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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 coro 
