher orders of animal and veg-
etable life would be destroyed. We can only reply to it that
the general analogies of nature lead us to believe that we
need not feel any apprehension of such a catastrophe. Not
436 THE STELLAR UNIVERSE.
the slightest certain variation of the solar heat has been de-
tected since the invention of the thermometer, and the gen-
eral constancy of the light emitted by ninety-nine stars out of
every hundred may inspire us with entire confidence that no
sudden and destructive variation need be feared in the case
of our sun.
4. Double Stars.
Telescopic examination shows that many stars which seem
single to the naked eye are really double, or composed of a
pair of stars lying side by side. There are in the heavens
several pairs of stars the components of which are so close
together that, to the naked eye, they seem almost to touch
each other. One of the easiest and most beautiful of these
is in Taurus, quite near Aldebaran. Here the two stars 1
Tauri and 2 Tauri are each of the fourth magnitude. An-
other such pair is a Capricorni, in which the two pairs are un-
equal. Here an ordinary eye has to look pretty carefully to
see the smaller star. Yet another pair is e Lyrse, the com-
ponents of which are so close that only a good eye can dis-
tinguish them. These pairs, however, are not considered as
double stars in astronomy, because, although to the naked eye
they seem so close, yet, when viewed in a telescope of high
power, they are so wide apart that they cannot be seen at the
same time. The telescopic double stars are formed of com-
ponents only a few seconds apart ; indeed, in many cases, only
a fraction of a second. The large majority of those which
are catalogued as doubles range from half a second to fifteen
seconds in distance. When they exceed the latter limit, they
are no longer objects of special interest, because they may
be really without any connection, and appear together only
because they lie in nearly the same straight line from our
system.
The most obvious question which suggests itself here is
whether in any case there is any real connection between the
two stars of the pair, or whether they do not appear close to-
gether, simply because they chance to lie on nearly the same
DOUBLE STAHS. 437
straight line from the earth. That some stars do appear dou-
ble in this way there is no doubt, and such pairs are called
" optically double. 5 ' But notwithstanding the immense num-
ber of visible stars, the chance of many pairs falling within
a few seconds of each other is quite small ; and the number
of close double stars is so great as to preclude all possibility
that they appear together only by chance. If any further
proof was wanted that the stars of these pairs are really phys-
ically connected, and therefore close together in reality as well
as in appearance, it is found in the fact that many of them
constitute systems in which one revolves round the other, or,
to speak more exactly, in which each revolves round the cen-
tre of gravity of the pair. Such pairs are called Unary sys-
tems, to distinguish them from those in which no such revolu-
tion has been observed. The revolution of these binary sys-
tems is generally very slow, requiring many centuries for its
accomplishment ; and the slower the motion, the longer it
will take to perceive and determine it. Generally it has been
detected by astronomers of one generation comparing their
observations with those of their predecessors ; for instance,
when the elder Struve compared his observations with those
of Ilerschel, and when Dawes or the younger Struve compared
with the elder Struve, a great number of pairs were found to
be binary. As every observer is constantly detecting new
cases of motion, the number of binary systems known to as-
tronomers is constantly increasing.
A brief account of the manner in which these objects are
measured may not be out of place. For the purpose in ques-
tion, the eye-piece of the telescope must be provided with a
" filar micrometer," the important part of which consists of a
pair of parallel spider-lines, one of which can be moved side-
ways by a very fine screw, and can thus be made to pass back
and forth over the other. The exact distance apart of the
lines can be determined from the position of the screw. The
whole micrometer turns round on an axis parallel to the tel-
escope, the centre of which is in the centre of th field of
view. To get the direction of one star from the other, the ob-
438 THE STELLAR UNIVERSE.
server turns the micrometer round until the spider-lines are
parallel to the line joining the two stars, as shown in Fig. 98,
and he then reads the position circle. Knowing what the
position circle reads when he turns the wires so that the star
shall run along them by its diurnal motion, the difference of
the two angles shows the angle which the line joining the
two stars makes with the celestial parallel. To obtain the
distance apart of the stars, the observer turns the micrometer
90 from the position in Fig. 98, and then turns the screw and
moves the telescope, until each star is bisected by one of the
wires, as shown in Fig. 99. The position of the wires is then
interchanged, and the measure is repeated. The mode in
N
FIG. 98. FIG. 99. FIG. 100.
which the direction of one star from another is reckoned is
this: Imagine a line, SN, in Fig. 100, drawn due north from
the brighter star, and another, SP, drawn through the smaller
star. Then the angle NSP which these two lines make with
each other, counted from north towards east, is the position
angle of the stars, the changes in which show the revolution
of one star around the other.
In a few of the binary systems the period is so short that
a complete revolution, or more, of the two stars round eacli
other has been observed. As a general rule, the pairs which
have the most rapid motion are very close, and therefore of
comparatively recent discovery, and difficult to observe. One
or two are suspected to have a period of less than thirty years,
but they are very hard to measure.
Binary /Systems of Short Period. The following table shows
DOUBLE STARS.
431)
the periods of revolution in the case of those stars which have
been observed through a complete revolution, or of which the
periods have been well determined :
42 Comas 26 years.
K Ilerculis 35
Struve, 3121 40
V Corona* 40
Sirius 50
Cancri 58
Ursae Majoris 03 years.
r\ Corona) Borealis (>7
a Centauri 77
fj, Ophiuchi..... 92
\ Ophiuchi 9G
Scorpii... 1)8
Two or three others are suspected to move very rapidly, but
they are so very close and difficult that it is only on favora-
ble occasions that they can be seen to be double. One of
the most remarkable stars in this list is Sirius, the period of
which is calculated, not from the observations of the satel-
lite, but from the motion of Sirius itself. It has long been
known that the proper motion of this star is subject to cer-
tain periodic variations ; and, on investigating these varia-
tions, it was found by Peters and Auwers that they could be
completely represented by supposing that a satellite was re-
volving around the planet in a certain orbit. The elements
of this orbit were all determined except the distance of the
satellite, which did not admit of determination. Its direction
could, however, be computed from time to time almost as ac-
curately as if it were actually seen with the telescope. But,
before the time of which we speak, no one had ever seen it.
Indeed, although many observers must have examined Sirius
from time to time with good telescopes, it is not likely that
they made a careful search in the predicted direction.
Such was the state of the question until February, 1862,
when Messrs. Alvan Clark & Sons, of Oambridgeport, were
completing their eighteen-inch glass for the Chicago Observa-
tory. Turning the glass one evening on Sirius, for the pur-
pose of trying it, the practised eye of the younger Clark soon
detected something unusual. " Why, father," he exclaimed,
" the star has a companion !" .The father looked, and there
was a faint companion due east from the bright star, and dis-
tant about 10". This was exactly the predicted direction for
MO THE STELLAR UNIVERSE.
that time, though the discoverers knew nothing of it. As the
news went round the world, all the great telescopes were
pointed on Sirius, and it was now found that when observers
knew where the companion was, many telescopes would show
it. It lay in the exact direction which theory had predicted
for that time, and it was now observed with the greatest inter-
est, in order to see whether it was moving in the direction of the
theoretical satellite. Four years' observation showed that this
was really the case, so that hardly any doubt could remain that
this almost invisible object was really the body which, by its at-
traction and revolution around Sirius, had caused the inequal-
ity in its motion. At the same time, the correspondence has
not since proved exact, the observed companion having moved
about half a degree per annum more rapidly than the theo-
retical one. This difference, though larger than was expected,
is probably due to the inevitable errors of the very delicate
and difficult observations from which the movements of the
theoretical companion were computed.
The visibility of this very interesting and difficult object
depends almost as much on the altitude of Sirius and the state
of the atmosphere as on the power of the telescope. When
the images of the stars are very bad, it cannot be seen even
in the great Washington telescope, while there are cases of its
being seen under extraordinarily favorable conditions with tel-
escopes of six inches aperture or less. These favorable condi-
tions are indicated to the naked eye by the absence of twinkling.
A case of the same kind, except that the disturbing satellite
lias not been seen, is found in Procyon. Bessel long ago sus-
pected that the position of this star was changed by some at-
tracting body in its neighborhood, but he did not reach a defi-
nite conclusion on the subject. Auwers, having made a care-
ful investigation of all the observations since the time of Brad-
ley, found that the star moved around an invisible centre 1"
distant, which was probably the centre of gravity of tue star
and an invisible satellite. This satellite has been carefully
searched for with great telescopes during the last few years,
but without success.
CLUSTERS OF STARS.
Triple and Multiple Stars. Besides double stars, groups
of three or more stars are frequently found. Such objects
are known as triple, quadruple, etc. They commonly occur
through one of the stars of a wide pair being itself a close
double star, and very often the duplicity of the component
has not been discovered till long after it was known to form
one star of a pair. For instance, jm Herculis was recognized
as a double star by Sir W. Herschel, the companion star being
about 30" distant, and much smaller than n itself. In 1856,
Mr. Alvan Clark, trying one of his glasses upon it, found that
the small companion was itself double, being composed of two
nearly equal stars, about V apart. This close pair proves to
be a binary system of short period, more than half a revolu-
tion of the two stars around each other having been made
since 1856. Another case of the same kind is y Andromedsa,
which was found by Herschel to have a companion about 10"
distant, while Struve found this companion to be itself double.
Many double and multiple stars are interesting objects for
telescopic examination. We give in the Appendix a list of
the more interesting or remarkable of them.
5. Clusters of Stars.
A very little observation with the telescope will show that
while the brighter stars are scattered nearly equally over the
whole celestial vault, this is not the case with the smaller ones.
A number of stars which it is not possible to estimate are
found to be aggregated into clusters, in which the separate
stars are so small and so numerous that, with insufficient tele-
scopic power, they present the appearance of a mass of cloudy
light. We find clusters of every degree of aggregation. At
one extreme we may place the Pleiades, or "seven stars"
which form so well-known an object in our winter sky, in
which, however, only six of the stars are plainly visible to the
naked eye. There is an old myth that this group originally
consisted of seven stars, one of which disappeared from the
heavens, leaving but six. But a very good eye can even now
see eleven when the air is clear, and the telescope shows from
442 TEE STELLAR UNIVERSE.
fifty to a hundred more, according to its power. We present a
view of this group as it appears through a small telescope.
No absolute dividing-line can be drawn between such wide-
ly extended groups as the Pleiades and the densest clusters.
Fio. 101. Telescopic view of the Pleiades, after Engelmann. The six larger stars are those
eawily seen by ordinary eyes without a telescope, while the four next in size, having
four rays each, can be seen by very good eyes. About au inch from the upper right-
hand corner is a pair of small stars which a very keen eye can see as a single star.
The cluster Praesepe, in the constellation Cancer (Map III.,
right ascension, 8 hours 20 minutes; declination, 20 10' N.),
is plainly visible to the naked eye on a clear, moonless night,
as a nebulous mass of light. Examined with a small tele-
CLUSTERS OF STARS. 448
scope, it is found to consist of a group of stars, ranging from
the seventh or eighth magnitude upwards. For examination
with a small telescope, one of the most beautiful groups is in
the constellation Perseus (Map I., right ascension, 2 hours 10
minutes ; declination, 57 N.). It is seen to the best advantage
with a low magnifying power, between twenty-five and fifty
times, and may easily be recognized by the naked eye as a
little patch of light.
The heavens afford no objects of more interest to the con-
templative mind than some of these clusters. Many of them
are scTclistant that the most powerful telescopes ever made
show them only as a patch of star-dust, or a 'mass of light so
faint that the separate stars cannot be distinguished. Their
distance from ns is such that they are beyond, not only all
onr means of measurement, but all our powers of estimation.
Minute as they appear, there is nothing that we know of to
prevent our supposing each of them to be the centre of a
group of planets as extensive as our own, and each planet to
be as full of inhabitants as this one. We may thus think of
them as little colonies on the outskirts of creation itself, and
as we see all the suns which give them light condensed into
one little speck, we might be led to think of the inhabitants
of the various systems as holding intercourse witli each other.
Yet, were we transported to one of these distant clusters, and
stationed on a planet circling one of the suns which compose
it, instead of finding the neighboring suns in close proximity,
we should only see a firmament of stars around us, such as we
see from the earth. Probably it would be a brighter firma-
ment, in which so many stars would glow with more than the
splendor of Sirius, as to make the night far brighter than
ours ; but the inhabitants of the neighboring worlds would as
completely elude telescopic vision as the inhabitants of Mars
do here. Consequently, to the inhabitants of every planet in
the cluster, the question of the plurality of worlds might be
us insolvable as it is to ns.
To give the reader an idea what the more distant of these
star clusters looks like, we present two views from Sir John
444
THE STELLAR UNIVERSE.
Herschel's observations at the Cape of Good Hope. Fig. 102
shows the cluster numbered 2322 in Herschel's catalogue, and
known as 47 Toucani. That astronomer describes it as "a
most glorious globular cluster, the stars of the fourteenth mag-
nitude immensely numerous. It is compressed to a blaze of
light at the centre, the diameter of the more compressed part
being 30" in right ascension." Fig. 103 is No. 3504 of Her-
schel : " The noble globular cluster w Centauri, beyond all
comparison the richest and largest object of the kind in the
heavens. The stars are literally innumerable, and as their
North.
FIG. 102. Cluster 47 Toucani. Right aecen- FIG. 103. Cluster o> Centauri. Right ascen-
sion, hours IS minutes ; declination, slow, 13 hours 20 minutes ; declination,
72 45' S. 46 52' S.
total light when received by the naked eye aft'ects it hardly
more than a star of the fifth or fourth to fifth magnitude, the
minuteness of each star may be imagined."
6. Nebulce.
Nebulae appear to us as masses of soft diffused light, of
greater or less extent. Generally these masses are very ir-
regular in outline, but a few of them are round and well-
defined. These are termed planetary nebulce. It may some-
times be impossible to distinguish between star clusters and
nebulae, because when the power of the telescope is so low
that the separate stars of a cluster cannot be distinguished,
they will present the appearance of a nebula. To the naked
eye the cluster Prsesepe, described in the last chapter, looks
NEBULAE. 445
exactly like a nebula, though a very small telescope will re-
solve it into stars. The early observers with telescopes de-
scribed many objects as nebulae which the more powerful in-
struments of Herschel showed to be clusters of stars. Thus
arose the two classes of resolvable and irresolvable nebulae,
the first comprising such as could be resolved into stars, and
the second such as could not. It is evident, from what we
have just said, that this distinction would depend partly on
the telescope, since a nebula which was irresolvable in one
telescope might be resolvable in another telescope of greater
power. This suggests the question whether all nebulae may
not really be clusters of stars, those which are irresolvable ap-
pearing so merely because their distance is so great that the
separate stars which compose them cannot be distinguished
with our most powerful telescopes. If this were so, there
would be no such thing as a real nebula, and everything
which appears as such should be classified as a star cluster.
The spectroscope, as we shall presently show, has settled this
question, by showing that many of these objects are immense
masses of glowing gas, and therefore cannot be stars.
Classification and Forms of Nebulae. The one object of this
class which, more than all others, has occupied the attention
of astronomers and excited the wonder of observers, is the
great nebula of Orion, It surrounds the middle of the three
stars which form the sword of Orion. Its position may be
found on Maps II. and III., in right ascension 5 hours 28
minutes, declination 6 S. A good eye will perceive that
this star, instead of looking like a bright point, as the other
stars do, has an ill-defined, hazy appearance, due to the sur-
rounding nebulae. This object was first described by Iluy-
ghens in 1659, as follows :
" There is one phenomenon among the fixed stars worthy
of mention which, so far as I know, has hitherto been noticed
by no one, and indeed cannot be well observed except with
large telescopes. In the sword of Orion are three stars quite
close together. In 1656, as I chanced to be viewing the mid-
dle one of these with the telescope, instead of a single star,
446 THE STELLAR VNIVEIiSE.
twelve showed themselves (a not uncommon circumstance).
Three of these almost touched each other, and, with four oth-
ers, shone through a nebula, so that the space around them
seemed far brighter than the rest of the heavens, which was
entirely clear, and appeared quite black, the effect being that
of an opening in the sky, through which a brighter region
was visible."*
Fio. 104. The great nebula of Orion, as drawn by Trouvelot with the twenty-six-inch
Washington telescope.
Since that time it lias been studied with large telescopes
by a great number of observers, including Messier, the two
* Systema Saturnium, p. 8. The last remark of Huyghens seems to have pro-
duced the impression that he or some of the early observers considered the nebula;
to be real openings in the firmament, through which they got glimpses of the
glory of the empyrean. But it may be doubted whether the old ideas of the firma-
ment and the empyrean were entertained by any astronomer after the invention
of the telescope, and there is nothing in the remark of Huyghens to indicate that
he thought the opening really existed. His words are rather obscure.
NEBULA. 447
Ilerschels, Rosse, Struve, and the Bonds. The representation
which we give in Fig. 104 is from a drawing made by Mr.
Trouvelot with the great Washington telescope. In brilliancy
and variety of detail it exceeds any other nebula visible in
the northern hemisphere. The central point of interest is oc-
cupied by four comparatively bright stars, easily distinguished
by a small telescope with a magnifying power of 40 or 50,
combined with two small ones, requiring a nine-inch telescope
to be well seen. The whole of these form a sextuple group,
included in a space a few seconds square, which alone would
be an interesting and remarkable object. Besides these, the
nebula is dotted with so many stars that they would almost
constitute a cluster by themselves.
In the winter of 1864-'65, the spectrum of this object was
examined independently by Secchi and Huggins, who found
that it consisted of three bright lines, and hence concluded
that the nebula was composed, not of stars, but of glowing
gas. The position of one of the lines was near that of a line
of nitrogen, while another seemed to coincide with a hydrogen
line. There is, therefore, a certain probability that this object
is a mixture of hydrogen and nitrogen gas, though this is a
point on which it is impossible to speak with certainty.
Another brilliant nebula visible to the naked eye is the
great one of Andromeda (Maps II. and V., right ascension,
hours 35 minutes ; declination, 40 K). The observer can
see at a glance with the naked eye that this is not a star, but
a mass of diffused light. Indeed, untrained observers have
sometimes very naturally mistaken it for a comet.* It was
first described by Marine, in 1614, who compared its light to
that of a candle shining through horn. This gives a very
good idea of the singular impression it produces, which is that
of an object not self-luminous, but translucent, and illuminated
by a very brilliant light behind it. With a small telescope, it
* A ship-captain who had crossed the Atlantic once visited the Cambridge Ob-
servatory, to tell Professor Bond that he had seen a small comet, which remained
in sight during his entire voyage. The object proved to be the nebula of An-
dromeda.
448 THE STELLAR UNIVERSE.
is easy to imagine it to be a solid like horn ; but with a large
one, the effect is much more that of a great mass of matter,
like fog or mist, which scatters and reflects the light of a brill-
iant body in its midst That this impression can be correct,
it would be hazardous to assert; but the result of a spectrum
FIG. 105. The annular nebula in Lyra. Drawn by Professor E. S. Holden.
analysis of the light of the nebula certainly seems to favor it.
Unlike most of the nebulae, its spectrum is a continuous one,
similar to the ordinary spectra from heated bodies, thus indi-
cating that the light emanates, not from a glowing gas, but
from matter in the solid or liquid state. This would suggest
NEBULA
the idea that the object is really an immense star- cluster, so
distant that the most powerful telescopes cannot resolve it.
Though we cannot positively deny the possibility of this, yet
in the most powerful telescopes the light fades away so softly
and gradually that no such thing as a resolution into stars
seems possible. Indeed, it looks less resolvable and more like
a gas in the largest telescopes than in those of moderate size.
If it is really a gas, and if the spectrum is continuous through-
out the whole extent of the nebula, it would indicate either
that it shone by reflected light, or that the gas was subjected
to a great pressure almost to its outer limit, which hardly seems
possible. But, granting that the light is reflected, we cannot
say whether it originates in a single bright star or in a num-
ber of small ones scattered about through the nebula.
Another extraordinary object of this class is the annular, or
ring-nebula of Lyra, situated in that constellation, about half-
way between the stars j3 and 7. In the older telescopes it
looked like a perfect ring; but the larger ones of modern tim0s
show that the opening of the ring is really filled with nebu-
lous light ; in fact, that we have here an object of very regular
outline, in which the outer portion is brighter than the inte-
rior. Its form is neither circular nor exactly elliptic, but egg-
shaped, one end being more pointed than the other. A mod-
erate-sized telescope will show it, but a large one is required
to see it to good advantage.
It would appear, from a comparison of drawings made at
different dates, that some nebulae are subject to great changes
of form. Especially does this hold true .of the nebula sur-
rounding the remarkable variable star ij Argus. In many
other nebrite changes have been suspected ; but the softness
and indistinctness of outline which characterize most of these
objects, and the great difference of their aspect when seen in
telescopes of very different powers, make it difficult to prove a
change from mere differences of drawing. One of the strong-
est cases in favor of change has been made out by Professor
Ilolden from a study of drawings and descriptions of what is
culled the "Omega nebula," from a resemblance of one of
450
THE STELLAR UNIVERSE.
Fm. 106. The Omega nebula ; Herscbel 2008. Right ascension, 18 hours 13 minutes ;
declination, 16 14' S. After Holden and Trouvelot.
its branches to the Greek letter Q,. We present a figure of
this object as it now appears, from a drawing by Professor
Holden and Mr. Trouvelot, with the great Washington tele-
scope. It is the branch on the left-hand end of the nebula
which was formerly supposed to have the form of Q,.
As illustrative of the fantastic forms which nebulae some-
times assume, we present Herschel's views of two more neb-
ulae. That shown in Fig. 108 he calls the " looped nebula,"
and describes as one of the most extraordinary objects in the
heavens. It cannot be seen to advantage except in the south-
ern hemisphere.
Distribution of the Nebulw. A remarkable feature of the
distribution of the nebulae is that they are most numerous
where the stars are least so. While the stars grow thicker as
we approach the region of the Milky Way, the nebulae dimin-
ish in number. Sir John Ilerschel remarks that one-third of
NEBULAE.
451
FIG. 107. Nebula Hevschel 3722. Right ascension, IT honrs 56 minutes; declination, 24"
21' S. After Sir John Herschel.
the nebulous contents of the heavens are congregated in a
broad, irregular patch occupying about one -eighth the sur-
face of the celestial sphere, extending from Ursa Major in the
north to Virgo in the south. If, however, we consider, not the
true nebulae, but star clusters, we find the same tendency to
condensation in the Milky Way that we do in the stars. W^
thus have a clearly marked dis-
tinction between nebulae and
stars as regards the law of their
distribution. The law in ques-
tion can be most easily under-
stood by the non-mathematical
reader by supposing the starry
sphere in such a position that
the Milky Way coincides with
the horizon. Then the stars and
star clusters will be fewest at the
zenith, and will increase in number as we approach the horizon.
Also, in the invisible hemisphere the same law will hold, the
stars and clusters being fewest under our feet, and will increase
as we approach the horizon. But the true nebute will then
FIG. 108. The looped nebula ; Herschel
2941. Right ascension , 5 hours 40 min-
utes ; declination, 69 6' S.
452 THE STELLAR UNIVERSE.
be fewest in the horizon, and will increase in number as we ap-
proach the zenith, or as, going below the horizon, we approach
the nadir. The positions of the nebulae and clusters in Sir John
Herschel's great catalogue have been studied by Mr. Cleve-
land Abbe with especial reference to their distance from the
galactic circle, and the following numbers show part of his re-
sults. Imagine a belt thirty degrees wide extending around
the heavens, including the Milky Way, and reaching fifteen
degrees on each side of the central circle of the Milky Way.
This belt will include nearly one-fourth the surface of the ce-
leStial sphere, and if the stars or nebulae were equally distrib-
uted, nearly one-fourth of them would be found in the belt.
Instead, however, of one-fourth, we find nine-tenths of the star
clusters, but only one-tenth of the nebulae.
The discovery that the nebulas are probably masses of glow-
ing gas is of capital importance as tending to substantiate the
view of Sir William Herschel, that these masses are the crude
material out of which suns and systems are forming. This
view was necessarily an almost purely speculative one on the
part of that distinguished astronomer ; but unless we suppose
that the nebulae are objects of almost miraculous power, there
must be some truth in it. A nebulous body, in order to shine
by its own light, as it does, must be hot, and must be losing
heat through the very radiation by which we see it. As it
cools, it must contract, and this contraction cannot cease un-
til it becomes either a solid body or a system of such bodies
revolving round each other. We shall explain this more fully
in treating of cosmical physics and the nebular hypothesis.
7. Proper Motions of the Stars,
To the unassisted eye, the stars seem to preserve the same
relative positions in the celestial sphere generation after gen-
eration. If Job, Hipparchus, or Ptolemy should again look
upon the heavens, he would, to all appearance, see Aldebaran,
Orion, and the Pleiades exactly as he saw them thousands of
3 r ears ago, without a single star being moved from its place.
But the refined methods of modern astronomy, in which the
PROPER MOTIONS OF THE STARS. 453
telescope is brought in to measure spaces absolutely invisible
to the eye, have shown that this seeming unchangeability is
not real, and that the stars are actually in motion, only the
rate of change is so slow that the eye would not, in most cases,
notice it for thousands of years. In ten thousand years quite
a number of stars, especially the brighter ones, would be seen
to have moved, while it would take a hundred thousand years
to introduce a very noticeable change in the aspect of the con-
stellations.
As a general rule, the brighter stars have the greatest
proper motions. But this is a rule to which there are many
exceptions. The star which, so far as known, has the greatest
proper motion of all namely, Groombridge 1830 is of the
seventh magnitude only. Next in the order of proper motion
comes the pair of stars 61 Cygni, each of which is of the sixth
magnitude. Next are four or five others of the fourth and
fifth magnitudes. The annual motions of these stars are as
follows :
Groombridge 1830 7".0
01 Cygni 5".2
Lalande 21185 4". 7
c Indi 4". 5
Lalande 21258 4".4
o'Kridani 4".l
p Cassiopeia} 3".8
a Centuuri 3". 7
The first of these stars, though it has the greatest proper
motion of all, would require 185,000 years to perform the
circuit of the heavens, while JJL Cassiopeia would require near-
ly 340,000 years to perform the same circuit. Slow as these
motions are, they are very large compared with those of most
of the stars of corresponding magnitude. As a general rule,
the stars of the fourth, fifth, and sixth magnitudes move only
a few seconds in a hundred years, and would therefore re-
quire many millions of years to perform the circuit of the
heavens.
So far as they have yet been observed, and, indeed, so far
as they can be observed for many centuries to come, these
motions take place in perfectly straight lines. If each star is
moving in some orbit, the orbit is so immense that no curva-
4-iiivn /.mi Ko vivm vo.H in flu> salmH-. o.iv \vln<li lifts hpPTl Hf>-
454 THE STELLAR UNIVERSE.
scribed since accurate determinations of the positions of the
stars began to be made. So far as mere observation can in-
form us, there is no reason to suppose that the stars are sever-
ally moving in definite orbits of any kind. It is true that
Madler attempted to show, from an examination of the proper
motions of the stars, that the whole stellar universe was revolv-
ing around the star Alcyone, of the Pleiades, as a centre a
theory the grandeur of which led to its wide diffusion in popu-
lar writings. But not the slightest weight has ever been given
it by astronomers, who have always seen it to be an entirely
baseless speculation. If the stars were moving in any regular
circular orbits whatever having a common centre, we could
trace some regularity among their proper motions. But no
such regularity can be seen. The stars in all parts of the
heavens move in all directions, with all sorts of velocities. It
is true that, by averaging the proper motions, as it were, we
can trace a certain law in them ; but this law indicates, not .a
particular kind of orbit, but only an apparent proper motion,
common to all the stars, which is probably due to a real mo-
tion of our sun and solar system.
The Solar Motion. As our sun is merely one of the stars,
and rather a small star too, it may have a proper motion as
well as the other stars. Moreover, when we speak of the
proper motion of a star, we mean, not its absolute motion, but
only its motion relative to our system. As the sun moves, he
carries the earth and all the planets along with him ; and if
we observe a star at perfect rest while we ourselves are thus
moving, the star will appear to move in the opposite direc-
tion, as we have already shown in explaining the Copernican
system. Hence, from an observation of the motion of a sin-
gle star, it is impossible to decide how much of this apparent
motion is due to the motion of our system, and how much to
the real motion of the star. If, however, we should observe a
great number of stars on all sides of us, and find them all ap-
parently moving in the same direction, it would be natural to
conclude that it was really our system which was moving, and
not the stars. Now, when Herschel averaged the proper mo-
PROPER MOTIONS OF THE STARS. 455
tions of the stars in different regions of the heavens, he found
that this was actually the case. In general, the stars moved
from the direction of the constellation Hercules, and towards
the opposite point of the celestial sphere, near the constella-
tion Argus. This would show that, relatively to the general
mass of the stars, our sun was moving in the direction of the
constellation Hercules. Herschel's data for this conclusion
were, necessarily, rather slender. The subject was afterwards
very carefully investigated by Argelander, and then by a num-
ber of other astronomers, whose results for the point of the
heavens towards which the sun is moving are as follows:
Right Ascension.
Declination.
Argelander ...
257 49'
28 50' N
O. Strove
261 22'
37 36' N
Ijiindahl
252 24'
14 20' N
Gallowav
260 1 '
34 23' N.
Madler
261 38'
39 54' N
Airv and Dunkin
262 29'
28 58' N.
It will be seen that while there is a pretty wide range among
the authorities as to the exact point, and, therefore, some un-
certainty as to where we should locate it, yet, if we lay the
different points down on a star-map, we shall find that they
all fall in the constellation Hercules, which was originally as-
signed by Herschel as that towards which we were moving.
As to the amount of the motion, Struve found that if the
sun were viewed from the distance of an average star of the
first magnitude placed in a direction from us at right angles
to that of the solar motion, it would appear to move at the
rate of SS^.O per century. Dunkin found the same motion to
be 33".5 or ^l/'.O, according to the use he made of stars hav-
ing large proper motions.
Motion of Groups of Stars. There are in the heavens sev-
eral cases of widely extended groups of stars, having a com-
mon proper motion entirely different from that of the stars
around and among them. Such groups must form connected
systems, in the motion of which all the stars are carried along
together without any great change in their positions relative
.456 THE STELLAR UNIVERSE.
to each other. The most remarkable case of this kind oc-
curs in the constellation Taurus. A large majority of the
brighter stars in the region between Aldebaran and the Plei-
ades have a common proper motion of about ten seconds per
century towards the east. How many stars are included in
this group no one knows, as the motions of the brighter ones
only have been accurately investigated. Mr. K. A. Proctor
has shown that five out of the seven stars which form the
Dipper, or Great Bear, are similarly connected. He proposes
for this community of proper motions in certain regions the
name of Star-drift. Besides those we have mentioned, there
are cases of close groups of stars, like the Pleiades, and of
pairs of widely separated stars, in which star -drift has been
noticed.
Motion in the Line of Sight. Until quite recently, the only
way in which the proper motion of a star could be detected
was by observing its change of direction, or the change of the
point in which it is seen on the celestial sphere. It is, how-
ever, impossible in this way to decide whether the star is or is
not changing its distance from our system. If it be moving
directly towards us, or directly away from us, we could not
see any motion at all. The complete motion of the stars can-
not, therefore, be determined by mere telescopic observations.
But there is an ingenious method, founded on the undulatory
theory of light, by which this motion may be detected with
more or less probability by means of the spectroscope, and
which was first successfully applied by Mr. Huggins, of Eng-
land. According to the usual theory of light, the luminosity
of a heated body is a result of the vibrations communicated
by it to the ethereal medium which fills all space ; and if the
body be gaseous, it is supposed that a molecule of the gas vi-
brates at a certain definite rate, and thus communicates only
certain definite vibrations to the ether. The rate of vibration
is determined by the position of the bright line in the spec-
trum of the gas. Now, if the vibrating body be moving
through the ether, the light-waves which it throws behind it
will be longer, and those which it throws in front of it will be
PROPER MOTIONS OF THE STARS. 457
shorter, than if the body were at rest. The result will be, that
in the former case the spectral lines will be less refrangible,
or nearer the red end of the spectrum, and in the latter case
nearer the blue end. If the line is not a bright one which the
gas emits, but the corresponding dark one which it has ab-
sorbed from the light of a star passing through it, the result
will be the same. If such a known line is found slightly
nearer the blue end of the spectrum than it should be, it is
concluded that the star from which it emanates is approach-
ing us, while in the contrary case it is receding from us.
The question may be asked, How can we identify a line as
proceeding from a gas, unless it is exactly in the position of
the line due to that gas ? How do we know but that it ijjay
be due to some other gas which emits light of slightly differ-
ent refrangibility \ The reply to this must be, that absolute
certainty on this point is not attainable ; but that, from the
examination of a number of stars, the probabilities seem large-
ly in favor of the opinion that the displaced lines are really
due to the gases near whose lines they fall. If the lines were
always displaced in one direction, whatever star was exam-
ined, the conclusion in question could not be drawn, because
it might be that this line was due to some other unknown sub-
stance. But as a matter of fact, when different stars are ex-
amined, it is found that the lines in question are sometimes
on one side of their normal position and sometimes on the
other. This makes it probable that they really all belong to
one substance, but are displaced by some cause, and the motion
of the star is a cause the existence of which is certain, and the
sufficiency of which is probable.
Mr. Hnggins's system of measurement has been introduced
by Professor Airy into the Royal Observatory, Greenwich,
where very careful measures have been. made during the past
two years by Mr. Christie and Mr. Maunder. To show how
well the fact of the motion is made out, we give in the tables
on the following page the results obtained by Mr. Hugging
and by the Greenwich observers for those stars in which the
motion is the largest :
458
THE STELLAR UNIVERSE.
STARS RECEDING PROM US.
By Mr. Hugtjins.
By Greenwich.
Sirius
20 miles per sec.
25 miles per sec.
a Orionis
22 " "
76 " "
/3 Orionis
15 " "
receding.
a Gem inorum
25 " "
25 miles per sec.
a Iieonis
15 " "
30 " "
STARS APPROACHING US.
By Mr. Muggins.
By Greenwich.
A returns
55 miles per sec.
41 miles per sec.
50 " "
36 " "
a Cygni
89 " "
41 " u
(3 Geminorum
49 " "
approaching.
a Ursae Majoris
46 " u
approach ing
There are several collateral circumstances which tend to
confirm these results. One is that the general amount of mo-
tion indicated is, in a rough way, about what we should expect
the stars to have, from their observed proper motions, com-
bined with their probable parallaxes. Another is that those
stars in the neighborhood of Hercules are mostly found to bo
approaching the earth, and those which lie in the opposite di-
rection to be receding from it, which is exactly the effect which
would result from the solar motion just described. Again, the
five stars in the Dipper which we have described as having a
common proper motion are also found to have a common mo-
tion in the line of sight. The results of this wonderful and
refined method of determining stellar motion, therefore, seem
worthy of being received with some confidence so far as the
general direction of the motion is concerned. But the dis-
placement of the spectral lines is so slight, and its measure-
ment a matter of such difficulty and delicacy, that we are far
from being sure of the exact numbers of miles per second
given by the observers. The discordances between the results
of Greenwich and those of Mr. Huggins show that numerical
certainty is not yet attained.
A necessary result of these motions will be that those stars
which are receding from us will, in the course of ages, appear
less brilliant, owing to their greater distance, while those which
PROPER MOTIONS OF THE STARS. 459
are approaching us will, as they come nearer, appear brighter,
always supposing that their intrinsic brightness does not vary.
But so immense is the distance of the stars, that many thou-
sands of years will be required to produce any appreciable
change in their brightness from this cause. For instance,
from the best determinations which have been made, the dis-
tance of Sirius from our system is more than a million radii
of the earth's orbit. With a velocity of twenty miles per sec-
ond, it would require more than one hundred and fifty thou-
sand years to pass over this distance.
It will, of course, be understood that the velocities found by
the spectroscopic method are not the total velocities with
which the stars are moving, but only the rate at which they
are approaching to or receding from the earth, or, to speak
mathematically, the component of the velocity in the direc-
tion of the line of sight. To find the total velocity, this com-
ponent must be combined with the telescopic velocity found
from the observed proper motion of the star, which is the ve-
locity at right angles to the line of sight. None of the stars
are moving exactly towards our system, and it is not likely
that any will ever pass very near it. In the preceding list,
the star a Cygni is the one which is coming most directly
towards us. Its telescopic proper motion is so slight that,
though we suppose its distance to be two million radii of the
earth's orbit, yet its velocity at right angles to the line of sight
will hardly amount to one-third of a mile per second. If the
Bpectroscopic determination is correct, then, after an interval
which will probably fall between one hundred thousand and
three hundred thousand years, a Cygni will pass by our sys-
tem at something like a hundredth of its present distance,
and w r ill, for several thousand years, be many times nearer and
brighter than any star is now.
460 THE STELLAR UNIVERSE.
CHAPTER II.
THE STRUCTURE OF THE UNIVERSE.
HAVING in the preceding chapter described those features
of the universe which the telescope exhibits to us, we have
now, in pursuance of our plan, to inquire what light telescopic
discoveries can throw upon the structure of the universe as a
whole. Here we necessarily tread upon ground less sure than
that which has hitherto supported us, because we are on the
very boundaries of human knowledge. Many of our conclu-
sions must be more or less hypothetical, and liable to be modi-
fied or disproved by subsequent discoveries. We shall en-
deavor to avoid all mere guesses, and to state no conclusion
which has not some apparent foundation in observation or
analogy. The human mind cannot be kept from speculating
upon and wondering about the order of creation in its widest
extent, and science will be doing it a service in throwing ev-
ery possible light on its path, and preventing it from reaching
any conclusion inconsistent with observed facts.
The first question which we reach in regular order is, How
are the forty or fifty millions of stars visible in the most pow-
erful telescopes arranged in space ? We know, from direct
observation, how they are arranged with respect to direction
from our system ; and we have seen that the vast majority of
small stars visible in great telescopes are found in a belt span-
ning the heavens, and known as the Milky Way. But this
gives us no complete information respecting their absolute po-
sition : to determine this, we must know the distance as well
as the direction of each star. But beyond the score or so of
stars which have a measurable parallax, there is no known
way of measuring the stellar distances ; so that all we can do
VIEWS OF MODERN 'ASTRONOMERS. 401
is to make more or less probable conjectures, founded on the
apparent magnitude of the individual stars and the probable
laws of their arrangement. If the stars were all of the same
intrinsic brightness, we could make a very good estimate of
their distance from their apparent magnitude ; but we know
that such is not the case. Still, in all reasonable probability,
the diversity of absolute magnitude is far less than that of the
apparent magnitude; so that a judgment founded on the lat-
ter is much better than none at all. It was on such consider-
ations as these that the conjectures of the first observers with
the telescope were founded.
1. Views of Astronomers before fferschcl
Before the invention of the telescope, any well-founded
opinion respecting the structure of the starry system was out
of the question. We have seen how strong a hold the idea of
a spherical universe had on the minds of men, so that even
Copernicus was fully possessed with it, and probably believed
the sun to be, in some way, the centre of this sphere. Before
any step could be taken towards forming a true conception of
the universe, this idea had to be banished from the mind, and
the sun had to be recognized as simply one of innumerable
stars which made up the universe. The possibility that such
might have been the case seems to have first suggested itself
to Kepler, though he was deterred from completely accepting
the idea by an incorrect estimate of the relative brilliancy of
the stars. He reasoned that if the sun were one of a vast
number of fixed stars of equal brilliancy scattered uniformly
throughout space, there could not be more than twelve which
were at the shortest distance from us. We should then have
another set at double the distance, another at triple the dis-
tance, and so on ; and since the more distant they are, the
fainter they would appear, we should speedily reach a limit
beyond which no stars could be seen. In fact, however, we
often see numerous stars of the same magnitude crowded
closely together, as in the belt of Orion, while the total num-
ber of visible stars is reckoned by thousands. He therefore
462 THE STELLAK UNIVERSE.
concludes that the distances of the individual stars from each
other are much less than their distances from our sun, the lat-
ter being situated near the centre of a comparatively vacant
region.
Had Kepler known that it would require the light of a hun-
dred stars of the sixth magnitude to make that of one of the
first magnitude, he would not have reached this conclusion.
A simple calculation would have shown him that, with twelve
stars at distance unity, there would have been four times that
number at the double distance, nine times at the treble dis-
tance, and so on, until, within the tenth sphere, there would
have been more than four thousand stars. The twelve hun-
dred stars on the surface of the tenth sphere would have
been, by calculation, of the sixth magnitude, a number near
enough to that given by actual count to show him that the
hypothesis of a uniform distribution was quite accordant with
observations. It is true that, where many bright stars were
found crowded together, as in Orion, their distance from each
other is probably less than that from our sun. But this ag-
glomeration, being quite exceptional, would not indicate a gen-
eral crowding together of all the stars, as Kepler seemed to
suppose. In justice to Kepler it must be said that he put
forth this view, not as a well-founded theory, but only as a
surmise, concerning a question in which certainty was not
attainable.
Ideas of Kant Those who know of Kant only as a specula-
tive philosopher may be surprised to learn that, although he
was not a working astronomer, he was the author of a theory
of the stellar system which, with some modifications, has been
very generally held until the present time. Seeing the Gal-
axy encircle the heavens, and knowing it to be produced by
the light of innumerable stars too distant to be individually
visible, he concluded that the stellar system extended much
farther in the direction of the Galaxy than it did elsewhere.
In other words, he conceived the stars to be arranged in a
comparatively thin, flat layer, or stratum, our sun being some-
where near the centre. When we look edgewise along this
VIEWS OF MODERN ASTRONOMERS. 403
stratum, we see an immense number of stars, but in the per-
pendicular direction comparatively few are visible.*
This thin stratum suggested to Kant the idea of a certain
resemblance to the solar system. Owing to the small inclina-
tions of the planetary orbits, the bodies which compose this
system are spread out in a thin layer, as it were ; and we have
only to add a great multitude of planets moving around the
sun in orbits of varied inclinations to have a representation in
miniature of the stellar system as Kant imagined it to exist.
Had the zone of small planets between Mars and Jupiter then
been known, it would have afforded a striking confirmation of
Kant's view by showing a yet greater resemblance of the plan-
etary system to his supposed stellar system. Were the num-
ber of these small planets sufficiently increased, we should see
them as a sort of Galaxy around the zodiac, a second Milky
Way, belonging to our system, and resolvable with the tele-
scope into small planets, just as the Galaxy is resolved into
small stars. The conclusion that two systems which were so
similar in appearance were really alike in structure would
have seemed very well founded in analogy.
As the planets are kept at their proper distances, and pre-
vented from falling into each other or into the sun by the
centrifugal force generated by their revolutions in their or-
bits, so Kant supposed the stars to be kept apart by a revolu-
tion around some common centre. The proper motions of
the stars were then almost unknown, and the objection was
anticipated that the stars were found to occupy the same po-
sition in the heavens from generation to generation, and there-
fore could not be in motion around a centre. To this Kant's
reply was that the time of revolution was so long, and the
motion so slow, that it was not perceptible with the imper-
fect means of observation then available. Future genera-
tions would, he doubted not, by comparing their observations
* The original idea of this theory is attributed by Kant to Wright, of Durham,
England, a writer whose works are entirely unknown in this country, and whose
authorship of the theory has been very generally forgotten.
464 THE STELLAR UNIVERSE.
with those of their predecessors, find that there actually was a
motion among the stars.
This conjecture of Kant, that the stars would be found to
have a proper motion, has, as we have seen, been amply con-
firmed ; but the motion is not of the kind which his theory
would require. On this theory, all the stars ought to move in.
directions nearly parallel to that of the Milky Way, just as in
the planetary system we find them all moving in directions
nearly parallel to the ecliptic. But the proper motions actually
observed have no common direction, and follow no law what-
ever, except that, on the average, there is a preponderance of
motions from the constellation Hercules, which is attributed
to an actual motion of our sun in that direction. Making al-
lowance for this preponderance, we find the stars to be appar-
ently moving at random in every direction ; and therefore
they cannot be moving in any regularly arranged orbits, as
Kant supposed. A defender of Kant's system might indeed
maintain that, as it is only in a few of the stars nearest us
that any proper motion has been detected, the great cloud of
stars which make up the Milky Way might really be moving
along in regular order, a view the possibility of which we shall
be better prepared to consider hereafter.
The Kantian theory supposes the system which we have
just been describing to be formed of the immense stratum of
stars which make up the Galaxy and stud our heavens, and
to include all the stars separately visible with our telescopes.
But he did not suppose this system, immense though it is, to
constitute the whole material universe. In the nebulas he
saw other similar systems at distances so immense that the
combined light of their millions of suns only appeared as a
faint cloud in the most powerful telescopes. This idea that
the nebulae were other galaxies was more or less in vogue
among popular writers until a quite recent period, when it
was refuted by the spectroscope, which shows that these ob-
jects are for the most part masses of glowing gas.. T has,
however, not received support among astronomers since the
time of Sir William TIerschel.
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 465
System of Lambert. A few years after the appearance of
Kant's work, a similar but more elaborate system was sketched
out by Lambert. He supposed the universe to be arranged in
systems of different orders. The smallest systems which we
know are those made up of a planet, with its satellites circu-
lating around it as a centre. The next system in order of
magnitude is a solar system, in which a number of smaller
systems are each carried round the sun. Each individual star
which we see is a sun, and has its retinue of planets revolving
around it, so that there are as many solar systems as stars.
These systems are not, however, scattered at random, but are
divided up into greater systems which appear in our telescopes
as clusters of stars. An immense number of these clusters
make up our Galaxy, and form the visible universe as seen in
our telescopes. There may be yet greater systems, each made
up of galaxies, and so on indefinitely, only their distance is so
immense as to elude our observation.
Each of the smaller systems visible to us has its central body,
the mass of which is much greater than that of those which
revolve around it. This feature Lambert supposed to extend
to other systems. As the planets are larger than their satel-
lites, and the sun larger than its planets, so he supposed each
stellar cluster to have a great central body around which each
solar system revolved. As these central bodies are invisible to
us, he supposed them to be opaque and dark. All the systems,
from the smallest to the greatest, were supposed to be bound
together by the one universal law of gravitation.
As not the slightest evidence favoring the existence of these
opaque centres has ever been found, we are bound to say that
this sublime idea of Lambert's has no scientific foundation.
Astronomers have handed it over without reservation to the
lecturers and essayists.
. .r 2. Researches of Hersdiel and his Successors.
Her'Lhel was the first who investigated the structure of
the stellar system by a long-continued series of observations,
executed with a definite end in view. His plan was that of
466 THE STELLAR UNIVERSE.
" star - gauging," which meant, in the first place, the simple
enumeration of all the stars visible with a powerful tele-
scope in a given portion of the heavens. He employed a
telescope of twenty inches aperture, magnifying one hundred
and sixty times, the field of view being a quarter of a degree
in diameter. This diameter was about half that of the full
moon, so that each count or gauge included all the stars visi-
ble in a space having one-fourth the apparent surface of the
lunar disk. From the number of stars in any one field of
view, he concluded to what relative distance his sight ex-
tended, supposing a uniform distribution of the stars through-
out all the space included in the cone of sight of the telescope^
When an observer looks into a telescope pointed at the heav-
ens, his field of vision includes a space which constantly
widens out on all sides as the distance becomes greater ; and
the reader acquainted with geometry will see that this space
forms a cone having its point in the focus of the telescope, and
its circular base at the extreme distance to which the telescope
reaches. The solid contents of this cone will be proportional
to the cube of the distance to which it extends ; for instance,
if the telescope penetrates twice as far, the cone of sight will
be not only twice as long, but the base will be twice as wide
in each direction, so that the cone will have altogether eight
times the contents, and will, on Herschel's hypothesis, contain
eight times as many stars. So, when Herschel found the stars
eight times as numerous in one region as in another, he con-
cluded that the stellar system extended twice as far in the
direction of the first region.
To count all the stars visible with his telescope, Herschel
found to be out of the question. He would have had to point
his instrument several hundred thousand times, and count all
the visible stars at each pointing. He therefore extended his
survey only over a wide belt extending more than half-way
round the celestial sphere, and cutting the Galaxy at right
angles. In this belt he counted the stars in 3400 telescopic
fields. Comparing the average number of stars in different
regions with the position of the region relative to the Galaxy,
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 467
he found that the stars were thinnest at the point most distant
from the Galaxy, and that they constantly increased in num-
ber as the Galaxy was approached. The following table will
give an idea of the rate of increase. It shows the average
number of stars in the field of view of the telescope for each
of six zones of distance from the Galaxy.
First zone 90 to 75 from Galaxy 4 stars per field.
Second zone 75
Third zone GO C
Fourth zone 45 C
Fifth zone 30 C
Sixth zone 15 C
60
45
30
15
14
24
53
A similar enumeration was made by Sir John Herschel for the
corresponding region on the other, or southern, side of the Gal-
axy. He used the same telescope, and the same magnifying
power. His results were :
First zone 6 stars per field.
Second zone 7 " "
Third zone 9 " "
Fourth zone 13 stars per field.
Fifth zone 2G " "
Sixth zone 59 " "
The reader will, perhaps, more readily grasp the significa-
tion of these numbers by the mode of representation which
was suggested in describing the distribution of the nebulae.
Let him imagine himself standing under a clear sky at the
time when the Milky Way encircles the horizon. Then, the
first zone, as we have defined it, will be around the zenith, ex-
tending one -sixth of the way to the horizon on every side;
the second zone will be next below and around this circular
space, extending one-third of the way to the horizon ; and so
each one will follow in regular order until we reach the sixth,
or galactic, zone, which will encircle the horizon to a height
of 15 on every side. The numbers we have given show that
in the position of the observer which we have supposed the
stars would be thinnest around the zenith, and would con-
stantly increase in number as we approached the horizon.
The observer being supposed still to occupy the same posi-
tion, the second table shows the distribution of the stars in the
468 THE STELLAR UNIVERSE.
opposite or invisible hemisphere, which he would see if the
earth were removed. In this hemisphere the first, or thinnest,
zone would be directly opposite the thinnest zone in the ob-
server's zenith ; that is, it would be directly under his feet.
The successive zones would then be nearer the horizon, the
sixth or last encircling it, arid extending 15 below it on every
side.
The numbers we have given are only averages, and do not
give an adequate idea of the actual inequalities of distribu-
tion in special regions of the heavens. Sometimes there was
not a solitary star in the field of the telescope, while at oth-
ers there were many hundreds. In the circle of the Galaxy
itself, the stars are more than twice as thick as in the average
of the first zone, which includes not only this circle, but a
space of 15 on each side of it.
Adopting the hypothesis of a uniform distribution of the
stars, Herschel concluded from his first researches that the
stellar system was of the general form supposed by Kant, ex-
tending out on all sides five times as far in the direction of
the Galaxy as in the direction perpendicular to it. The most
important modification he made was to suppose an immense
cleft extending edgewise into the system from its circumfer-
ence about half-way to the centre. This cleft corresponded to
the division in the Milky Way which commences in the sum-
mer constellation Cygnus in the north, and passes through
Aquila, the Serpent, and Scorpius far into the southern hemi-
sphere. Estimating the distance by the arrangement and ap-
parent magnitude of the stars, he was led to estimate the mean
thickness of the stellar stratum from top to bottom as 155
units, and the diameter as 850 units, the unit being the aver-
age distance of a star of the first magnitude. Supposing this
distance to be that which light would travel over in 16 years
a supposition which is founded on the received estimate of
the mean parallax corresponding to stars of that magnitude
then it would take light nearly 14,000 years to travel across
the system from one border to the other, and 7000 years to
reach us from the extreme boundary.
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 469
The foregoing deduction of
Herschel was founded on the
hypothesis that the stars were
equally dense in every part of
the stellar system, so that the
number of stars in any direc-
tion furnished an index to the
extent of the stars in that di-
rection. Further study show-
ed Herschel that this assump-
tion might be so far from cor-
rect that his conclusions would
have to be essentially modi-
fied. Binary and other double
stars and star clusters evident-
ly offered cases in which sev-
eral stars were in much closer
association than were the stars
in general. To show exactly
on what considerations this
change of view is founded, we
remark that if the increase of
density in the direction of the
Milky Way were quite regu-
lar, so that there were no cases
of great difference in the thick-
ness of the stars in two adjoin-
ing regions, then the original
view would have been sound
so far as it went. But such ir-
regularities are very frequent,
and it would lead to an obvi-
ous absurdity to explain them
on Ilerschel's first hypothesis ;
for instance, when the tele-
scope was directed towards
the Pleiades there would be FIG. m-Hechei'8 view of the form of the
universe.
470 THE STELLAR UNIVERSE.
found, probably, six or eight times as many stars as in the ad-
joining fields. But supposing the real thickness of the stars
the same, the result would be that in this particular direction
the stars extended oat twice as far as they did in the neigh-
boring parts of the sky ; that is, we should have a long, nar-
row spike of stars pointing directly from us. As there are
many such clusters in various parts of the sky, we should have
to suppose a great number of such spikes. In other regions,
especially around the Milky Way, there are spaces nearly void
of stars. To account for these we should have to suppose
long narrow chasms reaching through towards our sun. Thus
the stellar system would present the form of an exaggerated
star-fish with numerous deep openings, a form the existence
of which is beyond all probability, especially if we reflect
that all the openings and all the arms have to proceed from
the direction of our sun.
The only rational explanation of a group of stars showing
itself in a telescope, with a comparatively void space surround-
ing it, is that we have here a real star cluster, or a region in
which the stars are thicker than elsewhere. Now, one can see
with the naked eye that the Milky Way is not a continuous
uniform belt, but is, through much of its course, partly made
up of a great number of irregular cloud-like masses with com-
paratively dark spaces between them. The conclusion is un-
avoidable that we have here real aggregations of stars, and
not merely a region in which the bounds of the stellar-sys-
tem are more widely extended. Whether Herschel clearly saw
this may be seriously questioned ; but however it may have
been, he adopted another method of estimating the relative
distances of the stars visible in his gauges.
This method consisted in judging of the distances to which
his telescope penetrated, not by the number of stars it brought
into view, but by their brightness. If all the stars were of the
same intrinsic brightness, so that the differences of their ap-
parent magnitude arose only from their various distances from
us, then this method would enable us to fix the distance of
each separate star. But as we know that the stars are by no
RESEARCHES OF HEESCHEL AND HIS SUCCESSORS. 471
means equal in intrinsic brightness, the method cannot be
safely applied to any individual star, a fact which Herschel
himself clearly saw. It does not follow, however, that we
cannot thus form an idea of the relative distances of whole
classes or groups of stars. Although it is quite possible that
an individual star of the fifth magnitude may be nearer to us
than another of the fourth, yet we cannot doubt that the av-
erage distance of all the fifth-magnitude stars is greater than
the average of those of the fourth magnitude, and greater,
too, in a proportion admitting of a tolerably accurate numeri-
cal estimate. Such an estimate Herschel attempted to make,
proceeding on the following plan :
Suppose a sphere to be drawn around our sun as a centre
of such size that it shall be
equal to the average space
occupied by a single one of
the stars visible to the naked
eye; that is, if we suppose
that portion of the space of
the stellar system occupied
by the six thousand bright-
er stars to be divided into
six thousand parts, then the
sphere will be equal to one
of these parts. The radius
of this sphere will probably
not differ much from the dis-
tance of the nearest fixed star,
a distance we shall take for
unity. Then, suppose a series
of larger spheres, all drawn
around our sun as a centre,
and having the radii 3, 5, 7,
9, etc. The contents of the
spheres being as the cubes
of their diameters, the first Fig . no ._ Illustmting Herders orders of dis-
sphere will have 3 x 3 x 3 = 27 tauce of the stars.
472
THE STELLAR UNIVERSE.
times the bulk of the unit sphere, and will therefore be large
enough to contain 27 stars; the second will have 125 times
the bulk, and will therefore contain 125 stars, and so with
the successive spheres. Fig. 110 shows a section of portions
of these spheres up to that with radius 11. Above the centre
are given the various orders of stars which are situated be-
tween the several spheres, while in the corresponding spaces
below the centre are given the number of stars which the re-
gion is large enough to contain ; for instance, the sphere of
radius 7 has room for 343 stars, but of this space 125 parts
belong to the spheres inside of it : there is, therefore, room for
218 stars between the spheres of radii 5 and 7.
Herschel designates the several distances of these layers of
stars as orders ; the stars between spheres 1 and 3 are of the
first order of distance, those between 3 and 5 of the second
order, and so on. Comparing the room for stars between the
several spheres with the number of stars of the several magni-
tudes, he found the result to be as follows :
Order of
Distance.
Number of
Stars there
Is room for.
Magnitude.
Number of
Stars of that
magnitude.
1
26
1.
17
2
08
2
57
3
218
3
206
4
386
4
454
5
602
5
1161
G
866
6
6103
7
1178
7
6146
8
1538
There is evidently no correspondence between the calculat-
ed orders of distance and the magnitudes as estimated on the
usual scale. But Herschel found that this was because the
magnitudes as usually estimated corresponded to an entirely
different scale of distance from that which he adopted. In
his scale the several distances increased in arithmetical pro-
gression; while in the order of magnitudes the increase is
in geometrical progression. In consequence, the stars of the
sixth magnitude correspond to the eighth, ninth, or tenth order
of distances; that is, we should have to remove a star of the
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 473
first magnitude to eight, nine, or ten times its actual distance
to make it shine as a star of the sixth magnitude.
Attempting on this system to measure the extent of the
Milky Way, Herschel concluded that it was unfathomable
with his twenty -foot telescope, which, he calculated, would
penetrate to the 900th order of distances, that is, to stars
which were 900 times as far as the average of those of the
first magnitude. He does not seem to have made any very
extended examination with his forty-foot telescope, but con-
cluded that it would leave him in the same uncertainty in
respect to the extent of the Milky Way as the twenty-foot one
did. This unrivalled man, to whom it was given to penetrate
farther into creation than man had ever done before him,
seems to have rested from his labors without leaving any more
definite theory of the boundaries of the stellar system than
that they extended, at least in the direction of the Milky Way,
beyond the utmost limit to which his telescope could penetrate.
If we estimate the time it would require light to come from
the utmost limit to which he believed his vision to extend,
we shall find it to be about fourteen thousand years, or more
than double that deduced from his former gauges. We can
say with confidence that the time required for light to reach
us from the most distant visible stars is measured by thou-
sands of years. But it must be admitted that Herschel's esti-
mate of the extent of the Milky Way may be far too great, be-
cause it rests on the assumption that all stars are of the same
absolute brightness. If the smallest stars visible in his tele-
scope were, on the average, of the same intrinsic brilliancy as
the brighter ones, the conclusion would be well founded. But
if we suppose a boundary, it is impossible to decide from Her-
schel's data whether the minuteness of those stars arises from
their great distance or from their small magnitude. Notwith-
standing this uncertainty, it has been maintained by some, not-
ably by Mr. Proctor, that the views of Herschel respecting the
constitution of the Milky Way, or stellar system, were radical-
ly changed by this second method of star-gauging. I see no
evidence of any radical change. Although Herschel does not
474 THE STELLAR UNIVERSE.
express himself very definitely on the subject, yet, in his last
paper on the distribution of the stars (Philosophical Trans-
actions for 1817), there are several remarks which seem to im-
ply that he still supposed the stellar system to have the gen-
eral form shown in Fig. 109, and that, in accordance with that
view, he supposed the clustering of stars to indicate protuber-
ant parts of the Milky Way. He did, indeed, apply a differ-
ent method of research, but the results to which the new meth-
ods led were, in their main features, the same as those of the
old method.
Since the time of Herschel, one of the most eminent of the
astronomers who have investigated this subject is Strove -the
elder, formerly director of the Pulkowa Observatory. His re-
searches were founded mainly on the numbers of stars of the
several magnitudes found by Bessel in a zone thirty degrees
wide extending all round the heavens, fifteen degrees on each
side of the equator. With these he combined the gauges of
Sir William Herschel. The hypothesis on which he based his
theory was similar to that employed by Herschel in his later
researches, in so far that he supposed the magnitude of the
stars to furnish, on the average, a measure of their relative
distances. Supposing, after Herschel, a number of concentric
spheres to be drawn around the sun as a centre, the successive
spaces between which corresponded to stars of the several
magnitudes, he found that the farther out he went, the more
the stars were condensed in and near the Milky Way. This
conclusion may be drawn at once from the fact we have al-
ready mentioned, that the smaller the stars, the more they are
condensed in the region of the Galaxy. Struve found that if
we take only the stars plainly visible to the naked eye that
is, those down to the fifth magnitude they are no thicker in
the Milky Way than in other parts of the heavens. But those
of the sixth magnitude" are a little thicker in that region, those
of the seventh yet thicker, and so on, the inequality of distri-
bution becoming constantly greater as the telescopic power is
increased.
From all this, Struve concluded that the stellar system might
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 475
be considered as composed of layers of stars of various densi-
ties, all parallel to the plane of the Milky Way. The stars are
thickest in and near the central layer, which he conceives to
be spread out as a wide, thin sheet of stars. Our sun is situ-
ated near the middle of this layer. As we pass out of this
layer, on either side we find the stars constantly growing thin-
ner and thinner, but we do not reach any distinct boundary.
As, if we could rise in the atmosphere, we should find the air
constantly growing thinner, but at so gradual a rate of prog-
ress that we could hardly say where it terminated ; so, on
Struve's view, would it be with the stellar system, if we could
mount up in a direction perpendicular to the Milky Way.
Struve gives the following table of the thickness of the stars
on each side of the principal plane, the unit of distance being
that of the extreme distance to which Herschel's telescope
could penetrate :
Distance from Principal Plane.
Density.
Mean Distance
between Neigh-
boring Stars.
In the principal piano
1.0000
.000
0.05 from principal plane
0.48568
.272
0.10
t
0.33288
.458
0.20
0.23895
.611
0.30
0.17980
.772
0.40
0.13021
.973
0.50
0.08646
2.261
0.60
0.05510
2.628
0.70
0.03079
3.190
0.80
0.01414
4.131
0.866
0.00532
5.729
This condensation of the stars near the central plane, and
the gradual thinning-out on each side of it, are only designed
to be the expression of the general or average distribution
of those bodies. The probability is that even in the central
plane the stars are many times as thick in some regions as in
others, and that as we leave the plane, the thinning-out would
be found to proceed at very different rates in different re-
gions. That there may be a gradual thinning -out cannot be
denied ; but Struve's attempt to form a table of it is open to
the serious objection that, like Ilerschel, he supposed the dif-
476 THE STELLAR UNIVERSE.
ferences between the magnitudes of the stars to arise entirely
from their different distances from us. Although where the
scattering of the stars is nearly uniform this supposition may
not lead us into serious error, the ease will be entirely differ-
ent where we have to deal with irregular masses of stars, and
especially where our telescopes penetrate to the boundary of
the stellar system. In the latter case we cannot possibly dis-
tinguish between small stars lying within the boundary and
larger ones scattered outside of it, and Struve's gradual thin-
ning-out of the stars may be entirely accounted for by great
diversities in the absolute brightness of the stars.
Among recent researches on this subject, those of Mr. R.
A. Proctor are entitled to consideration, from being founded
on facts which were not fully known or understood by the
investigators whom we have mentioned. The strongest point
which he makes is that all views of the arrangement of the
stellar system founded upon the theory that the stars are
either of similar intrinsic brightness, or approach an equality
of distribution in different regions, are entirely illusory. He
cites the phenomena of star-drift, described in the last chap-
ter, as proving that stars which had been supposed widely sep-
arated are really agglomerated into systems; and claims that
the Milky Way may be a collection of such systems, having
nothing like the extent assigned it by Herschel.
How far the considerations brought forward by Mr. Proc-
tor should make us modify the views of the subject hitherto
held, cannot be determined without further observations on the
clustering of stars of different magnitudes. We may, howev-
er, safely concede that there is a greater tendency among the
stars to be collected into groups than was formerly supposed.
A curious result of Mr. J. M. Wilson, of Rugby, England, re-
specting the orbits of some binary stars, throws light on this
tendency. It was found by Struve that although the great
common proper motion of the pair of stars 61 Cygni, cele-
brated for the determinations of their parallax, was such as to
leave no reasonable doubt that they were physically connect-
ed, yet not the slightest deviation in their courses, arising
EESEAHCHES OF HEESCHEL AND HIS SUCCESSORS. 477
from their mutual attraction, could be detected. Mr. Wilson
has recently confirmed this result by an examination of the
whole series of measures on this pair from 1753 to 1874,
which do not show the slightest deviation, but seem to indi-
cate that each star of the pair is going on its course indepen-
dently of the other. But, as just stated, they move too nearly
together to permit of the belief that they are really indepen-
dent. The only conclusion open to us is that each of them de-
scribes an immense orbit around their common centre of grav-
ity, an orbit which may be several degrees in apparent diam-
eter, and in which the time of revolution is counted by thou-
sands of years. Two thousand years hence they will be so
far apart that no connection between them would be sus-
pected.
It is a question whether we have not another instance of
the same kind in the double star Castor, or a Geminorum.
Mr. Wilson finds the orbit of this binary to be apparently
hyperbolic, a state of things which would indicate that the
two stars had no physical connection whatever, but that, in
pursuing their courses through space, they chanced to come
so close together that they were brought for a while within
each other's sphere of attraction. If this be the case, they
will gradually separate forever, like two ships meeting on the
ocean and parting again. We remark that the course of each
star will then be very different from what it would have
been if they had not met. We cannot, however, accept the
hyperbolic orbit of Mr. Wilson as an established fact, because
the case is one in which it is very difficult to distinguish be-
tween a large and elongated elliptic orbit and a hyperbolic
orbit. The common proper motion of the two objects is such
as to lead to the belief that they constitute a pair, the compo-
nents of which separate to a great distance.
Now, these discoveries of pairs of stars moving around a
common centre of gravity, in orbits of immense -extent, sug-
gest the probability that there exist in the heavens great num-
bers of pairs, clusters, and systems of this sort, the members
of which are so widely separated that they have never beeu
i78 THE STELLAR UNIVERSE.
suspected to belong together, and the widely scattered groups
having a common proper motion may very well be systems of
this kind.
3. Probable Arrangement of the Visible Universe.
The preceding description of the views held by several gen-
erations of profound thinkers and observers respecting the
arrangement of the visible universe furnishes an example of
what we may call the evolution of scientific knowledge. Of
no one of the great men whom we have mentioned can it be
said that his views were absolutely and unqualifiedly errone-
ous, and of none can it be said that he reached the entire
truth. Their attempts to solve the mystery which they saw
before them were like those of a spectator to make out the ex-
act structure of a great building which he sees at a distance
in the dim twilight. He first sees that the building is really
there, and sketches out what he believes to be its outlines. As
the light increases, he finds that his first outline bears but a
rude resemblance to what now seems to be the real form, and
he corrects it accordingly. In his first attempts to fill in the
columns, pilasters, windows, and doors, he mistakes the darker
shades between the columns for windows, other lighter shad-
ows for doors, and the pilasters for columns. Notwithstand-
ing such mistakes, his representation is to a certain extent cor-
rect, and he will seldom fall into egregious error. The suc-
cessive improvements in his sketch, from the first rough out-
line to the finished picture, do not consist in effacing at each
step everything he has done, but in correcting it, and filling in
the details.
The progress of our knowledge of nature is generally of this
character. But in the case now before us, so great is the dis-
tance, so dim the light, and so slender our ideas of the princi-
ples on which the vast fabric is constructed, that we cannot
pass beyond a few rough outlines. Still there are a few feat-
ures which we can describe with a near approach to certainty,
and others respecting which, though our knowledge is some-
what vague, we can reach a greater or less degree of proba-
PROBABLE ARRANGEMENT OF THE VISIBLE UNIVERSE. 479
bility. We may include these under the following seven
heads :
1st. Leaving the nebulae out of consideration, and confining
ourselves to the stellar system, we may say, with moral cer-
tainty, that the great mass of the stars which compose this
system are spread out on all sides, in or near a widely extend-
ed plane passing through the Milky Way. In other words,
the large majority of the stars which we can see with the tele-
scope are contained in a space having the form of a round, flat
disk, the diameter of which is eight or ten times its thickness.
This was clearly seen by Kant, and has been confirmed by
Herschel ai)d Struve. In fact, it forms the fundamental base
of the structures reared by these several investigators. When
Kant saw, in this arrangement, a resemblance to the solar
system, in which the planets all move round near one central
plane, he was correct, so far as he went. The space, then, in
which we find most of the stars to be contained is bounded
by two parallel planes forming the upper and lower surfaces
of the disk we have described, the distance apart of these
planes being a small fraction of their extent probably less
than an eighth.
2d. Within the space we have described the stars are not
scattered uniformly, but are for the most part collected into
irregular clusters or masses, with comparatively vacant spaces
between them. These collections have generally no definite
boundaries, but run into each other by insensible gradations.
The number of stars in each collection may range from two
to many thousands ; and larger masses are made up of smaller
ones in every proportion, much as the heavy clouds on a sum-
mer's day are piled upon each other.
3d. Our sun, with its attendant planets, is situated near the
centre of the space we have described, so that we see nearly
the same number of stars in any two opposite quarters of the
heavens.
4th. The six or seven thousand stars around us, which are
easily seen by the naked eye, are scattered in space with a
near approach to uniformity, the only exception being local
480 THE STELLAR UNIVERSE.
clusters, the component stars of which are few in number and
pretty widely separated. Such are the Pleiades, Coma Bere-
nices, and perhaps the principal stars of many other constella-
tions, which are so widely separated that we do not see any
connection among them.
5th. The disk which we have described does not represent
the form of the stellar system, but only the limits within
which it is mostly contained. The absence of any definite
boundary, either to star clusters or the stellar system, and the
number of comparatively vacant regions here and there among
the clusters, prevent our assigning any more definite form to
the system than we could assign to a cloud of dust. The thin
and widely extended space in which the stars are most thickly
clustered may, however, be called the galactic region.
6th. On each side of the galactic region the stars are more
evenly and thinly scattered, but probably do not extend out to
a distance at all approaching the extent of the galactic region.
If they do extend out to an equal distance, they are very few
in number. It is, however, impossible to set any definite boun-
daries, not only from our ignorance of the exact distance of
the smallest stars we can see in the telescope, but because the
density of the stars probably diminishes very gradually as we
go out towards the boundary.
7th. On each side of the galactic and stellar region we have
a nebular region, in which we find few or no stars, but vast
numbers of nebulse. The nebulae diminish greatly in num-
ber as we approach the galactic region, only a very few being
found in that region.
The general arrangement of the stars and nebulse which we
have described is seen in Fig. Ill, which shows what is prob-
ably the general aspect of a section of the visible universe per-
pendicular to the Milky Way. In the central part of the fig-
ure we have the galactic region, in which the stars are mostly
aggregated in large masses. Of the arrangement of these
masses nothing certain is known ; they are, therefore, put in
nearly at random. Indeed, it is still an undecided question
whether the aggregations of stars which make up the Milky
PROBABLE ARRANGEMENT OF THE VISHtLE UNIVERSE. 481
Way extend all the way across the diameter of the galactic
region, or whether they are arranged in the form of a ring,
with our sun and his surrounding stars in the centre of it.
In the latter case, the masses of stars near the centre should
be less strongly marked. This central region being that in
which our earth is situated, this uncertainty respecting the
density of stars in that region implies an uncertainty whether
FIG. 111. Probable arrangement of the stars and nebulae visible with the telescope. In
the Galaxy the stars are not evenly scattered, but are agglomerated into clusters.
the stars visible with the naked eye are part of one of the
masses which make up the Galaxy, or whether we are in a
comparatively thin region. Although this question is still
unsolved, it is one which admits of an answer by telescopic
research. When we described Sir William Ilerschel's ar-
rangement of the stars in concentric spheres, we saw that. in
the more distant spheres the stars were vastly more dense
32
482 THE STELLAR UNIVERSE.
around the galactic belt of each sphere than they were in
other parts of it. To answer the question which has been
presented, we must compare the densities of the stars at the
circumferences of these spheres with the density immediately
around us. In other words, the question is, Suppose a human
being could dart out in the direction of the Milky Way, and
pass through some of the masses of stars composing it, would
he find them thicker or thinner than they are in the visible
heavens around us ?
A question still left open is, whether all the celestial objects
visible with the telescope are included within the limits of the
three regions we have just indicated, or whether the whole
Galaxy, with everything which is included within its limits,
is simply one of a great number of widely scattered stellar
systems. Since any consideration of invisible galaxies and
systems would be entirely idle, the question may be reduced
to this : Are the most distant star clusters which the telescope
shows us situated within the limits of the stellar system, or. far
without them, a great vacant space intervening? The latter
alternative is the popular one, first suggested by Kant, it be-
ing supposed that the most distant nebulas constituted other
Milky Ways or stellar systems as extensive as our own.
Although the possibility that this view is correct cannot be
denied, yet the arrangement of the star clusters or resolvable
nebulae militates against it. We have shown that the major-
ity of the latter lie near the direction of the plane of the
Milky Way, comparatively few being seen near the perpen-
dicular direction. But if these objects were other galaxies,
far outside of the one which surrounds us, they would be as
likely to lie in one direction as in another, and the probabil-
ity against the great mass of them lying in one plane would
be very great. The most probable conclusion, therefore, is
that they constitute part of our stellar system. They may, in-
deed, be scattered around or outside of the extreme limits with-
in which single stars can be seen, but not at distances so great
that they should be considered as separate systems. The most
probable conclusion, in the present state of our knowledge,
DO THE STARS REALLY FORM A SYSTEM? 483
seems to be that the scheme shown in Fig. Ill includes the
whole visible universe.
The differences of opinion which now exist respecting the
probable arrangement and distance of the stars arise mainly
from our uncertainty as to what is the probable range of ab-
solute magnitude of the stars, a subject to which we have al-
ready several times alluded. The discovery of the parallax
of several stars has enabled us not only to form some idea of
this question by comparing the brilliancy of these stars with
their known distances, but it has enabled us to answer the in-
teresting question, How does our sun compare with these stars
in brightness ? The curious result of this inquiry is, that our
sun is really a star less than the average, which would mod-
estly twinkle among the smaller of its fellows if removed
to the distance from us at which they are placed. Zollner
found, by comparing the light of the sun with that of Capella,
or a Aurigse, that it would have to be removed to 236,000
times its present distance to appear equally bright with that
star, which we may take as an average star of the first magni-
tude. But the greater number of the stars of this magnitude
are situated at four or five times this distance ; so that if our
sun were placed at their average distance, it would probably
not exceed the third or fourth magnitude. Still, it would by
no means belong among the smallest stars of all, because we
do find stars with a measurable parallax which are only of
the fifth, sixth, or even the seventh magnitude. Altogether, it
appears that the range of absolute brilliancy among the stars
extends through eight or ten magnitudes, and that the largest
ones emit several thousand times as much light as the small-
est. It is this range of magnitude which really forms the
greatest obstacle in tliQ way of determining the arrangement
of the stars in space.
4. Do the Stars really form a System?
We have described the sublime ideas of Kant and Lam-
bert, who, seeing the bodies of our solar system fitted to go
through their revolutions without permanent change during
THE STELLAR UNIVERSE.
an indefinite period of time, reasoned by analogy that the
stellar universe was constructed on the same general plan,
and that each star had its appointed orbit, round which it
would run its course during endless ages. This speculation
was not followed up by Herschel and Struve, who, proceeding
on a more strictly scientific plan, found it necessary to learn
how the stars are now situated before attempting to decide
in what kinds of orbits they are moving. In the absence of
exact knowledge respecting the structure and extent of the
stellar system, it is impossible to say with certainty what will
be the state of that system after the lapse of the millions of
years which woujd be necessary for the stars to perform a
revolution around one centre. But, as in describing the con-
stitution of the stellar system, we found certain features on
which we could pronounce with a high degree of probability,
so, in respect to the motions and orbits of the stars, there are
some propositions which we may sustain with a near approach
to certainty.
Stability of the System. We may first assert, with a high de-
gree of probability, that the stars do not form a stable system
in the sense in which we say that the solar system is stable.
By a stable system we mean one in which each star moves
round and round in an unchanging orbit, every revolution
bringing it back to its starting-point, so that the system as a
whole shall retain the same general form, dimensions, and
arrangement during innumerable revolutions of the bodies
which compose it. It is almost necessary to the existence of
such a system that it have a great central body, the mass of
which should be at least vastly greater than that of the indi-
vidual bodies which revolve around it. At least, such a cen-
tral body could be dispensed with only by the separate stars
having a regularity of motion and arrangement which cer-
tainly does not exist in the stellar system as we actually see
it. The question, then, reduces itself to this : Are there any
immense attracting centres around which the separate collec-
tions of stars revolve ; or is there any centre around which all
the stars which compose the visible universe revolve ? In all
DO THE STAES REALLY FORM A SYSTEM? 485
human probability, these questions must be answered in the
negative. All analogy leads us to believe that if there were
any such central masses, they would be not only larger than
the other stars, but brighter in a yet greater proportion. It
is, of course, possible to conceive of immense dark bodies,
such as Lambert supposed to exist, but we cannot but believe
the existence of such bodies to be very improbable. Al-
though there is, as we have seen, great diversity among the
stars in respect to their magnitudes, there are none of them
which seem to have that commanding preeminence above
their fellows which the sun presents above the planets which
surround him.
But the most conclusive proof that the stars do not revolve
round definite attracting centres is found in the variety and
irregularity of their proper motions, which we have already
described. We have shown (1) that when the motions of
great numbers of stars are averaged, there is found a general
preponderance of motions from the constellation Hercules,
which is supposed to be due to a motion of our sun with his
attendant planets in that direction ; and (2) that when the
motions of stars in the same region are compared, there is
often found to be a certain resemblance among them. But
this tendency towards a regular law affects only large masses
of stars, and does not imply any such regularity in the mo-
tions of individual stars as would be apparent if they moved
in regular circular orbits, as the planets move round the sun.
The motion of each individual star is generally so entirely
different from that of its fellows as seemingly to preclude all
reasonable probability that these bodies are revolving in defi-
nite orbits around great centres of attraction.
The most extraordinary instances of the irregularities of
which we speak are found in the stars of unusually rapid
proper motion, which are moving forward at such a rate that
the gravitation of all the known stars cannot stop them until
they shall have passed through and beyond the visible uni-
verse. The most remarkable of these, so far as we know, is
Groombridge 1830, it having the largest apparent proper mo-
486 THE STELLAR UNIVERSE.
tion of any known star. The most careful determinations of
its parallax seem to show that its distance is so immense that
the parallax is only about a tenth of a second ; that is, a line
drawn from the sun to the earth would subtend an angle of
only a tenth of a second when viewed from this star. But
the apparent motion of the star, as we actually see it, is more
than seven seconds per annum, or seventy times its parallax.
It follows that the star moves over a space of more than sev-
enty times the distance of the sun from us in the space of a
year. If, as is likely, the motion of the star is oblique to the
line in which we see it, its actual velocity must be yet greater.
Leaving this out of account, we see that the star would pass
from the earth to the sun in about five days, so that its veloci-
ty probably exceeds two hundred miles per second.
To understand what this enormous velocity may imply, we
must advert to the theorem of gravitational astronomy that
the velocity which a body can acquire by falling towards an
attracting centre is, at each point of its path, limited. For ex-
ample, a body falling from an infinite distance to the earth's
surface, and acted on by the attraction of the earth alone, would
acquire a velocity of only about seven miles per second. Vice
versa,& body projected from the earth with this velocity would
never be stopped by the earth's attraction alone, but would
describe an elliptic orbit round the sun. If the velocity ex-
ceeded twenty-seven miles per second, the attraction of the sun
himself could never stop it, and it would wander forever
through the stellar spaces. The greater the distance from the
sun at which the body is started, the less the velocity which
will thus carry it forever away from the sun. At the orbit of
Uranus the required velocity would be only six miles per sec-
ond ; at Neptune, it would be less than five miles per second ;
half-way between the sun and a Centauri, it would be a mile
in twelve seconds, or a fourth the speed of a cannon-ball. If
we knew the masses of 'each of the stars, and their arrange-
ment in space, it would be easy to compute this limiting ve-
locity for a body falling from an infinite distance to any point
of the stellar system. If the motion of a star were found to
DO THE STARS REALLY FORM A SYSTEM? 487
exceed this limit, it would show that the star did not belong
to the visible universe at all, but was only a visitor flying
on a course through infinite space at such a rate that the
combined attraction of all the stars could never stop it.
Let us now see how the case may stand with our flying star,
arid what relation its velocity may bear to the probable attrac-
tion of all the stars which exist within the range of the tel-
escope. The number of stars actually visible with the most
powerful telescopes probably falls short of fifty millions ; but,
to take a probable outside limit, we shall suppose that within
the regions occupied by the farthest stars which the telescope
will show, there are fifty millions more, so small that we cannot
see them, making one hundred millions in all. We shall also
suppose that these stars have, on the average, five times the
mass of the sun, and that they are spread out in a layer across
the diameter of which light would require thirty thousand years
to pass. Then, a mathematical computation of the attractive
power exerted by such a system of masses shows that a body
falling from an infinite distance to the centre of the system
would acquire a velocity of twenty -five miles per second.
Vice versa, a body projected from the centre of such a system
with a velocity of more than twenty-five miles per second in
any direction whatever would not only pass entirely through
it, but would fly off into infinite space, never to return. If the
body were anywhere else than in the centre of the system, the
velocity necessary to carry it away would be less than the
limit just given. But this calculated limit is only one-eighth
the probable velocity of 1830 Groombridge. The force re-
quired to impress a given velocity on a body falling through
any distance is proportional to the square of the velocity, four
times the force being required to give double the velocity, nine
times to increase it threefold, and so on. To give eight times
the velocity would require sixty-four times the attracting mass.
If, then, the star in question belongs to our stellar system, the
masses or extent of that system must be many times greater
than telescopic observation and astronomical research indicate.
We may place the dilemma in a concise form, as follows :
488 1HE STELLAR VNIVEESE.
Either the bodies which compose our universe are vastly
more massive and numerous than telescopic examination
seems to indicate, or 1830 Groornbridge is a runaway star,
flying on a boundless course through infinite space with such
momentum that the attraction of all the bodies of the universe
can never stop it.
Which of these is the more probable alternative we cannot
pretend to say. That the star can neither be stopped, nor bent
far from its course until it has passed the extreme limit to
which the telescope has ever penetrated, we may consider
reasonably certain. To do this will require two or three mill-
ions of years. Whether it will then be acted on by attractive
forces of which science has no knowledge, and thus carried
back to where it started, or whether it will continue straight
forward forever, it is impossible to say.
Much the same dilemma may be applied to the past history
of this body. If the velocity of two hundred miles or more
per second with which it is moving exceeds any that could be
produced by the attraction of all the other bodies in the uni-
verse, then it must have been flying forward through space
from the beginning, and, having come from an infinite dis-
tance, must be now passing through our system for the first
arid only time.
It may be asked whether, in Lambert's hypothesis of im-
mense attracting bodies, invisible on account of their being
dark, we have not at once the centres required to give general
stability to the stellar system, and to keep the star of which
we have spoken in some regular orbit. We answer, no. To
secure such stability, stars equally distant from the attracting
centres must move with nearly the same velocity. An at-
tracting centre sufficiently powerful to bring a body moving
two hundred miles per second into a regular orbit would
draw most of the other stars moving with small velocities into
its immediate neighborhood, arid thus subvert the system. We
thus meet the double difficulty that we have good reason to
doubt the existence of these opaque, dark bodies, and that if
they did exist, they would not fulfil our requirements.
DO THE STARS REALLY FORM A SYSTEM? 4:89
The general result of our inquiry is that the stellar uni-
verse does not seem to possess that form of unvarying stabil-
ity which we see in the solar system, and that the stars move
in irregular courses depending on their situation in respect
to the surrounding stars, and probably changing as this situa-
tion changes. If there were no motion at all among the stars,
they would all fall to a common centre, and universal ruin
would be the result. But the motions which we actually see
are sufficient to prevent this catastrophe, by supplying each
star with a reserve of force which will generally keep it from
actual collision with its neighbors. If, then, any one star
does fall towards any attracting centre, the velocity which it
acquires by this fall will carry it away again in some other
direction, and thus it may keep up a continuous dance, under
the influence of ever- vary ing forces, as long as the universe
shall exist under its present form.
To those who have been enraptured with the sublime specu-
lations of Kant and Lambert, this may seem an unsatisfactory
conclusion; while to those who look upon the material uni-
verse as something made to last forever, it may seem improba-
ble. But when we consider the immense periods which would
be required for the mutual gravitation of the stars to effect
any great change in the stellar system, we may be led to alter
such views as these. We have shown that tens of thousands
of years would be required to make any great change in the
arrangement of the stars which we see with the naked eye.
The time required for all the stars visible with the telescope
to fall together by their own attraction is to be counted by
millions of years. If the universe had existed in its present
state from eternity, and were to exist forever, the immensity
of these periods would not be at all to the point, because a
million of years is no more a part of eternity than a single
day. But all modern science seems to point to the finite
duration of our system in its present form, and to carry us
back to the time when neither sun nor planet existed, save as
a mass of glowing gas. How far back that was, it cannot tell
us with certainty ; it can only say that the period is counted
490 THE STELLAR UNIVERSE.
by millions of years, but probably not by hundreds of mill-
ions. It also points forward to the time when the sun and
stars shall fade away, and nature shall be enshrouded in dark-
ness and death, unless some power now unseen shall uphold
or restore her. The time required for this catastrophe cannot
be calculated ; but it is probably not so great that the stellar
system can, in the mean time, be subverted by the mutual
gravitation of its members.
It would thus appear as if those nicely arranged adjust-
ments which secure stability and uniformity of motion are
not found where they are not necessary to secure the system
from subversion during the time it is to last, much as the
wheel of an engine which is to make but two or three revo-
lutions while the engine endures need not be adjusted to
make thousands of revolutions. The bodies which form our
solar system are, on the other hand, like wheels which have
to make millions of revolutions before they stop. Unless there
is a constant balance between the opposing forces under the
influence of which they move, there must be a disarrangement
of the movement long before the engine wears out. Thus,
although the present arrangement of the stars may be studied
without any reference to their origin, yet, when we seek to
penetrate the laws of their motion, and foresee the changes
of state to which their motions may give rise, we are brought
to face the question of their duration, and hence of their be-
ginning and end.
THE COSMOGONY.
CHAPTER III.
THE COSMOGONY.
THE idea that the world has not endured forever in the
form in which we now see it, but that there was a time when
it either did not exist at all, or existed only as a mass " with-
out form, and void," is one which we find to have been always
held by mankind. The " chaos" of the Greeks the rude and
formless materials, subject to no law, out of which all things
were formed by the creative power corresponds in a striking
manner to the nebulous masses of modern astronomy. These
old ideas of chaos were expressed by Milton in the second
book of "Paradise Lost," before such a thing as a nebula
could be said to be known, and he would be a bold astrono-
mer who, in giving a description of the primeval nebulous
mass, would attempt to improve on the great poet :
" a dark,
Illimitable ocean, without bound,
Without dimension, where length, breadth, and height,
And time and place, are lost ; where eldest Night
And Chaos, ancestors of Nature, hold
Eternal anarchy amidst the noise
Of endless wars, and by confusion stand :
For hot, cold, moist, and dry, four champions fierce,
Strive here for mastery, and to battle bring
Their embryon atoms.
*******
Chaos umpire sits,
And by decision more embroils the fray
By which he reigns : next him, high arbiter,
Chance governs all. Into this wild abyss
The womb of Nature, and perhaps her grave,
Of neither sea, nor shore, nor air, nor fire,
But all these in their pregnant causes mixed
Confusedly, and which thus must ever fight,
4:92 THE STELLAR UNIVERSE.
Unless the almighty Maker them ordain
His dark materials to create more worlds
******
Some tumultuous cloud
Instinct with fire and nitre."
If we classify men's ideas of the cosmogony according to
the data on which they are founded, we shall find them divis-
ible into three classes. The first class comprises those formed
before the discovery of the theory of gravitation, and which,
for this reason, however correct they might have been, had no
really scientific foundation. The second are those founded on
the doctrine of gravitation, but without a knowledge of the
modern theory of the conservation of force ; while the third
are founded on this theory. It must not be supposed, how-
ever, that the ideas of the last-mentioned class are antagonistic
to those of the other classes. Kant and Laplace founded the
nebular hypothesis on the theory of gravitation alone, the con-
servation of force being then entirely unknown. It was, there-
fore, incomplete as it came from their hands, but not neces-
sarily erroneous in its fundamental conceptions.
The consideration of the ancient ideas of the origin of the
world belongs rather to the history of philosophy than to as-
tronomy, for the reason that they were of necessity purely
speculative, and reflected rather the mode of thought of the
minds in which they originated than any definite system of
investigating the operations of nature. The Hindoo concep-
tion of Brahma sitting in meditation on a lotus-leaf through
long ages, and then producing a golden egg as large as the
universe, out of which the latter was slowly evolved, is not
founded on even the crudest observation, but is purely a result
of the speculative tendency of the Hindoo mind. The Jew-
ish cosmogony is the expression of the monotheistic views of
that people, and of the identity of their tutelary divinity with
the maker of heaven and earth. Hipparchus and Ptolemy
showed the scientific turn of their minds by confining them-
selves to the examination of the universe as it is, without mak-
ing any vain effort to trace its origin.
THE MODEEN NEBULAR HYPOTHESIS. 493
Though the systems to which we refer are essentially un-
scientific, it must not be supposed that they were all errone-
ous in their results, or that they belong exclusively to ancient
times. Thus, the views of Swedenborg, though they belong
to the class in question, are remarkably in accordance with
recent views of the subject as regards the actual changes which
took place during the formation of the planets. A great deal
of what is written on the subject at present is to be included
in this same ancient class, as being the production of men who
are not mathematicians or working astronomers, and who,
therefore, cannot judge whether their views are in accordance
with mechanical laws and with the facts of observation. Pass-
ing over all speculation of this sort, no matter when or by
whom produced, we shall consider in historical order the works
of those who have actually contributed to placing the laws of
cosmogony on a scientific foundation.
1. The Modern Nebular Hypothesis.
From a purely scientific point of view, Kant has probably
the best right to be regarded as the founder of the nebular
hypothesis, because he based it on an examination of the actual
features of the solar system, and on the Newtonian doctrine
of the mutual gravitation of all matter. His reasoning is
briefly this: Examining the solar system, we find two remark-
able features presented to our consideration. One is that six
planets and nine satellites (the entire number then known)
move around the sun in circles, not only in the same direction
in which the sun himself revolves on his axis, but very nearly
in the same plane. This common feature of the motion of
so many bodies could not, by any reasonable possibility, have
been a result of chance ; we are, therefore, forced to believe
that it must be the result of some common cause originally
acting on all the planets.
On the other hand, when we consider the spaces in which
the planets move, we find them entirely void, or as good as
void ; for if there is any matter in them, it is so rare as to be
without effect on the planetary motions. There is, therefore,
494 THE STELLAR UNIVERSE,
no material connection now existing between the planets
through which they might have been forced to take up a com-
mon direction of motion. How, then, are we to reconcile this
common motion with the absence of all material connection ?
The most natural way is to suppose that there was once some
such connection which brought about the uniformity of mo-
tion which we observe ; that the materials of which the plan-
ets are formed once filled the whole space between them. " I
assume," says Kant, " that all the materials out of which the
bodies of our solar system were formed were, in the begin-
ning of things, resolved in their original elements, and filled all
the space of the universe in which these bodies now move."
There was no formation in this chaos, the formation of sepa-
rate bodies by the mutual gravitation of parts of the mass be-
ing a later occurrence. But, naturally, some parts of the mass
would be more dense than others, and would thus gather
around them the rare matter which filled the intervening
spaces. The larger collections thus formed would draw the
smaller ones into them, and this process would continue until
a few round bodies had taken the place of the original chaotic
mass.
If we examine the result of this hypothesis by the light of
modern science, we shall readily see that all the bodies thus
formed would be drawn to a common centre, and thus we
should have, not a collection of bodies like the solar system,
but a single sun formed by the combination of them all. In
attempting to show how the smaller masses would be led to
circulate around the larger ones in circular orbits, Kant's rea-
soning ceases to be satisfactory. He seems to think that the
motion of rotation could be produced indirectly by the repul-
sive forces acting among the rarer masses of the condensing
matter, which would give rise to a whirling motion. But the
laws of mechanics show that the sum total of rotary motion in
a system can never be increased or diminished by the mutual
action of its separate parts, so that the present rotary motions
of the sun and planets must be the equivalent of that which
they had from the beginning.
THE MODERN NEBULAR HYPOTHESIS. 495
HerscheVs Hypothesis. It is remarkable that the idea of
the gradual transmutation of nebulse into stars seems to have
been suggested to Herschel, not by the relations of the solar
system, but by his examinations of the nebulae themselves.
Many of these bodies seemed to him to be composed of im-
mense masses of phosphorescent vapor, and he conceived that
these masses must be gradually condensing, each around its
own centre, or around those parts where it is most dense, until
it should be transmuted into a star or a cluster of stars. On
classifying the numerous nebuke which lie discovered, it
seemed to him that he could see each stage of this operation
going on before his eyes. There were the large, faint, diffused
nebulae, in which the process of condensation seemed to have
hardly begun ; the smaller but brighter ones, which had been
so far condensed that the central parts would soon begin to
form into stars ; yet others, in which stars had actually begun
to form ; and, finally, star clusters in which the condensation
was complete. As Laplace observes, Herschel followed the
condensation of the nebulso in much the same way that we
can, in a forest, study the growth of the trees by comparing
those of the different ages which the forest contains at the
same time. The spectroscopic revelations of the gaseous nat-
ure of the true nebulse tend to strengthen these views of Her-
schel, and to confirm us in the opinion that these masses will
all at some time condense into stars or clusters of stars.
Laplace s View of the Nebular Hypothesis. Laplace was led
to the nebular hypothesis by considerations very similar to
those presented by Kant a few years before. The remarkable
uniformity among the directions of rotation of the planets be-
ing something which could not have been the result of chance,
he sought to investigate its probable cause. This cause, he
thought, could be nothing else than the atmosphere of the sun,
which once extended so far out as to fill all the space now oc-
cupied by the planets. He does not, like Kant, begin with a
chaos, out of which order was slowly evolved by the play of
attractive and repulsive forces, but with the sun, surrounded
by this immense fiery atmosphere. Knowing, from mechan-
496 THE STELLAR UNIVERSE.
ical laws, that the sum total of rotary motion now seen in the
planetary system must have been there from the beginning, he
conceives the immense vaporous mass forming the sun and
his atmosphere to have had a slow rotation on its axis. The
mass being intensely hot would slowly cool off, and as it did so
would contract towards the centre. As it contracted, its ve-
locity of rotation would, in obedience to one of the funda-
mental laws of mechanics, constantly increase, so that a time
would arrive when, at the outer boundary of the mass, the cen-
trifugal force due to. the rotation would counterbalance the at-
tractive force of the central mass. Then, those outer portions
would be left behind as a revolving ring, while the next inner
portions would continue to contract until, at their boundary,
the centrifugal and attractive forces would be again balanced,
when a second ring would be left behind, and so on. Thus,
instead of a continuous atmosphere, the sun would be sur-
rounded by a series of concentric revolving rings of vapor.
Now, how would these rings of vapor behave ? As they
cooled off, their denser materials would condense first, and
thus the ring would be composed of a mixed mass, partly solid
and partly vaporous, the quantity of solid matter constantly
increasing, and that of vapor diminishing. If the ring were
perfectly uniform, this condensing process would take place
equally all around it, and the ring would thus be broken up
into a group of small planets, like that which we see between
Mars and Jupiter. But we should expect that in general
some portions of the ring would be much denser than others,
and the denser portions would gradually attract the rarer por-
tions around it until, instead of a ring, we should have a sin-
gle mass, composed of a nearly solid centre surrounded by an
immense atmosphere of fiery vapor. This condensation of the
ring of vapor around a single point would have produced no
change in the amount of rotary motion originally existing in
the ring ; the planet, surrounded by its fiery atmosphere, would
therefore be in rotation, and would be, in miniature, a repro-
duction of the case of the sun surrounded by his atmosphere
with which we set out. In the same way that the solar at-
THE MODERN NEBULAR HYPOTHESIS. 497
mosphere formed itself first into rings, and then these rings
condensed into planets, so, if the planetary atmospheres were
sufficiently extensive, they would form themselves into rings,
and these rings would condense into satellites. In the case of
Saturn, however, one of the rings was so perfectly uniform
that there could be no denser portion to draw the rest of
the ring around it, and thus we have the well-known rings
of Saturn.
If, among the materials of the solar atmosphere, there were
any so rare and volatile that they would not unite themselves
either into a ring or around a planet, they would continue to
revolve around the sun, presenting an appearance like that
of the zodiacal light. They would offer no appreciable re-
sistance to the motion of the planets, not only on account of
their extreme rarity, but because their motion would be the
same as that of the planets which move among them.
Such is the celebrated nebular hypothesis of Laplace which
has given rise to so much discussion. It commences, not with
a purely nebulous mass, but with the sun surrounded by a
liery atmosphere, out of which the planets were formed. On
this theory the sun is older than the planets ; otherwise it
would have been impossible to account for the slow rotation
of the sun upon his axis. If his body had been formed of ho-
mogeneous matter extending out uniformly to near the orbit
of Mercury, it would not have condensed into a globe revolv-
ing on its axis in twenty-five days, but into a flat, almost lens-
shaped, body, which would have been kept from forming a
sphere by the centrifugal force. But the denser materials be-
ing condensed first, perhaps into such a body as we described,
the friction of the vmcondensed atmosphere would have di-
minished the rotation of the sun, the rotating energy which he
lost being communicated to the embryo planets and throwing
them farther away.
In accordance witli the hypothesis of Laplace, it has al-
ways been supposed that the outer planets were formed first.
There is, however, a weak point in Laplace's theory of the for-
mation of rings. lie supposed that when the centrifugal and
33
498 THE STELLAR UNIVERSE.
centripetal forces balanced each other at the outer limit of
the revolving mass, the outer portions were separated from the
rest, which continued to drop towards the centre. If the plan-
etary rings were formed in this way, then, after each ring was
thrown off, the atmosphere must have condensed to nearly
half its diameter before another would have been thrown off,
because we see that each planet is, on the whole, nearly twice
as far as the one next within it. But there being no cohe-
sion between particles of vapor, such thro wing-off of immense
masses of the outside portions of the revolving mass was im-
possible. The moment the forces balanced, the outer portions
of the mass would, indeed, cease to drop towards the sun, and
would partially separate from the portions next to it ; then
these would separate next, and so on ; that is, there would be
a constant dropping-off of matter from the outer portions, so
that, instead of a series of rings, there would have been a flat
disk formed of an infinite number of concentrating rings all
joined together.
If we examine the subject more closely, we shall see that
the whole reasoning by which it is supposed that the inner
portions of the mass would drop away from the outer ones
needs important modifications. In its primeval state, when it
extended far beyond the present confines of the solar system,
the rare nebulous atmosphere must have been nearly spherical.
As it gradually contracted, and the effect of centrifugal force
thus became more marked, it would have assumed the form
of an oblate spheroid. When the contraction had gone so
far that the centrifugal and attracting forces nearly balanced
each other at the outer equatorial limit of the mass, the result
would have been that contraction in the direction of the equa-
tor would cease entirely, and be confined to the polar regions,
each particle dropping, not towards the sun, but towards the
plane of the solar equator. Thus, we should have a constant
flattening of the spheroidal atmosphere until it was reduced
to a thin flat disk. This disk might then separate itself into
rings, which would form planets in much the same way that
Laplace supposed. But there would probably be no marked
PROGRESSIVE CHANGES IN OUR SYSTEM. 499
difference in the age of the planets ; quite likely the smaller
inner rings would condense into planets more rapidly than the
wide-spread outer ones.
Kant and Laplace may be said to have arrived at the neb-
ular hypothesis by reasoning forward, and showing how, by
supposing that the space now occupied by the solar system
was once filled by a chaotic or vaporous mass, from which the
planets were formed, the features presented by this system
could be accounted for. We are now to show how our mod-
ern science reaches a similar result by reasoning backward
from actions which we see going on before our eyes.
2. Progressive Changes in our System.
During the short period within which accurate observations
have been made, no actual permanent change has been ob-
served in our system. The earth, sun, and planets remain of
the same magnitude, and present the same appearance as al-
ways. The stars retain their brilliancy, and, for the most part,
the nebute their form. Not the slightest variation has been
detected in the amount of heat received from the sun, or in
the average number and extent of the spots on his surface.
And yet we have reason to believe that these things are all
changing, and that the time will come when the state of the
universe will be very different from that in which we now see
it. How a change may be inferred when none is actually vis-
ible may be shown by a simple example.
Suppose an inquiring person, walking in what he sup-
posed to be a deserted building, to find a clock running. If
he is ignorant of mechanics, he will see no reason why it may
not have been running just as he now sees it for an indefinite
period, and why the pendulum may not continue to vibrate,
and the hands to go through their revolutions, so long as the
fabric shall stand. He sees a continuous cycle of motions, and
can give no reason why they should not have been going on
since the clock was erected, and continue to go on till it shall
decay. But let him be instructed in the laws of mechanics,
and let him inquire into the force which keeps the hands and
500 THE STELLAR UNIVERSE.
pendulum in motion. lie will then find that this force is
transmitted to the pendulum through a train of wheels, each
of which moves many times slower than that in front of it,
and that the first wheel is acted upon by a weight, with which
it is connected by a cord. He can see a slow motion in the
Avheel which acts on the pendulum,- and perhaps in the one
next behind it, while during the short time he has for exami-
nation he can see no motion in the others. But if he sees how
the wheels act on each other, he will know that they must all
be in motion ; and when lie traces the motion back to the first
wheel, he sees that its motion must be kept up by a gradual
falling of the weight, though it seems to remain in the same
position. He can then say with entire certainty: "I do not see
this weight move, but I know it must be gradually approach-
ing the bottom, because I see a system of moving machinery,
the progress of which necessarily involves such a slow falling
of the weight. Knowing the number of teeth in each wheel
CD O
and pinion, I can compute how many inches it falls each day ;
and seeing how much room it has to fall in, I can tell how
many days it will take to reach the bottom. When this is
done, I see that the clock must stop, because it is only the fall-
ing of the weight that keeps its pendulum in motion. More-
over, I see that the weight must have been higher yesterday
than it is to-day, and yet higher the day before, so that I can
calculate its position backward as well as forward. By this
calculation I see backward to a time when the weight was
at the top of its course, higher than which it could not be.
Thus, although I see no motion, I see with the eye of reason
that the weight is running through a certain course from the
top of the clock to the bottom ; that some power must have
wound it up and started it ; and that unless the same power
intervenes again, the weight must reach the bottom in a cer-
tain number of days, and the clock must then stop."
The corresponding progressive change exhibited by the
operations of nature consists in a constant transformation of
motion into heat, and the constant loss of that heat by radia-
tion into space. As Sir William Thomson has expressed it,
PROGRESSIVE CHANGES IN OUR SYSTEM. 501
a constant " dissipation of energy" is going on in nature.
We all know that the sun has been radiating heat into space
during the whole course of his existence. A small portion of
this heat strikes the earth, and supports life and motion on its
surface. All this portion of the sun's heat, after performing
its function, is radiated off into space by the earth itself. The
portion of the sun's radiant heat received by the earth is, how-
ever, comparatively insignificant, since our luminary radiates
in every direction equally, while the earth can receive only a
part represented by the ratio which its apparent angular mag-
nitude as seen from the sun bears to the whole celestial sphere,
which a simple calculation shows to be the ratio of 1 to
2,170,000,000. The stars radiate heat as well as the sun.
The heat received from them, when condensed in the focus of
a telescope, has been rendered sensible by the thermo-multi-
plier, and there is every reason to believe that stellar heat and
light bear the same proportion to each other that solar heat
and light do. Wherever there is white stellar light, there
must be stellar heat ; and as we have found that the stars in
general give more light than the sun, we have reason to be-
lieve that they give more heat also. Thus we have a contin-
uous radiation from all the visible bodies of the universe,
which must have been going on from the beginning.
Until quite recently, it was not known that this radiation
involved the expenditure of a something necessarily limited in
supply, and, consequently, it was not known but that it might
continue forever without any loss of power on the part of the
sun and stars. But it is now known that heat cannot be pro-
duced except by the expenditure of force, actual or potential,
in some of its forms, and it is also known that the available
supply of force is necessarily limited. One of the best-estab-
lished doctrines of modern science is that force can no more
be produced from nothing than matter can : to find it so pro-
duced would be as complete a miracle as to see a globe created
from nothing before our eyes. Hence, this radiation cannot
go on forever unless the force expended in producing the heat
be returned to the sun in some form. That it is not now
502 THE STELLAR UNIVERSE.
so returned we may regard as morally certain. There is no
known law of radiation, except that it proceeds out in straight
lines from the radiating centre. If the heat were returned
back to the sun from space, it would have to return to the
centre from all directions ; the earth would then intercept as
much of the incoming as of the outgoing heat ; that is, we
should receive as much heat from the sky at night as from
the sun by day. We know very well that this is not the case ;
indeed, there is no evidence of any heat at all reaching us from
space except what is radiated from the stars.
Since, then, the solar heat does not now return to the sun,
we have to inquire what becomes of it, and whether a com-
pensation may not at some time be effected whereby all the
lost heat will be received back again. Now, if we trace the
radiated heat into the wilds of space, we may make three pos-
sible hypotheses respecting its ultimate destiny :
1. We may suppose it to be absolutely annihilated, just as it
was formerly supposed to be annihilated when it was lost by
friction.
2. It may continue its onward course through space forever.
3. It may, through some agency of which we have no con-
ception, be ultimately gathered and returned to the sources
from which it emanated.
The first of these hypotheses is one which the scientific
thinkers of the present day would not regard as at all philo-
sophical. In our scientific philosophy, the doctrine that force
cannot be annihilated is coequal with that that it cannot be
created; and. the inductive processes on which the latter doc-
trine is founded are almost as unimpeachable as those from
which we conclude that matter cannot be created. At the
same time, it might be maintained that all these doctrines re-
specting the uncreatableness and indestructibility of matter
and force can have no proper foundation except induction
from experiment, and that the absolute truth of a doctrine
like this cannot be proved by induction. Especially may this
be claimed in respect of force. The most careful measures of
force which we can make under all circumstances show that it
PROGRESSIVE CHANGES IN OUR SYSTEM. 503
is subject to no sensible loss by either transmission or transfor-
mation. But this alone does not prove that it can be subject
to no loss in a passage through space requiring hundreds of
thousands or millions of years. There is also this essential
difference between force and matter, that we conceive the lat-
ter as made up of individual parts which preserve their iden-
tity through all the changes of form which they undergo ;
while force is something in which we do not conceive of any
such identity. Thus, when I allow a drop of water to evapo-
rate from iny hand, I can in imagination trace each molecule
of water through the air, into the clouds, and down to the
earth again in some particular drop of rain, so that, if I only
had the means of actually tracing it, I could say, " This cup
contains one, or two, or twenty of the identical molecules
which evaporated from my hand a week or a month ago."
It is on this idea of the separate identity of each molecule
of matter that our opinion of the indestructibility of matter is
founded, because matter cannot be destroyed without destroy-
ing individual molecules, and any cause which could destroy a
single molecule might equally destroy all the molecules in the
universe.
But neither parts nor identity is possible in force. A cer-
tain amount of heat may be expended in simply raising a
weight. Here heat has disappeared, and is replaced by a
mere change of position something which cannot be con-
ceived as identical with it. If we let the weight drop, the
same amount of heat will be reproduced that was expended
in raising the weight; but, though equal in quantity, it can-
not be regarded as identical in the way that the water con-
densed from steam is identical with that which was evapo-
rated to form the steam. If measures showed it to be less
in quantity, we could not say there was a destruction of an
identical something which previously existed, as we could if
the condensed steam were not equal to the water evaporated.
Therefore, while the doctrine of the indestructibility of force
is universally received as a scientific principle, it can hardly
be claimed that induction has established its absolute correct-
504 THE STELLAR UNIVERSE.
ness ; and, in a case like the present, where we see something
which transcends scientific explanation, the failure of the
widest induction may be considered among the possible alter-
natives.
The second alternative that the heat radiated from the
sun and stars continues its onward course through space for-
ever is the one most in accord with our scientific concep-
tions. We actually receive heat from the most distant star
visible in our telescopes, and this heat has, according to the
best judgment we can form, been travelling thousands of
years without any loss whatever. From this point of view,
every radiation which has ever emanated from the earth or
the sun is still pursuing its course through the stellar spaces,
without any other diminution than that which arises from its
being spread over a wider area. A very striking presentation
of this view is, we believe, clue to some modern writer. If
an intelligent being had an eye so keen that he could see the
smallest object by the faintest light, and a movement so rapid
that he could pass from OTIC bound of the stellar system to the
other in a few years, then, by viewing the earth from a dis-
tance much less than that of the farthest sttfr, he would see it
by light which had left it several thousand years before. By
simply watching, he would see the whole drama of human his-
tory acted over again, except where the actions had been hid-
den by clouds, or under other obstacles to the radiation of light.
The light from every human action performed under a clear
sky is still pursuing its course among the stars, and it needs
only the powers we have mentioned to place a being in front
of the ray, and let him see the action again.
If the hypothesis now under consideration be the correct
one, then the heat radiated by the sun and stars is forever lost
to them. There is no known way by which the heat thus sent
off can be returned to the sun. It is all expended in produc-
ing vibrations in" the ethereal medium which constantly ex-
tend out farther and farther into space.
The third hypothesis, like the first, is a simple conjecture
permitted by the necessary imperfection of our knowledge.
THE SOURCES OF THE SUN'S HEAT. 505
All the laws of radiation and all our conceptions of space
lead to the conclusion that the radiant heat of the sun can
never be returned to it. Such a return can result only from
space itself having such a curvature that what seems to us a
straight line shall return into itself, as has been imagined by a
great German mathematician ;* or from the ethereal medium,
the vibrations in which constitute heat being limited in extent ;
or, finally, through some agency as yet totally unknown to sci-
ence. The first idea is too purely speculative to admit of dis-
cussion, while the other two suppositions transcend our science
as completely as does that of an actual annihilation of force.
3. The Sources of the Sun's Heat.
We may regard it as good as an observed fact that the sun
has been radiating heat into void space for thousands or even
millions of years, without any apparent diminution of the sup-
ply. One of the most difficult questions of cosmical physics
a question the difficulty of which was not seen before the dis-
covery of the conservation of force has been, How is this sup-
* This idea belongs to that transcendental branch of geometry which, rising
above those conceptions of space derived from our experience, investigates what
may be possible in the relations of parts of space considered in their widest range.
Jt is now conceded that the supposed a priori necessity of the axioms of geom-
etry has no really sound logical foundation, and that the question of the limita-
tions within which they arc true is one to be settled by experience. Especially is
this true of the theorem of parallels, no really valid demonstration either that two
parallel straight lines will never meet or never diverge being possible. By reject-
ing the limitations imposed upon our fundamental geometrical conceptions, yet
without admitting anything which positively contradicts them, several geometrical
svstems have been constructed in recent times, which are included under the gen-
eral appellation of the non-Euclidian Geometry. The most celebrated and re-
markable of these systems is that of Riemann, who showed that although w r e are
obliged to conceive of space as unbounded, since no position is possible which has
not space on all sides of it, yet there is no necessity that we shall consider it as
infinite. It may return into itself in something the manner of the surface of a
sphere, which, though it has no boundary, yet contains only a finite number of
square feet, and on which one who travels straight forward indefinitely will finally
arrive at his starting-point. Although this idea of the finitude of space transcends
our fundamental conceptions, it does not contradict them, and the most that ex-
perience can tell us in the matter is that, though space be finite, the whole extent
of the visible universe can be but a very small fraction of the sum total of space.
506 THE STELLAR UNIVERSE.
ply of heat kept up ? If we calculate at what rate the tem-
perature of the sun would be lowered annually by the radia-
tion from its surface, we shall find it to be 2^- Fahrenheit per
annum, supposing its specific heat to be the same as that of
water, and from 5 to 10 per annum, if we suppose it the
same as most of the substances which compose our globe. It
would, therefore, have entirely cooled off in a few thousand
years after its formation if it had no other source of heat
than that shown by its temperature.
That the temperature could be kept up by combustion, as
terrestrial fires are kept up, is out of the question, as new fuel
would have to be constantly added in quantities which cannot
possibly exist in the neighborhood of the sun. But an allied
source of heat has been suggested, founded on the law of the
mechanical equivalency of heat and force. If a body should
fall into the sun from a great height, all the force of its fall
would be turned into heat, and the heat thus produced would
be enormously greater than any that would arise from the
combustion of the falling body. An instance of this law is
shown by the passage of shooting-stars and aerolites through
our atmosphere, where, though the velocity rarely amounts to
more than forty miles a second, nearly all such bodies are con-
sumed by the heat generated. Now, the least velocity with
which a body could strike the sun (unless it had been merely
thrown from the sun and had fallen back) is about 280 miles
per second ; and if the body fell from a great height, the ve-
locity would be over 350 miles per second. The meteoric
theory was founded on this law, and is, in substance, that the
heat of the sun is kept up by the impact of meteors upon his
surface. The fact that the earth in its course around the sun
encounters millions of meteoroids every day is shown by the
frequency of shooting - stars, and leads to the result that the
solar system is, so to speak, crowded with such bodies revolv-
ing in all sorts of erratic orbits. It is therefore to be sup-
posed that great numbers of them fall into the sun ; and the
question whether the heat thus produced can be equal to that
radiated by the sun is one to be settled by calculation. It is
THE SOURCES OF THE SUN'S HEAT. 507
thus found that, in order to keep up the solar heat, a mass of
matter equal to our planet would have to fall into the sun ev-
ery century.
This quantity of meteoric matter is so far beyond all rea-
sonable possibility that it requires little consideration to show
that the supply of solar heat cannot be thus accounted for.
Only a minute fraction of all the meteoroids or other bodies
circulating through space or revolving around the sun could
strike that luminary. In order to reach the sun, they would
have to drop directly to it from space, or be thrown into it
through some disturbance of their orbits produced by planet-
ary attraction. If meteors were as thick as this, the earth
would be so pelted with them that its whole surface would be
made hot by the force of the impact, and all life would be
completely destroyed. While, then, the sun may, at some past
time, have received a large supply of heat in this way, it is
impossible that the supply could always be kept up.
The Contraction Theory. It is now known that there is
really no necessity for supposing the sun to receive heat from
any outward source whatever in order to account for the
preservation of his temperature through millions of years.
As his globe cools off it must contract, and the heat gener-
ated by this contraction will suffice to make up almost the en-
tire loss. This theory is not only in accordance with the laws
of matter, but it admits of accurate mathematical investiga-
tion. Knowing the annual amount of energy which the sun
radiates in the form of heat, it is easy, from the mechanical
equivalent of the heat thus radiated, to find by what amount
he must co 
