TEXT-BOOKS OF SCIENCE
ADAPTED FOR THE USE OF
ARTISANS AND STUDENTS IN PUBLIC AND SCIENCE SCHOOLS
ASTRONOMY
ELEMENTS
OF
ASTRONOMY
BY
SIR ROBERT STAWELL BALL, LL.D., F.R.S.
LOWNDBAN PROFESSOR OF ASTRONOMY IN THB
UNIVERSITY OF CAMBRIDGE
NEW IMPRESSION
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
1910
All rights reserved
PREFACE.
THE READER of this volume is expected to possess such
knowledge of Mathematics as may be gained by studying
the Elements of Euclid and Algebra, together with a rudi-
mentary acquaintance with the geometry of Planes and
Spheres.
While the book is mainly intended for beginners, yet it
is believed that more advanced students may find portions
of it useful. This will perhaps be especially the case in the
last chapter, where a somewhat extended account is given
of the important constants of Astronomy, with references to
the original sources of information.
Many of the illustrations have been taken from Delau-
nay's 'Cours Elementaire d' Astronomic,' and a few from
Secchi's ' Le Soleil,' from Guillemin's ' Le Ciel,' and other
sources. In the last chapter extensive use has been made
of Houzeau's * Repertoire des Constantes Astronomiques.'
ROBERT S. BALL.
DUNSINK : June 4, 1880.
In the present edition the work has been revised through-
out. Special care has been taken in the endeavour to bring
the chapter on Astronomical Constants up to a recent
standpoint. The author acknowledges with many thanks
the help he has received from his friend Dr. J. L. E.
Dreyer, Director of Armagh Observatory.
ROBERT S. BALL.
CAMBRIDGE: March 1896.
335925
CONTENTS.
CHAPTER I.
ON THE INSTRUMENTS USED IN ASTRONOMICAL
OBSERVATIONS.
PAGE
Introduction ...... . . . . i
Astronomical Instruments ........ i
Angular Magnitude ......... 2
Brightness of a Distant Object ....... 3
Lenses 4
Formation of Images ......... 6
The Telescope 8
Achromatic Object Glasses 1 1
Reflecting Telescope . . . . . . . .14
The Measurement of Angles . . . . . . . 16
Circular Measure . . . . . . . . 19
Instruments for Measuring Angles . . . . . . 21
Method of Reading an Angle . . . . . . 26
Error of Eccentricity . . . . . . . . 28
The Measurement of Time -. . . . . . . 30
The Clock . . ... 33
The Compensating Pendulum . . . . . -37
Composition of Light ......... 38
Construction of the Spectroscope 39
CHAPTER II.
THE EARTH.
Form of the Earth 43
The Atmosphere ......... 46
Atmospheric Refraction . . . . . . . . 47
viii Contents.
CHAPTER III.
THE DIURNAL MOTION OF THE HEAVENS.
PAGE
The Celestial Bodies 53
The Celestial Sphere 54
The Fixed Stars .... . ... 55
Constellations 58
Diurnal Motion of the Heavens ...... 65
The Equatorial Telescope 67
Circles of the Celestial Sphere 72
Circumpolar Stars ......... 74
The Globe ^76
Rotation of the Earth 78
Shape of the Earth connected with its Rotation .... 80
Definition of Terms ......... 80
The Transit Instrument ........ 83
Error of Collimation . . . . . . . . . 85
Error of Level .......... 86
Error of Azimuth ......... 88
Determination of Right Ascensions ...... 92
The Meridian Circle ......... 96
Latitude 101
Phenomena dependent on Change of Place . . . . . 103
Determination of Latitude . . . . . . .107
Numerical Illustration , . . . 108
Star Catalogues . . . . . . . no
CHAPTER IV.
APPARENT MOTION OF THE SUN.
Annual Motion of the Sun . . m
Observations of the Sun 116
The Micrometer . . . . . . . . . . 119
Apparent Diameter of the Sun . . . . . . .127
The Heliometer 128
Effect of Refraction . . . . . . . . .132
Right Ascension and Declination of the Sun 134
Mean Time and Sidereal Time. . . . . . .138
The Ecliptic 140
Day and Night 142
Contents. ix
PAGE
Zones into which the Earth is Divided . . . . . 153
Effect of Refraction on the Length of the Day . . . 1 56
Twilight 157
Changes of Temperature on the Earth . . . . 161
Mean Temperature . . . . . . . 164
Effect of the Atmosphere . . . . . . . .166
The Origin of Right Ascensions . . . . . . . 167
Celestial Latitude and Longitude . . . . ' . .176
The Sun's Path in Space 177
Velocity of the Sun 181
Changes in the Length of the Seasons . . . . . . 186
CHAPTER V.
THE STRUCTURE OF THE SUN.
Dimensions of the Sun . . . . . . . .187
Sun Spots ........... 188
The Nature of Sun Spots . . . . .- . . .191
The Solar Spectrum . . . 194
The Chromosphere and the Prominences . . . . .196
The Corona . . .198
Constitution of the Sun * 199
Zodiacal Light . ... . . . ... 200
CHAPTER VI.
MOTION OF THE EARTH AROUND THE SUN.
Revolution of the Earth . . . 201
Precession of the Equinoxes ....... 209
Numerical Determination of the Precession . . . .215
Gradual Displacement of the Perihelion of the Earth's Orbit . . 216
The Aberration of Light 2I 7
Velocity of Light . . . . . 2I 9
Nutation of the Earth's Axis .... 22 3
Annual Parallax of Stars 22(3
CHAPTER VII.
THE MOON.
Apparent Movements of the Moon 2 3 2
Phases of the Moon 2 33
x Contents.
^i
PAGE
The Eccentricity of the Moon's Orbit ..... 237
Motion of the Perigee 237
Mean Motion of the Moon ....... 238
Figure of the Moon 238
Parallax of the Moon ........ 239
Dimensions of the Moon . . . 242
Movements of the Moon ........ 243
Motion of the Moon's Nodes ....... 244
Sidereal Revolution of the Moon ...... 245
Rotation of the Moon ......... 246
Mountains in the Moon ........ 247
Periods connected with the Sun and the Moon . . . . 250
Eclipses . . . 251
Prediction of Eclipses 254
Eclipses of the Sun 255
Frequency of Eclipses ......... 256
Prediction of Solar Eclipses ....... 257
Occultations of Fixed Stars ........ 258
Determination of Longitudes by the Moon .... 259
CHAPTER VIII.
THE PLANETS.
Determination of Planets . . ... . . . . 263
The Zodiac ' f . . . .265
Kepler's Laws .......... 265
The Planet Venus 268
Mercury ........... 276
The Superior Planets ........ 279
The Planet Mars . . . ... . . . 279
Appearance of Mars 285
Satellites of Mars 286
Jupiter 289
Saturn . . . 292
Law of Bode . 294
Discovery of New Planets 295
The Minor Planets 297
Elements of the Movements of a Planet 299
The Parallax of the Sun 302
Contents. xi
CHAPTER IX.
COMETS AND METEORS.
PAGE
Comets 3 o 7
Periodic Comets ......... 309
Halley's Comet 3 IO
Distinction between Planets and Comets 311
Shooting Stars 312
CHAPTER X.
UNIVERSAL GRAVITATION.
The Law of Gravitation ........ 322
Perturbations of the Planets 328
Masses of the Planets 330
Gravitation at the Surface of the Celestial Bodies . . . . 332
Perturbations of the Moon . . . . . . 332
The Secular Acceleration ........ 334
Cause of the Precession of the Equinoxes . , . . -335
Nutation . . . . . . . . ... 338
CHAPTER XI.
STARS AND NEBUL/E.
Star Clusters . . . 338
Spectra of Stars . . . . ... . . 340
Telescopic Appearance of a Star . . . . . 341
Stellar Photometry . . . . . . . 343
Variable Stars . . . . .... . . . 344
Proper Motion of Stars ........ 345
Motion of the Sun through Space 346
Real Proper Motion of the Stars 348
Double Stars .......... 349
The Double Star Castor . 350
Motion of a Binary Star 351
Dimensions of the Orbit of a Binary Star 354
Determination of the Mass of a Binary Star .... 355
Colours of Double Stars . . . . . ... 356
Nebulae ........... 357
Classification of Nebulae . . . . . . 357
Spectra of Nebulae 360
Application of Photography to the Study of Stars and Nebulae . 360
xii Contents
CHAPTER XII.
ASTRONOMICAL CONSTANTS.
PAGE
Obliquity of the Ecliptic 362
Secular Diminution of the Obliquity of the Ecliptic . . . 363
Precession of the Equinoxes 364
Nutation 365
Aberration .......... 366
Refraction ........... 367
Twilight 367
Semidiameter of the Sun ........ 368
The Sun's Parallax 369
Elements of the Sun's Rotation ....... 372
Rotation of the Sun ......... 372
Bodies seen Passing across the Sun . . . . . . 372
Heating and Actinic Power of the Sun ..... 373
On the Physical Constitution of the Sun ..... 373
Period of the Solar Spots ........ 374
Elements of the Orbit of Mercury . . . . . . 374
Transits of Mercury across the Sun ...... 375
Diameter of Mercury 375
Mass of Mercury ......... 376
Rotation of Mercury on its Axis . . * . . . . . 376
Plane of the Equator of Mercury ...... 377
Physical Conditions of the Surface of Mercury . . . . 377
Brightness of Mercury ........ 377
Elements of the Orbit of Venus . . . . . 377
Transits of Venus across the Sun ...... 378
Apparent Diameter of Venus 378
Ellipticity .......... 379
Mass of Venus . . . . . . ... 379
Rotation of Venus . . . ...... 380
Brilliancy of Venus . . . . . . . . 380
The Earth Duration of the Year 381
Perihelion ........... 382
The Eccentricity and Equation of the Centre .... 383
Tables of the Sun . . 383
Dimensions of the Earth ........ 384
Ellipticity of the Earth . . . . . . . . 385
Gravitation .......... 385
Rotation of the Earth . . . . . . . . 386
Density .......... . 387
Mass of the Earth . . . , . , . , . 387
Contents. xiii
PAGE
The Moon Secular Variation .. . . ./ , . . 388
Periods of the Lunar Movements ...... 389
The Inclination of the Lunar Orbit to the Ecliptic . . . 390
The Parallax of the Moon * .- 390
Semidiameter of the Moon 391
The Mass of the Moon 391
The Lunar Equator 392
Libration .......... 392
Figure of the Moon ......... 393
Moments of Inertia of the Moon 393
Topography of the Moon ........ 394
Brilliancy of the Moon . . . . . . . '395
Heat from the Moon 395
Elements of Mars ......... 396
Diameter of Mars . . . . . . . . 397
Rotation of Mars ......... 397
Direction of the Axis of Rotation of Mars ..... 398
Mass of Mars . . 398
Brilliancy of Mars . . ... . . . . . 399
Physical Condition of Mars . , . . . , . . 399
Satellites of Mars 399
Eccentricities of the Minor Planets . . . . . . 400
Inclinations . . . . . . . . . . 401
General Features . . . . . . . . . . 401
Elements of Jupiter ......... 402
Great Inequality of Jupiter . . . . .. . 402
Dimensions of Jupiter . . . . .... . . 403
Rotation of Jupiter . . . . . . . . 403
Situation of the Axis of Rotation of Jupiter ..... 404
Mass of Jupiter and his System ....... 405
Brilliancy of Jupiter ......... 46
Physical Conditions of Jupiter ....... 406
Satellites of Jupiter 47
Elements of the Four Outer Satellites 408
Synodic Revolutions . . . . . 408
Eccentricities and Inclinations of the Satellites .... 409
Masses of the Satellites 49
Perturbations of the Satellites 410
Rotation of Jupiter's Satellites 41
Elements of Saturn . . . . . . . . .411
Great Inequality of Saturn . . . . . . . . 411
Rotation of Saturn 4*3
Mass of Saturn . . . . . . . ... 413
xiv Contents.
Brilliancy of Saturn .........
Rings of Saturn ..........
Mass of Saturn's Ring ........
Satellites of Saturn
Elements of Uranus ........
Equatorial Diameter of Uranus at its Mean Distance from the Sun
Mass of Uranus .........
Rotation and Brilliancy of Uranus . . . . . .
Satellites of Uranus .........
Elements of Neptune .........
Diameter, Brilliancy, Mass .......
The Satellite of Neptune
Comets Determined by a Single Apparition ....
Halley's Comet
Tuttle's Comet .
Faye's Comet
Biela's Comet ..........
D'Arrest's Comet .........
Winnecke's Comet .........
Brorsen's Comet ..........
Encke's Comet .........
Other Periodic Comets ,..,....
Physical Theory of Comets .......
Showers of Shooting Stars ........
The Leonides ..........
Radiant Points ........
The Invariable Plane ........
Motion of the Solar System through Space
Star Catalogues .........
Magnitudes of the Stars ........
Measurement of the Brightness of Stars
Variable Stars ........ . .
Colours of Stars .........
Scintillation ....'......
Stellar Spectroscopy .... ...
Parallaxes of the Stars .... ...
Proper Motions of the Stars . . , . : .
Double Stars . ... . . . . . .
Nebulae List of Authorities .......
The Milky Way
The Zodiacal Light
INDEX
ASTRONOMY,
CHAPTER I.
ON THE INSTRUMENTS USED IN ASTRONOMICAL
OBSERVATIONS
1. Introduction. The sun, the moon, and the other
objects which shine in the heavens on a clear night constitute
what are known as the celestial bodies. To study the celestial
bodies is to pursue the branch of science which is called
astronomy. This includes all that can be learned of the
motions of the celestial bodies, of their actual dimensions
and distances, and of their physical constitution.
2. Astronomical Instruments. The instruments which
are employed in making astronomical observations may be
conveniently divided into three classes. Instruments of the
first class are for the purpose of extending our powers of vision,
so as to permit us to use our eyes to greater advantage than
would be possible v ithout such assistance. By instruments
of this class we e enabled to view the features of the
celestial bodj if they were much nearer to us than they
really are. We can thus become acquainted to a certain
extent with the shapes and appearance of many of the
celestial bodies which would otherwise be very imperfectly
known. By the help of these instruments we are also
enabled to perceive large numbers of celestial bodies which
2 " * j&$(ronomy,
are not Sufffelentty : conspicuous to be detected by the
unaided eye. The instruments of this class are termed
telescopes.
We shall subsequently see that the position of a celes-
tial body on the surface of the heavens is to be expressed
by certain angular magnitudes, and therefore the means
by which these magnitudes can be determined must be ex-
plained. The various appliances which are used in making
such measurements of angles form the second class of instru-
ments.
The celestial bodies are in constant motion, real or
apparent. In order to study these motions it is not only
necessary to ascertain the different positions which the
bodies assume, but it is also essential to have the means of
measuring with accuracy the intervals of time which elapse
during which the celestial body is passing from one position
to the positions which it subsequently occupies. We must
therefore be pi jvided with instruments for the purpose of
measuring time. Clocks or chronometers, therefore, consti-
tute the third class of instruments.
3. Angular Magnitude. It will first be necessary for
us to consider briefly the circumstances of ordinary vision
with the unaided eye. We shall then be able to compre-
hend what is the nature of the assistance which is afforded
when a telescope is interposed between the eye and a distant
object
FIG. i.
Let A B (Fig. i ) be an object viewed by an eye placed at
the position o. Then the line A B which connects two
points of the object is seen to subtend an angle A#B at the
point o. If the eye be moved to the point o' t which is
at one-half the distance from M, the line A B will subtend an
Instruments used in Astronomical Observations. 3
angle A o' B. It is obvious that the angle A o' B is greater
than the angle A o B ; and if the line A B be very small in
comparison with its distance from 0, the angle A o' B will be
approximately double the angle A o B. It thus appears that
when the distance of an object is halved the angle under
which the object is seen is doubled. In the same way it
can be shown that if the distance of the object be reduced
to one-third, the angle which it subtends will be increased
threefold, or more generally that if the distance be dimi-
nished in any ratio the angle subtended at the eye will be
increased in the same ratio. It will be convenient to speak
of the angles A0 B, A o' B as the apparent magnitudes of the
line A B, and we are thus led to the following law :
The apparent magnitude of a linear dimension of an
object varies inversely as the distance of the object from the eye.
Since the areas of similar figures are proportional to the
squares of their linear dimensions, it is obvious that the ap-
parent area of an object is proportional tr .the square of the
apparent magnitude of one of its dimensions, and hence we
are led to the result that
The apparent area of a distant object varies inversely as
the square of the distance of the object from the eye. _ ..
4. Brightness of a Distant Object. A luminous object,
whether it shines by its own light or by the light from some
other body reflected
from it, radiates light
in all different direc-
tions. Let us consider
a certain point m of the
body M (Fig. 2), and en-
quire how the apparent
brightness of this point
depends upon the dis-
tance at which the eye
is placed. From the
point m rays of light diverge in all directions, and of these
FIG. 2.
B 2
4 Astronomy.
rays a certain number enter the pupil a b of the eye. The
rays that enter the pupil will all be contained in the cone
of which m is the vertex, while the base of the cone is the
area of the pupil. If, however, the eye be moved to a
distance which is one-half its former distance, so that the
pupil occupies the position a' V , then the rays which enter
the eye will be those contained in the cone, which has the
pupil at 'a' b' for its base and the point m as its vertex. It
is obvious that the angle a m b, which the pupil subtends at
m, is half the angle a' m b'^ which is subtended when the
pupil moves into the new position. It therefore follows
that the apparent area of the pupil a! b' subtended at the
point m is four times as large as it is when the pupil has the
position a b. The quantity of light received by the pupil
from a given point of the body must therefore vary inversely
as the square of the distance. It does not, however, follow
that the brightness of the object increases as the eye ap-
proaches thereto ; for although the quantity of light re-
ceived from a small spot of the body increases as the eye
approaches the body, yet the apparent area of the spot
increases in the same ratio. The quantity of light received
is, therefore, always proportional to the apparent illumi-
nated area, so that the intrinsic brightness of the object is
always the same whatever be the distance from which it is
viewed.
Some modification of this statement would be required
when, as in the case of distant terrestrial objects, a great
thickness of air has to be traversed by the rays. In this
case the absorption of the light by the atmosphere has the
effect of diminishing the brightness of a distant object.
5. Lenses. Telescopes are usually made by inserting
into a tube a certain number of specially shaped pieces of
glass, termed lenses. It will be necessary for us to describe
some of the different forms of lenses and their properties,
in order to understand the combination of lenses which
forms a telescope.
Instruments used in Astronomical Observations. 5
If a converging lens D (Fig. 3) receive a pencil of rays
diverging from a point A, the rays will, after refraction, con-
verge towards a certain fixed point a. A converging lens
FIG. 3.
will act in the same way upon a pencil of rays which diverge
from a point A (Fig. 4) not situated exactly in the axis of
symmetry of the lens, and will bring them to intersect at a.
FIG.
Let us suppose that the point A recedes farther and farther
from the lens, then the point a will draw in closer and closer
towards it. When the point A has at last withdrawn to such
a distance that the rays which diverge from it have become
sensibly parallel, the point a will have moved in to a certain
distance o a, which is called ti\z focal length of the lens (Fig. 5).
6 Astronomy.
The influence of diverging lenses (Fig. 6) upon a pencil of
light is opposite to that of converging lenses. If a convergent
FIG pencil of rays falls upon a diverging lens
it renders them less convergent, or even
parallel or divergent. If the pencil consists
of parallel rays, the diverging lens renders
them divergent ; if the pencil consists of divergent rays, the
diverging lens will render them more divergent.
6. Formation of Images. An object AB (Fig. 7) is
placed in front of a converging lens, at a distance from that
lens which is greater than its focal length.
This object is supposed either to be self-luminous or to
be illuminated by the rays from some source of light. From
each point of the object a pencil of rays will diverge ; this
FIG. 7.
pencil will fall upon the converging lens, and after passing
through the lens the rays will converge to meet at a point on
the other side of the lens. Thiis from the point A of the
image a pencil of rays will diverge, which, after passing
through the lens, converge to the point a. In a similar
manner the pencil of rays proceeding from the point B will
converge to the point b.
It therefore appears that each point of the original
object will be the source of a pencil of rays, which converge
to a corresponding point after passing through the lens. The
figure produced in this way is called an image. If the object
A B be at an exceedingly great distance, then the image will
be formed at the principal focus of the lens.
When we wish to observe the details of a small object it
is usual to employ a single lens for the purpose, which is held
Instruments used in Astronomical Observations. 7
between the object and the eye. In this way the eye can
be brought much closer to the object than would be possible
for distinct vision without the assistance which the lens
affords. The structure of the eye is such that distinct vision
is only possible when the divergence of the rays which enter
the pupil does not exceed a certain amount. If the eye be
brought too close to an object for distinct vision, then the
divergence of the rays from that object is too large. By
placing a simple converging lens between the eye and the
object the divergence of the rays is diminished, and thus
distinct vision is rendered possible.
This effect of a lens can be illustrated by a figure. Let
A B be a small object which is to be examined, and let it be
FIG. 8.
placed between the lens and its focus F, the eye of course
being situated at the other side of the lens. The rays which
diverge from the point A will, after passing through the lens,
have their divergency diminished ; they will therefore appear
as if they diverged from a point a more remote from the
lens, and situated upon the line joining the centre of the
lens to the point A. In a similar way the rays from the
point B will appear to come from the point b, and thus the
whole object A B will appear of the same dimensions as its
image a b. The distance of the image from the eye will
depend upon the distance of the object from the lens, and
the latter maybe adjusted so that the image shall be situated
at the distance of distinct vision. The eye is thus able to
8 Astronomy.
see distinctly the details of the image, because the image is
larger than the object would appear if it were placed at the
distance of distinct vision and viewed without the aid of
the lens.
7. The Telescope. The telescope in its most simple
form consists of a combination of two lenses, one of which
forms an image of the distant object while the other mag-
nifies that image.
Let L (Fig. 9) be a lens, called the object lens, which
receives rays coming from a distant object. An image a b
is formed of this object where o A and o B are directed from
the centre of the lens to the extremities of the distant
object. The image a b is then magnified by the lens into
the image a' b'. The lens L' is termed the eye piece.
FIG. 9.
The distance at which the image a b is situated from the
object lens depends upon the distance of the object itself
from the object glass. When the latter is so great that the
rays from a point may practically be considered to form a
parallel beam, then the distance from a b to the object glass is
equal to the focal length of the object glass. This is of course
the case when the telescope is used for astronomical observa-
tions. The distance at which the lens L' is placed from the
image a b depends upon the eye of the observer, because
the image a' b' must lie at .the distance for distinct vision,
which is different in different persons.
We can now ascertain the effect which the telescope
produces in magnifying a distant object. The angle which
the object subtends at the object glass is equal to A o B.
Instruments tised in Astronomical Observations. 9
Since the length of the telescope may be regarded as quite
inappreciable when compared with the distance of the ob-
ject, it follows that A o B is also equal to the angle which the
object would subtend if viewed by the unaided eye. But
when we view the object through the telescope we see, instead
of the object, the image a' b ', and this image subtends an
angle b o' a. It therefore appears that the telescope augments
the angle at which an object is seen in the ratio of the angle
b o' a to the angle b o a. Since these angles are small we
shall be approximately correct in assuming that the angle
boa bears to the angle b o' a the same ratio as the distance
from b a to the eye lens bears to the distance from b a to the
object lens. The distance from b a to the eye lens is very
nearly the same thing as the focal length of the eye lens,
because the rays, on emerging from the eye lens, have to
be nearly parallel in order to have them in a suitable form
for distinct vision. We have also seen that -the distance
from b a to the object lens is equal to the focal length of the
object lens, and hence we deduce the imnertant result which
is thus stated :
The magnifying poiver of a telescope is equal to the ratio of
the focal length of the object glass to the focal length of the
eye piece.
An important practical consequence follows from this
law. We are enabled, by simply changing the eye piece, to
augment indefinitely the magnifying power of the telescope.
The advantage of increasing the magnifying power beyond
a certain point is, however, neutralised by the fact that the
brilliancy of the object is diminished.
Let us next consider the effect of the telescope upon the
brilliancy with which the object is seen. From each point
of the object a pencil of rays diverge, which may be consi-
dered to be parallel. Thus the entire surface of the object
glass receives rays from each point of the distant object.
These rays, after passing through the object glass, converge
to a point m in the image a b (Fig. 10). Diverging there, they
10
Astronomy.
fall upon the eye lens, and thence into the eye of the
observer. If the eye lens bad not been used, the eye of
the observer would have to be placed at the distance of dis-
tinct vision, about 8 or 10 inches from ;;/. The beam \vould
FIG.
accordingly have attained a considerable degree of diver-
gence, and only a portion of the rays would have been able
to enter the pupil. A portion of the light grasped by the
object glass would therefore have been wasted. By the inter-
vention of the eye piece the eye is enabled to be brought
much closer to the point whence rays are diverging, and
thus the beam is intercepted by the eye while the section of
the diverging cone is still smaller than the pupil. In this
way the eye piece enables us to avail ourselves of all the
light grasped by the object glass.
When all the light enters the pupil, then the quantity of
light which illuminates the point m of the image is equal to
the quantity of light which fell upon that point from the
object glass. It is therefore proportional to the area of the
object glass. It should be observed, however, that in what
has been said we have overlooked the loss of light which
occurs in consequence of its absorption by the glass both
in the object glass and the eye piece, and also the loss which
takes place by reflection at the different surfaces ; the effect
of these losses is to render-the quantity of light received by
the eye from a point of the object somewhat less than it
would have been had the object glass and the eye piece
been perfectly transparent
We have, then, seen that the magnifying power of a tele-
Instruments used in Astronomical Observations. 1 1
scope depends entirely upon the ratio of the focal lengths
of the object glass and the eye piece, while the quantity of
light transmitted from each point of the object to the eye
depends upon the aperture of the object glass.
It will now be obvious that the quantity of light with
which the image in a telescope is illuminated depends upon
the size of the object glass. If, therefore, the magnifying
power of the telescope be increased while the aperture of
the object glass remains the same, the intrinsic brilliancy of
the image is diminished, for the same quantity of light has
now to be spread over a larger area.
The same considerations will also explain how it is that
a telescope can render an object visible which, without such
aid, would be invisible. Take, for example, a telescopic
star. The rays from such a star, falling upon the pupil, fail
to produce an impression upon the retina, because the
aperture of the pupil is so small that a sufficiency of rays to
produce the required impression cannot enter the eye.
When the aid of a telescope is called in, all the rays which
fall upon the surface of the object glass are so modified that
they can enter the eye. In fact, if we may use the illustra-
tion, the telescope acts as a sort of funnel, and pours a large
quantity of the rays in through the small aperture of the
pupil. Omitting the sources of loss already referred to, we
may say that the quantity of light which enters the eye with
the aid of the telescope bears to *.he quantity which enters
without that aid the same proportion which the area of the
object glass bears to the area- of the pupil.
8. Achromatic Object Glasses. A beam of ordinary
white light consists of a number of rays of different coloured
lights mingled together. When a beam of white light is
refracted through a prism, the different coloured lights are
separated, and what are called prismatic colours are observed.
It will be found that the bluish rays are more bent than the
red, while the greenish tints occupy an intermediate position.
When a beam of white light falls upon a converging lens, the
12 Astronomy.
blue rays being more bent than the red, the focal length of
the lens for the blue rays is somewhat shorter than it is for
the red. The image of an object which emitted only blue
rays would therefore be formed somewhat nearer to the
object glass than the image of an object which emitted
only red rays. The light from the different celestial bodies
consists generally of a mixture of several different colours,
and it follows that a number of images will be produced at
the foci corresponding to the different colours. It is true that
these foci are all near together, but the effect is still sufficient
to render the image of the object, as seen through the
object glass, somewhat indistinct and fringed with colours.
It was, however, discovered by Dolland in 1758 that the
difficulty arising from this cause could be obviated. He
found that by a suitable combination of two lenses an
object glass could be constructed, in which the focus of the
red rays and that of the blue rays could be made to coincide.
The achromatic object glass, as this compound lens is termed,
is shown in Fig. 1 1. One of these lenses is convergent, and is
made of what is called crown glass ;
FlG ' 3I> the other is divergent, and is
formed of flint glass. There is a
remarkable difference between the
action of flint glass and crown
glass upon light. If we take a convergent lens of crown glass
and a convergent lens of flint glass, and if these lenses be such
that each of them has the same focal length for the red rays,
then the focal length of the blue rays will be shorter for
the flint lens than for the crown. In fact, the effect of the
flint glass in separating the rays of a compound beam is
more marked than that of the crown. If we take a diverg-
ing lens formed of flint glass, and unite it to a converging
lens formed of crown glass, then when a beam of light pours
through the compound lens the red rays are bent by the
converging lens and unbent by the diverging lens ; the blue
rays are also bent by the converging lens and unbent by
Instruments used in Astronomical Observations. 13
the diverging lens. But the lenses can be so apportioned
that the total effect will be to bend the red rays and the
blue rays by the same amount, and therefore to concentrate
them all at one focus. The effect of the union of the two
lenses is thus to produce what is equivalent to a single lens,
which acts equally upon the blue rays and the red rays.
When the blue rays and the red rays have thus been
brought to coincide, the intermediate rays of orange, yellow,
FIG. 12.
and green may practically be considered to have been
brought to the same point. The construction of the achro-
matic object glass so that the various corrections shall be
made with nicety is a most delicate mechanical operation.
Until recently good achromatic object glasses above 6 or 8
inches in diameter were very rare, but now object glasses
of 36 inches in aperture and upwards have been success-
fully accomplished. A section of an achromatic telescope
is shown in Fig. 12. The achromatic object glass A is
14 Astronomy.
fixed at the extremity of a tube, at right angles to its
axis. At F is the eye piece, which consists of two lenses
fitted into a tube which slides in and out of a tube D c by
the aid of a rack and pinion r. The eye piece sometimes
consists of only a single lens, and this arrangement is
undoubtedly preferable when the object under examina-
tion is situated near the centre of the field of view. There
is, however, so much distortion produced by a single eye
lens in those objects which lie near the margin of the field
of view that the compound eye piece, consisting of two
lenses, is generally preferred. By its aid the same magnifying
power is retained while the distortion is greatly diminished.
On the other hand, the introduction of a second lens is of
course attended with some sacrifice of light.
In focussing the telescope the eye piece is drawn in or
out by the rack until the object is seen distinctly. If the
telescope be intended for terrestrial objects it is usual to
replace the astronomical eye piece by another eye piece
which contains four lenses. The reason of this is that the
astronomical telescope always exhibits an object turned
upside down, and the second pair of lenses have to be
added to the eye piece for the purpose of showing objects
in their ordinary position.
9. Reflecting Telescope. Telescopes are also constructed
by means of the reflection of light from spherical mirrors.
Suppose a luminous object A B is placed in front of a
spherical mirror M (Fig. 13). The rays from the point A
form a diverging beam, which, after reflection from the
surface of the mirror, form, in accordance with the laws of
reflection, a converging beam, which comes to a focus at the
point a. In a similar way the rays diverging from B are
brought to a focus at the point b. Thus an image of the
entire object AB will be formed at the position ab.
There are various different forms in which the principle
of the mirror can be employed in the construction of a
reflecting telescope. The most simple arrangement, and
Instruments used in Astronomical Observations. 1 5
probably the best, is what is known as the Newtonian
telescope (Fig. 14). The rays of light from a distant object
A B fall upon a concave mirror M, and tend to form an image
of the object at the point a b. Before, however, the rays reach
the position a b, they are intercepted by a small diagonal
FIG. 13.
mirror N, which directs the rays to the side of the tube,
where they form the image a' b'. This image is then viewed
by the observer at the side of the telescope with the aid of
the eye piece o.
The magnifying power of a Newtonian reflecting telescope
is equal to the ratio of the focal length of the large mirror to
FIG. 14.
M
the focal length of the eye piece. The light-grasping power
is proportional to the area of the large mirror.
The construction of a large mirror is an exceedingly
delicate and difficult operation ; the size is, however, not so
limited as that of achromatic object glasses. The largest
1 6 Astronomy.
telescope which has yet been constructed is of the Newtonian
form. This magnificent instrument was constructed by the
late Earl of Rosse at Parsonstown, and the large mirror is six
feet in diameter. The amount of concavity in the mirror is de-
signedly exaggerated in the figure. In the case of the great
mirror at Parsonstown the depression at the centre is only
about half an inch, and the focal length is about sixty feet.
The polished surface of the mirror differs but little from a
small portion of a sphere with a radius of 120 feet.
Another form of reflecting telescope is represented in
Fig. 15, and is called the Gregorian telescope. In this case
the large mirror M is pierced by a circular aperture, and the
small mirror N is also concave, and is situated in the axis of
the tube, The rays from the distant object, after reflection at
FIG. 15.
the surface of the large mirror, form an image of the object at
a b. The rays diverging from this image fall upon the small
mirror at N. After reflection from the small mirror they are
returned through the aperture in the large mirror, and form
another image at a' b'. They are then viewed by the eye piece,
placed at o. In the Cassegrain telescope the small mirror is
convex, and is placed at the other side of the focus of the
large mirror.
The mirrors were formerly composed of what is called
speculum metal, an alloy consisting of two parts of copper
and one of tin. Of late years, however, they are usually
constructed of silvered glass.
10. The Measurement of Angles. If a right angle be
divided into ninety equal parts, each one of the parts thus
obtained is termed a degree. If a degree be subdivided into
sixty equal parts, each one of these parts is termed a minute ;
Instruments used in Astronomical Observations. 17
and if a minute be subdivided into sixty equal parts, each
of these parts is termed a second.
An angle is, therefore, to be expressed in degrees,
minutes, and seconds, and, if necessary, decimal parts of
one second. For brevity certain symbols are used : thus
49 13' n"-4 signifies 49 degrees, 13 minutes, n seconds,
and four-tenths of one second.
We shall now explain what is meant by a graduated
circle. Let the circumference of a circle A D B (Fig. 16)
be divided into 360 parts of equal length. The division
270
lines separating these parts are denoted by o, i, 2, up to
359. It is usual in small circles to engrave upon the circle
only those figures which are appropriate to every tenth
division. The actual numbers found on the circle are,
therefore, o, 10, 20, &c. There is, however, no difficulty
in finding at a glance the number appropriate to any in-
termediate division. To facilitate this operation the divisions
5, 15, 25, which are situated half-way between each of the
numbered divisions, are sometimes marked with a larger line,
so that they can be instantly recognised.
The interval between two consecutive divisions on a
c
i8 Astronomy.
circle is often, for convenience, termed a degree. The
reader must, however, carefully remember that the word
degree means an angle and not an arc. With this caution,
no confusion will arise from the occasional use of the word
to denote the small arc of the circle instead of the angle
which this arc subtends at the centre.
For the more refined purposes of science the subdivision
of the circle must be carried much further than the division
into degrees. The extent of the subdivision of each arc of
one degree into smaller arcs depends upon the particular
purpose for which the graduated circle is intended.
The most familiar instance of a graduated circle is the
ordinary drawing instrument termed a protractor. The pro-
tractor is employed for drawing angles of a specified size.
For example, suppose that from a point c in a straight line
AB (Fig. 1 6) it is required to draw a line c D so that the
angle BCD shall be equal to 43. The centre of the pro-
tractor is to be placed at c, and the division marked o upon
the protractor is to be placed upon the line A B. Then a
dot is to be placed upon the paper at the division 43, and
a line c D drawn through the dot from the point c is the line
which is required.
The extent of the subdivisions is limited by the size of
the instrument. Thus in a protractor six inches in diameter
the length of the arc of one degree is about the twentieth
of an inch. If much further subdivision be attempted, the
divisions are so close together that they cannot be con-
veniently read without a magnifier. A protractor of this
size is, therefore, usually only divided to 3o-minute spaces.
For astronomical instruments the graduated circles are
generally subdivided to a greater extent than 3o-minute
spaces. In the instrument known as the meridian circle the
divisions of the circles are usually engraved on silver, and
two consecutive divisions are only five minutes, or in some
instruments only two minutes, apart. In the latter case the
entire circumference contains 30x360=10800 divisions.
Instruments used in Astronomical Observations. 19
The circles in this case are about three feet in diameter,
and the divisions are read by microscopes.
Mechanical ingenuity has, however, obviated the neces-
sity for carrying the subdivisions of the circumference of a
graduated circle to an excessive degree of minuteness. By
the graduated circles attached to large astronomical instru-
ments we are now able to 'read off' angles to the tenth
part of a second. If this had to be effected by divisions
alone there would require to be 12,960,000 distinct marks
upon the circumference, and this is clearly impossible
with circles of moderate dimensions. We shall presently
explain the contrivances by which this vast extension of the
accuracy with which angles can be measured has been
obtained.
11. Circular Measure. There is another mode by which
the magnitude of angles may be expressed, which, though
unsuited for the graduation of astronomical instruments, is
still of the greatest importance in many astronomical calcu-
lations. If we measure upon the circumference of a circle
an arc of which the length is equal to the radius of the circle,
and if we draw straight lines from the two extremities of this
arc to the centre of the circle, the joining lines include a
certain definite angle, which is termed the unit of circular
measure. This is sometimes called the radian. It can easily
be shown that the unit of circular measure is independent of
the length of the radius of the circle. Whether the radius
of the circle be an inch or a yard, the number of degrees,
minutes, and seconds in the radian always remains the
same.
We can now see how the magnitude of any angle what-
ever may be expressed by the number of radians and frac-
tional parts of one radian to which the given angle is
equivalent. This number is called the circular measure of
the angle. It is often necessary to convert the expression
for the magnitude of an angle in radians into the equiva-
lent expression in degrees, minutes, and seconds. To
c 2
20 Astronomy.
accomplish this we first calculate the number of seconds in
one radian.
Since the circumference of a circle is very nearly equal
to 3-14159 times its diameter, the arc of a semicircle is very
nearly equal to 3 '141 59 times the radius. The angle sub-
tended at the centre of the circle by the arc of a semicircle
is of course 180. It therefore follows that 180 must be
almost exactly equal to 3-14159 radians. By reducing 180
degrees to seconds, and dividing by 3-14159, it is found that
one radian is very nearly equal to 206265 seconds.
It is frequently necessary in astronomical calculations
to make use of the principle that when the length of an arc
of a circle is very small in comparison with the radius, the
length of the arc may generally be taken as the length of
the chord.
To illustrate the application of this principle we shall
state here a problem which very often occurs in astronomy.
A distant object, of which theap-
FIG. 17. J
parent diameter is A B (Fig. 17),
subtends a known angle at the
eye placed at o. If the distance
OA from the eye to the object
be known, it is required to find
the length A B. It generally happens in astronomical calcu-
lations that although the length A B may be exceedingly
great, yet the ratio of the length A B to the distance o A
is comparatively small. If a circle be described of which
o is the centre and o A the radius, this circle will pass
through the points A, B, and the length of the chord A B
will practically be equal to the length of the arc. We may
therefore compute the arc instead of the chord. The
angles subtended at the centre of a circle by arcs upon
its circumference are proportional to the lengths of those
arcs; it therefore follows that the required distance A B must
bear to the length o A the same ratio which the angle A o B
bears to the angle subtended by an arc equal to o A i.e. to
Instruments used in Astronomical Observations. 21
an angle of one radian. If be the angle o A B expressed
in seconds, we therefore have the relation
AB : gA::0 : 206265,
from which A B is determined.
12. Instruments for Measuring Angles. In practical
astronomy it is frequently necessary to measure the angle
which two distant points subtend at the eye. Take, for
example, two stars, which may be regarded as almost mathe-
matical points on the surface of the heavens ; then it may
be required to measure the angle which is formed by
the two lines which may be conceived to be drawn from the
eye of the observer to the two stars. In effecting this mea-
surement it is first of all necessary to bring two radii of a gra-
duated circle into coincidence with the two sides of the angle
which Is to be measured, and then to ascertain the number
of degrees, minutes, and seconds between the two radii.
Before the invention of the telescope one of the methods
of bringing the radius of the graduated circle into coinci-
dence with the visual ray was by the operation known as
' sighting/
At one end A of a bar A B (Fig. 18) a vertical slit is
fixed, while at the other end B is a pin. The eye being
FIG. 1 8.
placed at the slit, the bar can be so placed that the object
under observation appears exactly behind the pin. The
bar containing the sights can turn about the centre of a
graduated circle, of which a quadrant is represented (Fig.
19). When the sights have been properly directed to one
of the objects to be observed, the position of the bar on
the graduated circle is read off. The sights are then
directed to the other object, and the position of the bar
22
Astronomy.
FIG. 19.
is again read off. The difference between the two readings
gives the angle between the two objects.
The great drawback to this contrivance is its want of
accuracy, which renders it quite (unfitted for astronomical
observations in the
present state of the
science. In fact, it
is impossible to avoid
errors, which may
amount to some or
even many minutes
of arc, in measuring
angles by such a con-
trivance. Even the
improved sights used
by Tycho Brahe could
FIG.
scarcely distinguish less than a minute. The sighting is
therefore now replaced for astronomical purposes by the
incomparably superior contrivance which the invention of
the telescope has placed in our hands.
At the focus of the object glass of a telescope a dia-
phragm with a circular aperture is placed, and across this
circular aperture two extremely fine lines, usually taken from
a spider's web, are stretched (Fig. 20). The intersection of
these lines marks a certain point in the field of view, and the
telescope is to be directed to the distant object, so that the
object or a specified point thereof shall coincide with the
intersection of the wires.
It remains to be shown what specific line in the tele-
Instruments tised in Astronomical Observations. 23
scope is to be actually regarded as the line of vision which
is to replace the line joining the two sights in the com-
paratively rude apparatus already described. Let A repre-
sent (Fig. 21) the distant object, the rays from which fall
FIG. 21.
I
upon the object glass at o and are then brought to a focus at
a point B, which coincides with the intersection of the two
cross wires. The rays which fall upon the object glass must
in general be deflected in passing through the glass, but
there is one ray among those which diverge from A which
the object glass does not deflect. If the line A B be drawn,
it cuts the object glass at a point o. A ray passing along the
direction A o cannot be deflected by the object glass, for
otherwise it would not travel to the point B after passing
through the object glass. This ray must pass through a
certain point, which is called the optical centre of the object
glass. The line joining the optical centre of the object
glass to the intersection of the cross wires is actually
denned in the telescope itself, without reference to external
objects. This line is adopted as the line of sight of the
telescope, and is known as the optic axis. It is necessary to
observe that the optic axis need not necessarily coincide
with the actual axis of the cylindrical tube of the telescope
itself, nor is it either the line joining the centres of the
object glass and the eye piece. The eye piece, in fact, may
be displaced without altering the optic axis. If it be
desired to effect a small change in the position of the optic
axis of the telescope, this is effected by moving the diaphragm
containing the cross wires in a direction transverse to the
tube itself; the line joining the optic centre of the object
glass to the intersection of the cross wires can thus be
moved within certain limits.
24 Astronomy.
We can now understand how the telescope, when pro-
vided with the cross wires, affords a much more exact
instrument than the sights placed on a bar. In the latter
case the slit of the one sight and the pin of the other have
to be of considerable dimensions, in order to be readily seen,
and consequently the sighting of the object can only be very
coarsely accomplished. But in the telescope the optic
centre of the object glass may be considered almost a
mathematical point, while the intersection of two exceedingly
fine lines is perhaps the most definite method we possess for
indicating the position of a point. It follows that the optic
axis of the telescope has extreme precision, for it is the line
joining two definite points.
The lines furnished by the spider possess in a high
degree the necessary qualities for forming the cross lines
we have described. In the first place, they are exceedingly
fine and uniform in thickness, and they are also sufficiently
elastic to ensure that when once adjusted with the right
degree of tension they shall remain constantly stretched.
The spiders' webs with which we are all so familiar are
often used for this purpose, but the cocoons formed by some
species of spiders are perhaps the most convenient source
whence these lines can be derived.
At night it is necessary to illuminate the wires, as other-
wise they could not be seen against the dark background of
the sky. This is accomplished in two different ways. In the
first of these methods the light from a lamp is thrown into
the tube, so as to illuminate the entire field, and then the
lines are seen as dark objects against the bright background.
This is the most satisfactory method of rendering the wires
visible whenever it is applicable. In the case, however, of
very faint stars the illumination of the field will sometimes
render them invisible. It then becomes necessary to resort
to a different method of making the wires visible. By
certain optical arrangements, which need not here be de-
scribed, the light from a lamp is thrown across the field so
Instruments used in Astronomical Observations. 25
that it illuminates the lines while the field still remains
dark. In this case, therefore, bright lines are seen in a dark
field, while in the other dark lines are on a bright field.
Arrangements are provided by which either kind of illu-
mination can be adopted, according to circumstances. The
illuminated lines are, however, not so sharply seen as the
dark lines, and therefore the latter are always preferred
when the objects under examination are sufficiently bril-
liant to be visible in the illuminated field.
The telescope is to be attached to the divided circle
in place of the sights which we have already described.
The optic axis of the telescope could not conveniently
be placed in the actual plane of the divided circle. It is,
however, quite sufficient that it should be parallel thereto,
nor is it even necessary that the optic axis should pass
through a perpendicular to the plane of the graduated circle
drawn through its centre.
Let us suppose that the angle between two distant points
has to be measured. The plane of the graduated circle is
first to be placed so that it passes through the two points ;
the telescope is to be turned so that the image of one of the
points coincides with the intersection of the wires. The
graduated circle is then to be 'read off' by means of a
pointer, fixed quite independently of the telescope and the
circle. The reading having been made, the telescope,
bearing with it the graduated circle, to which it is rigidly
attached, is to be turned round until the optic axis is directed
towards the other point, the plane of the graduated circle
remaining unaltered. The circle is again to be read off by
the same fixed pointer. The difference between the two
readings determines the angle through which the optic axis
of the telescope must be turned in order to be moved from
one object to the other. This angle is the angular distance
of the two objects, which has thus been determined quite
independently of the position of the telescope itself with
respect to the graduated circle.
26
A stronomy.
The degree of precision which can be attained in the
measurement of angles by the aid of a telescope may be
estimated by a consideration of the thickness of a spider's
line. A line taken from a cocoon ordinarily used has a
thickness of about 0*003 mcn - I n a telescope of about
20 feet focal length the thickness of a line of this size
will subtend at the object glass an angle of about one-quarter
of a second. This, therefore, indicates the degree of ex-
actitude with which the telescope might be directed to-
wards a distant point.
For many purposes it is found more accurate to have
two parallel spider lines tolerably close together, and then to
bring the image of a distant point so as to bisect the distance
between the lines. As the eye can judge with considerable
delicacy of the equality of the distances of the point from
the two lines, this method has much to recommend it for
certain kinds of observation.
13. Method of Reading an Angle. The reading micro-
scope consists of an object glass at B (Fig. 22) and an
FIG. 22.
FIG. 23.
eye piece at A, connected by a
tube. At the focus of the object
glass a pair of cross lines are
inserted, and the diaphragm
which carries the cross lines is
capable of being moved by a
screw, which carries a graduated
head at a. A portion of the
graduated circle, which is rigidly
attached to the telescope, is shown at c D (Fig. 23). The
Instruments used in Astronomical Observations. 27
microscope is adjusted so that a distinct image of a portion
of the graduated limb of the circle can be seen when the
eye is placed at A. The appear- FlG
ance presented in the field of the
microscope is shown in Fig. 24.
It may be supposed that the circle
is so divided that the distance from
one division line to the next is
equal to 5 minutes. A few of
these division lines will be seen in
the field, and also the cross wires
which are attached to the screw of the micrometer. As
the telescope, carrying with it the graduated circle, is
moved the division marks are seen to move through the
field of the microscope, while the cross lines of course
remain fixed. If the microscope screw be set so that the
divided head stands at zero, then the optic axis of the
microscope intersects the graduated limb of the circle at a
definite point, which is the reading of the circle. If this
optic axis actually passed through one of the division lines,
then this division line would be seen to pass through the
intersection of the cross lines, and the degrees and minutes
corresponding to that division line would be the reading of
the circle.
It will, however, generally happen that the optic axis of
the microscope will intersect the limb of the graduated circle
at a point lying between two adjacent division lines. In
this case the two division lines will be seen, as in Fig. 24, to be
lying one on each side of the point defined by the intersec-
tion of the cross wires. To accomplish the reading of the
circle it becomes necessary to determine the accurate reading,
which corresponds to the point in which the intersection of
the cross wires divides the distance between the two
adjacent divisions. Assuming that the divisions of the
graduated circle increase from the top of the figure to the
bottom, then the distance from the mark ;;/ to the intersec-
28 Astronomy.
tion of the cross wires has to be ascertained. The distances
between the division lines being 5 minutes, we shall suppose
that the thread of the screw at the head of the microscope
is such that five complete revolutions of the screw would
be sufficient to carry the intersection of the cross wires
from one division line to that next adjacent. It follows
that each revolution of the screw corresponds to one minute
of arc. If, therefore, the head of the screw be subdivided
into sixty equal parts, it is plain that a rotation of the head
through one of these parts will carry the cross lines over a
distance of one second.
The reading is effected by moving the cross lines in the
direction of the arrow until their intersection is brought to
coincide with ///. The number of entire revolutions will
give the number of minutes, and the number of fractional
parts the number of seconds, between the division mark m
and the point of the graduated limb, which was intersected
by the optic axis of the microscope when the cross wires
were set at zero.
In order to illuminate the graduated limb at night,
a mirror is placed between the object glass and the
graduated limb. The light from a lamp falling upon the
mirror is reflected upon the limb, while a hole in the centre
of the mirror allows the limb to be seen by the micro-
scope.
14. Error of Eccentricity. In large circles it is usual
to have four microscopes, or sometimes more, placed sym-
metrically round the circumference, and the reading is made
at each of the microscopes separately. By this means an
important source of error is entirely eliminated. This must
now be explained, and for simplicity we shall take an
example.
A meridian circle was turned through a certain angle,
and the value of that angle was measured by four micro-
scopes placed round the circumference at angles of 90 apart.
The value of the angle by
Instruments used in Astronomical Observations. 29
Microscope I. is 104 56' 47 // 'i
II. 104 56 51-3
III. 104 56 47-1
IV. 104 56 41-4
If everything had been perfectly right, then it is obvious that
these four angles ought to be equal to each other. But various
sources of error are present.
1. There are doubtless actual errors of judgment in
making the coincidence of the cross wires with the division
mark. These errors are, however, but small, and in a good
instrument should not amount to a single second.
2. There are also errors of workmanship in the execution
of the division marks upon the limb of the graduated circle,
and also in the screws of the different microscopes. Still
these errors are but small, and in the instrument with which
the measurements now under discussion were made they
certainly do not exceed a single second.
It is therefore plain that we must look to some other
source for an explanation of the discrepancies between the
four values which have been found.
The chief source of the error is the eccentricity, which
arises from an unavoidable' lack of absolute coincidence be-
tween the centre of the graduated circle and the axis about
which the telescope and the graduated circle revolve. The
existence of an error from this cause is inevitable whenever
a graduated circle is mounted upon an axis, but fortunately
we can easily eliminate its effects, so that they shall not
vitiate our results.
It must first be observed that what we want to measure
is the angle A o B (Fig. 25), through which the telescope has
been rotated. What we actually do measure is the number
of divisions of the circle between A and B. It is, however,
obvious that the arc of the circle (which is proportional to
the number of divisions) will not be proportional to the angle
at o, unless the point o, about which the telescope rotates,
Astronomy.
FIG. 25.
coincides with the centre of the graduations. If, however,
we have two microscopes diametrically opposite, one of them
will indicate the arc A' B' and
the other the arc A B. Draw
B c parallel to A A' ; then
since c A' is equal to A B, the
sum of the two measured arcs
is c B' ; but the angle which
c B' subtends at the circum-
ference is obviously equal to
the angle at o. It follows
that \ c B' subtends an angle
o at the centre, and therefore
we have the following im-
portant result :
The arithmetic mean of the readings of two diametrically
opposite microscopes is independent of the error of eccentri-
city.
In the case at present under consideration the mean read-
ings of the diametrically opposite Microscopes I. and III. is
104 56' 47"'i,
while the mean given by Microscopes II. and IV. is
104 56' 4 6"' 4
The small discrepancy between these two results may fairly
be attributed to some of the other sources of error to which
we have . referred. It will, therefore, be natural to take the
mean of all four microscopes as the final result, which is
accordingly
104 56' 4 6"75.
15. The Measurement of Time. In many astronomical
investigations it is necessary to have an accurate method of
measuring time. This is best effected by the astronomical
clock. The clock is really only an arrangement for counting
Instruments used in Astronomical Observations. 31
FIG. 26.
the vibrations of a pendulum, while at the same time it
sustains the motion of the pendulum. It will first be
necessary to give an outline of the principles upon which
the motion of the pendulum depends. ^
If a weight A (Fig. 26) be attached to a cord A B which is
suspended from a fixed point B,
the contrivance forms what is
known as a simple pendulum.
When at rest the cord will
hang in the vertical position B c,
with the weight directly under
the point of support B. If the
cord BC be drawn out of the
vertical position into the position
B A, and if the weight A be re-
leased, it will descend until the
cord occupies the vertical posi-
tion B c, after passing which the
cord will ascend into the position B A'. If we could sup-
pose that the resistance of the air were entirely removed,
then it would be found that the weight would rise at A 7
to precisely the same vertical height that it had at A, or
that the angle A B c is equal to the angle A' B c. After a
momentary pause in the position B A', the weight will again
descend, pass through the position c, and rise again to A.
Again pausing, it will commence to descend, and again rise
to A 7 , and so on indefinitely. Owing, however, to the resist-
ance of the air, and also, it should be added, to the rigidity
of the cord at the point of suspension, the weight A will
not on each occasion rise quite to the same height that it
occupied before, and consequently the amplitude of the
swing will gradually diminish until finally the weight comes
to rest again in the position c. We shall, however, in what
follows overlook the effect of the resistance of the air ; for
the motion of the pendulum can be indefinitely sustained,
notwithstanding the resistance of the air.
32 Astronomy.
A certain definite time is required for the weight to pass
from the point A to the point A', and we shall first proceed
to enquire into the circumstances by which the duration of
that time called the time of vibration is to be determined.
In the first place, it is to be observed that if the arc A A' form
but a small portion of the entire circumference of the circle
which could be described around the centre B with the
radius B A, the time taken to move from A to A' is inde-
pendent of the length of the arc. For example, if the length
of the cord A B be one yard, and if the length of the arc A A'
be one inch, then the time taken by the weight to move
from A to A' is very nearly the same as it would have been
had the arc A c A' been half an inch or had it been two
inches, the length of the cord A B being the same in all
three cases. It is no doubt true that there is a minute
difference of time, that the short arc is described in a some-
what shorter time than the long arc ; but this difference
bears such an exceedingly small ratio to the total time that
for all practical purposes it may be omitted. We are thus
enabled to state the following remarkable law :
The time of vibration of a simple circular pendulum
through a small arc is independent of the length of the arc.
This property of the pendulum is often known as its
isochronism.
It is also easy to show that the time of vibration does
not depend upon the weight of the pendulum. If the weight
A be replaced by one which is double the amount or half
the amount, the time of vibration is still found to be the
same, and still found to be nearly independent of the
length of the arc.
Nor is the case altered when the material of which the
weight of the pendulum is composed is changed. A ball
of lead, of iron, or of wood will vibrate precisely in the
same time, whatever be its weight or whatever be the arc
(supposed ' small) through which it swings, provided only
that the length of the cord by which it is suspended remains
unaltered.
Instruments used in Astronomical Observations 33
We have thus ascertained that the time of vibration
depends solely upon the length of the cord by which the
weight is supported. It can be shown from theoretical con-
siderations, and it can also be readily verified by actual
experiment, that the following law expresses the true relation
between the length of a pendulum and the time of its
vibration.
The time of vibration of a simple circular pendulum is
proportional to the square root of its length^ and the length of
the pendulum which at the latitude of London vibrates in one
mean solar second is 36 '139 inches.
It will thus be perceived that the pendulum provides
an admirable method of determining intervals of time.
It is only necessary to count the number of vibrations
made by a pendulum of known length, and the required
interval of time is at once ascertained. For this purpose we
must sustain the motion of the pendulum by occasionally
giving it a suitable impulse ; but, owing to the principle
of isochronism, it is fortunately unnecessary to impose
the condition that the arc of vibration shall remain strictly
constant.
16. The Clock. A pendulum of the simple form which
we have been describing would not be adapted for use in a
clock. The pendulum in a clock consists of a heavy mass
of metal attached to a rigid rod, which is suspended from a
fixed point by a steel spring, which acts as a sort of hinge to
permit the vibrations of the pendulum. It is, however,
possible to apply the principles of the simple circular pen-
dulum to the clock pendulum, only observing that the
length of the circular pendulum, which would vibrate in
precisely the same way as the clock pendulum, is somewhat
less than that of the latter.
The first duty of the clock is to sustain the motion of
the pendulum, which the resistance of the air is constantly
striving to bring to rest. To attain this end the clock is
supplied with a motive power, which gives the pendulum a
D
34
Astronomy.
small impulse in each vibration, and thus retains the arc of
vibration approximately constant.
The motive power employed in those clocks which are
used for astronomical purposes is generally afforded by a
weight, rather than by a spring. The cord attached to
the weight is wound around a drum, and as the weight
descends the drum . is forced to revolve. On the axis
of the drum is a toothed wheel, which sets in motion a
series of toothed wheels, by which the hands are turned
round, and the motion of the whole is controlled by the
pendulum. This control is exercised through the medium
Instruments used in Astronomical Observations. 35
of that important part of a clock which is known as the
escapement, while the escapement also discharges the im-
portant duty of sustaining the motion of the pendulum.
The action of the escapement maybe understood from Fig.
2 7. A toothed wheel E is connected with the wheelwork driven
by the weight. Above this is suspended a piece A B c D
which is free to oscillate about the centre D. From the axis
D a rod F (Fig. 28) descends, which by means of a fork at G
catches the rod of the pendulum. Thus as the pendulum
oscillates so does the rod F, and hence also the piece ABC.
In the course of the vibration the portioned enters between
a pair of consecutive teeth of the escapement wheel, and the
tooth then falls upon the arc. In this condition the escape-
ment wheel remains fixed until, in the return motion of the
pendulum, the part c p withdraws from between the teeth suffi-
ciently to allow the poin t of the tooth to glide down the inclined
face p q, and the tooth escapes, as it is called. Immediately
afterwards, however, the tooth at the other side drops upon
the arc at m, and is there detained until the pendulum gains a
position which will enable the point of the tooth to slide down
the face m n. It will thus be seen that the revolution of the
escapement wheel, and therefore of the whole train of wheels,
is controlled by the motion of the pendulum. In the act
of descending the inclined planes at / q and m n the point
of the tooth imparts a slight impulse to the piece ABC;
this impulse is, through the medium of the fork G, transmitted
to the pendulum, and so the oscillations of the pendulum are
sustained.
When the clock is wound up a store of energy is imparted
thereto, and this is doled out to the pendulum in a very
small impulse which it receives at each vibration. The clock
weight is of such a magnitude that it shall just be able to
counterbalance the retarding forces when the pendulum has
a proper amplitude of vibration. In all machines there is
a certain amount of energy lost in setting the parts in motion
and in overcoming friction and other resistances ; in clocks
D2
36 Astronomy.
this represents the whole amount of the energy consumed,
as there is no external work to be performed.
A good construction of the escapement wheel is essential
to the correct performance of the clock. Although the
pendulum must have its motion sustained by receiving an
impulse at every vibration, yet it is desirable that the vibra-
tion of the pendulum should be hampered as little as pos-
sible by mechanical constraint. The isochronism of the
pendulum, on which depends its utility as a timekeeper,
is a property of a pendulum which is swinging quite freely.
Hence we must endeavour to approximate the clock pen-
dulum as nearly as possible to a pendulum hung freely.
To effect this and at the same time to maintain the arc of
vibration constant is the property of a good escapement.
The operations are so timed that the pendulum receives
its impulse when at the middle of its stroke, and the pendulum
is then unacted upon until it reaches a similar position in
the next vibration. There is still a certain resisting force
acting to retard the pendulum ; this arises from the pressure
of the teeth upon the circular surfaces, where some friction is
unavoidable, however carefully the surfaces maybe polished.
It is essential for the correct performance of a clock
that the pendulum should vibrate at a proper rate, as a
very small irregularity may produce an appreciable effect
upon the clock. Thus suppose the pendulum vibrates in
I'ooi second instead of in one second ; the clock loses one-
thousandth of a second at each beat, and, since there are
86,400 seconds in a day, it follows that the clock will lose
about 86 seconds, or nearly a minute and a half, daily. The
time of vibration depends upon the length of the pendulum,
and therefore the rate of the clock will be constant, pro-
vided the length of the pendulum remain constant. To
alter the rate of the clock the length of the pendulum must
be altered ; thus, for example : if the length of the pendulum
be altered by one-tenth of an inch the clock will lose or gain
nearly two minutes daily, according to whether the pendulum
Instruments used in Astronomical Observations. 37
be lengthened or shortened. This explains the well-known
practice of raising or lowering the bob of the pendulum when
the clock is going too slow or too fast.
17. The Compensating Pendulum. Let us suppose that
the length of the pendulum has been properly adjusted, so
that the clock keeps accurate time. It is necessary that
the pendulum should not alter in length. But, as all bodies
expand by heat, a pendulum which consists of a single rod
to which the weight is attached must be longer in hot
weather than it is in cold weather, and hence a clock will
generally have a tendency to go faster in winter than in
summer. For a pendulum with a steel rod the difference of
temperature between summer and winter will cause a differ-
ence in the rate of five seconds daily, or about half a minute
in a week. The amount of error thus introduced is of no
great consequence in clocks which are intended for ordinary
use, but in astronomical clocks, where seconds, or even
portions of a second, are of the utmost consequence, in-
accuracies of this magnitude would be quite inadmissible.
There are, it is true, substances for example, slips of
white deal in which the rate of expansion is less than that
of steel ; consequently the irregularities introduced by em-
ploying a pendulum whose rod is a slip of deal would be
less than that of the steel pendulum we have mentioned ;
but no substance is known which would not undergo greater
variations than are admissible in the pendulum of an
astronomical clock.
We must, therefore, devise some means by which the
effect of changes of temperature in altering the time of
vibration of a pendulum can be avoided. Various contri-
vances have been proposed for this purpose ; we shall de-
scribe one which is often adopted.
In Fig. 29 is shown what is known as the mercurial
compensating pendulum. The rod a, by which the pen-
dulum is suspended, is made of steel, and at its lower
extremity two cylindrical glass jars are supported, which
FIG. 29.
38 Astronomy.
are partly filled with mercury. The distance of the centre
of gravity of the mercury from the point of suspension
is very nearly equal to the length of the simple pendulum,
which would vibrate isochronously with
the compound arrangement here described.
Mercury and steel both expand when their
temperature is raised, but the rates at which
they expand are widely different, and it is
upon this difference in the coefficients of
expansion that the action of the compensat-
ing pendulum depends. For a given rise
of temperature the linear coefficient of ex-
pansion of mercury is several times greater
than that of steel. If the height of the
column of mercury in the two jars b, b has
a proper ratio to the length of the steel rod,
the compensation will be complete. For
suppose the temperature of the pendulum to
be raised, the steel rod would be lengthened,
and therefore the vessels of mercury would
be lowered. On the other hand, the surface
of the column of mercury in the jars would
be varied by the expansion of the mercury. The centre of
the column of mercury will be raised by half the amount
which its surface is raised. It can be arranged that the
centre of the column of mercury is raised by its own ex-
pansion as much as it is lowered by the expansion of the
steel. By this contrivance the time of oscillation of the
pendulum is rendered independent of the temperature.
The mercurial compensating pendulum possesses the
great advantage that it is easy to alter the quantity of mer-
cury so as to adjust the compensation with precision.
18. Composition of Light. We shall now give a brief
account of a very remarkable method which has been ap-
plied with great success to the examination of the heavenly
bodies. This method is termed spectrum analysis. Its
peculiar feature is that, with the assistance of a telescope, it
Instruments used in Astronomical Observations. 39
actually gives us information as to the nature of the elemen-
tary substances which are present in some of the celestial
bodies. To explain how this is accomplished it will be
necessary for us to refer again to some properties of light
which were already alluded to ( 8). A ray of ordinary
sunlight consists in reality of a number of 'rays of different
colours blended together. The ' white ' colour of ordinary
sunlight is due to the joint effect of the several different rays.
We have, however, the means of separating the constituent
rays of a beam of light and examining them individually.
This is due to the circumstance that the amount of bending
which a ray of light undergoes when it passes through a
prism varies with the colour of the light.
19. Construction of the Spectroscope. Suppose ABC
(Fig. 2pA) to represent a prism of flint glass. If a ray of
ordinary white light tra-
velling along the direc-
tion P Q falls upon the
prism at Q, it is bent by
refraction, so that the
direction in which it
traverses the prism is
different from the direc-
tion in which it was
moving when it first encountered the prism. The amount
of the bending is, however, dependent upon the colour of
the light. In a beam of white light we have blended
together the seven well-known prismatic colours, viz. red,
orange, yellow, green, blue, indigo, violet. We shall trace
the course of the first of these and the last. The red light
is the least bent ; it travels along (let us suppose) the direc-
tion Q R until it meets the second surface of the prism at R ;
it is then again bent at emergence, and finally travels along
the direction R s. On the other hand, the violet portion of
the incident beam, which originally travelled along the
direction P Q, is more bent at each refraction than the red
rays. Consequently after the first refraction it assumes the
Astronomy.
FIG.
293.
direction Q R', and after the second refraction, the direction
R' s'. The intermediate rays of orange, yellow, green, blue,
and indigo, after passing the prism, are found to be more
refracted than the red rays, and less refracted than the
violet rays ; they are, therefore, found in the interval
between the lines R s and R' s'.
We have therefore, in the prism, a means of decomposing
a ray of light and examining the different constituents of
which it is made. We shall now show how this is practi-
cally applied in the instrument
known as the spectroscope. The
principle of this instrument
may be explained by reference
to Fig. 2913. At s is a narrow
slit, which is supposed to be
perpendicular to the plane of
the paper. Through this slit
a thin line of light passes, and
it is this thin line of light
which is to be examined in the spectroscope. After passing
through s, the light diverges until it falls upon an achro-
matic lens placed at A. This lens is to be so placed that
the distance A s is equal to the focal length of the lens ; it
therefore follows that the beam diverging from s will, after
refraction through the lens A, emerge as a beam of which all
the constituent rays are parallel. Let us now for a moment
fix our attention upon the rays of some particular colour.
Suppose, for example, the red rays. The parallel beam of
red rays will fall upon the prism P. Since each of these
rays has the same colour, it will, on passing through the
prism, be deflected through the same angle, and, therefore,
the beam which consisted of parallel rays before incidence
upon the prism will consist of parallel rays after refraction
through the prism, the only difference being that the entire
system of parallel rays will be bent from the direction which
they had before. In this condition the rays will fall upon
the achromatic lens B, which will bring them to a focus at a
Instruments used in Astronomical Observations. 41
point R, where we shall suppose a suitable screen to be
placed. Thus the red rays which pass through the slit at s
will form a red image of the slit upon the screen at R.
But what will be the case with the violet constituents of
the light which passes through s ? The violet rays will fall
upon the lens A, and will emerge as a parallel beam (for we
have supposed the lenses A and B to be both achromatic),
the parallel violet beam will then fall upon p, and it will
emerge from p also as a beam of parallel rays. It will, how-
ever, be more deflected than the beam of red rays, but still
not so much so as to prevent it falling upon the lens B,
which will make it converge so as to form an image at T
near to the red image at R, but somewhat below it.
Let us suppose the slit at s to be exceedingly narrow,
and let us suppose that the beam of light which originally
passed through s contained rays of every degree of refrangi-
bility from the extreme red to the extreme violet. We
should then have on the screen an indefinitely great number
of images of the slit in different hues, and these images
would be so exceedingly close together that the appearance
presented would be a band of light equal in width to the
length of the image of the slit, and extending from R to T.
This band, the colour of which gradually changes from red
at R to violet at T, is known as \h& prismatic spectrum. In-
stead of the screen the eye itself may be employed to receive
the light which emerges from the lens B, so that the spec-
trum is impressed upon the retina. For the more delicate
purposes of spectrum analysis this plan is always adopted.
Suppose that the light which was being examined con-
sisted only of rays of certain special refrangibilities, the
spectrum which would be produced would then only show
images of the slit corresponding to the particular rays which
were present in the beam. Consequently, the spectrum
would be * interrupted,' consisting of a number of detached
lines, and the character of the spectrum would reveal the
nature of the light of which the beam was composed.
This may be made to give us most valuable information
42 Astronomy.
with reference to the nature of the source from which the
light emanates. In order to concentrate as much light as
possible on the slit of a ' spectroscope,' this slit is placed
in the focus of an astronomical telescope, and instead of the
single prism p (Fig. 2911) a train of prisms is generally used
to increase the dispersion of the parallel rays coming from
the ' collimating lens ' A. The lens B belongs to a small
viewing telescope which can be turned slightly along a
graduated arc so as to bring different parts of the spectrum
into the field of view, and enable the observer to measure
the relative positions of the various lines in the spectrum.
If a glass tube contain a small quantity of gas, and if an
electric current be passed through the tube, the gas inside
the tube may be raised to a temperature so exceedingly high
that it will become luminous, and the light which emanates
from it can be examined by means of the spectroscope. It
is found that gases under low pressure yield a spectrum con-
sisting of bright lines (really separate images of the slit), the
same gas always giving the same lines, so that the nature of
the gas under observation may be ascertained from its spec-
trum. An incandescent solid or liquid body or a gas under
high pressure emits light of all refrangibilities, and there-
fore yields a continuous spectrum. On the other hand, a
gaseous substance absorbs from light passing through it
exactly the same rays which its own spectrum shows. The
spectrum of the sun therefore consists of a continuous band
of all the colours from red to violet, interrupted by a great
number of dark lines caused by absorption of light passing
from the body of the sun through the gaseous atmosphere
of that luminary, and by measuring the positions of these
lines and comparing with tables of the spectral lines of the
various chemical elements (prepared from spectroscopic
researches in the laboratory), the nature of the gases consti-
tuting the solar atmosphere may be ascertained (see 70).
43
CHAPTER II.
THE EARTH.
20. Form of the Earth. To an observer who is limited,
as we are, to the surface of the earth, the contrast is at
first sight very wide indeed between the appearance of
the earth and the appearances presented by the sun and
moon. The earth appears to be a flat plain, more or less
diversified ; the sun and moon appear to be globular ; the
earth appears to be at rest, while the sun and moon are ap-
parently in constant motion ; and, lastly, the earth appears to
have a bulk incomparably greater than that of either the
sun or the moon.
If, however, we could change our point of view to a
suitable position in space, we should form a more just con-
ception of the relation of the earth to the sun and moon.
We should then see that each of the three bodies was really
spherical, that each of them was really in motion, and that
the earth, though larger than the moon, was very much less
than the sun.
It need hardly be said that it is impossible for observers
on the earth to obtain such a bird's-eye view as we have
here described. A balloon might indeed convey the ob-
server to a point from which he would have a very extensive
view, but it would be necessary to ascend to a height vastly
beyond that to which any balloon could attain before the
shape of the earth would be discerned as we discern the
shape of the sun and the moon. Our knowledge of the
figure of the earth is only to be attained by indirect means,
the nature of which we shall now explain.
The most simple method of becoming actually convinced
that the surface of the earth (or rather of the sea) is not an
indefinitely extended plain is by taking a station on a high
44 Astronomy.
cliff near the sea-side, from which an uninterrupted view of
the sea can be obtained. We shall also suppose that a
number of vessels are dotted over the surface of the sea at
different distances, and that the 'station which the observer
has chosen is at a greater vertical height above the sea than
are the tops of the masts of any of the vessels.
If the surface of the sea extended as an indefinite plane,
then this plane must be intersected by a line drawn from
the eye of the observer to the topmost point of the mast of
any one of the vessels. It is, therefore, obvious that the
entire of each of the vessels must be seen projected upon the
surface of the water. But this is obviously not the case.
The view which the observer has of the sea is shown in Fig.
30. The vessel in the foreground is no doubt entirely
FIG. 30.
projected on the surface of the sea, but the more distant
vessel is almost entirely projected against the sky, while the
most distant vessel of all is so far from being projected on
the surface of the water that the hull of the vessel is
rendered invisible by the interposition of a protuberant
mass of water, while the masts are seen projected against
the sky. We are, therefore, forced to the conclusion that
the sea is not a flat plain, but that it is a convex surface.
At whatever part of the earth the observations which we
have just described be made, it is invariably found that the
surface of the ocean is convex. The degree of the curvature
may be estimated by the distance at which the hull of the
vessel becomes invisible. The observer being stationed at
1 a certain height, and the hull of the vessel having a certain
size, the greater the curvature the less is the distance at
The Earth. 45
which the hull is invisible. Tested in this way, the curvature
of the ocean appears nearly uniform over its entire extent.
The surface which has a curvature which is uniform at all
points must be a sphere. We are hence forced to the
conclusion that the surface of the sea is approximately
spherical.
It is somewhat more difficult to perceive that the general
surface of the land is also approximately spherical. The
irregularities on the surface of the earth, arising from hills
and mountains and valleys, appear at first sight to preclude
the possibility of making any general statement with refer-
ence to the figure of the earth. It is, however, to be observed
that these irregularities on the surface are of quite trivial
extent in comparison with the vast bulk of the earth itself.
It has been found that the figure of the earth, though
very approximately a sphere, differs therefrom to an appre-
ciable extent. It appears that the true figure of the earth
is nearly that of the surface produced by the revolution
of an ellipse A DEC (Fig. 31) about its minor axis AB.
The eccentricity of the ellipse is designedly much exagge-
rated in the figure. According
to the careful investigations of FlG - 3-
Colonel A. R. Clarke, C.B., we
have the following dimensions of
the ellipsoid of revolution which
most closely approximates to the
figure of the earth : Let a, b
be the equatorial and polar semi-
diameters respectively, then A
a = 6378207 metres = 20926062 feet,
b 6356584 metres = 20855121 feet;
while for the ellipticity
a 294*98
1 For certain purposes, and perhaps on the whole, the actual figure
of the earth can, it is believed, be represented with still greater accuracy
46 Astronomy.
It having been ascertained that the earth has an aproxi-
mately spherical figure, the next important point is to show
that the earth is free in space, and not supported by or
attached to any other object. This is clear from the
circumstance that though the surface of the earth has been
traversed in nearly every direction, no trace has been found
of any such support or connection, and we must therefore
admit that the earth is really an isolated object. At first it
may seem difficult to believe that this is really the case. It
might be thought that, as the earth is not supported, it
ought to fall somewhere or other. This will be subse-
quently explained.
21. The Atmosphere. At the exterior of the surface of
the earth, and entirely enveloping the earth, is what is known
as the atmosphere. At whatever height we ascend upon
the mountains, we still find that air is present. We know
that there is a limit to the atmosphere ; but the height
is far greater than any to which we can attain, though
we can ascertain its amount to some degree of approxi-
mation.
It can easily be shown that air is a substance which has
weight. A glass balloon filled with air weighs more than it
does when all the air has been removed from it. Air is
eminently compressible, and the air near the surface of the
earth, which has to bear the weight of all the superincum-
bent air, is much more compressed than the air which is
as an ellipsoid with three unequal axes. Colonel Clarke gives for the
lengths of the semiaxes
a = 20926629 feet = 6378390 metres,
b = 20925105 feet = 6377920 metres,
c = 20854477 feet = 6356390 metres.
The ellipticities of the two principal meridians are
I I
289-5 and 295^
The longitude of the greatest axis is 8 15' W.
The Earth.
47
FIG. 32.
higher up. It follows that the density of the air is a maxi-
mum at the surface of the earth, and that it diminishes as
we ascend until the confines of the atmosphere are reached,
where the density is zero. It is, therefore, plain that the real
height of the atmosphere must be much greater than it
would have been were the atmosphere homogeneous through-
out.
We shall subsequently allude to the phenomena of shooting
stars, and we shall show by what observations their height
is ascertained. It is known that these objects only become
visible when they enter our atmosphere, and therefore we
have the means of ascertaining a minor limit to the height
of the atmosphere. It is found that shooting stars are some-
times seen at a height of more than twt> hundred miles, and
therefore the atmosphere must
extend to at least that height.
There can be little doubt that
for a very great depth at the
upper surface of the atmo-
sphere the density is exceed-
ingly small.
22. Atmospheric Refrac- ^
tion. In viewing a celestial
body we have always to look
completely through the atmo-
spheric shell by which the
earth is surrounded. This
produces an apparent dis-
placement of the celestial body by what is called refraction.
Let D E (Fig. 32) be the surface of any transparent medium,
and let a ray A B fall upon the surface D E at B. Then
when the ray enters the medium it undergoes a certain
deflection, insomuch that it pursues the path B c instead
of the original path. The angle A B M is called the angle of
incidence, and the angle CBM' is the angle of refraction
where M M' is perpendicular to the surface D E. The rays. A B
4 8
Astronomy.
FIG. 33.
and CB both lie in a plane which contains the normal,
and the sine of the angle of incidence is in a constant ratio
to the sine of the angle of reflection.
We can now explain the effect which the atmosphere
has on the refraction of the light from a celestial body
suppose a star. We may for this purpose assume the earth
to be a spherical body whose centre is at o (Fig. 33). The
atmosphere may then be considered to consist of a number
of concentric spherical
shells, each of uniform
density, but the density
of each shell being
\ greater than that of the
shell immediately out-
side it. If these shells be
regarded as indefinitely
thin, this supposition
may accurately repre-
sent the atmosphere of
our earth.
A ray of light, after
passing through space
in the direction E a y falls
upon the first layer of
atmosphere at a ; after
entering the layer the
ray moves along the di-
rection a b, which is less
inclined to o a than was
the original line E a.
Having traversed the first layer, the ray enters the second
layer ; it is again deflected into the line b c. The same process
goes on as the ray enters each successive layer, until finally
it reaches the eye at the point A on the surface of the earth.
The actual direction of the ray at the moment it entered the
eye is A E'. This, then, will be the direction in which the
The Earth. 49
star is seen, and therefore the real position of the star would
be judged erroneously.
The line o A points upwards to the zenith of the
observer at A. The angle subtended at the eye by the
zenith point and the star is the zenith distance of the star.
The apparent zenith distance of the star is represented by
the angle z A E'. The real zenith distance of the star is the
angle between A z and a line through A parallel to a E.
Thus the effect of refraction is always to diminish the zenith
distance of a star, or to make the star appear nearer to
the zenith than it would be were refraction absent. The
effect of refraction on a star actually at the zenith is zero,
while the effect is a maximum on a star situated on the
horizon.
To compute with accuracy the precise amount of devia-
tion which a ray of light experiences in traversing the entire
thickness of our atmosphere, it would appear to be necessary
to know the precise density of each of the shells of which
we have supposed the atmosphere to be constituted. Our
knowledge of the pressure and temperature in the upper
regions of the atmosphere is, however, so imperfect that it
is impossible to form any accurate law which connects the
alteration of density in the atmosphere with the increase of
height. It is, however, fortunate that the refraction can be
computed in a much more simple manner whenever the
zenith distance is comparatively small.
The thickness of the atmosphere is, even on the largest
estimation, only a very small fraction of the radius of the
earth. We may therefore, without appreciable error, consider
the surface of the earth to be a plane, and consequently on
this assumption the successive shells of different densities
will be horizontal layers. When this assumption is made,
the problem of computing the refractions becomes greatly
simplified. It is, under these circumstances, quite unneces-
sary to know what the densities of the successive layers may
be, or to what height the atmosphere extends. The refrac-
E
5O Astronomy.
tion will, in fact, be the same as if the entire atmosphere
were of absolutely uniform density throughout, that density
being the same as is indicated by the barometer and thermo-
meter at the surface of the earth at the moment when the
observation is made.
This very remarkable result can be demonstrated with
facility. Let M, M', M", M"' represent media of different
FIG. 34.
FIG. 35.
degrees of refrangibility, through which a ray of light
originally moving in the direction A B is to be refracted.
It is assumed that the bounding surfaces of these media are
all parallel planes. After refraction in the medium M the
ray travels in the direction B c, then it is refracted by the
medium M' into the direction c D, and so on till in the last
medium the ray has the direction E F. It is to be proved
that the direction E F is the same as it would have been had
the ray A B fallen directly upon the medium M' /X without the
intervention of M, M', and M". It should, however, be
observed that we are here only concerned with the direction
of the ray ; the absolute situation, no doubt, is to a certain
extent altered by the superincumbent media.
This will be made clear by Fig. 35. A B is a ray of light
which impinges upon a single medium M bounded by two
parallel planes. After refraction at the first surface the ray
The Earth. 5 1
traverses the direction B D, then falls upon the second surface
and emerges in the direction c D. Since the surfaces are
parallel, it is clear that the ray B D makes the same angle with
the normal at B which it does with the normal at D ; it there-
fore follows that after emerging from the medium at D the
ray c D must be inclined to the normal at D at the same
angle at which A B was inclined to the normal at B, and that
consequently the ray A B is parallel to the ray c D. Hence
the effect of the transmission of a ray of light through a
medium bounded by parallel planes is merely to change
the situation of the ray while leaving its direction unaltered.
This principle can be applied to the explanation of the
property illustrated in Fig. 34. After the ray has traversed
M we may suppose it emerges parallel to its original direction,
and then immediately impinges upon M' in the same way ;
after passing M' it emerges still parallel to A B and falls
upon M" j thence emerging parallel to its original direction,
the ray falls upon M'". It is, therefore, obvious that the
refraction produced by the medium M'" is the same as if the
ray A B had directly impinged thereon.
It will be observed that the entire argument depends
upon the parallelism of the planes bounding the surfaces of
the media. The actual bounding surfaces in the atmosphere
being curved surfaces closely approaching to spheres, the
property we have just proved is only approximately true. It
has, however, been found that for all zenith distances not
exceeding 75 the calculations made upon this assumption
are sufficiently accurate for most purposes.
When the zenith distance exceeds 75 the amount of
the refraction depends upon the constitution of the different
layers of the atmosphere. It is also subject to considerable
changes in accordance with the variations in the temperature
and pressure of* the atmosphere.
The following table gives the amount of the refraction at
different zenith distances from o to 90, the height of the
barometer being 30 inches and the temperature being 50 :
E2
Astronomy.
Apparent
Zenith
Distance
Refraction j
Apparent
Zenith
Distance
Refraction
Apparent
Zenith
Distance
Refraction
o
O
O'O
35
4o'-8
o
70
2 38-8
5
5' 1
*o
48-9
75
3 34'3
10
10-3
45
58-2
So
5 19-8
15
15-6
5o
I 9'3
85
9 54'8
20
21-2
55
I 23-4
87
14 28-1
25
27-2
60
I 40*6
89
24 21-2
30
33-6
65
2 4'3
90
33 46-3
Thus, for example, the apparent zenith distance of an
object being 60, the real zenith distance is found by
augmenting the apparent zenith distance by i' 4o //- 6, and
therefore the true zenith distance is 60 i' 40" '6.
At moderate zenith distances we have the following
law :
The amoitnt of refraction is proportional to the tangent of
the zenith distance.
From the table of refractions it appears that the refraction
at the zenith distance 45 is 58" -2, whence we must have in
general the expression
$&"-2 tan z
for the value of the refraction at the distance z. It is, how-
ever, obvious that this law is incorrect near the horizon.
Under these circumstances the tangent of z approaches to
infinity, while the observed value of the refraction at the
horizon is 33' 46" -3.
53
CHAPTER IIT.
THE DIURNAL MOTION OF THE HEAVENS.
23. The Celestial Bodies. On a clear night the surface
of the heavens glitters with innumerable points of light,
commonly called stars. The objects which are popularly
known by this term comprise two different classes. The
great majority belong to what are called fixed stars, while
a few are known as planets.
The first feature of the fixed stars to which we must
direct attention is their apparent fixity in the heavens with
respect to each other. If we form figures by lines, joining
the different stars together, then it is found that these
figures remain unaltered even while centuries pass away. In
fact, if we could regard the surface of the heavens as a vault
of solid material, the stars appear as if they were rigidly
stuck on the interior of this vault.
The planets, on the other hand, do not remain fixed ;
they are, as their name implies, wanderers, and they move
about on the surface of the heavens among the stars. The
word planet is usually restricted to a very special group of
objects. There are other celestial bodies which are also
wanderers. Among these we may mention the moon, the
satellites of the planets, and comets.
At a superficial glance a planet resembles an ordinary
fixed star so closely that it is difficult to realise how funda-
mental and important is the distinction which separates
them. To test whether an object is really a planet or a
fixed star the position of the object should be carefully
noted with respect to the bright stars in its vicinity. After
some time the object should be again examined and the
place compared with the adjacent fixed stars. If it be found
that the place has altered, then the object is a planet. There
54 Astronomy.
is, however, another method of discriminating between a
star and a planet, which has the advantage of enabling the
decision to be pronounced immediately without waiting
until the planet, shall disclose its real character by move-
ment. If a telescope be directed to a fixed star the object
appears to be merely a point of light. No increase in the
power of the telescope will enable us to see the dimensions
of the small point from which the light comes, although the
brilliancy is increased with each increase of the power of
the telescope. The case is, however, widely different when
the telescope is directed to a planet. It is then seen that
the planet really has a circular disk of dimensions which are
quite appreciable. This test can be applied with facility to .
all the more conspicuous planets. In the case of planets
which are extremely minute or extremely distant this test
cannot be applied easily. In fact, there are numbers of
planets so minute that the telescope cannot show them to
be different from the stars in their vicinity. In these cases
the motion test has to be applied.
24. The Celestial Sphere. A sphere is a surface such
that every point upon it is equidistant from one point in the
interior which is called the centre. If a plane be drawn through
the centre of the sphere it cuts the sphere in a circle which
is called a great circle. A plane which cuts the sphere, but
which does not pass through the centre, has also a circle
for the line along which it intersects the sphere ; this is
called a small circle. The radius of a great circle is of
course equal to the radius of the sphere. The radius of a
small circle may be of any length less than the radius of the
sphere. We may suppose that a sphere is produced by the
revolution of a circle about its diameter, and the radius of
the sphere is then equal to the radius of the circle from
which it has been produced.
Let o be the centre of a sphere, and A B any two points
on its surface. Then a plane through the three points
o A B cuts the sphere in a great circle. This may, for
The Diurnal Motion of the Heavens. 5 5
simplicity, be termed the great circle A B. The length of
the arc of the great circle connecting two given points on a
sphere of known radius is most conveniently measured by
the angle which the arc subtends at the centre.
If we imagine the angle of a pair of compasses to be
placed at the eye while each leg of the compasses is directed
towards a particular star, the angle between the legs of tne
compasses is said to be the angular distance between the
two stars. By an instrument founded on this principle, it is
possible to measure the angular distance between two stars
with great accuracy, and from such measurements a celestial
globe can be constructed. Two points, A and B, are first to
be marked on the surface of the globe, so that the angle
which A and B subtend at the centre of the globe is equal
to the angle subtended at the eye by the two stars to
which A and B correspond. The angular distance of a third
star s is to be measured from both A and B, and the star s
is to be marked on the globe, so that the two arcs s A and
s B shall subtend at the centre of the globe the angles which
have been observed. In this way all the principal stars on
the surface of the heavens may be accurately depicted upon
the surface of a globe.
We shall now introduce a convention which is very
useful. The stars are, no doubt, at very varied distances
from the earth, but, nevertheless, we have seen that the
appearance of the heavens can be adequately represented on
a globe where all the stars are at the same distance from the
centre. Let us suppose a colossal globe to be described
with the earth at its centre and an enormously great radius.
Then if the stars were all bright points stuck on the interior
surface of this globe, the appearance of the heavens would
be the same as we actually find it This imaginary globe
we call the celestial sphere.
25. The Fixed Stars. It may be observed that the
planets which can be conspicuously seen with the unaided
eye are only five in number (viz. Mercury, Venus, Mars,
56 Astronomy.
Jupiter, Saturn). Uranus can be seen like a very faint star,
and one or two of the remaining planets have occasionally
been detected by exceptionally sharp vision. It is thus
evident that of the vast multitude of celestial objects visible
to the unaided eye every clear night, by far the greater
number are fixed stars.
The first feature connected with the stars to which we
shall direct attention is their very different degrees of bright-
ness. Astronomers have thus been led to classify the stars
accordingly. About twenty of the brightest stars in the
heavens are said to be of the first magnitude. Among these
we may mention a few which are particularly conspicuous
in northern latitudes. The brightest star in the whole
heavens is Sirius. Then come Arcturus, Vega, Capella,
Aldebaran, Rigel, Spica, and Betelgeuze.
Next in order to the stars of the first magnitude come
those of the second magnitude. Of these we may mention,
as examples which must be familiar to many, the four
brightest stars in the constellation sometimes known as Ursa
Major, the Great Bear (Fig. 36).
The stars immediately below those of the second magni-
tude in brightness are called stars of the third magnitude ;
next come the fourth, and so on down to the very smallest
stars that can be seen in the most powerful telescopes.
According to Engelmann, the number of stars of each of the
first nine magnitudes is as follows :
ist . . 19 4th . . 490 yth . . 19,900
2nd . . 65 5th .. 1,400 8th . . 68,000
3rd . . 200 6th . . 4,900 9th . . 241,000
From this it will be seen that the fainter stars are much
more numerous than the brighter ones. The number of stars
of each magnitude is greater than the number in any pre-
ceding magnitude, and less than in any following magnitude.
The stars of each magnitude are about 2^ times brighter
than those of the next magnitude below, so that the light of
a star of the first magnitude is a hundred times as great as
that of one of the sixth.
The Diurnal Motion of the Heavens 57
Of the total number of stars only a comparatively small
number are visible to the unaided eye. Stars of the fifth
magnitude are faint, those of the sixth very faint, and it
requires very good vision to perceive stars of the seventh
magnitude without the assistance of a telescope. The
number of stars which can be seen with the unaided eye in
England may be estimated at about 3,000.
It is hardly possible to form any very accurate conception
of the numbers of the stars of each magnitude when that
magnitude is expressed by a larger number than nine. This
arises partly from the prodigious numbers of the stars, and
partly from some uncertainty with which the estimation of
the magnitudes of very small stars are attended. Argelander
has published a most valuable catalogue of the stars in
the northern hemisphere. This catalogue is accompanied
by a series of maps on which these stars are depicted. All
stars of the first nine magnitudes are included in this
catalogue, as well as a very large number of stars which are
between the ninth and tenth magnitudes. The total number
of stars contained in the catalogue and on the maps amounts
to 324,188.
Maps have been formed of isolated portions of the
heavens which include stars much smaller than those here
referred to. Some of these maps contain stars of the
eleventh and twelfth magnitudes, if not actually smaller.
The enormous numbers of the very small stars render the
formation of such maps exceedingly laborious. The total
number of stars visible in powerful telescopes doubtless
amounts to many (perhaps very many) millions. A survey of
the starry contents of the heavens now being made by
photography tends still further to increase our estimate of
the number of the stars.
The prodigious multitudes of minute stars with which
the heavens are strewn is well illustrated by the nature of
what is commonly known as the Milky Way. The milky
way is an irregular band of faint luminosity which encircles
the whole heavens, and may be seen on any dark and clear
58 Astronomy.
night in the absence of the moon. The telescope shows
that this faint luminosity really arises from myriads of
minute stars, which, though individually so faint as to be
invisible to the naked eye, yet by their countless numbers
produce the appearance with which doubtless everyone is
familiar.
26. Constellations. For the purpose of marking out
different regions in the heavens, modern astronomers have
retained the method which was principally due to the
poetical imagination of the ancients. The whole surface of
the celestial sphere is, on this method, supposed to be
covered by imaginary human figures, and representations of
other objects. The stars on each of these figures are by
some grotesque conception supposed to point out the form
of the object. In this way different regions of the heavens
are known by special names, and the stars on each of these
regions are collectively termed a constellation. We thus
have, for example, the constellation of Orion, Ursa Major,
Ursa Minor, Leo, Lyra, &c. &c.
This arrangement provides a very convenient method of
indicating the stars. It is for this purpose only necessary
to mention the name of the constellation to which the star
belongs, and to append a letter or number by which the
different stars of each constellation may be distinguished.
Bayer published in the year 1603 a series of maps of the
stars, in which the letters of the Greek alphabet were
attributed to the principal stars of each constellation. To the
brightest star of the constellation the letter a was as-
signed, the next brightest is denoted by /3, the next
by y, and so on throughout the alphabet. When all the
Greek letters have been exhausted, the remaining stars
in the constellation are usually denoted by Latin letters and
numbers.
It is exceedingly desirable that the learner should make
himself acquainted . with the principal constellations. To
facilitate him in doing so, we shall give a few outline charts,
The Diurnal Motion of the Heavens. 59
in which the brighter stars in several of the constellations
will be shown.
There is no difficulty in recognising at once the con-
stellation of Ursa Major, of which the seven principal stars
FIG. 36.
Y * e*
are shown in Fig. 36. This constellation is perhaps the
most conspicuous object in the northern skies, and in these
latitudes it never sets. Ursa Major can thus be seen every
clear night in the year, and in April it is near the zenith at
1 1 P.M. When once this group of stars has been recognised,
many of the other important stars and constellations can be
determined with facility.
We shall first point out how the position of the Pole
Star is to be ascertained by the help of Ursa Major. If
we imagine a line drawn through the stars ft and a in
FIG. 37.
Major and then continued on from a to a distance which is
about five times the distance from ft to a, the extremity of this
line will be found to be close to a bright star. This bright
60 Astronomy.
star is called the Pole Star. The Pole Star is also the star
a of the constellation Ursa Minor, Fig. 37. This group
contains seven principal .stars, of which /3 arid y, in addition
of course to the Pole Star, are the most conspicuous. The
point which is known as the pole of the heavens, lies exceed-
ingly near to the Pole Star (Fig. 37), whence the latter has
received its name.
If we join c in Ursa Major to the Pole Star, and produce
the joining line nearly as far on the other side of the Pole
Star, we come to a remarkable group of stars, forming the
constellation Cassiopeia. Thus Ursa Major and Cassiopeia
are so situated, that the Pole Star lies almost exactly half-
way between them. These are the constellations which
should first be made familiar to the eye and memory of the
student, and then he can proceed to the others now to be
described.
The great Square of Pegasus is a remarkable group.
Unlike Cassiopeia and Ursa Major, the constellation now
under consideration rises and sets daily. It cannot be seen
FIG. 38.
Square of Pegasus
A ft^ oc
\> _- ^T 1
:^---
-""^ole Star
conveniently during the spring and summer, but during
autumn and winter the four stars forming the great Square
The Diurnal Motion of the Heavens. 6 1
of Pegasus form a remarkable object every evening. These
stars are of the second magnitude. The square may be
determined by drawing two lines through a and S Ursae
Majoris to the Pole Star. These lines continued on beyond
Cassiopeia to about the same distance as Cassiopeia is from
the Pole Star, include between them the great square of
Pegasus (Fig. 38).
Three of the stars in the square, viz. a, /3, y, belong to
the constellation Pegasus, but the fourth star, which is also
marked <, belongs to the constellation Andromeda, of which
it is the brightest object. Two other stars, /3and y, belong-
ing to Andromeda can also be readily determined from the
circumstance that they are near the corner of the square,
where a Andromedse is situated (Fig. 38). The line joining
/3 and y in Andromeda, produced away from Pegasus,
points to the brightest star a in the constellation Perseus.
The seven stars, viz. a Persei, a, /3, y Andromedse, and
a, /3, y Pegasi, form a very remarkable group of stars, and
once they have been recognised they will aid in the indica-
tion of several other constellations.
o Persei lies between two other stars y and belonging
to the same constellation. These stars form an arc (Fig. 39)
which, produced on a little distance,
includes the bright star Capella, belong-
ing to the constellation Auriga. On #,.^
the convex side of this arc lies the Capelk'
remarkable variable star /3 Persei, more
usually known as Algol. If the arc
formed by y, a, c Persei be prolonged
so as to be concave towards Algol, it
points out the stars e, Persei ; and
continued on further in the same direc-
tion, we come upon the very remarkable
group of small stars close together which are called the
Pleiades.
Joining the Pole Star to Capella, and producing the join-
62
Astronomy.
ing line beyond Capella, the splendid constellation of Orion
is arrived at (Fig. 40). The brightest star of this constellation
is a Orionis, often called Betelgeuze, which is remarkable for
its ruddy hue. The Belt of Orion is formed by the three stars
c), e, The belt is surrounded by the quadrilateral formed
by the four stars a, /3, y, /.-. Of the seven stars a and /3 are
FIG. 40.
FIG. 41.
Aldebaran*
Orion I
* *
of the first magnitude, while the five
remaining stars are of the second mag-
nitude.
The three stars in the Belt of Orion
point downwards to a most conspicuous
star called Sirius. This is by far the
most brilliant of all the stars. In con-
junction with a few inconspicuous
stars it forms the constellation of Cam's
Major. Pollux *
If the line of the Belt of Orion be
prolonged in the other direction, it
points out the star Aldebaran. This \
is the brightest star in the constellation \
of Taurus. * ***** '
The line joining the stars /3 and r> in Ursa Major, and
produced on sufficiently far, points out the two stars of the
second magnitude termed Castor and Pollux in the constel-
lation Gemini (Fig. 41). This same line continued a little
farther passes near the star Procyon, of the first magnitude,
in the constellation of Cam's Minor (Fig. 41).
Castor
*
The Diurnal Motion of the Heavens. 63
The line joining the two stars a, /3 in Ursa Major, pro-
longed on beyond (3 to a distance five times as far as from a
to /3, points out the constellation of FIG
Leo (Fig. 42). The stars in this con-
stellation have a remarkable form. ^J ^
The four principal stars a, /3, y, S f j "^\/
are shown in the figure, a, other- 1 ; / "\^
wise called Regulus, is of the first ~~"~-/--..^ r -"" 3 %D
magnitude. The three remaining /
stars of the quadrilateral are of the /
second magnitude. '
The tail of Ursa Major, when j
prolonged, points to the brilliant /
star of the first magnitude called /
ArcturuS) which is the principal /
object in the constellation Bootes ^ ^
(Fig. 43). The stars ft y, a, e in \
the same constellation are also SK xx
TT *^t-'-"~'*f*
shown in the figure. *"* Af a -
Close to Bootes, and in a direc-
tion which may be found by following the line of the stars
/3, S, e, Z, in Ursa Major, is the constellation Corona Borealis.
This consists of a number of stars arranged nearly in a semi-
circle, the largest of them being of the second magnitude.
FIG. 43-
t Corona
V-i
If a line be drawn through a and y in Ursa Major, and
if this line be curved so as to present its convexity towards
6 4
Astronomy.
Arcturus, as in Fig. 44, it points to a brilliant star termed
Spica,) which is the brightest star in the constellation Virgo.
FIG. 44 .
*r\,
\
Denebola
The star /3 Leonis, otherwise called Denebola, which is situ-
ated at the tail of Leo, forms one vertex of a very striking
FIG. 45.
Star
equilateral triangle of which Arcturus and Spica are the
two remaining vertices.
The Diurnal Motion of the Heavens. 65
One of the most brilliant stars in the northern sky is the
bright star in the constellation Lyra, which is known gene-
rally by the term Vega. Vega may readily be recognised as
the vertex of a nearly right-angled triangle constructed on
the line joining the Pole Star to Arcturus. Four other stars 1
in the constellation Lyra form a parallelogram which may
be noticed. These stars are /3, y, , '.
The constellation Cygnus will be recognised as lying
between Vega and the great Square of Pegasus. There are
five principal stars in Cygnus which form a remarkable con-
figuration (Fig. 46).
FIG. 46.
'
**. , ,. ^
It
!
Altalr
The last constellation which will be noticed is Aquila.
This will be easily determined, because a line drawn from
Vega across /3 Cygni passes a little above the group of three
stars which form the most conspicuous part of Aquila (Fig.
46). The star a Aquilae, otherwise called Altair, is of the
first magnitude.
27. Diurnal Motion of the Heavens. After the learner
has become familiar with the appearance and names of the
leading constellations, he is recommended to notice the
apparent movements which they perform on the surface of
the heavens.
The constellation Ursa Major is to be looked at early in
66 Astronomy.
the evening, and its position with regard to the trees, or
houses, or other terrestrial objects is to be noted. If the
observation be renewed a few hours later, a very remarkable
change will be perceived. The relative positions of the stars
have not indeed altered. All the angular distances between
the several pairs of stars in the constellation are the same
on the two occasions. Nor have the stars changed their
positions with reference to the stars in the adjacent constel-
lations, but the whole system of stars has moved bodily.
Observation will also show that the position of the Pole
Star does not appreciably change its place either with respect
to the stars or with respect to the terrestrial objects by which
its position may be indicated. At different hours of the
night, or at different seasons of the year, the Pole Star will
constantly be seen in the northern sky at about the same
elevation above the horizon. We shall hereafter have to
explain that with more careful methods of measurement this
statement would not be found strictly accurate. The Pole
Star does really change its position, though the amount of
that change is not sufficient to be readily appreciable in the
coarse, naked- eye observations which we are at present dis-
cussing.
A marked contrast is thus perceptible between the fixity
of the Pole Star and the large movements which are made
by the stars in Ursa Major. It is, however, to be noticed
that the two stars a and /3 (Fig. 37), which point towards
the Pole Star, continue to point to the Pole Star, notwith-
standing the great movements which they undergo in com-
mon with all the other stars of the constellation. The idea
is thus suggested that the stars of Ursa Major really move
as if they were all fastened together by invisible rods, and as
if each of the stars was also fastened by an invisible rod to
the Pole Star, about which the whole system is free to turn.
If the observations be renewed at intervals through the
night, and then with the help of a telescope through the
following day, it would be seen that Ursa Major, after as-
The Diurnal Motion of the Heavens. 67
cending from the east, passes over the observer's head, then
down towards the west, under the Pole Star in the north,
and round again to the east, and the observer would find
that in about twenty-four hours the constellation had re-
turned to its original position.
This movement of the constellations by which each of
them moves (or appears to move) round the heavens in
about twenty-four hours is termed the Diurnal Motion. It
will be instructive to trace the same series of movements in
some other celestial objects. Take, for example, the re-
markable group of small stars known as the Pleiades (Fig.
39). This beautiful group is visible at night throughout the
greater part of the year, but it need not be looked for from
the middle of April to the middle of June. Winter is the
best season for observing it. In November this little group
may be detected in the east shortly after sunset. It will
then gradually rise until about midnight, when it reaches
its greatest height. After passing the highest point the
group begins to descend, and gradually gets lower and lower,
until it disappears in the west There is, however, this very
remarkable difference between the motion of the Pleiades
and that of Ursa Major. The latter could be followed (with
a telescope) through a complete revolution (at least in our
latitude), but this is not the case with the Pleiades, for they
actually disappear in the west, and after some hours reappear
again in the east. If, however, the time be noted which
elapses between two consecutive returns of the Pleiades to
the same position, the interval will be found to be equal to
the time of revolution of Ursa Major.
28. The Equatorial Telescope. To study the apparent
diurnal motion of the heavenly bodies with the accuracy
which its great importance demands, we call in the aid of
the astronomical instrument called the Equatorial Telescope.
The equatorial in its essential features consists of an
astronomical telescope attached at its centre o to an axis A B,
called the polar axis. The telescope is capable of being
F 2.
68 Astronomy.
turned round the axis passing through o, while the polar
axis is capable of being turned round the two pivots at A
and B. By the combination
of these two motions it is pos-
sible to direct the telescope
towards any required point.
To render this instrument
serviceable for astronomical
purposes, the polar axis must
be carefully adjusted in a very
special direction. The axes
of the two pivots at A and B
being supposed to form parts of the same straight line, the
direction of this straight line should point towards a par-
ticular point on the surface of the heavens in the immediate
vicinity of the Pole Star. This point is the Pole. It will
be subsequently explained how this adjustment of the polar
axis of the equatorial is to be made, but for our present pur-
pose we may assume that the adjustment is perfect.
The equatorial telescope may be employed in watching
the apparent diurnal movement of a star by the following
method. Point the telescope to the star shortly after the
star has made its appearance in the east. Then damp the
telescope so that it can no longer turn around the axis
through o, but leaving the polar axis carrying the telescope
along with it quite free to turn round the pivots A, B. It
will then be found that by the simple operation of turning
the polar axis round at the proper speed, the star can be
kept continually in the field of view, although the magnitude
of the angle B o Q made by the telescope with the polar axis
remains unaltered.
To appreciate the full significance of the lesson which
the observations with this instrument teaches, let the tele-
scope be directed to any other star. For this purpose it
must be undamped, and after the angle B o Q has been
suitably altered, so as to enable the star to be seen in the
The Diurnal Motion of the Heavens. 69
telescope, the instrument is again clamped, so as to pre-
serve the angle B o Q from alteration. , It is again found
that the movement of the star can be followed by simply
rotating the polar axis, which carries with it the telescope.
If the polar axis of the equatorial be not directed exactly
to the correct point of the heavens, it will not be found that
the diurnal motion of a star can be followed by simply
rotating the polar axis without altering the angle B o Q.
It is to be particularly observed that when the polar axis
is set correctly for one star it is set correctly for all stars.
The Pole Star itself is no exception to this law. If the
instrument be directed to the Pole Star, we shall now see
what the coarser methods of observing failed to indicate
namely, that the Pole Star is itself in motion. In this case
the telescope, when adjusted on the Pole Star, is inclined at a
very small angle to the polar axis. The angle B o Q is, in
fact, only about i 15'.
The other extremity of the polar axis may be supposed
to be prolonged downwards through the earth, and it will
then point towards a point in the southern heavens which is
called the South Pole. It happens, unfortunately for astro-
nomers in the Southern hemisphere, that there is no bright
star situated so conveniently near to the South Pole as the
Pole Star is to the North Pole.
These two poles of the celestial
sphere are of the very utmost im-
portance in astronomy.
The polar axis of an equatorial
having been correctly adjusted, we
shall suppose that its direction is
E P (Fig. 48) ; and if P be the point
in which the direction of the polar
axis intersects the celestial sphere,
then P is the pole of the heavens.
Let s denote the position of a star on the celestial sphere
which is being observed, then the axis of the telescope
7O Astronomy.
has the direction E s. We have seen that the diurnal mo-
tion of the star can be followed by rotating the telescope
about the polar axis without at the same time making any
alteration in the angle at which the telescope is inclined to
the polar axis. Let us, then, suppose that the star, in con-
sequence of the diurnal motion, assumes the various posi-
tions L, M, N, &c. When the star has arrived at L, the
telescope must have moved into such a position that its
axis is directed along the line E L. It follows that the angle
between the polar axis and the telescope must be equal to
the angle PEL. But this angle has remained unchanged
notwithstanding the diurnal motion, and therefore we see
that the angle p E s is equal to the angle PEL. The arcs
p s and P L on the surface of the celestial sphere subtend at
the centre the angles PES and PEL respectively, and as
these two angles are equal the two arcs must also be equal.
In the same way it is shown that the arcs p M, p N, &c., are
each equal to P s.
We have therefore ascertained that the diurnal move-
ment of a star on the celestial sphere is always subject to
the condition that the length of the arc drawn from the pole
to the star is a constant. From s let fall a perpendicular
s H upon the polar axis P E. Then, since the length of E s,
the angle PES, and the right angle at H remain unaltered
during the motion of the star, it follows that the triangle s E H
remains unaltered, and therefore also the lengths of the
sides E H and s H. The line s H will therefore be always
contained in the plane drawn through the point H per-
pendicular to the axis E P. The path of the star will
always be in this plane, and, as the path is also on
the celestial sphere, it follows that the actual path appar-
ently described by the star will be the intersection of a plane
and a sphere, and will therefore be a small circle of the
sphere. The same process may be applied in the case of
other stars, and therefore we are led to the following very
important result :
The Diurnal Motion of the Heavens. 7 1
The apparent diurnal motions of the stars are performed
in small circles of the celestial 'sphere -, and all these small circles
lie in a system of parallel planes.
The next question to be considered is the rate at which
the apparent motion of each star in its small circle is per-
formed. While the star moves from s to L (Fig. 48) the
polar axis of the telescope must be rotated through an angle
equal to that between the planes P s E and p L E. This angle
is equal to that between the two arcs of the celestial sphere
p s and P L. Thus while the star moves from s to L the polar
axis of the telescope must be turned through an angle s P L.
By means of a graduated circle, called the hour circle, of
which the plane is perpendicular to the direction of the
polar axis, it is easy to measure the angle through which the
polar axis has been rotated when the telescope is turned
from the position E s to the position E L. The observations
are, then, to be made in the following manner : When the
star is at s, and when the telescope is pointed to it, note
the position of the polar axis as indicated by the hour circle,
and also the time as shown by a clock, and repeat the
observation when the star arrives at other points L, M, N of
its path. From the readings of the hour circle the angles
s P L, L P M, M P N, &c., become known, while from the
recorded clock times we have the times of moving from s
to L, from L to M, and from M to N, &c. It is, then, found
that the time intervals are proportional to the angles through
which the polar axis has been rotated. The distance through
which the star appears to move is therefore proportional to
the time, and hence we have the following important law of
the diurnal motion :
The velocity of a star in the small circle which it appears
to describe in the diurnal motion is uniform.
It follows from this law that when the equatorial telescope
is to be moved so as to keep the star continually in the field
of view, the angular velocity with which the polar axis re-
volves must be uniform. To secure this condition a clockwork
72 Astronomy.
arrangement is usually attached to the telescope, which carries
the polar axis (and of course the telescope attached thereto)
with the correct velocity.
So far we have only been considering the movement of
a single star in its small circle. We have now to make a
comparison between the movements of different stars in their
appropriate small circles. This can also be effected by the
equatorial, in the following manner : Point the telescope to
a star, and note the time when the star passes the centre of
the field ; then, without altering the position of the telescope
or the polar axis, observe the time when the star, after having
performed a complete revolution of the heavens, returns again
to the centre of the field. This time will be found to be
equal to
Turn the telescope to any other star, and make the same
observation. It will be found that for the second star the
time will be precisely the same. This conclusion may be
extended to other stars, and thus we are led to the following
important result :
The time occupied by a star in performing its diurnal path
around the heavens, is the same for all stars, and is equal to
23 h 56 4 s of mean solar time.
29. Circles of the Celestial Sphere. -The study of the
apparent diurnal motion of the heavens is of such funda-
mental importance that we shall proceed to illustrate it in
a somewhat different manner. It will first be necessary to
explain some terms which are of frequent use.
An observer, situated on a ship out of sight of land, ob-
serves that the celestial sphere is bounded by a circle, below
which he cannot see. This circle, when regarded as one of
the great circles of the celestial sphere, is the horizon.
If a weight be suspended by a thread from a fixed point,
then when the weight is at rest the thread is said to be
vertical. That point of the heavens to which the thread
The Diurnal Motion of the Heavens.
73
points, and which it would appear to reach if it could be
prolonged indefinitely upwards, is the zenith, while if the
direction of the thread be prolonged downwards through
the earth it will point to that part of the celestial sphere
which is termed the nadir.
A straight line which is perpendicular to a vertical line is
called a horizontal line, and all the straight lines which can
be drawn perpendicular to a vertical line through any one
point in it lie in one and the same plane, which is called a
horizontal plane.
If the face of an observer in the northern hemisphere be
directed towards that part of the heavens where the sun is
at noon, the part of the heavens in front of him is termed the
south, that behind him is the north, while the east is on his
left hand and the west upon his right.
The great circle of the celestial sphere which passes
through the poles, and also through the zenith, is called the
meridian. The meridian may also be defined as the great
circle which passes through the north and south points of
the horizon, and also through the zenith.
FIG. 49-
Let the circle H M H' (Fig. 49) represent the horizon, and
let z be the zenith, the position of the observer being at o.
74 Astronomy.
If M be the south point of the horizon, then the great circle
z M is a portion of the meridian. Let E c E' represent
the apparent path of a star. Let H be the point on the
horizon vertically beneath the star in the position E. This
point will be found by drawing a great circle from z to E,
and producing it on to cut the horizon at H. The angle
E o H is termed the altitude of the star at E. It is observed
that the altitude of the star increases until the star arrives
at the meridian z M, which it crosses at the point c. When
the star has this position its altitude is the arc c M, or the
angle which that arc subtends at o. The altitude at this
point is a maximum, and the star is said to culminate. After
passing the meridian the star moves along the arc c E', and
begins to descend towards the horizon when it reaches the
point E' its altitude is only E' o H', and this altitude gradu-
ally diminishes until the star crosses the horizon, or sets, as it
is called. In the case here represented only a portion of
the path of the star is visible, the remainder lying below
the plane of the horizon. It is important to observe that
the path of the star is symmetrical with respect to the
meridian. It cuts the meridian at right angles, and at
equal distances on either side of the meridian the altitudes
are equal.
30. Circumpolar Stars. In this case we have supposed
the star is placed at a considerable distance from the
pole ; let us now take the case of a star situated compara-
tively near the pole. For this purpose the observer must
turn his face towards the north (Fig. 50). p is the pole, z is
the zenith, and the great circle z p is the meridian which
cuts the horizon at the northern point. Let E denote the
position of the star, which is in the act of crossing the meri-
dian by the diurnal motion. Then in the course of a little
less than twelve hours the star will have moved round to the
position E' below the pole. We have already seen that the
diurnal motion is performed subject to the condition that
the distance from the pole to the star measured along the
The Diurnal Motion of the Heavens. 75
celestial sphere remains constant ; we must therefore have
the arc p E equal to the arc p E'. The star, when at the posi-
tion E, is said to be at its upper culmination^ while at E' the
star is at its lower culmination.
FIG. 50.
A star which is situated at a distance from the pole
which is less than the altitude of the pole above the horizon
will be visible both at upper and lower culmination. Such
a star will never either rise or set, and is said to be a cir-
cumpolar star. If, however, the distance from the star to
the pole be exactly equal .to the altitude of the pole, then
the star at its lower culmination will just graze the horizon.
If the polar distance of the star exceed the altitude of the
pole, then the star will pass below the horizon, and its lower
culmination will not be visible.
It should be mentioned that the phenomena we have
described are to a certain small extent modified by the
influence of atmospheric refraction. For example, the arc p E
(Fig. 50) is not precisely equal to the arc p E', because the
refraction has acted unequally upon the position of the star
in both cases. We can, however, allow for the amount of
refraction, and thus we can ascertain what the distances
would be if we could see them without the modification
which the atmosphere produces. When these allowances
Astronomy.
FIG. 51.
have been made it is found that the laws enunciated are
accurately fulfilled.
31. The Globe. We are now in a position to form a
distinct idea of the varied series of phenomena which the
diurnal rotation brings before us.
Let us take a globe A (Fig. 51), which is movable about
an axis p Q. The axis P Q is supported by a ring M M, which
is sustained by another ring H H. We may conceive the
axis P Q to be adjusted so
that it is parallel to the line
joining the two poles of the
heavens or to the polar axis
of the equatorial (Fig. 47).
The plane H H is to be made
1 horizontal. Then the globe
may be taken to represent
the celestial sphere, of which
p, Q are the two poles, the
ring H H indicates the hori-
zon, while M M, which passes
through the zenith and the
pole P, is the meridian. On
this globe we may suppose
that the principal stars of the
celestial sphere are marked
in their proper relative places,
and thus we have a miniature representation of the celestial
sphere.
The globe is supposed to be free to turn around the
polar axis P Q, and we may assume that by suitable clock-
work such a motion is given to the globe as will turn it
round its axis in 23** 56 4 s , while the velocity with
which the motion is effected is uniform. It is easy to show
that under these circumstances all the phenomena of the
diurnal motion will be faithfully represented.
A star will, in consequence of this motion, gradually
The Diurnal Motion of the Heavens. 77
ascend above the circle H H and thus rise ; it will ascend
farther and farther until it reaches the meridian M M,
or culminates ; after culmination it will gradually descend
again to H H, or set. So also a circumpolar star will be
seen to pass the meridian M M at its upper culmination, and
then in n h 58 m 2" afterwards to cross the meridian at
the lower culmination.
It will further be seen that the laws of the diurnal
motion will be preserved in this miniature representation
of the phenomenon. In the first place, the distance from
the pole to the star measured along the surface of the sphere
remains unaltered ; the velocity of each star in its path is
also obviously uniform, while the time of a complete revo-
lution is the same for each star as the time of revolution of
the sphere i.e. 23 h 56 m 4 s .
We are, therefore, led to the important conclusion that
the apparent diurnal motion of the heavens is performed in
the same manner as if all the stars were actually stuck on
the surface of a hollow sphere which revolved uniformly
about an axis passing through its two poles in 23 h 56 m 4*.
The period of revolution of the celestial sphere is prac-
tically a constant quantity. It is, therefore, very natural to
adopt this period as the unit of time, and it is known as the
sidereal day. The sidereal day is subdivided into twenty-
four hours, each hour into sixty minutes, and each minute
into sixty seconds. An interval of time expressed in these
fractional parts of a sidereal day is termed sidereal time.
The difference, amounting to nearly four minutes, by which
the sidereal day falls short of the ordinary day of civil
reckoning will be subsequently explained.
The polar axis of an equatorial telescope prolonged both
ways to the celestial sphere cannot be distinguished from
the axis about which the celestial sphere rotates. This
is true wherever the equatorial be situated It would,
therefore, appear that the axis of the celestial sphere may
be considered to pass through any point on the surface of
78 Astronomy.
the earth. It is, however, obvious that there is really but
one axis about which the celestial sphere is turning. The
only way by which these discrepancies can be reconciled is
by supposing that the dimensions of the earth are exceed-
ingly small in comparison with the distance at which the
stars are situated. The axis must actually occupy some de-
finite position in the earth ; but the earth is, comparatively
speaking, so small that the observer must always be so near
to the axis that the observed phenomena are the same as
they would be were he actually situated on the axis. The
polar axes of the equatorials all over the earth are absolutely
parallel to each other, and they all intersect the celestial
sphere in two small regions which for all practical purposes
are undistinguishable from the north and south poles of the
celestial sphere.
32. Rotation of the Earth. The apparent diurnal
motion of the heavens might be no doubt explained by
the hypothesis that the celestial bodies were all attached
to the interior surface of a colossal globe of which the earth
was the centre, and that this globe revolved around one of
its diameters once every sidereal day. There is, however,
another method of explaining the diurnal motion, which
demands our careful attention. The earth itself is, as we
have seen, an isolated body in the universe, and is attached
to no other object. What is there, then, to prevent the
earth being actually in motion? It may be said that we,
as dwellers on the earth, do not feel the motion ; but this
is no argument. If you are seated in the cabin of a canal
boat and have no opportunity of looking out, you cannot
tell whether you are in motion or not. If you can look out
and see the trees and other objects on the bank apparently
moving, you will at once refer the motion to yourself and
acknowledge the trees are at rest. In this way if the earth
were moving equably it would be impossible for us to detect
that motion except by comparing our positions with the
positions of external objects. It is, therefore, reasonable
The Diurnal Motion of the Heavens. 79
for us to ask whether we can obtain from external objects
any information of the state of the earth as to rest or
motion.
A solid body like the earth may have either of two
different descriptions of movement, or, more generally, it
may possess both forms of movement combined together.
The body may have a movement of translation, by which
all points of the body are at any moment moving in parallel
lines, or it may have a movement of rotation about an axis,
or it may have, and generally has, the movements of trans-
lation and of rotation combined. Setting aside for the
present the question of translation, let us enquire whether
the earth possesses the features that we might expect if it
were actually rotating about an axis. The celestial bodies
are the only external objects by the observation of which
we are to see whether the earth has any movement of rota-
tion or not. If the earth be rotating in the opposite direction
about the axis of the sphere, and with the uniform velocity
which would complete the revolution in a sidereal day, then
the apparent diurnal motion would be completely explained.
We have, therefore, two solutions of the problem of the ap-
parent diurnal motion. We may suppose that the celestial
sphere is revolving around the earth from east to west, while
the earth is at rest ; or we may suppose that the celestial
.sphere is at rest, and that the earth is revolving from west
to east, and thus produces the apparent motion.
Which of these two solutions are we to adopt? W r e
shall see hereafter that many of the celestial bodies are
vastly larger than the earth, that they are situated at very
great distances from the earth, and that some of these dis-
tances are very much greater than others. It therefore
seems much more reasonable to suppose that the earth,
which is a comparatively small body, should be in a con-
dition of rotation rather than that the vast fabric of the
universe should all be moving round the earth once every
day. Astronomers, therefore, now universally admit that
8o Astronomy.
the true explanation of the apparent diurnal motion of the
heavens is to be found in the fact that the earth revolves
on its axis once every sidereal day from west to east.
33. Shape of the Earth connected with its Rotation. A
remarkable confirmation of this conclusion is presented by
the shape of the earth itself. Conceive a straight line
drawn from the centre of the earth towards the north pole
of the celestial sphere. This straight line will cut the surface
of the earth in a point which is called the north pole of the
earth. By means of the surveying operations which have
determined the figure of the earth we are enabled to ascertain
the point on the earth's surface which is the extremity of the
shorter axis of the ellipse by the rotation of which the figure
of the earth can be produced. It will be noticed that the
apparent diurnal motion has nothing whatever to do with
the surveying operations, so that it is exceedingly remark-
able to find that the north pole of the earth is close to,
if not actually identical with, the extremity of the shorter
axis of the ellipse. Thus we see that the axis about which
the earth actually rotates coincides with the shortest diameter
of the earth. In this we have another very remarkable
proof of the reality of the earth's rotation. It is generally
believed that at some very remote epoch the earth was in a
fluid or a semifluid condition. At the time that this was so
the effect of the centrifugal force would make the earth bulge
out at the equator and flatten it down at the poles, and
thus impart to it the shape of an ellipsoid of revolution.
The shortest axis of this ellipsoid would coincide with the
axis of rotation. We are thus led to the belief that the
observed coincidence between the axis of the apparent
diurnal rotation of the celestial sphere and the shortest
axis of the earth is a proof that the apparent diurnal motion
of the heavens is really due to the rotation of the earth
on its axis.
34. Definition of Terms. To enable us to define the
positions of the various celestial bodies on the surface
The Diurnal Motion of the Heavens. 8 1
of the celestial sphere it is necessary to imagine certain
circles traced upon its surface, with reference to which
the positions of the bodies may be specified. There is
considerable convenience in choosing these circles, so as
to be symmetrical with reference to the diameter of the
celestial sphere about which the apparent diurnal motion is
performed.
Let the point c be the centre of the celestial sphere
(Fig. 52), and let the diameter PQ be the axis of the ap-
parent diurnal rotation. The earth may be regarded as
a particle of exceedingly small
magnitude situated at the centre
c. If through the point c a
plane be drawn which is per-
pendicular to the polar axis P Q,
this plane will cut the surface
of the celestial sphere in a great
circle E E, which is called the
celestial equator. The celestial
equator divides the celestial
sphere into two equal portions,
in which the poles P and Q
occupy two symmetrical positions. The hemisphere which
contains the north pole is called the northern hemisphere,
while that which contains the south pole is termed the
southern hemisphere.
If the celestial sphere be cut by a plane s s which is
parallel to the plane of the equator, the section of the
celestial sphere is termed a parallel. The circles T T and
R R are &\$Q parallels. The effect of the diurnal motion is
to make each star move around the celestial sphere in the
parallel which is appropriate to it. A plane passing through
the axis P Q cuts the celestial sphere in a circle, called a
decimation circle.
By the aid of the various parallels and declination circles
drawn upon the surface of the celestial sphere we are
G
82 Astronomy.
enabled to specify the position of a star on that sphere
with the greatest facility. It must be understood that we are
not now speaking of the absolute position of the body in
space ; for this it would be necessary to know the actual
distance of the body from the earth, of which in the great
majority of cases we are entirely ignorant. What we now
refer to is merely the direction in space where the body is
situated.
Let A be a star on the celestial sphere. Then we are to
draw a great circle from the pole through A, and this great
circle cuts the equator at the
point M. Taking an arbitrary
point o upon the equator from
which to make our measure*
ments, it is clear that the
decimation circle PAQ will be
completely defined if we know
the length of the arc o M. If
the distance of A from M be
also knownj then we have a
complete method of specifying
the position of the point A.
Instead of the arcs o M and A M we may speak of the angles
which those arcs subtend at the centre of the celestial sphere,
and thus we may define the position of the star A by two
angles as well. as by their corresponding arcs.
The arc o M, which is the distance between the declina-
tion circle passing through A and the standard point o, is
called the right ascension of the star A ; while the arc A M,
which is the arc of the great circle drawn through the star
perpendicular to the equator, is termed the declination.
The position of a star is thus completely specified
when its right ascension and declination are known. It is
only necessary to mark off a distance o M upon the equator
equal to the given right ascension, and take off the
distance M A equal to the given declination. In this way
The Diurnal Motion of the Heavens.
the position of the star can be expressed in a manner
which is quite unambiguous. If the right ascension of the
star only were given, then all we would know as to its posi-
tion is that it is somewhere on the declination circle passing
through A. If the declination of the star only were given,
then all that would be known is that the star lies somewhere
on the ' parallel ' passing through A.
The point o, from which the right ascensions of the stars
are measured, might be chosen anywhere. For example, we
might agree that o should be denned to be the point in
which a declination circle, passing through a certain con-
spicuous star, such as Vega or Sirius, cuts the equator.
Astronomers have, however, adopted a different method,
and the point o is defined by the motion of the sun, in a
manner which will be explained subsequently.
Right ascensions are measured from west to east, and
increase from o to 360. Declinations are measured above
and below the equator, and are taken as positive when the
star lies between the equator and the north pole, and
negative when the star lies between the equator and the
south pole.
35. The Transit Instrument. For the determination
of the right ascensions of the celestial bodies use is made
of the transit instrument ', the
principle of which will now be
described.
A telescope A B (Fig. 54) is
fixed to an axis XY, the direc-
tion of which is at right angles
to the line of collimation of the
telescope. The shapes of the
axis and the telescope are so
designed as to secure as much
rigidity as possible. At the ex-
tremities of the axis are two
cylindrical pivots x, Y, which turn in suitable bearings sup-
G 2
FIG.
8 4
Astronomy.
ported on solid masonry piers L, M. The transit instrument
is capable of turning around these pivots, but it can have
no other motion. As the axis of A B is at right angles to
the line of pivots x Y, the movement of the line A B must
obviously be limited to the plane perpendicular to x Y.
In the focus of the object glass of the telescope are
stretched a number of parallel spider-lines A B, &c. (Fig. 55).
These lines are placed perpen-
dicular to the axis XY, and
therefore parallel to the plane in
which the movements of the axis
of the telescope are confined.
y , ^ These lines are at equal dis-
tances apart, and their number
depends upon the particular
kind of observations which are
made. It is sometimes as low
as five, and sometimes as great
as twenty-five. The vertical
system of spider lines is also crossed at right angles by one
or more horizontal spider-lines c D.
When the telescope is pointed to a star the image of the
star is formed in the same plane which contains the system
of spider lines. Consequently, when the eye piece has
been adjusted, the star and the spider lines will be clearly
seen together. If the telescope be at rest the apparent
diurnal motion of the celestial sphere carries the star across
the spider lines one after the other ; and the instrument
must be adjusted so that the path of each star across the
field will be parallel to the horizontal wire c D, and therefore
parallel to the axis about which the telescope revolves.
We have now to explain how the transit instrument is to
be adjusted and placed in its proper position. If the point
o, which is the intersection of the horizontal line with the
central vertical line, be joined by an imaginary line to the
centre of the object glass, this line is the axis of collimation.
The Diurnal Motion of the Heavens. 85
The pivots at x and Y, about which the instrument rotates,
are presumed to be perfectly cylindrical, and the diameters
of these cylinders are presumed to be equal and their axes to
be collinear. The straight line which contains the axes of the
two pivots is the axis around which the telescope revolves.
The first adjustment of the transit instrument which we
shall consider is purely instrumental. It consists in fixing
the telescope to the axis in such a manner that the line of
collimation shall be exactly perpendicular to the axis of
revolution. The astronomical instrument maker can, no
doubt, effect this adjustment to a high degree of approxima-
tion so far as mere mechanical measurement is concerned.
But the delicacy of astronomical observations renders errors
visible which would entirely elude a less subtle method of
detecting them, and it is therefore necessary to point out
how we can avoid the effects of the errors into which inac-
curacies in the construction of the instrument would lead us.
This is attained not so much by endeavouring to correct
these errors as by ascertaining their amount and then allow-
ing for the effects which they produce on the various obser-
vations. For the present, however, we shall merely point
out how the errors can be detected.
36. Error of Collimation. The amount by which the
angle between the line of colli-
mation and the axis of revolu-
tion exceeds or falls short of a
right angle is termed the error
of collimation.
Let A B (Fig. 56) be the axis
of revolution and x Y be the
line of collimation. (We have
purposely greatly exaggerated
the error of collimation in the
figure.) Suppose that the tele-
scope is pointed to a fixed object, suitably placed at a con-
siderable distance, and that a certain point P of the object
86 Astronomy.
is noted, of which the image in the field of view is coinci-
dent with the point o in the field of view (Fig. 55). Let
the telescope be lifted from its bearings and replaced with
the pivots reversed i.e. the pivot which was previously at
the west is now at the east, and rice versa and let the
telescope be again directed to the distant mark. If the axis
of collimation be at right angles to the axis of revolution,
then it is plain that the line of collimation would still point
in the direction which it had before the reversal. But if the
two axes are not at right angles, then the line of collimation,
instead of having the direction x Y, will have the direction
x' Y'. This will be made manifest at once from the circum-
stance that the point of the distant body, which had its
image at o before the reversal, will not have its image at
that point after the reversal. This points out the method
of correcting the error of collimation. It is to be remem-
bered that the line of collimation is found by joining o to
the centre of the object glass. The system of spider lines
are set in a frame, and this frame is attached to the tube of
the telescope by adjusting screws. If the frame be moved
by these screws, then the point o is moved, and thus the
line of collimation is moved. To get rid of the error of
collimation it is therefore necessary to move the frame con-
taining the system of wires until the point on the distant
mark whose image coincides with the point o is the same
after the reversal of the instrument as it was before.
When this adjustment has been made the line of colli-
mation moves in a plane, and this plane cuts the celestial
sphere in a great circle. It is the object of the subsequent
adjustments to arrange that this great circle shall be coincident
with the meridian.
37. Error of Level. The second adjustment which we
shall describe consists in placing the axis of revolution in a
horizontal plane. This is most directly accomplished by
means of the spirit level A A (Fig 57), which is suspended
between the arms B, B. These arms are provided with hooks
The Diurnal Motion of the Heavens. 87
at the extremities, by means of which the level can be sus-
pended from the pivots in the manner shown in Fig. 58. The
FIG. 58.
FIG. 57-
bubble in the level assumes a certain position, which can
be read off by means of a graduated scale. The level is
then to be reversed, so that the hook which previously hung
from one pivot now hangs from the other, and after allowing
a few moments for the bubble to come to rest its position is
to be read off again. If the two pivots be accurately hori-
zontal, then the position of the bubble will be the same after
the reversal as it was before ; but if there be the slightest
departure of the bubble from its original position the axis of
revolution is not horizontal. This can, so far as its grosser
portion is concerned, be corrected by raising or lowering
one of the bearings of the pivots until the bubble retains the
position after reversal which it had before.
We may here mention that by the help of the level we
can also scrutinise another detail in which the instrument
may be more or less imperfect. We have assumed that
the diameters of the two cylinders which constitute the
pivots are equal, but this may not be (indeed, generally is not)
strictly true. Their equality may be tested in the follow-
ing way : Adjust the pivots so that they appear horizontal ;
then reverse the axis of the telescope, so as to interchange
88 Astronomy.
the pivots in the bearings, just as was done in the case of
determining the collimation. If the pivots be equal the
level will show that they are horizontal after the reversal ;
but if the two pivots, being horizontal before the reversal,
are found not to be horizontal after the reversal, then the
pivots are not of the same size. By these observations the
actual difference (if any) between the diameters of the two
pivots can be ascertained, and the effect of this difference
upon the observations can be calculated and allowed for.
By the adjustment of the bearings the greater portion
of the error of level can be actually corrected, but it is not
possible to make this adjustment as perfectly as the accuracy
of astronomical observations requires. Even if the axis were
once made level, it would not remain so. Slight changes in
the temperature, and possibly changes in the earth itself,
alter to a minute extent the piers upon which the bearings
rest. The level is thus continually undergoing small fluctua-
tions. The effect of these may be obviated by deter-
mining, in the course of the observations each night, the
actual inclination of the axis, and then correcting the obser-
vations by calculation, so as to reduce them to what they
would have been, had the telescope been perfectly adjusted.
38. Error of Azimuth. By correcting the telescope
for the error of collimation it is provided that the line of
collimation moves in a plane perpendicular to the axis of
revolution. The effect of making the line of pivots hori-
zontal is to cause this plane to pass exactly through the
zenith. All the planes passing through the zenith are
vertical planes, and the last adjustment of the transit instru-
ment consists in so placing it that the particular vertical
plane to which the movements of the telescope are restricted
shall coincide with the meridian of the place. As the
meridian is defined to be the great circle which passes
through the zenith and the celestial pole, the adjustment
now under consideration will be secured if the plane in
which the telescope moves be caused to pass through the
The Diurnal Motion of the Heavens. 89
celestial pole. For this purpose we have to resort to obser-
vations of the stars, as it is by this means alone that this
adjustment can be effected.
It is easy to arrange the bearings so that the axes of
the pivots shall lie approximately in its correct position due
east or west, or, what is the same thing, that the central
spider line shall be very close to the meridian. If the Pole
Star were actually at the pole, then it would only be necessary
to move one of the bearings horizontally northwards or
southwards until the Pole Star, when viewed through the
telescope, would be seen to coincide with the central wire.
As the Pole Star is really a degree and a half from the pole,
the operation is not quite so simple. Still the Pole Star
(like every other star) crosses the meridian twice in every
revolution of the celestial sphere. The times at which the
Pole Star is on the meridian can be found from the ' Nautical
Almanac/ and the approximate adjustment of the transit in-
strument may be made by making the observation at that
time, and then moving the bearing until the Pole Star is
seen to coincide with the central wire.
Though this adjustment is susceptible of a considerable
degree of accuracy, yet, just as in the case of the level, it is
hopeless to atterapt to place the instrument absolutely
correctly. Nor, if it were once placed in the true position,
would it be safe to calculate that that position would be
retained. It is therefore necessary, on each occasion when
the telescope is used for accurate observations, to have the
means of computing to what extent the axis of revolution
really departs from the true east and west position. This
is called the error of azimuth.
For the determination of the error of azimuth we require
the assistance of a good clock, and we choose for the obser*
vations some conspicuous star situated near the pole, pre-
ferably the Pole Star itself. LetACBD (Fig. 59) represent
the apparent path of the Pole Star in its diurnal motion, the
point o, which is the centre of the circle A c B D, being of
9O Astronomy.
course the celestial pole. The meridian passes through the
pole, and we may denote that small portion of the meridian
which lies within the circle by the
line A B. The telescope having
been approximately adjusted, the
vertical circle which the axis of col-
limation describes will pass very
close to the pole, and we may de-
note that portion of it which lies
within the path of the Pole Star
by the line E F. The diameter
of the small circle A B is less
than three degrees of arc on the
celestial sphere, and consequently we may often regard
A B and E F as straight lines, though of course they are really
parts of great circles. In a period of one sidereal day the
Pole Star moves completely round the circle A c B D ; this
motion is described uniformly, so that the time taken to
move from A through c to B is equal to the time taken to
move from B through D to A. The telescope being directed
to the Pole Star, the time is to be noted when the star crosses
the central wire of the system ; the star is then at the point
E. After an interval somewhat exceeding half a sidereal day
the Pole Star will again be visible at its lower culmination,
and will again cross the central wire of the system at the
point F. The instant of crossing is to be again noted by
the help of the clock. In another period of somewhat less
than half a sidereal day, the star will have returned to upper
culmination, and the clock time is to be taken again when
the star is at E. If the telescope were correctly adjusted, so
that the vertical circle described by the line of collimation
coincided with A B, then the time interval between the
observed upper and lower culmination would be equal to
that between the lower and upper ; if, however, the telescope
be not perfectly adjusted, there will be a discrepancy between
these two intervals, arising from the fact that the arc E c F
The Diurnal Motion of the Heavens. 91
exceeds the arc E D F. It is thus easy to see that by these
observations we have the means of ascertaining if the tele-
scope be correctly placed, while if the telescope be not
FIG. 60.
correctly placed the observations give the means of ascer-
taining how much that place is erroneous.
The general appearance of the transit instrument as it is
actually used in astronomical observations is shown in Fig.
60. The bearings of the pivots repose on massive masonry
9 2 Astronomy.
piers c, c. In order to ensure that the form of the pivots
shall not be injured by friction, the weight of the telescope
and axis is to a large extent relieved by the counterpoises
D, D, which, by means of hooks B, B furnished with friction
rollers, support the instrument. Just sufficient pressure is left
on the pivots to ensure that they shall work steadily in the
bearings. When the telescope is used at night it is necessary
to make provision for illuminating the spider lines, which
would otherwise be invisible against the dark sky. There
are various methods for effecting this illumination. In the"
instrument shown in Fig. 60 this is effected by a lamp,
which is attached to the centre of the tube of the telescope.
By suitable arrangement of reflectors the light from the
lamp is brought down to the spider lines, which are close to
the eye piece.
39. Determination of Right Ascensions. We have ex-
plained ( 34) that the right ascension of a star is the arc
on celestial equator between the declination circle passing
through the star and a standard point upon the equator.
We may also define the right ascension to be the angle be-
tween the declination circle drawn through the star and the
declination circle drawn to the standard point of the equator.
If, therefore, we can measure the angle between these two de-
clination circles we have ascertained the right ascension.
The transit instrument and its auxiliary, the astronomical
clock, enable us to measure the angle be -{- 90 = 1 80 ^ c.
In order that a star may be visible, it is necessary that
its zenith distance at the time of observation be less than
io6 Astronomy.
90. Hence for a star to be visible at the moment of
lower culmination we must have
1 80 (D
or
We thus have the following result :
When the north declination of a star exceeds the colatiiude,
both culminations of the star will take place above the horizon
of a station in the northern hemisphere.
Next suppose a southern star at T. The zenith distance
of the star is z T, but
ZT=PT PZ
Hence when the upper culmination of the star takes place
above the horizon, we must have
or
and we have the following result :
When the south declination of a star is less than the
colatitude, then the upper culmination of the star will take
place above the horizon of a station in the northern hemi-
sphere.
For example, the latitude of Greenwich is 51 28' 38'' '4,
and therefore the colatitude is 38 31' 21" '6. The upper
culmination of every star in the northern hemisphere will
be seen at Greenwich, as well as of all the southern stars
whose south declination does not exceed 38 31' 21" '6.
All stars are visible at both culminations at Greenwich
of which the declinations exceed +38 31' 21" -6.
These statements require some modification on account
of the effects of refraction, but this need not be considered
at present. It should also be observed that, owing to the
loss of light incurred when the rays have to pass through a
The Diurnal Motion of the Heavens. 107
great thickness of the atmosphere, stars cannot be seen when
close to the horizon. The actual rising or setting of a star
is perhaps never witnessed.
43. Determination of Latitude. Since the altitude of
the pole above the horizon is equal to the latitude, the
angular distance from the zenith to the pole is equal to the
complement of the latitude, or the colatitude. By suitable
observations made with the meridian circle the colatitude
can be ascertained, and thence the latitude is known. We
select for this purpose a circumpolar star, preferably the Pole
Star itself, and we determine the zenith distance of the star
at its upper and then at its lower culmination.
Let z s, z s' (Fig. 64) be the zenith distances at upper
and lower culmination respectively, then if refraction be
omitted, we have
or the colatitude is the arithmetic mean of the zenith distances
of a circumpolar star at upper and lower culmination.
Owing, however, to the effect of refraction, the actual
distances z p found by different circumpolar stars will be
seen to vary. A star, for example, which, at its lower
culmination, passed close to the horizon would be largely
affected by refraction, while at its upper culmination it would
be but very slightly affected ; the Pole Star would be affected
very nearly equally on both occasions. We have seen that
the refractions of stars are nearly proportional to the tangent
of the zenith distance. They are therefore equal to this
tangent multiplied by a certain coefficient, termed the
coefficient of refraction, which has to be determined by
observation. It is by observations of the kind we are de-
scribing that the coefficient of refraction is to be determined.
This coefficient must have such a value that, when the
corresponding corrections are applied to the zenith distances,
the resulting values of the colatitude shall be all equal from
whatever star they have been derived. In this way the
io8 Astronomy.
colatitude has been ascertained, and therefore also the
latitude.
The declination of a star can now be readily found.
For the declination S is the complement of the polar dis-
tance, which is equal to the zenith distance at upper cul-
mination added to the colatitude. If z be the zenith
distance, and X the latitude, we have therefore
90 2=
whence
or
We therefore see that
The zenith distance of a star at upper culmination added
to its declination is equal to the latitude,
and also it can be easily shown that
The zenith distance of a star at lower culmination added
to its declination is equal to the supplement of the latitude.
44. Numerical Illustration. In applying the correction
for refractions, it is necessary to take account of the tern,
perature of the air (/ degrees Fahr.), as well as its barometric
pressure (h inches of mercury). The following formula,
which has been derived from the observations we have just
described, fairly represents the refractions except in the
neighbourhood of the horizon.
Refraction (in seconds) =99 2 "-> , tan z.
For the sake of illustration we shall show how the lati-
tude of Dunsink Observatory and the declination of the star
y Draconis have been ascertained by observations of this
star at its upper and lower culmination respectively.
At the lower culmination the nadir distance of the star
was observed, and appeared to be
104 56' 46"-8.
The zenith distance is therefore
75 3' is"'*-
The Diurnal Motion of the Heavens. 109
Twelve hours later y Draconis crossed the meridian
again, and its south zenith distance on that occasion was
found to be
i 53' i8"-6.
We have first to correct these apparent zenith distances
for the effect of refraction, so as to bring them to what they
would have been had the atmosphere been absent. It
appears that at the time of lower culmination the temperature
was 40, and the barometric pressure is 2 9'' "86. Under
these circumstances the refraction is
3' 4i"'9-
The corrected value of the zenith distance at the lower cul-
mination is
75 6' 55-1.
The observations at the upper culmination are also affected
to a small extent by refraction, the amount being
i- 9 .
Applying this correction, we have for the zenith distance at
upper culmination the result
i 53' 2o"- 5 .
We therefore have the following two equations from which
the latitude A and the declination 5 are to be ascertained :
i8o-A=75 6' 55"-i + a
X=i 53' 2C/-5 + 2,
whence we deduce
A = 53* 23' T2" 7
=51 29' 52"'2.
By repeating these observations, using different stars for
the purpose, the latitude can be determined with great
accuracy, and in the case of those observatories which are
furnished with large meridian instruments the latitude is
known accurately to a small fraction of a second.
HO A stronomy.
45. Star Catalogues. The results of the observations
on the positions of the stars are given in what are called
Star Catalogues. These catalogues contain the appropriate
designation of the star, either by a special name, or more
usually by the constellation in which it lies, together with
the number or letter by which the star is distinguished.
Then follow columns containing the right ascensions and
declinations of the stars, and it is usual to place the stars in
the catalogue in the order of their right ascensions. Such
catalogues of stars are of the greatest service in astronomy.
When once the place of a star has been accurately found
and recorded, that place becomes a faithful point of reference
from which other measurements can be made. For example,
suppose a comet appears which cannot be conveniently
observed by a meridian instrument; it is only necessary
to select some star in the neighbourhood of the comet,
whose place is known by the catalogue. It is then easy to
determine the difference of the right ascensions and de-
clinations of the star and the comet by means of an equa-
torial telescope, which can be directed to whatever point of
the heavens the comet may happen to be situated. These
differences being determined, the absolute position of the
comet is deduced, because the right ascension and declination
of the star is known from the catalogue.
Ill
CHAPTER IV.
APPARENT MOTION OF THE SUN.
46. Annual Motion of the Sun. Passing from the
consideration of the apparent diurnal rotation of the heavens,
which is, as we have seen, due to the rotation of the earth
upon its axis, we must proceed to consider the movements of
those heavenly bodies which do not occupy a fixed position
with regard to the stars and constellations. Among this
class of bodies we can have no hesitation in regarding the
sun as the most important as far as the inhabitants of the
earth are concerned. We shall therefore begin by studying
the nature of those movements on the surface of the celestial
sphere which are performed by the sun.
It is, in the first place, obvious that the sun partakes in
the apparent diurnal rotation of the heavens which we have
already considered. Like the stars, the sun rises in the
east, and having run its course across the heavens, it descends
again to set towards the west. When, however, we study
the apparent movements of the sun with more attention, we
see that the motions of the sun are not simply due to the
apparent motion of the entire celestial sphere, but that the
sun actually possesses a certain motion on the sphere, which
is blended with the apparent motion which it also receives
by the diurnal rotation of the sphere. The actual move-
ments of the sun are, however, so slow when compared with
the movement arising from the apparent diurnal motion,
that it requires some little attention to perceive them. The
difficulty would be greatly lessened if it were possible to see
the stars on the celestial sphere in the neighbourhood of the
sun. No doubt it is possible by the aid of telescopes to see
bright stars in the daylight, but these stars to be visible
112 Astronomy.
must be at least 15 from the sun, otherwise the overwhelm-
ing brilliancy of the sun would obliterate the feeble rays
from the star. There are, however, several indirect methods
by which we can easily see that the circumstances attending
the apparent motions of the sun are different from those
connected with the stars. In the first place, if we note care-
fully the point of the heavens at which a star first becomes
visible after it has risen, and if we compare this position
with the surrounding terrestrial objects, we shall find that the
point of the horizon at which the star actually rises is con-
stant, so that it remains from one end of the year to the
other at the same distance from the north or south point.
This constancy of the point of rising is an obvious conse-
quence of the diurnal motion of the heavens, when it is
remembered that the star remains in a constant position on
the surface of the celestial sphere. The rising of the sun is,
however, very different from that of a star ; for the point of
the horizon at which the sun rises changes periodically. This
is seen by noting the position of the sun at sunrise with regard
to the adjacent terrestrial objects. If the distance of the point
at which the sun rises from the southern point of the hori-
zon be measured, it is found that this distance fluctuates
between certain limits, and the period in which these
changes are accomplished is one year. Precisely similar
phenomena are witnessed at sunset ; the point at which the
sun descends below the horizon oscillates between certain
limits. This is seen in a very striking manner at certain
places on the western coasts of Europe, where the sun
appears to set in the sea, and where the point at which it
sets is easily defined by the aid of islands which are seen
near the horizon.
There is also another point in which the movement ot the
sun is seen to differ from the apparent movements which the
stars make in virtue of the diurnal rotation of the heavens.
When a star culminates, the altitude of that star is a maxi-
Apparent Motion of the Sun 1 1 3
mum. It is easily perceived that this maximum altitude of
a fixed star is always the same, whatever may be the season
of the year at which it is observed. This is, however, not
the case with the sun. At or near noon each day the sun
culminates, but everybody knows that the altitude which
the sun has at culmination is far from constant. In winter
the sun is low when it culminates, while in summer it is
high. In the arctic regions this feature of the sun's move-
ments is so strongly marked that in midwinter the sun
actually does not come above the horizon at all, while in
midsummer the sun never sets. These points of contrast
between the movements of the sun and those of the stars
can only be explained by the supposition that the posi-
tion of the sun on the celestial sphere is constantly chang-
ing. We can confirm this by observing the heavens in
the west as soon after sunset as the decreasing twilight has
rendered the stars visible. If we note the positions of
the stars with respect to the terrestrial objects, and if the
observation be repeated after an interval of two or three
weeks, it is seen that the stars which at the first observation
were considerably above the western horizon at sunset have
now closely approached it. Again repeating the observation
after the same interval, it will be found that the stars
already mentioned are now actually below the horizon at
sunset. After the lapse of some time it will be found that
these stars, having ceased to be visible in the west after
sunset, will become visible in the east shortly before sunrise.
These phenomena can only be explained by the supposition
that the sun is in motion on the surface of the celestial
sphere.
It will be instructive for the learner to observe these
phenomena for himself, and it may facilitate his doing
so if we describe the appearance presented by a certain
region of the heavens at the different seasons. We shall again
take for the purpose of illustration the well-known group in
114 Astronomy.
the constellation Taurus known as the Pleiades ( 27), and we
shall describe the position occupied by the Pleiades at
eleven o'clock P.M. on the nights of January i, March i,
May i, July i, September i, November i. If the weather
be unfavourable on any of the nights we have named, then
the next fine night at the same hour will answer instead.
We shall also assume that the observer is situated in the
northern hemisphere, at about the latitude of the British
Islands.
At eleven P.M. on January i, the Pleiades may be found
high up in the sky, a little to the west of south. At the
same hour on the evening of the ist of March they will be
visible rather low in the west. On the ist of May they are
not visible ; on the ist of July they are not visible. On the
ist of September they are visible low in the east. On the
ist of November they are high in the heavens, a little to the
east of south. On the next ist of January they will be
in the same position as they were on the last, and in the
course of the following year the same cycle of changes
which we have described will be repeated.
It would therefore seem as if the Pleiades were at first
gradually moving from the east to the west, that then they
dipped below the horizon, and after a short time reappeared
again in the east, so as to regain at the end of a year the
position they had at the beginning.
The reader will, it is hoped, not confuse the annual
motion which we are here considering with the apparent
diurnal motion previously discussed (27). In the apparent
diurnal motion the phenomenon is observed by looking
out at different hours on the same night. To observe
the apparent annual motion we must look at the same
hour on different nights separated by a considerable in-
terval.
We shall now endeavour to explain the apparent annual
motion of the Pleiades. We have chosen the hour at
Apparent Motion of the Sun. 115
eleven P.M. because by this time in the summer months
the heavens are sufficiently dark to enable the stars to be
visible. We might, however, have traced the same series
of changes had we adopted any other constant hour, and
used a telescope whenever the daylight would not permit
the stars to be seen without its aid. It will also be under-
stood that the Pleiades have merely been taken as an illus-
tration : many other objects would have answered equally
well.
We must first ask, What does eleven P.M. really mean?
It will be necessary to anticipate to some trivial extent
certain points to be more fully discussed hereafter ; we may }
however, assume that the sun crosses the meridian each day
very near noon, and that, consequently, at eleven P.M.
the sun has passed the meridian about eleven hours pre-
viously. We find that at eleven P.M. on March i, the
Pleiades are farther from the meridian than they were
at eleven P.M. on January i. But as the sun is nearly at
the same distance from. the meridian in the two cases, it
follows that the Pleiades must be nearer to the sun on
March i than on January i. It is, therefore, plain that
the relative positions of the sun and the Pleiades on the
surface of the heavens must be changing. By comparing
the sun in the same way with any other stars, it is found
that the stars to the east of the sun appear to be ap-
proaching the sun. But we have already noticed that
the positions of the stars inter se do not change, and there-
fore we are obliged to come to one of two conclusions :
either, firstly, that all the stars in the universe have an
annual motion from east to west relatively to the sun,
which remains fixed, or that the sun has an apparent
annual motion from west to east, while the stars remain
fixed. We cannot hesitate to choose the latter alterna-
tive as the correct one. The apparent diurnal motion we
have already explained to be due to the real rotation of
i 2
ii6 Astronomy.
the earth upon its axis. Were this rotation to cease, the
stars would appear immovable, but the apparent annual
motion of the sun among the stars would remain as before.
In the discussions of the motion of the sun, which we shall
now commence, we shall only consider the apparent annual
motion of the sun among the stars, for, of course, that part
of the sun's apparent motion which is due to the diurnal
motion which it shares in common with the stars needs no
other explanation than the rotation of the earth upon its
axis.
47. Observations of the Sun. We shall first consider
how the position of the sun may be ascertained by observa-
tions made with instruments capable of giving numerical
results. The instruments first to be described are of ex-
ceedingly simple construction, and though the results they
give are only to be regarded as coarse approximations,
yet in the early epochs of astronomy it was by their means
that acquaintance was made with the apparent movements
of the sun, and that the laws of those movements were dis-
covered.
The most simple instrument of the class now under con-
sideration depends upon the shadow which the sun casts on
a fixed object. As the sun moves, the shadow moves in a
corresponding manner, and by the measurements of the
position of the shadow on the plane the movements of the
sun can be deduced. This instrument in its simplest form
is represented in Fig. 65. A rod AB is fixed vertically, so
as to project from the horizontal plane ABC. On this
plane a line A c is traced north and south for the purpose of
facilitating the measurements.
The shadow of the vertical rod A B occupies the position
A D on the horizontal plane, and by the position and length
of this shadow the position of the sun can be ascertained.
The plane BAD which contains the rod and its shadow is
vertical, and the intersection of this plane with the hori-
Apparent Motion of the Sun.
117
zontal plane makes with the line A c an angle equal to
the azimuth of the sun. Thus the azimuth of the sun can
be ascertained by measurement of the angle B A c. It is also
easy to obtain the zenith distance of the sun. For the line
joining the end of the shadow D to the top B of the rod
must point directly towards the sun, and as the line A B
points directly towards the zenith, it follows that the angle
z B s or A B D must be equal to the zenith distance of the
sun. The angle BAD being a right angle, it follows that the
FIG. 65.
tangent of the zenith distance is equal to A D-f-A B, and, as
A B is constant, it appears that the tangent of the zenith dis-
tance of the sun is proportional to the length of the shadow.
At noon each day the zenith distance of the sun is at its
smallest value, and the shadow of the sun, which is then
on the line A c, has its smallest value also. It is, however,
found that the length of the shadow at noon is different on
different days. In midsummer the length of the shadow
has its minimum value, and as the season advances so does
Ii8 Astronomy.
the length of the shadow, until in midwinter the length
attains its greatest value. This shows that the zenith dis-
tance of the sun at noon has its least value in midsummer,
and its greatest value in midwinter, and by measurement
of the length of the shadow and dividing the result by the
length of the vertical rod, the tangent of the zenith distance
can be computed.
The accuracy of this instrument is greatly impaired by
the circumstance that the apparent size of the sun is so con-
siderable. Each luminous point on the surface of the sun
emits rays of light, and will throw a shadow of the vertical
rod. We thus see not a single shadow, but a great number
of shadows partially superposed on each other. This com-
posite nature of the shadow entails a certain degree of
ambiguity and want of sharpness in the shadow itself, and is
a very serious obstacle in the way of exact measurement
So crude an instrument as this is therefore quite unsuited
for the exact measurements required in modern astronomy.
It has been sought in some degree to rectify the uncer-
tainty attendant upon measurements of the shadow by using
FIG. 66.
FIG. 67.
a modified form of this instrument, shown in (Fig. 66). The
vertical rod A B (Fig. 66) carries at its summit a plate B
Apparent Motion of the Sun. 1 19
pierced with a small orifice. The shadow of this plate is
thrown on the horizontal plane, and the measurements are
made from*-the.point A to the centre of the illuminated disk
(Fig. 67). In this way it is found that measures can be
made with a considerably greater degree of precision than is
attainable when the extremity of the shadow of the rod is
the point whose distance is to be measured. It might be
thought that if the orifice were made exceedingly small
the point in the centre of the shadow of the disk would
also be an exceedingly small point ; but in this case again
the apparent size of the sun intervenes, and prevents the
point in the centre of the shadow from being so sharply
defined, as it would be were the apparent diameter of the
sun smaller than it actually is. All instruments of this class
are, however, replaced for accurate work by suitably
mounted telescopes, which enable measurements to be made
that are incomparably more accurate than anything which
can be attempted by the contrivances we have just been
describing.
Before the indications of these accurate instruments can
make known to us the precise place of the sun, it is neces-
sary to have some acquaintance with the apparent shape and
form of the sun's disk as we see it. We shall therefore first
turn our attention to this subject. The disk of the sun on
the celestial sphere appears, at first sight, to be a circle : it is,
however, necessary to make the shape of this disk the sub-
ject of exact measurement, in order to show how far the disk
is exactly circular, and also to determine the angular value of
its radius.
48. The Micrometer. The instrument which is used in
these investigations is generally attached to the eye end of a
telescope, and is employed for measuring the dimensions of
the images of the objects in the field of view. There are
several different contrivances used : we shall describe the
form which is known as the parallel wire micrometer.
In the focus of the object glass of the telescope are
120 A stronomy.
stretched three spider lines. Two of these are parallel, and
the third is at right angles to them. Each of the parallel
wires is mounted in a frame, by which it is enabled to be
moved parallel to itself in the plane of the focus, and the
movements of the two wires are completely independent.
The movement of each wire is effected by a screw called
the micrometer screiv^ and it is on the accuracy with which this
screw is made that the utility of the micrometer mainly
depends. If the screw be strictly uniform in the shape of
its thread, then the distance through which the wire is moved
is always proportional to the number of whole revolutions
and parts of a revolution which the screw has made.
Means are provided by which the entire number of revolu-
tions by which the screw has been turned from a standard
position can be ascertained. The head of the screw is also
usually subdivided into hundredths, and by estimation each
hundredth part may be subdivided into tenths. It is there-
fore possible to record the distance through which the screw
has been moved from a standard position accurately to the
thousandth part of a revolution. The single wire which
intersects the movable wires passes through the centre of
the field of view. It has no motion of the kind we have just
described, but, in common with the two movable wires
and the eye piece, is capable of being rotated around the
axis of the telescope. There is also a graduated circle
attached to the micrometer, so as to enable the angle,
through which the micrometer has been rotated, to be
ascertained.
To illustrate the method of using this instrument we
shall suppose the case of three stars in the field of view, and
we shall describe how the relative positions and distances of
these stars are to be ascertained. To enable the measure-
ments to be made with facility and accuracy the micrometer
ought to be attached to a telescope, which is mounted
equatorially ( 28), and which is furnished with a clock-work
apparatus. When the clock is going the stars will remain
Apparent Motion of the Sun. 1 2 1
constantly in the field of view, and the attention of the
observer will not be distracted by the diurnal motion, which,
if uncompensated by the action of the clock, would entirely
preclude any accurate results. The circles which are
attached to the telescope are not employed in connection
with the measurements now to be described. In fact, in an
equatorial instrument, these circles are generally only
intended for the purpose of pointing the telescope in the
right direction, so as to bring the right object into the field
of view, but they are not generally intended to serve any
purpose in the making of exact measurements.
For convenience we speak of the three stars as A, B, c,
and we propose to measure the sides and angles of the
triangle ABC. The triangle which we see is of course not
the actual triangle, which has the three stars at its vertices :
it is only the projection of this triangle on the surface of the
celestial sphere which is amenable to our measurements.
Thus the triangle with which we are dealing is really a
spherical triangle, but as the field of view is always only a
very minute portion of the entire celestial sphere, it follows
that the portion of the celestial sphere visible in the tele-
scope differs but little from an exact plane, and may gene-
rally for our present purposes be simply regarded as a plane.
We have then to measure the angles subtended by the sides of
the plane triangle, ABC, by the aid of the micrometer. We
proceed as follows. Turn the micrometer, and of course its
wire system also, so as to place the single wire approximately
parallel to one of the sides of the triangle (suppose A B) ;
then, by means of the slow movements which are provided
for the purpose of slightly changing the telescope in right
ascension and declination, bring the telescope into such a
position that the stars A and B are close to the single wire.
Then adjust the single wire so that it passes symmetrically
across the two stars. The two movable wires are next
to be placed so that one of the wires is exactly on A and
the other on B. These adjustments having been carefully
122 Astronomy.
made, the micrometer is to be read off. First the posi-
tion of the graduated circle is to be noted, and then the
positions of the screws, as well as the indications of their
graduated heads, are to be recorded. Without altering the
position of the single wire, the two movable wires are to be
brought into coincidence, and the indications of the screws
are again to be read off. It is thus known how far each of
the wires has been moved from the point where they
coincide to the position which it occupied when it was
coincident with the star, and thus the entire distance be-
tween the two stars, expressed in terms of the revolutions of the
screws, is ascertained.
The whole micrometer is now turned so as to bring the
single wire across A c, and the operations already described
are to be repeated. The difference between the readings
of the graduated circle in the two positions of the micro-
meter will give the angle BAG, while the readings of the
screws gives the distances A B and A c, so that the whole
triangle is ascertained. The results may be verified by
actually measuring the distance between B and c, and com-
paring it with the distance ascertained by calculation.
It remains, however, to show how the apparent distances
thus found, which are expressed by the arbitrary value of
the revolutions of the screw, can be evaluated in angular
magnitude. In fact, what we want actually to find is the
angle which two stars A and B, for example subtend at
the eye. It therefore becomes necessary to ascertain the
number of seconds of arc which are equivalent to one
revolution of the screw. We may put the question now
under consideration in a somewhat different manner. Sup-
pose that two stars on the surface of the celestial sphere
were separated by a distance equal to one revolution of the
micrometer screw : it is required to find how many seconds
of arc these stars subtend at the eye. There are different
methods by which this important problem may be solved.
One of these methods depends uuon direct measurement,
Apparent Motion of the Sun. 123
while others are founded upon astronomical observations.
We shall proceed to describe the two processes, taking first
the method of direct measurement.
By means of an accurately graduated scale we can
measure the actual distance in inches or fractions of an
inch at which the wires are separated. We are then to
measure the distance from the wires to the optical centre
of the object glass, which is in fact the focal length of the
object glass. The angle subtended at the object glass by
the two points in which the fixed wire intersects the mov-
able wires, is obviously equal to the angle which the stars
subtend at the centre of the object glass when the stars are
situated at the two points of intersection. But the angle
subtended by the two points at the centre of the object
glass is easily found when the measurements have been
made. The distance between the points divided by the
focal length gives the circular measure of the angle, and
multiplying the circular measure by 206265, we obtain the
required angle in seconds. The difficulty attending this
method of determining the value of the micrometer screw
principally arises from the uncertainty with which the
measurements of the distance of the wires and the focal
length of the telescope are affected. Any error in the
determination of the distance between the wires will pro-
duce a corresponding error in the determination of the
value of the screw. This source of uncertainty may to a
large extent be obviated by separating the wires as far as
possible, so that the distance between them shall be fifty or
more revolutions of the screw. Any error that is made in
the measurement of the distance will thus be subdivided by
fifty, when we come to the evaluation of a single revolution,
and thus when two stars, tolerably near together, are
measured, the error arising from using the incorrect value
of the micrometer screw will be intrinsically insignificant.
The measurement of the focal length of the telescope is
also a matter of some difficulty. It is no doubt easy to
124 Astronomy.
define the focal length to be the distance from the optical
centre of the object glass to the point where all the con-
stituents of a beam of parallel light falling on the object
glass converge. The optical centre, however, is not a point
which is accessible to measuring instruments, nor is it easy
to find at what point of the thickness of the object glass it
is really situated. There is thus no insignificant degree of
uncertainty about the actual focal length of a telescope.
These causes render the method of determining the value
of the micrometer screw by direct measurement to be of
comparatively little reliability and it is seldom resorted to
in practice.
With a telescope which is really well and steadily
mounted, the value of the micrometer screw is most con-
veniently and accurately found by observations of the Pole
Star. For this purpose a clock or chronometer accurately
rated to sidereal time is required. The micrometer is first
to be adjusted so that the Pole Star, when carried by the
diurnal motion, will run accurately along the fixed wire.
The two movable wires are then to be placed at a con-
venient distance apart, and the telescope is to be firmly
clamped in right ascension. The time shown by the clock
is to be noted when the Pole Star crosses the first of the
wires, and then when it crosses the second wire. The dif-
ference between the two recorded times, corrected, if necessary,
for the rate of the clock, gives the time occupied by the
Pole Star in passing from one of these wires to the other.
This determination should be repeated several times, and
the mean of the several results chosen as the final value.
It is desirable, for the reasons already explained, to have the
interval between the two wires as great as possible. On the
other hand, the success of the method depends entirely upon
the telescope remaining absolutely fixed while the Pole Star
is crossing the interval between the two wires. If this dis-
tance be too great, some uncertainty is apt to arise, par-
ticularly when the telescope is not mounted in a very
Apparent Motion of the Sun. 125
substantial manner. When the observations are finished,
it is usually necessary to make some trifling allowance on
account of refraction. What we actually observe is the
time in which the image of the Pole Star as deranged by
refraction moves over a certain distance. What we want
to find is the time in which the image of the Pole Star would
have moved over the same distance had there been no such
thing as atmospheric refraction. We do not enter into the
details of the method by which the small correction which
the time is to receive is computed ; indeed, except for the
more refined branches of observational astronomy, such
accuracy is not required. We shall therefore proceed at
once to show how from the observed time which the Pole
Star requires to move over a certain number of revolutions
the value of a single revolution is to be ascertained.
We have already explained how the declination of a
celestial object is determined, and we may therefore assume
that the declination of the Pole Star is known. The Nautical
Almanac contains the apparent declination of the Pole Star
for every day in the year, and we cannot do better than
adopt the declination there given as the basis of the cal-
culations which are to be made. From the declination the
polar distance can be ascertained, and in this way the
dimensions of the small circle on the celestial sphere, in
which the Pole Star moves in its diurnal motion, is known.
The Pole Star performs its journey round this circle in
twenty-four hours of sidereal time. As we know the length
of the circumference of the small circle expressed in degrees,
minutes, and seconds, we are able to ascertain the number
of degrees, minutes, and seconds that the Pole Star travels
in a given time. We are, therefore, able to find the distance
in minutes and seconds which the Pole Star will accomplish
in the time which it takes to move from one of the wires to
the next, and thus we are enabled to ascertain the minutes
and seconds of arc on a great circle by which those two
wires are separated. As we also know the number of revo-
j 2 6 A stronomy.
lutions of the micrometer screw which corresponds to the
interval between the two wires, we are enabled to deduce
the value of one revolution.
A word should be added as to the grounds on which
the Pole Star is chosen for the purpose of these observations.
There is really no particular virtue about the Pole Star for
this purpose, save that it is near the pole. Any other star
tolerably near the pole would do equally well. For some
reasons, indeed, a star a little more removed from the pole
than the Pole Star is perhaps preferable. But a star very
far from the pole moves across the field of view so rapidly
that a small error in the determination of the time of transit
from one wire to the other will be a comparatively large
fraction of the total time observed ; by choosing a star
close to the pole, the interval of time will be greatly in-
creased, and the effect of an error in the time will have a
much less appreciable effect.
The Pole Star is attended by a small companion star, which
is visible in a small telescope and is a very conspicuous object
in a large telescope. In the Litter case it is often preferable
to use the companion of the Pole Star, rather than the Pole
Star itself. The moment when the small star crosses the
wire can generally be more accurately noted than in the case
of the larger star. In this case, of course, it is the declination
of the companion which must be employed in the calcula-
tions instead of that of the Pole Star.
Another method of finding the values of the micro-
meter screw has also much to recommend it. This
consists of measuring with the micrometer the distance of a
pair of stars which have already been measured by a previous
observer, and of which the distance is therefore known.
For the application Of this method, certain stars in
the Pleiades ( 27) are especially suitable. The arcual
distances of several of the stars in this group have been
accurately determined by Bessel, and by these the value
of the revolution of a screw in any micrometer can be
Apparent Motion of the Sun. 127
readily ascertained It is only necessary to choose two of
Bessers stars which are at a suitable distance for the par-
ticular micrometer under consideration, and then to measure
them with the micrometer. By comparing this with
Bessel's measures, the number of seconds of an arc of the
great circle on the celestial sphere which corresponds to
a certain number of revolutions and parts of a revolution
of the micrometer screw is determined. From this of course
it is easy to ascertain the number of seconds of arc in one
revolution.
The value of a revolution of the micrometer screw
depends, as we have seen, upon the focal length of the
telescope as well as upon the actual linear distance between
the wires. The latter generally, and perhaps the former
also, depends to a certain extent upon the temperature of
the instrument. The effect of temperature upon the value
of the screw can only be obtained empirically. This is
done by using any of the methods we have described,
and noting the temperature by a thermometer. These
observations being repeated at different seasons, when the
temperature is different, enable a table to be formed which
will give the value of the screw for any given tempe-
rature.
49. Apparent Diameter of the Sun. Having determined
the value of the micrometer screw, we shall now show how
it may be used for measuring the apparent dimensions of
the sun on the surface of the celestial sphere. For this
purpose the micrometer should be fitted to a telescope
mounted equatorially, and the telescope being directed to
the sun, should be clamped in declination while the clock
movement carries it on in right ascension. The single
wire should be placed on that diameter of the sun which
it is proposed to measure, and the movable wires are
then to be brought so as to form tangents to the disk of the
sun at the extremities of the diameter. It is important in
placing the wires to observe that the screws are always
128 Astronomy.
turned in the same direction ; for example, it is a convenient
rule whenever a wire is being set to draw it up to its final
position, so that its motion is towards the head of the screw.
If this precaution be not taken, irregularities will be apt to
arise from the presence of a certain degree of shake in the
bearings of the screw. After the two movable wires have
been set, the positions of the screws are to be read off and
recorded. We may then proceed in two different methods :
the simplest method is that already described, of bringing
the two wires into coincidence, reading off the screws, and
then calculating the distance in arc through which each
screw has been moved. This method is, however, very in-
ferior to the somewhat more tedious plan of reversing the
wires, i.e. moving the wire from one extremity of the diameter
to the other, and vice versa, and then reading the screws
again. It can be proved that the required length of the
diameter is equal to the arithmetical mean of the distances
over which the two screws have been moved. After a
measure has been made in this way, it is desirable to turn
the entire micrometer through 180, and then repeat the
measurement and adopt the mean of the results as the final
value of the sun's diameter. If increased accuracy be desired,
it is well to make two settings of the wires before reversal,
then two settings after reversal, and the same series again
after the micrometer has been turned through 180.
50. The Heliometer. Another instrument which may
be used for the purpose of measuring the diameter of the sun
is termed the heliometer, and is founded upon quite a different
principle to the parallel wire micrometer. The heliometer
is essentially an achromatic telescope, the object glass of
which is divided in half by a plane which passes through
the optic axis of the telescope. If the disc in Fig. 68 re-
present the object glass, then the diameter of the disc shown
in the figure is the line in which the object glass is cut.
One half of the object glass A may be fixed in the tube of
the telescope, but the other half B is mounted in a frame so
Apparent Motion of the Sun. 1 29
that it moves in a plane perpendicular to the optic axis of
the telescope, and is thus enabled to assume the position
shown in Fig. 69. The movement of B is effected by a screw
which has a graduated head, and also an arrangement by
which the entire number of revolutions can be counted.
It is thus possible to measure with the greatest accuracy the
precise distance through which the half of the object glass
has been moved, and it is by the indications of this screw
that the measurements are effected by the heliometer.
To understand the action of this instrument let us first
suppose the heliometer to be directed to some small celestial
object a fixed star, for example and let us see what effect
the movement of the half of the object glass will have on
the appearance of the field of view. When the two halves
FIG. 68. FIG. 69.
of the object glass are together in the position shown in Fig.
68, then the instrument performs exactly in the same way
as an ordinary astronomical telescope ; but when the two
halves of the object glass have the relative positions shown
in Fig. 69, the condition of affairs is altered. It is to be
remembered that the function of an achromatic object glass
is to convey to a single point all the rays of a parallel beam
falling upon it near the direction of its optic axis. Every part
of the object glass bends the rays which it receives in the
required direction. It therefore appears that if parts of
the object glass were covered over, the rays which fell on
the uncovered portions would be brought to a focus and
form an image of the object, which would only differ from
the image formed by the whole object glass in being
proportionally less brilliant. When, therefore, the object
130 Astronomy.
glass has been divided in the heliometer, each portion
of the glass forms its own image of the object. If
the two halves are in the position of Fig. 68, the two
images made by the two halves are coincident ; but when the
halves are in the position of Fig. 69, the two images are
separated by a distance which depends upon the distance
through which one half of the glass has been displaced
Relatively to the other.
We can now understand how this instrument can be
applied to the measurement of the apparent diameter of the
sun. When the two halves are coincident, the image of the
sun appears single in the telescope, because in this case the
separate images formed by the two halves of
the object glass are superposed ; but when the
halves are separated, then the image of the
sun produced by the moving half of the object
glass withdraws from the other, and a double
image of the sun is the result. The observer
at the eye piece having the movement of the
half object glass under his control, gradually
increases the separation, until the two images
of the sun s and s' are in contact, and in fact
just on the point of being separated. It is
then clear that the image of the sun has moved through a
distance equal to D c, or the apparent diameter of the sun.
The actual distance through which the half object glass
has been moved is ascertained from the screw, and hence
we learn the apparent diameter of the sun in terms of the
revolutions of the screw.
By this means we are enabled to determine the apparent
diameter of the sun in terms of the revolutions of the screw,
which moves the half of the object glass. It remains to
point out how the actual distance in arc of the celestial
sphere, which corresponds to a revolution of this screw, can
be ascertained. This may be found by drawing a circle of
white on a black ground and observing this circle with the
Apparent Motion of the Sun. 1 3 1
heliometer, when placed at a considerable distance. If the
diameter of .the circle is known, and also its distance from
the telescope, then the angle which a diameter of the circle
subtends at the object glass of the telescope can be calcu-
lated. By the screw of the heliometer, the white circle can
be measured in the same manner we have just described
with reference to the sun. We have thus the means of find-
ing the actual value of a revolution of the micrometer screw,
and therefore of determining the apparent diameter of the sun.
Either the wire micrometer or the heliometer may be
employed to determine the shape of the sun's disk as it
appears to us. For this purpose it is only necessary to
measure different diameters of the sun drawn through the
centre in various directions. It appears from these measures
that the lengths of the various diameters are all equal, and
therefore the measurements show that the sun's disk is not
appreciably distinct from a perfect circle. The diameter
of this circle is not always the same. In midwinter its ap-
parent diameter is 32' 36", and in midsummer 31' 32" : these
are the extreme limits within which the fluctuations of the
diameter are confined. We shall generally not be far wrong
in assuming the sun's diameter to have its mean value of 32'.
We shall subsequently explain the cause of these apparent
fluctuations in the diameter, and it is only necessary here to
remark that they are not due to any intrinsic changes in the
body of the sun itself.
It is very instructive to contrast the circular figure of the
sun with the elliptical figure of the earth. If the sun really
presented to us the figure of an ellipse similar to that which
is produced by a section of the earth drawn through its polar
axis, there would then be a difference of no less than 7"
between the greatest diameter of the sun and the least
diameter. A difference so great as this would be readily
appreciated in measurements so exact as those which can
be made with the heliometer or the parallel wire micro-
meter. We are therefore led to the conclusion that even if
K 2
132 Astronomy,
the figure of the sun (or rather that projection of the figure
which we see in the celestial sphere) be elliptical, its
ellipticity must be very much smaller than the ellipticity
of the section of the earth which is obtained by a plane
drawn through the polar axis.
51. Effect of Refraction. To observe that the apparent
disk of the sun is circular, the opportunity should be chosen
when the sun is situated at a considerable altitude above the
horizon. When the sun is very low down, the refraction of
the atmosphere surrounding the earth distorts the apparent
disk of the sun, so that it is no longer circular, but assumes
approximately the form of an ellipse with its smaller axis
vertical. It is not difficult to explain how refraction causes
this curious transformation in the apparent shape of the sun.
.It will be remembered that the effect of refraction on a
celestial body is to raise the apparent place of that body up
towards the zenith. It therefore follows that the entire disk
of the sun is raised up by refraction, so as to appear higher in
the heavens than it would do if we could see the sun without
the intervention of the atmosphere. But besides this effect
of refraction in bodily raising the whole image of the sun, it
has also the effect of slightly distorting that image. The
upper edge of the sun is nearer to the zenith than the lower
edge, the difference in the zenith distances being of course
equal to the diameter of the sun, when the highest point of
the sun is compared with the lowest point. The refraction,
however, increases with the zenith distance, and hence it
follows that while both the upper and lower edges of the sun
are raised by refraction, the lower edge is raised more than
the upper edge ; consequently, in the refracted image of the
sun, the vertical distance, between the highest point and the
lowest point, must be less than it would be in an unrefracted
image. Refraction, however, can have no appreciable effect
in altering the length of the horizontal diameter of the sun.
But if the vertical diameter be shortened while the hori-
zontal diameter is unchanged, the image of the sun has
Apparent Motion of the Sun. 133
ceased to be circular, and has assumed a form which is
nearly that of an ellipse.
When the sun is actually at the horizon, the effects pro-
duced by atmospheric refraction are of a very marked
character. Let us take the case when the sun appears
to be on the point of setting, and select for special con-
sideration that particular phase in which the lower edge
of the sun appears just to have come in contact with the
horizon.
The appearance of the sun in these circumstances is re-
presented in Fig, 71 ; the horizontal line is the horizon,
and the elliptical figure
s' denotes the apparent
shape of the sun, the
lower edge being in
contact with the hori-
zon. At the moment
when the sun appears
to have this distorted
shape, and to be just in
contact with the hori-
zon, the real position
of the sun is altogether
below the horizon at s.
The atmospheric refraction has both raised the sun above
the horizon to the position s', and also altered its shape.
The amount of the distortion of the figure when the sun
is in this position is very considerable ; in fact, the vertical
diameter is shortened to the extent of one-sixth part of its
total amount. This distortion, though necessarily always
present, decreases very rapidly indeed, as the altitude of
the sun above the horizon is augmented. At the altitude
of 45 the sun's vertical diameter is only diminished by i",
which is about one three-hundredth part of the effect which
is produced near the horizon.
When the sun is in the vicinity of the horizon, either
134 ^ stronomy.
shortly after rising or shortly before setting, it is often re-
marked that his apparent size seems considerably greater
than when he is high in the heavens at noon. This is
really only an illusion, but none the less it is worthy of a
word of explanation. Measurement lends no countenance
to this illusion. We have already seen that the horizontal dia-
meter is unchanged as the sun approaches the horizon, while
the vertical diameter is actually shortened. The apparent
dimensions of the sun, when tested by measuring instruments,
are therefore less near the horizon than high up, though
to the unaided eye the reverse seems the case. The
explanation of this illusion is found in the circumstance
that near the horizon we tacitly compare the size of the sun
with the various terrestrial objects in its vicinity. We can-
not then fail to observe that the sun is more distant from
us than any of the terrestrial objects. Ordinary experience
shows us that if two objects subtend the same angle at the
eye, the more distant of the objects must be larger than the
other. Hence, seeing that the sun is more distant than
any terrestrial object, and yet observing that the apparent
dimensions of the sun are considerable, we naturally con-
sider the sun to be larger than in the case where, as it is
high in the heavens, we have no terrestrial objects with which
to compare it.
52. Right Ascension and Declination of the Sun. As
the apparent disk of the sun is circular, it is convenient to
define the position of the sun on the celestial sphere by the
position of the centre of the circle. We may therefore
speak of the right ascension and declination of the sun,
meaning thereby the right ascension and declination of the
sun's centre. The centre of the sun, being only marked out
by geometrical considerations, is not a visible point capable
of being observed by the telescope, like a star. We are
therefore obliged to resort to indirect means to ascertain the
position of the sun's centre.
For this purpose the meridian circle which we have
described in 40 is very suitable. It is, however, necessary,
Apparent Motion of the Sun. 135
when employing a telescope to observe the sun, to take
precautions which will counteract the effects of the excessive
heat and light of the sun. For this purpose a diaphragm
may be placed over the end of the telescope, which inter-
cepts a portion of the sun's rays before they fall upon
the object glass. The total light and heat received at the
eye piece is thus reduced to a fraction of what it would be
were the telescope to be used in its ordinary condition.
But even with this precaution the light and heat, though
greatly reduced, are still too considerable to allow .the un-
protected eye to be placed at an ordinary eye piece.
Further protection is afforded by using an eye piece modi-
fied in a suitable manner. The most simple arrangement
for this purpose is to cover the eye piece with a piece of
glass which, though very deeply coloured, is still sufficiently
transparent to allow a portion of the sun's light to pass
through it. One disadvantage of this contrivance is that
the observer retains no power of adjusting the light so as to
make the image more or less brilliant according as circum-
stances may require. This difficulty has been obviated by
using eye pieces of a more elaborate construction, one of
which may be here referred to.
It is well known to those who are acquainted with the
properties of light, that when a beam of rays falls upon a
plane glass surface at a particular angle, the rays which are
reflected from that surface are polarised. If a polarised
beam fall perpendicularly upon a plate of the mineral called
tourmaline, the amount of light which will pass through the
tourmaline depends entirely upon the position of the plane
of polarisation of the rays with respect to a certain axis of
the tourmaline. When this axis is parallel to the plane of
polarisation, the tourmaline is comparatively transparent.
When this axis is normal to the plane of polarisation the
tourmaline is almost opaque. By rotating the plate of tour-
maline in its plane, the quantity of light which is transmitted
can be varied at will. This property of polarised light is
applied in the construction of a solar eye piece. The rays
136 Astronomy.
from the sun, after passing through the object glass and
down the tube of the telescope, fall on the glass plane near
the eye piece. A great portion of those rays pass directly
through the glass and never reach the eye of the observer.
A portion of the rays are, however, reflected from the plate,
and the plate being placed at the proper angle, the reflected
beam is polarised, and in this state falls upon the eye piece.
Between the eye of the observer and the first lens of the
eye piece a plate of tourmaline is interposed. This is so
mounted as to be capable of being rotated, and by its aid
the observer has the most complete control over the degree
of illumination of the image. A very simple eye piece is that
of Herschel, in which a piece of unsilvered glass reflects
about a tenth part of the rays coming from the object glass
at right angles and sends them through an ordinary eye
piece, after which their intensity is further reduced by means
of a piece of neutral tinted glass.
With his eye protected by one of the methods we have
described, or by other analogous contrivances, the observer
proceeds to determine the right ascension and declination
of the sun by observations made with the meridian circle.
As the centre of the sun is not a recognisable point, the
observations are always made by noting the contact of the
circular margin of the sun's disk, or what is technically called
the limb of the sun, with the wires stretched in the focus of
the telescope. As the sun enters the field of view, the
observer counts the seconds in the same way as if he were
observing a star, and he notes the times when the preceding
limb touches the first and subsequent wires, from which he
can ascertain the moment when the preceding limb of the
sun crosses the central wire ; then allowing for the errors
of the instrument, he deduces the right ascension of the sun's
preceding limb. The observer also notes the contacts of
the following limb of the sun with the successive wires, and
in that way the right ascension of the following limb is
determined. As the disk of the sun is known to be circular,
we can find at once the right ascension of its centre by
Apparent Motion of the Sun. 137
taking the mean of the right ascensions of the preceding and
following limbs. At the same time as these observations are
made, the meridian circle will also enable the declination of
the sun's centre to be determined. While the sun is passing
across the wires, the telescope is to be moved so as to bring
the horizontal wire to touch the upper limb of the sun. The
four microscopes are then to be read off rapidly, and ere the
sun has passed out of the field the telescope is to be moved
so as to bring the horizontal wire into coincidence with the
sun's lower limb, and the microscopes are to be read again.
From the indications of the microscopes the declinations of
the upper and lower limbs of the sun are to be ascertained
in the way already explained (Chap. III.), due allowance
being made for the effect of refraction. The mean of these
observations gives the declination of the sun's centre.
If we determine the right ascension and declination of
the centre of the sun on different days, we shall find that
neither of these quantities remains constant. The right
ascension, for example, is continually increasing. Ex-
pressing the right ascension in arc of a great circle, we find
that the daily increase is about i. If the right ascension
be expressed in the more usual method as an interval of
time, then it appears that the daily increase of the sun's right
ascension is about 4 minutes. Nor are the variations in the
declination more difficult to recognise. The northern declina-
tion of the sun in the spring gradually increases until it
reaches a maximum in midsummer of about 23 27'; after
attaining this value, the declination decreases, reaches zero
in the autumn ; then the centre of the sun crosses the equator,
till in midwinter the southern declination has attained the
same value as the northern declination had in midsummer.
Again the sun approaches the equator, and crossing it, the
declination repeats the cycle of changes to which we have
referred.
The changes in right ascension and declination of the
sun stand out in marked contrast to the fixity of the right
ascension and declination of the stars ; they indicate that the
138 A stronomy.
sun is not at rest upon the surface of the heavens, but that it
has, or appears to have, a motion which is constantly changing
its position with respect to the stars and constellations.
As the right ascension of the sun is increasing, the return
of the sun to the meridian, when expressed in sidereal time,
is later and later each sidereal day. The difference
being on an average about four minutes, the interval
between two successive transits of the sun's centre across
the meridian is four minutes longer than the sidereal
day. Thus, if a star came on the meridian to-day at the
same moment as the sun's centre, when the star reached
the meridian to-morrow, the sun would have moved
away from the place it originally occupied, and its centre
would not cross the meridian until about four minutes after
the star.
53. Mean Time and Sidereal Time. The interval
between two successive transits of the sun is called an appa-
rent solar day and as the sun is of such transcendent im-
portance to the earth, it is necessary to regulate our ordinary
avocations by solar days rather than by sidereal days. There
is, however, an apparent difficulty in adopting the solar day
as the measure of time. The interval between two con-
secutive returns of the centre of the sun to the meridian is
not exactly constant. The sun, in fact, does not augment
its right ascension with uniformity, but the motion is some-
times more rapid than at other times. The length of the
apparent solar day is thus not absolutely constant, though
the limits between which it fluctuates are narrow. We there-
fore introduce the conception of the mean solar day, of which
the length is equal to the average of a very great number
of consecutive apparent solar days. This mean solar day
is the unit used for all ordinary civil reckoning: its duration
is absolutely constant, and generally different from, though
always very close to, the length of the apparent solar day.
The mean solar day is equal to 24** 3 56 S *56 of sidereal
time. The mean solar day is (like the sidereal day) sub-
Apparent Motion of the Sun. 139
divided into twenty-four hours, each hour into sixty minutes,
and each minute into sixty seconds.
The reader may, perhaps, think that needless complexity
is introduced by using two different methods of measuring
time. He might suppose that simplicity would be gained
either by making all astronomical measurements in ordinary
mean solar time, or possibly he might suppose that the
sidereal day could be used for ordinary civil purposes.
We must therefore show why the two distinct measures of
time must be maintained.
The great convenience which sidereal time possesses for
astronomical purposes arises from the circumstance that
when sidereal time is used each star crosses the meridian
daily at the same moment of time. Thus when the sidereal
clock is going correctly, a star which crosses the meridian
at 4 h 30 to-day will cross it at the same hour to-morrow,
and every day (subject only to very minute variations,
which need not be further considered at present). The
time of culmination as shown by a sidereal clock is, in fact,
the right ascension of the star. If we were to take the
time from an ordinary mean solar clock, then the time of
culmination of the star would be continually changing, being
about four minutes earlier every day. The inconvenience
arising from this would be intolerable, so that the sidereal
clock must be the regulator of time in the observatory. For
the ordinary purposes of life, on the other hand, sidereal time
would not answer. We are obliged to regulate the time
used in daily life by the movements of the sun. Our notion
of a day is so inseparably connected with the sun that the
length of the day must be the average duration of the appa-
rent diurnal revolution of the sun around the earth. Custom
has decreed that our measurement of time shall commence
from a moment which is always close to the time of cul-
mination of the sun, and at that moment a correct mean
solar clock should show o h o m o s , or, as it is more commonly
called, twelve o'clock. When we speak of any other hour for
140 Astronomy.
example, 2 RM. then everyone knows that the sun has at
that hour passed the meridian about two hours previously.
But were we to attempt to use sidereal time, endless con-
fusion would be the consequence. By the sidereal clock
the sun comes on the meridian about four minutes later every
day, so that in a month the time of culmination would have
changed by a couple of hours, and in the course of a year
the time of culmination would have been at every hour of
the twenty-four. We are therefore obliged to use a mean-
time clock regulated by the sun for the purposes of civil
life, while in the observatory we use a sidereal clock regulated
by the stars.
In consequence of the continual increase in the right
ascension of the sun, it is found that after the lapse of 365
days, or, more strictly, of 365-2421 days, the right ascension
has gained 360, or twenty-four hours of sidereal time. At the
same time it is found that the movements of the sun in
declination have also run through their cycle, so that at the
close of the epoch just mentioned, which is approximately
365^ days, the right ascension and declination of the sun
have both regained the values they had at its commence-
ment. The sun has, therefore, in the course of this time
leturned to the point of the heavens from which it originally
departed.
54. The Ecliptic. To ascertain what the actual move-
ments of the sun during the interval have been, we make
use of a celestial globe. By the observations of the right
ascension and decimation of the sun's centre made at stated
intervals of time, we are enabled to plot down on the celes-
tial globe the actual position which the centre of the sun
occupied on the celestial sphere at the corresponding epochs.
When this is done we find that all the points, which have
been laid down, lie on the circumference of a great circle,
and we therefore see that the sun moves in a great circle
on the surface of the celestial sphere. This great circle is
called the ecliptic.
Apparent Motion of the Sun.
141
It is desirable to dwell for a moment on the important
result which is thus obtained. That the path of the sun on
the celestial sphere must be a closed curve of some kind is
obvious from the consideration that, at the termination of a
period of 365^ days, the sun returns to the position which
it originally had at the commencement of that period. The
number of closed curves which can be drawn on the surface
of a sphere are of course of unlimited variety. If, however,
the sun's motion takes place in a plane, then its apparent
motion on the surface of the sphere can only be in such a
curve a?s lies on the surface of the sphere, and also in a
plane ; but a section of a plane by a sphere is a circle, and
as the sun appears to move in a circle, it follows that the
sun moves in a plane. There is a very remarkable circum-
stance with respect to this plane, for as the circle in which
the sun moves is a great circle, the plane must pass through
the centre of the celestial sphere. The earth is stationed
at the centre of the celestial sphere, and hence we see that
the apparent motion of the sun takes place in a plane
which passes through the earth.
Let the sphere P Q (Fig. 72) represent the celestial sphere,
of which the points P and
Q are the north and south
poles respectively. The
great circle c E A E is the
celestial equator. The
ecliptic is the great circle
A B c D, which intersects
the equator in the points
A c, called the Equinoxes.
The plane of the ecliptic is
inclined to the plane of the
equator by an angle which
is called the Obliquity of
the Ecliptic, and is equal
to about 23 27'. The points on the ecliptic B D, which are
142
A stronomy.
situated at the middle points B and D of the semi-circum-
ferences ABC and ADC, are termed the Solstices. The sun
moves round the ecliptic in the direction indicated by the
arrow. He passes through the point A about March 21,
whence that point is termed the Vernal equinox. In three
months afterwards, about June 22, he reaches B, the summer
solstice, and c, the autumnal equinox, on September 23, and
D, the winter solstice, on December 22.
55. Day and Night. To study the variations in the
length of the day, a celestial globe is specially convenient
FIG. 73.
(Fig. 73). The earth is supposed to have shrunk into a
small point at the centre o of the celestial globe. The plane
of the horizon, drawn at the place where the observer is
supposed to be stationed, must cut the celestial sphere in a
great circle. This great circle corresponds to the ring H F H,
which is attached to the frame by which the globe is sup-
Apparent Motion of the Sun. 143
ported. A celestial object will be visible to the observer if
it be on that part of the globe which is above the plane
H F H. All objects on the hemisphere below that plane are
invisible.
To examine the variations in the length of the day, the
globe must first be set correctly for the latitude of the place
where the observer is stationed. We have shown in 41
that the elevation of the pole of the heavens above the
horizon is equal to the latitude. To set the globe it is,
therefore, necessary to place the axis P Q, about which the
globe revolves, so that it makes with the plane H F H an
angle equal to the latitude.
Let z be the zenith ; then the great circle passing through
z and P is the meridian, which of course cuts the horizon
at right angles. The meridian on the globe is represented
by the ring H z M. The great circle E F G, drawn perpen-
dicular to the polar axis P Q, is the equator. Since two
great circles must mutually bisect each other, it is obvious
that the equator is bisected by the horizon at F and G, and
therefore half of the equator is below the horizon and half
is above. A celestial object which is situated on the equator
will, in the course of one revolution of the heavens, remain
above the horizon for precisely the same time that it is below.
When the sun is in the equator the length of the day must
be equal to the length of the night. If the sun always
moved in the equator then the day and night would be con-
stantly equal. The path of the sun lies, however, in the
ecliptic ; which crosses the equator at the vernal and autumnal
equinoxes. The sun is, therefore, in the equator when, and
only when, he is in the act of passing through one or other
of the equinoctial points on March 21 or September 23.
At either of the dates mentioned the length of the day is
equal to the length of the night.
After passing the vernal equinox on March 2 1 the sun
gradually increases his declination. The path of the sun as
caused by the diurnal rotation ceases to be a great circle
1 44 A stronomy.
after the equinox is passed. It is then a small circle, of
which the dimensions gradually decrease until June 22, when
the sun having attained its greatest north declination, the
small circle which it appears to describe in virtue of its
apparent diurnal rotation is a minimum. At a date inter-
mediate between March 21 and June 22 the path of the
sun will be the small circle I I (Fig. 73). It is plain
that this circle is bisected by the great circle F p G, and
therefore the part of the small circle, which is above the
plane of the horizon, is greater than that which is below it.
When the*sun appears to move in this circle it continues
above the horizon for a longer period than it is below, and
consequently the length of the day exceeds that of the night.
The disparity between the length of the day and night will
increase as long as the sun increases in north declination,
until the difference attains its maximum value on June 22,
when the sun, having attained the declination of 23 27', is
in the summer solstice. In this case the sun passes the
meridian at the point b, the distance a b being equal to
23 27'.
The sun having passed the summer solstice, begins
to return towards the equator. On September 22 the sun
reaches the equator, and the length of the day is again
twelve hours, and equal, of course, to the length of the night.
After this date the sun is below the equator, its south
declination gradually increasing to the value 23 27', which
it has on December 22. The sun each day after passing
the autumnal equinox will describe a small circle of the
celestial sphere parallel to the plane of the .equator, and
lying to the south of it. The dimensions of this circle
gradually diminish, until the winter solstice is reached. Let
j j be the circle described by the sun on a date between the
autumnal equinox and the winter solstice. Part of this
circle is above the plane of the horizon and part is below,
and it is easy to see that the latter part is greater than the
former. The plane P F Q must obviously bisect this circle,
Apparent Motion of the Sun. 145
and the two points of bisection, and therefore more than
half the circle, are below the plane of the horizon.
When the apparent diurnal motion of the sun is per-
formed in this circle j j, the sun is below the horizon for a
longer period in each revolution than it is above, and hence
the day is shorter than the night. The disparity between
the length of the day and that of the night goes on augment-
ing until the winter solstice, when the shortest day is attained.
In the movement of the sun from the summer solstice to the
winter solstice we see that the length of the day changes
from its greatest value to its least. After passing the winter
solstice the same series of changes in the relative lengths of
the day and night is repeated in the inverse order, and in
the course of 365!- days, or one year, a complete cycle of
changes has been gone through and a new cycle is com-
menced.
There are, however, remarkable phenomena connected
with the recurrence of day and night in countries near either
of the poles, that merit special attention.
The globe is set in Fig. 74 so as to correspond to a con-
siderable northern latitude, which we shall suppose is not less
than 66 33'. The distance of the pole P from the zenith z
is equal to the complement of the altitude of the pole, and
as the altitude of the pole is equal to the latitude, it follows
that the zenith distance of the pole in the present case is
less than 23 27'. Let us now consider the circumstances
under which the sun can rise above the horizon in a case
like the present. Whenever the sun is above the horizon,
its distance from the zenith must be less than 90. The
zenith distance of the sun is always smaller when the sun is
on the meridian than when the sun is either approaching to
the meridian or after he is past it. We have, therefore, to
see under what circumstances the sun, when on the meridian,
is above the horizon, or, what is the same thing, when the
meridian zenith distance of the sun is smaller than 90. To
give definiteness to what we have to say on this subject, let
L
146
Astronomy.
us take in the first instance a latitude of 75, so that the
angle between z and P is equal to 15. The distance from
the pole to the equator is equal to 90 : hence the distance
in the present case from the zenith to the equator is 90
15 = 75. If then the sun were on the equator, its zenith
distance at the moment of culmination would be 75. The
sun must then be visible every day, because the zenith dis-
tance at culmination is less than 90. As the sun moves
from the equinox towards the summer solstice, the meridional
zenith distance gradually diminishes. When the sun is at
the solstice, its declination is 23 27'. It is, therefore, north
of the equator by this amount, and consequently the zenith
distance at culmination is 75 23 2 7'= 51 33'. The sun
crosses the meridian twice daily, viz. at noon and at mid-
night ; in the former case the zenith distance has its smallest
value, and in the latter the zenith distance has its greatest
Apparent Motion of the Sun. 147
value. We have seen that the southern point E of the
equator is 75 from z. The northern point of the equator
is below the horizon, and its distance from z must be 90
-f- 15= 105. On June 22, when the sun is in the summer
solstice, the north declination is 23 27', and when the sun
is on the meridian at midnight it will be 23 27' nearer the
zenith than the north point of the equator. It follows that
the zenith distance of the sun at midnight will be 105
23 27'=8i 33'. As this is less than 90, we learn the very
remarkable fact that the sun under these circumstances does
not descend below the horizon at all, so that, in fact, as long
as this state of things continues we have perpetual day.
Thus is explained the midnight sun in the Arctic regions.
It is plain that as the sun sets every day, even in mid-
summer, in the latitude of the United Kingdom, while it
does not set at midsummer in the latitude of 75, there must
be some intermediate latitude where the sun just reaches the
horizon at midnight in midsummer. The determination of
this latitude is very easily effected by the celestial globe.
The polar distance of the sun is equal to the complement of
the declination, and therefore at midsummer the polar dis-
tance is 66 33'. When the sun is on the horizon at midnight,
the polar distance of the sun must be equal to the altitude
of the pole ; but the latter is the latitude, and hence when
the sun is on the horizon at midnight in midsummer the
latitude must be 66 33'. The parallel which passes through
all the points which have the north latitude 66 33' is called
the Arctic Circle. At all places to the north of this circle
the sun remains above the horizon, even at midnight, for a
certain portion of the summer. The number of days in the
year during which the midnight sun is to be seen increases
as the latitude increases, and may be found as follows.
After the sun has passed the vernal equinox its declina-
tion gradually increases, and the amount by which the
diurnal circle dips below the horizon gradually diminishes
until a declination is attained, when the diurnal circle i I
L 2
148 A stronomy.
(Fig. 74) just grazes the northern point of the horizon. On
the day when this declination is attained, the sun's centre
will therefore not set. The next day the sun's centre will at
midnight be some distance above the horizon, and the mid-
night sun will be continually witnessed until, after passing
the summer solstice, the sun has returned so far towards
the autumnal equinox that he is again performing his diurnal
motion in the circle i i. At midnight the centre of the sun
will then just graze the horizon, and on the following revolu-
tion the centre will pass below the horizon. When the
equinox has been reached, the length of the night has become
equal to that of the day, and the length of the latter gradually
diminishes until the sun has attained a declination so far to
the south that the circle j j, which its centre describes, only
just grazes the horizon. In this case when the sun is on
the meridian at noon, its centre has just reached the horizon,
and on the following day the centre of the sun will not
reach the horizon at all. Perpetual night will then reign
until the sun, having attained the winter solstice, has moved
so far towards the equator that it again performs its diurnal
motion in, the circle j j. When this point has been attained
the centre of the sun just grazes the horizon at noon, and
the following day the sun may be seen to rise : the length of
the day then gradually increases, and the cycle already
described is repeated.
It should also be observed that the limits of latitude in
which perpetual day is enjoyed at midsummer are identical
with the limits in which perpetual night is found in mid-
winter. At the winter solstice, the south declination of the
sun is 23 27'. If, therefore, the sun at culmination in the
winter solstice be on the horizon, the southern point of the
equator will be 23 27' above the horizon. The meridional
distance from the zenith to the equator will therefore be
90 23 27 / =66 33'. It is, however, easy to see that this
is the altitude of the pole, and therefore the latitude of the
place. It follows that in all localities of which the latitude
Apparent Motion of the Sun.
149
exceeds 66 33' there will be perpetual day for a certain
period at midsummer, and perpetual night for a correspond-
ing period at midwinter.
To take an extreme case, let us consider the condition of
day and night which could be presented to an observer who
was stationed at the latitude of 90, or, in other words, at the
pole itself. The pole would then coincide with the zenith,
and the celestial globe adapted to these circumstances is
shown in Fig. 75: The equator, being at every point 90
distant from the pole, must now be coincident with the
horizon, and the small circles in which the stars revolve
will be all parallel to the plane of the horizon. The altitude
of a star would then be a constant, and the phenomena of
rising and setting stars would be unknown. If the sun were
actually fixed in the ecliptic it would then always describe
the same small circle, and would be visible or not, according
150 Astronomy.
as that point of the ecliptic lay in the half which was
above or below the plane of the horizon. As, however, the
sun moves in the ecliptic, it will be seen constantly through
part of the year, and remain invisible during the remainder.
Suppose, for example, that the sun is in the vernal equinox.
The centre of the sun is then on the equator, and as the
equator is coincident with the horizon, the centre of the sun
will lie on the horizon. The diurnal motion will, therefore,
carry the sun round the horizon. As the declination increases
the sun will gradually become elevated above the horizon,
so that it will really describe a sort of spiral on the celestial'
sphere, each revolution being at a greater altitude than the
preceding one, until the summer solstice is attained, when
the sun will revolve nearly in a small circle parallel to the
horizon, at an altitude of 23 27'. After the summer solstice
has passed, the spiral course of the sun will recommence, but
its motion will now be gradually downwards, so that after a
number of complete revolutions it will again have reached the
horizon. Thus an observer stationed at the north pole
will find the sun above his horizon during the whole interval
from the vernal to the autumnal equinox. After the latter
equinox the sun descends below the horizon, and performs
a spiral movement in the southern hemisphere, until, at
the winter solstice, it has attained the south declination of
23 27'. It then commences to return towards the horizon,
to reappear in the northern hemisphere after the vernal
equinox. At the north pole, therefore (neglecting small
variations), one half of the year is day and the other half is
night. Finally, let us take the other extreme case of an
observer who was stationed at the equator. The globe set
for this case is shown in Fig. 76. As the latitude is now
equal to zero, the elevation of the pole above the horizon
must be zero, and therefore the pole must actually lie in the
plane of the horizon. All the small circles which are de-
scribed by the celestial bodies must, therefore, be perpen-
dicular to the plane of the horizon. It is easy to see that
Apparent Motion of the Sun. 1 5 1
half of each circle lies below the plane of the horizon, and
half is above. Thus every celestial object will (so far as
the diurnal motion is concerned) be above the horizon for
half the day, and below it for the other half. The sun is no
exception to this statement : the small circle in which the
sun moves each day is bisected by the horizon, and therefore
the day and night are of equal length.
At the equinox the sun at rising is stationed precisely at
FIG. 76.
the east point of the horizon ; it then ascends to the zenith,
and descends again to set in the western point of the horizon.
After the vernal equinox is past, the sun has moved into
the northern hemisphere, and the small circle described in
the diurnal motion, though still perpendicular to the plane
of the horizon, cuts the horizon at points less than 90 from
the north point. Thus each day the sun rises somewhat to
f he north of due east, ascends perpendicularly till it cul-
152 Astronomy.
minates at a point on the meridian to the north of the zenith,
then descends to set perpendicularly at a point of the
horizon somewhat to the north of west. The magnitude of
the diurnal circle gradually decreases until the summer
solstice is reached, when the sun at noon is 23 27' to the
north of the zenith ; the circle afterwards increases till it be-
comes a great circle passing through the zenith at the
autumnal solstice, and then repeats in the southern hemi-
sphere the series of changes that we have described in the
northern.
We give here a table for determining the length of the
longest and shortest day in the different latitudes, from the
equator up to 66 33'.
Latitude. Longest Day. Shortest Day.
o I2 h o m I2 h o m
5 12 17 ii 43
10 12 35 ii 25
T 5 12 53 ii 7
20 13 13 lo 47
25 13 34 Jo 26
3 *3 5 6 1 4
35 14 22 9 38
4o 14 5 1 9 9
45 15 26 8 34
5 16 9 7 51
55 17 7 6 53
60 18 30 5 30
65 21 9 2 51
66 33' 24 o oo
At localities above the latitude of 66 33' the length of
the longest day is never less than twenty-four hours, while
there is no day at all during a certain period at midwinter. It
is, however, of interest to calculate the connection between
the latitude and the number of days during which the sun does
Apparent Motion of tJie Sun.
153
not set in summer or
rise in winter.
in
the following table
North
Sun does not set
Latitude.
for about
66 33'
I day
70
65 days
75
103 ^
80
134
85
161
90
186
FIG. 77,
The results are given
Sun does not rise
for about
i day
60 days
97
127
153
179 ,
56. Zones into which the Earth is divided. The
parallels which pass through all the points of latitude 66 33'
in either hemisphere, con-
veniently mark off two
important regions in the
vicinity of the north and
south poles respectively.
These parallels are repre-
sented by A A' and B B'
(Fig. 77), and the regions
which they define are
A p A' and B Q B'. The
northern circle A A' is
called the Arctic Circle^
while B B' is the Antarctic
Circle. The regions with-
in these circles are characterised by the presence of con-
tinual day at midsummer, and continual night at midwinter.
They are the coldest portions of the earth, and are known
as the North Frigid Zone and South Frigid Zone respectively.
Another natural division of the earth is presented by
the equator E E', which divides the portion of the earth
between the Arctic and Antarctic circle into equal parts.
There is also a natural division by means of the circles
c c' and D D', which are known as the Tropic of Cancer and
154 Astronomy.
the Tropic of Capricorn. It will be necessary to explain
the significance of these circles.
The sun at midday attains its greatest elevation above
the horizon, so that the zenith distance of the sun is then a
minimum. At midsummer the sun at noon is nearer to the
zenith than it is at any other season. In European latitudes
it is always seen that even when the sun has its greatest
altitude it is still at a considerable distance from the
zenith. The question, therefore, arises as to whether there
are any localities on the earth's surface at which the sun,
when its altitude is greatest, is actually situated at the zenith.
The altitude of the pole being equal to the latitude, the
angular distance from the pole to the zenith is equal to the
complement of the latitude, or to what is called the co-
latitude. If, therefore, the sun at its moment of culmination
be situated in the zenith, the polar distance of the sun must
be equal to the co-latitude. The polar distance of any
celestial object is, however, equal to the complement of its
declination. It is, therefore, evident that when the sun is
in the zenith, the complement of its declination must be
equal to the complement of the latitude, but this can only
be the case when the latitude is equal to the declination ;
and hence we find that the sun will culminate in the zenith
whenever its declination is equal to the latitude.
As the ecliptic is inclined to the equator at the angle of
23 27', the greatest declination which the sun can have is
23 27', and this is only attained when the sun is at the
summer or winter solstice. As the sun can only attain the
zenith when its declination, is equal to the latitude, and as
the greatest declination is +23 27', it follows that the sun
cannot attain the zenith of localities which are situated at a
greater distance north and south of the equator than 23 27'.
The north and south parallels, which correspond to this
latitude, bound the regions in which it is possible for the
sun to attain the zenith.
As tne sun in the course of the year passes through every
Apparent Motion of the Sun. 155
phase of declination between +23 27' and 23 27', so it
follows that the sun will appear during the year at, or close
to, the zenith of every place contained between these two
parallels. It would not be correct to say that the sun would
actually culminate in the zenith, for it will generally happen
that at the time when the sun passes close to the zenith, its
declination on two consecutive days will be one a little
greater and the other a little less than the latitude. The
sun will, therefore, on one day culminate a little on one
side of the zenith, and the following day it will be a little on
the other side.
The circles c c' and D D', bounding this very naturally
marked region on the surface of the earth, are known as the
tropics. The name is given to them from the circumstance
that an observer on one of these circles will, as midsummer
approaches, find the sun daily approach nearer and nearer to
the zenith at the moment of culmination, until on midsummer
day the culmination will be exceedingly close to the zenith.
The centre of the sun will then be actually in the zenith if
it should happen that the moment of culmination is identical
with the moment when the sun has actually attained its
greatest north declination. After this point has been
attained, the sun will then begin to turn back, for at the
next culmination it will be a little south of the zenith in the
northern hemisphere, or north of the zenith in the southern
hemisphere.
A resident, either on the equator or at any station inter-
mediate between the two tropics, will have the sun in his
zenith twice each year. Suppose, for example, that the lati-
titude of the place be + 10. At the vernal equinox the
sun's declination is zero, but it gradually increases, and,
when it attains the value of. 10, being then equal to the
latitude, the culmination must take place at the zenith.
After the declination of 10 is passed, the sun gradually
moves to the summer solstice, when its declination is 23 27',
and then, in commencing to return towards the equator,
156 Astronomy.
the declination diminishes down to 10, and, therefore, the
culmination is again at the zenith. We thus see that a
station in the northern hemisphere which has a latitude less
than 23 27' will have the sun in its zenith on two occasions
between the vernal and the autumnal equinox.
At a place situated on the equator, the latitude is of
course zero, and hence the declination of the sun must be
zero when it culminates at the zenith. This is only the
case at the vernal and autumnal equinox. It is easy to
show that in the southern hemisphere the sun is twice near
the zenith, between the autumnal and the vernal equinox,
provided the latitude is less than 23 27' south of the
equator.
The regions between the equator and the tropic of
Cancer on the one hand, and the equator and the tropic
of Capricorn on the other, are known as the north and
south torrid zones respectively. The region between the
tropic of Cancer and the arctic circle is the north temperate
zone, while that between the tropic of Capricorn and the
antarctic circle is the south temperate zone. Each of the
two hemispheres into which the equator divides the earth
is thus conveniently divided into three zones, and the boun-
daries are indicated in a very natural manner, by the
apparent annual movements of the sun.
57. Effect of Refraction on the Length of the Day. In
what we have hitherto stated with respect to the variation
in the length of the day, in different seasons of the year and
at different latitudes on the earth, we have overlooked the
effect of atmospheric refraction in changing the apparent
place of the sun. It is, therefore, necessary to point out
briefly the modifications which must be introduced into our
results when refraction has to be taken into account. In
the tables given on pages 152-3, it has been assumed that the
day commences at the moment when the centre of the sun
is actually on the horizon, as it would be seen were there
no atmosphere. The refraction of the atmosphere tends to
Apparent Motion of the Sun. 157
raise all objects towards the zenith, and at the horizon this
is no less than 33'. In fact, as we pointed out in 51, the
sun's centre appears to be on the horizon, while in reality
the sun's centre has to ascend 33' in order to be on the
horizon. It therefore follows that, as the sunrise is appa-
rently accelerated and sunset retarded, the length of the
day really appears longer than calculations show, which
neglect the effect of the atmosphere.
At the north pole the effect of refraction upon the length
of the day is indicated in a somewhat remarkable manner.
We shall only consider the position of the centre of the sun,
so that some modifications are required when the dimensions
of the sun are taken into account. When the sun, in pass-
ing from the winter solstice to the vernal equinox, has ap-
proached so near to the latter that its south declination is
33', then the refraction of the atmosphere raises the sun's
centre to the horizon, and the perpetual daylight of summer
has commenced. Again, when the sun, after passing the
summer solstice, is again descending to the horizon, the
refraction appears to retard its setting, so that it is not
until the sun's centre has really passed below the horizon
to the distance of 33' that the phenomenon of setting is
witnessed. Remembering that for an observer stationed at
the north pole the celestial equator is coincident with the
horizon, we see that the arctic day will be enjoyed during
the whole time that the sun moves from 33' south decli-
nation to -{-23 27' north declination at the solstice, and
then back again to 33' south.
58. Twilight. The atmosphere has also an effect
upon the duration of daylight, which arises from a dif-
ferent source. After the sun has set, his rays still tra-
verse the higher regions of the atmosphere, and illuminate
the particles which the air retains in a state of suspen-
sion. This light from above diffuses a certain amount
of illumination on the surface of the earth, which gra-
dually decreases in intensity as the sun sinks below the
158 A stronomy.
horizon. The twilight in the evening is generally known
as dusk, while that which precedes the rising of the sun
is known as the dawn. Were it not for the effect of the air,
the brightness of the day would totally cease when the
last portion of the sun's disk disappeared below the horizon
at sunset, and the daylight* would only commence when
the disk commenced to ascend above the horizon at
sunrise.
The twilight either at dusk or dawn is only seen when
the sun is within a certain distance of the horizon. The
exact amount of the distance appears to be dependent upon
the state of the atmosphere. It may, however, be generally
stated that the distance is about 18. The dusk is thus
usually visible until the centre of the sun has been carried
by the diurnal motion to a perpendicular distance of 18
below the horizon. Similarly the earliest glimpses of dawn
may be caught when the sun, in his approach to the horizon,
has attained a distance of only 18 therefrom. It will of
course be understood that the distance from the horizon
which is here alluded to is the distance of the sun from
the nearest point of the horizon, or the arc which is inter-
cepted by the plane of the horizon on the great circle drawn
from the zenith to the sun. This will not, of course, be
generally coincident with the actual course in which the sun
is apparently moving by the diurnal motion, The sun will
generally have to move over a distance considerably greater
than 1 8 before it reaches the horizon after the first glimpses
of dawn have been perceived.
The duration of the twilight either at dusk or dawn
will be found to vary very considerably at different
seasons, as well as at different latitudes. To take a sim-
ple case, let us suppose the observer to be stationed at
the equator, and let us calculate the duration of twilight
when the sun is at either of the equinoxes. Under these
circumstances, as the sun is actually situated in the celestial
equator, and as the equator passes through the zenith, the
Apparent Motion of the Sun. 159
diurnal motion of the sun will be effected in the great circle
which passes through the zenith and the eastern and
western points of the horizon the circle, in fact, which is
often known as the prime vertical. Before sunrise the sun
will ascend perpendicularly to the horizon, and after sunset
it will descend perpendicularly below it. The twilight will
therefore continue in this special case during the time when
the sun moves through an arc of 18 on the celestial sphere,
in virtue of the apparent diurnal motion. As the diurnal
motion completes its revolution in twenty-four hours, a point
on the equator which moves through 360 in one revolution
must move through 15 in one hour. To move through an
arc of 18 a time of i h i2 m will therefore be required.
Hence it appears that under the circumstances we have
described the twilight at dusk and at dawn will last for a
period of i h 12.
At other places or seasons the duration of twilight can
be found by the celestial globe with sufficient accuracy for
most purposes. First set the globe to the latitude of the
place by placing the axis of the celestial sphere at the
correct inclination to the horizon. Then find on the globe
the point on the ecliptic which the sun occupies on the day
in question, and place this point on the horizon. The angle
through which the globe must be rotated in order to bring
the point from the horizon to a distance of about 18 below
it, converted into time at the rate of 15 to an hour, is the
duration of twilight.
It is well known that in our latitude, at midsummer, the
night is never perfectly dark even at midnight. Looking
towards the northern horizon, the midnight twilight is seen
to come from that region, and its origin can easily be
explained. When the sun crosses the meridian at midnight,
its distance below the horizon is greater than when the sun
is at any other point of its diurnal path ; if, therefore, the
depression of the sun below the horizon at midnight be not
greater than 18, the sun will, during the entire night, be
160 Astronomy.
within 18 of the horizon, and consequently the twilight will
never cease.
At midsummer, the sun's declination being 23 27', the
polar distance of the sun is 90 23 2 7 '=66 33'. If,
therefore, the sun be 18 below the horizon, the elevation of
the pole above the horizon will be 66 33' 18=48 33'.
It therefore appears that when the latitude of the place is
48 33', the sun at midsummer will only just attain the
distance below the horizon at which twilight ceases. At any
latitude exceeding 48 33' we shall, then, have twilight at
midnight in midsummer. Take, for example, the latitude
of 53, The elevation of the pole above the horizon is
therefore 53, and consequently the distance of the mid-
summer sun below the horizon at midnight is 66 33' 53
= 13 33'. As this is less than 18, the twilight will still be
seen at midnight.
Similar considerations will also enable us to find the
number of days at a given latitude during which the midnight
twilight will be seen. At the latitude of 53, which we may
adopt as before, for the sake of illustration, the elevation of
the pole is, of course, 53. If the sun comes to the meridian
at midnight at a point which is 18 below the horizon, the
distance from the pole to the sun is 534-18 71. The
declination of the sun is equal to the complement of the
polar distance, and hence the declination is 9071 = 19.
The midnight twilight will therefore be perceived whenever
the declination of the sun exceeds 19. To find the
number of days during which the midnight twilight continues,
it is therefore only necessary to find the number of days in
which the sun moves from the declination 19 to the
summer solstice, and then back again to the declination 19.
In the particular case now before us, the number of days is
about 74.
The effect of twilight in mitigating the darkness of the
long arctic winter should also be noted. In midwinter the
sun does not ascend above the horizon in the arctic regions,
Apparent Motion of the Sun. 161
but if the sun approaches the horizon to a distance less than
1 8, the twilight of course becomes visible. At the winter
solstice, the south declination of the sun is 23 27'. If the
sun at culmination be 18 below the horizon, it follows that
the equator must cut the meridian at an elevation of 23 27'
- 1 8 =5 27' above the southern horizon ; but it is easy to
show that this must be the complement of the elevation of
the pole above the horizon. The whole semicircumference
of the meridian is made up of the elevation of the pole,
the altitude of the point on the equator, and the distance
from the pole to the equator. As this last is equal to
90, the two former must be complementary. The elevation
of the pole at that latitude in the arctic region, where the
midday sun in winter just comes near enough to the horizon
to afford a glimpse of twilight, is 90 -5 27'=84 33' ; at
lower latitudes the number of days in which twilight is
witnessed in midwinter gradually increases. Within the
distance of 5 27' from the pole, there are a certain number
of days every winter, during which not even a glimpse of
twilight announces the fact that the sun has reached the
meridian at noon. This number gradually increases from
the latitude of 84 33' to the pole.
As the sun approaches the winter solstice, its south
declination gradually increases, until about the i3th of
November the Sun has descended 18 below the equator.
Assuming that the atmospheric conditions of twilight
at the pole resemble those which are found in latitudes
to which access is obtained, it would appear that the
twilight at midday will cease on the i3th of November, and
will continue absent until the sun, having passed the winter
solstice again, reaches the distance of 18 from the horizon
on January 29.
59. Changes of Temperature on the Earth . The earth is
constantly radiating out heat from its surface to the celestial
spaces, and tends to grow cooler and cooler by the continual
loss of heat which is thus sustained. On the other hand.
M
1 62 Astronomy.
the rays from the sun, besides their effect in illuminating the
earth which we have already considered, convey to us
heat which counteracts the continuous loss of heat to which
the earth is exposed by the effect of its radiation. During
the night this radiation is continually cooling the earth, and,
as there is no counterbalancing heat then derived from the
sun, the temperature goes on decreasing after sunset When
the sun rises, its rays begin to warm the earth, and though the
loss by radiation still continues, yet the increase of heat due
to the sun soon counterbalances the loss arising from radia-
tion, so that the temperature gradually rises. The efficiency
of the sun rays in warming the earth increases as the sun
approaches to the meridian, and attains a maximum when
the sun is on the meridian at noon. As the sun commences
to decline towards the western horizon in the afternoon, the
amount of heat received from his rays by the earth decreases.
Still, so long as the amount which is received exceeds that
which is lost by radiation towards the celestial spaces, the
temperature of the earth goes on increasing. Thus the
greatest temperature in the day is attained not actually at
noon, but some time afterwards. When the amount of heat
received just equals the amount lost, then the maximum
temperature of the twenty- four hours is reached. The loss
then exceeds the gain, and consequently the temperature
falls.
The series of changes in the temperature which occur
daily would be reproduced each day in precisely the same
manner if the apparent diurnal motion of the sun were
always performed in the same course. But as the sun has
an apparent annual motion on the surface of the celestial
sphere, so there are corresponding modifications in the path
of the diurnal motion from one day to another. For the
sake of illustration we may take the case of the northern
temperate region. As the length of the day commences to
increase in spring, the quantity of heat received from the sun
between sunrise and sunset increases also. This is due not
Apparent Motion of the Sun. 163
only to the longer continuance of the sun above the horizon,
but also to the increased elevation of the sun, which causes its
rays to descend more nearly perpendicularly on the earth.
The temperature is of course still diminished by radiation
from the earth during the night, but the decreasing length of
the night combined with the increase of heat during the day
soon makes the gain to exceed the loss, and consequently
the temperature steadily rises. As the summer is neared,
the daily gain in temperature approaches a maximum, so
that on midsummer day the region receives more heat during
the day, and loses less during the night, than on any other
day in the year. It does not, however, follow that the
hottest period of the year is precisely at midsummer day ;
just as in the case of the changes of temperature during the
day it appears that the maximum of temperature does not
coincide with the moment when the most heat is being
gained, so in the case of the annual changes of temperature
the day when most heat is received is not necessarily the
hottest day. At midsummer the gain during the day
largely exceeds the loss during the night, and though the
daily gain is less on subsequent days, yet the total heat must
be increasing so long as there is any gain at all. The
greatest temperature will, therefore, be attained at the
moment when the gain during the day is equal to the loss ;
this will be some little time after midsummer. On subse-
quent days the loss will exceed the gain, and consequently
the temperature will fall ; but just as the greatest heat is not
attained precisely at midsummer, so the greatest cold is not
attained precisely at midwinter. At midwinter no doubt
the loss of heat by radiation exceeds the gain during the day
by a greater amount than at any other season, but so long
as the loss is in excess of the gain, so long will the tempera-
ture continue to decrease ; nor will the decrease be arrested
until, by the gradual lengthening of the days during the
approach of spring, the amount of gain during the day will
precisely counterbalance that lost by radiation. When this
M 2
164 Astronomy.
point is attained, the temperature will have sunk to its
lowest amount for the year ; this point is readied about a
fortnight after the winter solstice. What has been said as
to the diurnal and annual variations of temperature may
also be applied to the southern temperate region, remem-
bering that midsummer here is midwinter there, and vice
versa. A somewhat different account must be rendered of
the variations of temperature between the tropics on the one
hand, or inside the arctic circles on the other.
On the equator the length of the day is equal to the
length of the night, whatever be the point of its apparent
path in which the sun is situated : the changes of tempera-
ture corresponding to different periods of the year are there-
fore much less marked than is the case in the temperate
latitudes, where the relative lengths of the day and night
undergo considerable fluctuations. Any changes in the
temperature at the equator are therefore limited to the
effects which can be produced by the fluctuations of the
sun's zenith distance. At the equinox, when the sun is in
the equator it passes through or close to the zenith at the
moment of culmination. At the solstices the sun is at cul-
mination 23 27' to the north or south of the zenith. As
the sun is therefore shining more perpendicularly upon the
earth at the period of the equinoxes, these periods are, so
far as this is concerned, the hottest parts of the year. At
regions in the tropics not situated on the equator there is
of course some difference between the lengths of the days
and nights, and a corresponding fluctuation in the tempera-
ture, but this is much less marked than in places situated in
the temperate regions- In the arctic regions the circum-
stances are modified by the fact that during part of the year
the sun remains entirely above the horizon, while during part
of the year it is as continuously below.
60. Mean Temperature. The mean temperature of
any spot on the earth depends chiefly upon the latitude.
At the equator the mean temperature is a maximum, and it
Apparent Motion of tlie Sun. 1 65
gradually decreases as the latitude increases until the pole
is attained. The variation in the mean temperature is
not to be explained by the relative proportions of daylight
and night : the number of hours of sunlight in the year is
pretty much the same whatever the latitude may be. Thus
at the equator we have twelve hours of sunlight out of every
twenty-four, and therefore the sun is above the horizon at
the equator for half the whole number of hours in the year,
and below it for the other half. This is the same as we find
at the pole, for the sun is there continuously above the
horizon for six months, and then continually below for six
months. At the intermediate latitudes, the great length of
the davs in summer is counterbalanced by the great length
FIG. 78.
A
of the nights in winter, so that here again we find that for
one half of the year the sun is above the horizon, and for
one half below. It is, therefore, necessary to search for some
other reason for explaining the great variations in the mean
annual temperature at the different latitudes. The explana-
tion will be found in the different elevations which the sun
attains in different latitudes, combined with the fact that
the efficiency of the sun's rays for warming the earth depends
upon the angle of incidence. This latter remark may be
explained by Fig. 78. Let s represent the sun, and E the
earth ; then the rays from the sun diverge in various directions
s P, s Q, s A. s B, and it may be assumed that the heat dis-
1 66 Astronomy.
tributed in the various directions is constant. If we conceive
a very large sphere to be drawn of which s is the centre,
then all the heat from the sun will fall upon the interior of
this sphere. This heat is uniformly spread over the surface,
so that a given area receives the same quantity of heat what-
ever be the situation which it occupies on the surface of the
sphere. For simplicity we may suppose the area under con-
sideration to be a small circle, and the quantity of heat
which falls on that circle will be proportional to the area of
the segment of the sphere which it cuts off. If the circum-
ference of the small circle be regarded as the base of a
cone of which the centre is at the point s, then the cone
contains a portion of the sun's rays which bear to the total
radiation the same proportion which the segment of the
sphere bears to the entire area of the sphere.
Let two right circular cones be drawn with equal vertical
angles, and let the section of these cones, by the plane of the
paper, be P s Q and A s B (Fig. 78), the former falling on the
earth near the pole, and the latter in the vicinity of the
equator. Since the angles at the vertices of these two cones
are equal, it is evident that an equal portion of the sun's
radiation passes through each, and that, consequently, a
certain area of the earth, of which PQ is a section, receives
the same quantity of heat as the area near the equator of
which the section is A B. It will at once be seen that the
area which the cone P s Q cuts on the earth's surface is
much larger than the area cut out by the cone A s B. The
same quantity of heat which falls on a certain region near
the equator has, therefore, to be distributed over a much
larger area near the pole; hence the temperature, per unit of
area, must be less at the neighbourhood of the pole than
in the neighbourhood of the equator. More generally it
appears that the temperature decreases as we pass from
the equator towards the poles.
61. Effect of the Atmosphere. All the considerations
which have here been brought forward with reference to the
Apparent Motion of the Sun. 167
efficiency of the sun in heating the earth, must receive
certain modifications when the existence of the atmosphere
surrounding the earth is taken into account. The heat of
the sun acting on one region of the earth raises the tem-
perature of that region. The air which is in contact with
the earth becomes warm, and as it expands by heat must
necessarily become lighter. Thus the air over a heated region
of the earth ascends, and its place is supplied by cooler
air rushing in along the surface of the earth. These cur-
rents of air, which rush towards the heated regions, form
what- we know as winds. Their regularity is, however,
greatly modified by the configuration of the land and other
circumstances. It would appear that the influence of the
winds, so far as their effect on the temperature is concerned,
is entirely of a moderating character. The hot region is
cooled by the cool air rushing in upon it, while the heated
air, which ascends, carries the heat with it to some less
favoured region of the earth.
So considerable are the effects produced by the action
of the winds, that the law of the diurnal changes of tem-
perature which we have laid down, and still more the law
of changes of temperature in the course of the year, are
often seriously incorrect. These laws are, therefore, to be
regarded as merely expressing tne mean or average state of
things from which the irregularities produced by the influ-
ence of the atmosphere have been eliminated.
62. The Origin of Right Ascensions. We are now in a
position to explain how the point is to be found on the
equator from which right ascensions are to be measured.
The two most important fixed circles of the celestial sphere
are unquestionably the equator and the ecliptic, for though
of course, at a given place, the meridian or the horizon are of
very great significance, yet these are not fixed circles on the
sphere, as their relation to the celestial objects changes
every moment. As the right ascensions are measured on the
equator, it is natural to make the measurements start from
1 68 Astronomy.
one of the two most remarkable points on the equator, these
being the two equinoxes or the intersections of the equator
with the ecliptic. There still remains a choice as to
which of the two equinoxes shall be selected as the zero o-
right ascension. Custom has settled on the vernal equinox,
through which the sun's centre passes about March 20
every year, when changing its declination from south to
north.
It has already been explained ( 39) that when the sidereal
clock is going correctly, the right ascension of any object
is the sidereal time at which that object crosses the meri-
dian. The determination of the origin from which right
ascensions are measured is, therefore, the same problem as
the setting of the sidereal clock so that it shall show correct
time. We shall, therefore, first direct our attention to the
problem of ascertaining both the rate of the sidereal clock
and its error.
The sidereal day is the interval between two successive
upper culminations of the same star. Let us, for the sake
of illustration, fix our attention upon the bright star Sirius.
The interval between the upper culmination of Sirius on
January i and January 2, 1877, is 24 h o m o s 'oo7 of sidereal
time. Is this interval constant or not ? If we repeat the
observations on March i and 2, we find for the interval
2 3 h 59 m 59 S '985- It is no doubt true that each of these
quantities only differs by an extremely small fraction of a
second from twenty-four hours, but still there is a difference,
Let us now compare the interval between two successive
culminations of another bright star, Vega, with what we have
already found for Sirius. It appears, when the observations;
are made, that the interval between the upper culmination!
of Vega, on January i -and January 2, 1877, is 2 4 h oTn
o s -013.
We have already explained how the successive returns
of the stars to the meridian, in the apparent diurnal motion,
are really due to the rotation of the earth upon its axis. It
Apparent Motion of the Sun. 169
may be reasonably objected to this explanation that, if it
be true, we ought to find the interval between two successive
returns to the meridian the same for all the stars and con-
stant for each one ; yet the observations appear to show a
difference in the case of Sirius and Vega, and that even the
period is not constant in either star. The reply to this
objection is that, if we could see the real culmination of the
stars, the interval between two successive culminations would
be exactly the same for each star, and constant for each
one, but that the apparent culminations, which alone we can
see, are affected by certain sources of error now wholly, or
in great part, understood. When due allowance is made
for the effect of these errors, in modifying the time of culmi-
nation, it is found that the interval between two successive
culminations is the same for each star, and that it is constant
for centuries.
By observing a pair of consecutive culminations of the
same star, the rate of the clock can be accurately determined.
It remains now to show how the hands are to be set so that
the time indicated by the clock shall really correspond with
the right ascension of the celestial bodies on the meridian.
As the right ascension of the vernal equinox is to be zero, it
follows that a correct sidereal clock should show o h o m o s
when the vernal equinox is on the meridian. What the
sidereal clock does actually show, when the vernal equinox
is on the meridian, is the error of the clock. These obser-
vations would be comparatively simple were the vernal
equinox a point so marked that its presence could be
detected in the telescope, or if a fixed star happened to
be situated at the equinox. As these conditions are not
fulfilled, it is necessary to resort to indirect means to ascer-
tain when the vernal equinox is actually culminating.
Let s s' (Fig. 79) be the ecliptic, and M M' the equator
in the neighbourhood of the vernal equinox A. The sun's
centre at culmination on the day previous to its passage
through the vernal equinox is at s, and on the following day
170 Astronomy.
it is at s' ; at some epoch between these two culminations
the centre of the sun must actually have been in the point
A. It will render the
FlG ' 79 ' process of calculation
which is employed more
easily understood, to
give in detail a series
of observations for the
purpose of determining
the error of the clock
on a special occasion.
The instrument used is a meridian circle, and the observa-
tions are presumed to have been made on March 19 and
20, 1877. At the culmination of the sun on March 19, the
declination of its centre was ascertained in the way already
described, and was found to be o 23' 21" -9. The next
day the sun's centre has passed to the north of the equator,
and its declination as determined by the meridian circle
at culmination is +oo' 20" -4. If from s an arc s M of a
great circle perpendicular to the equator be drawn, then
the arc SM is equal to 23' 2i //> 9 > Similarly the arc s' M' is
equal to o' 20" -4. We may for our present present assume
that the triangles A M s and A M' s' are plane triangles, and
as the angles at M and M' are both right angles, the two
triangles are obviously similar. We therefore have the re-
lation
AM : AM'::SM : S'M'.
The arc MM' intercepted on the equator by the two
declination circles through the sun, is the difference be-
tween the right ascensions of the sun on the two con-
secutive days of observation. But this difference is known
from the observations with the meridian circle. It is only
necessary to know the rate of the sidereal clock, and observe
the time when the centre of the sun crosses the meridian on
each of the two days. The difference between these times
Apparent Motion of the Sun. 171
is of course independent of the error of the clock, at present
an unknown quantity. On the days in question, it will be
found that the difference between the two times, after
making allowance for the rate of the clock, is 3 38 S> 52.
This is, therefore, the length of the arc M M' on the equator,
which is of course equal to the sum of the arcs A M and A M'.
We can therefore find the arcs A M and A M' measured in
time, as we know both their sum and their ratio. Thus we
have :
2V 2l"'Q
A M = 3 m 38 S X2 X -A - JT~
23 42"'3
=3 m 35 8 '39.
Similarly we have
Thus we see that the difference between the right
ascension of the sun and the equinox is 3 35 S> 39 on March
19, and o m 3 s -i3 on March 20. In the former case the
equinox comes to the meridian after the sun, and in the
latter the equinox precedes the sun. Let us, then, suppose
that on March 19 the clock showed 23 h 56 49 8 '8i at the
moment of culmination of the sun's centre. Then the clock
would show at the moment of culmination of the equinox
23 h 56m 49*81 + 3 35 s '39= h m 25 8 '2o.
This proves that the clock is o m 2^-20 fast, for if it had
been correct it should have shown o h o m o s at the moment
of culmination of the equinox.
The method of determining the clock error which we have
just described can only be conveniently applied when the
sun is in the immediate neighbourhood of either of the
equinoxes. Of course the time shown by a correct sidereal
clock, when the autumnal equinox culminates, is equal to
twelve hours, so that either equinox will answer for the
purpose.
It is no doubt true that any two complete observations
of the sun at culmination theoretically afford the means of
1 7 2 A stronomy.
determining the error of the clock. For let s and s' (Fig.
80) be the positions of the sun at the moments when the
observations are made, then the declinations s' M ; and SM
are determined by the meridian circle, while with the help
of the clock of which the rate is known the difference in
right ascension of the sun on the two occasions is known.
This difference converted into arc at the rate of 15 to an
hour is equal to M M'. We can therefore construct the
equinoctial point A, by taking an arc of a great circle of the
known length M M', and then drawing the arcs s M and s' M'
perpendicular thereto. We thus determine the points s, s',
and the great circle through s s', and therefore the point A in
which it cuts the line
FlG - 8a M M' is known. We
s' s have therefore reduced
the question to the
problem in spherical
geometry of calculating
the arc A M. This arc
is really the right ascen-
sion of the sun at the time of the first observation, and by
comparison with the observed time the error of the clock
is determined. In the neighbourhood of the equinoxes the
method just described coincides with that of which we have
already given an illustration. The method cannot be
satisfactorily applied except near the equinoxes.
The determination of the sun's declination is, like all
other measurements, open to some degree of error. It is
therefore proper to enquire whether the calculated distances
A M will be much affected by errors in the declination. It
appears that when s and s' are distant from the equinoxes, a
very trifling error in the observed declinations will produce
a very large error in the concluded value of A M. This can
easily be seen by taking s and s' near the solstices, when it
is plain that a very slight alteration in either of the lengths
s M or s' M' will produce a very considerable displacement of
Apparent Motion of the Sun. 173
the ecliptic upon the equator. The alteration in the sun's
decimation on two consecutive days at the solstice is only
about 4" -5 ; consequently an error in one of the declinations
of half a second will be a ninth part of the difference of
declinations, and hence the position of the equinox which is
concluded from the difference of declinations will be exposed
to a very large degree of uncertainty. At the equinox,
however, the sun's declination in a single day changes
through no less than 23' 42' ''$=142 2" -3. But there is no
reason to suppose that the observed declinations will be
more erroneous at the equinoxes than at the solstices. We
may therefore assume at the equinoxes as at the solstices
that the risk of an error of o"'5 is incurred. But this error,
which in the case of the solstices is one-ninth of the total
amount with which we have to deal, is in the case of
the equinoxes little more than the three-thousandth part
(1^-2844-6). We hence conclude that the equinoctial deter-
mination of the zero of right ascension is far less liable to
error than a determination made at any other season of the
year.
It is, however, manifest that, as no clock can be trusted
to run accurately during so long a period as from one
equinox to the next, we must have some practical method
for determining the error of the clock at intermediate times.
In fact, in an observatory, when great accuracy is required,
the error of the clock is of such importance that it requires
to be determined carefully every night on which observations
of right ascension are made, or indeed several times in the
course of a single mght Further, it may be added that
the determination of the error of the clock, by the method
we have described, can only be done in a well-equipped
observatory ; and even then it is a laborious operation, and
liable to be seriously interfered with by the weather at the
critical times during which alone it is possible. On all these
grounds, it is, therefore, obvious that some more practical and
simple method of determining the clock error is required,
1 74 Astronomy.
though it must be distinctly understood that the method to
be described is subsidiary to, and indeed ultimately based
upon, the fundamental method of equinoctial observations of
the sun.
Suppose that on one occasion of the sun passing through
the equinox we have succeeded in determining accurately
the error of the clock. We then observe the transit of a
fixed star with the same instrument at a time when the error
of the clock is certainly known. We can, therefore, find
with great precision the right ascension of the star at the
epoch in question. The process can be repeated for other
standard stars, and then, by observation of any one of these
stars at subsequent epochs, the clock error can be ascertained.
If the equinox remained absolutely fixed on the surface of
the celestial sphere, then the right ascensions of the stars
would remain absolutely constant, except in so far as the
actual proper motion of the star is capable of producing an
appreciable change. The position of the equinox is not,
however, constant, as will be explained subsequently, but
the nature of its motion is so well understood, that when
once the right ascension of a star has been ascertained at
any epoch, its right ascension at any subsequent epoch can
be calculated. We are thus able to predict, with a high
degree of accuracy, the actual right ascensions of a large
number of fundamental stars, and it is by the observations
of these fundamental stars that the errors of the sidereal
clock can be determined. The difference between the
right ascension of the star and the time of transit as shown
by the clock is the error of the clock.
By referring to the ' Nautical Almanac ' the astronomer
will always find a standard star which will shortly come on
his meridian ; he then makes an observation with the
transit instrument or the meridian circle, and determines the
moment of culmination of this star by his sidereal clock.
This is compared with the right ascension given for the
star in the ' Nautical Almanac ' for the day in question, and
Apparent Motion of the Sun. 175
the difference between the two is the error of the clock.
Thus, for example, we have from the * Nautical Almanac '
the following right ascensions of Vega at the corresponding
dates :
1877. January i . . . . . i8 h 32 m 44^85
April 2 18 32 47-28
July 3 18 32 49-46
October 2 18 32 48-13
Take, for the sake of illustration, an observation of the
transit of Vega on July 3, 1877. After the mean of the
results obtained at the different wires had been computed,
and after allowance had been made for the errors of the
instrument, due to level, collimation, and azimuth, it was
found that the clock time of crossing the meridian was
jgh ^ 2 m 5i s - 4 2. But had the clock been correct, it must
have indicated the true right ascension of the star,
which at this date, according to the 'Nautical Almanac,'
is i8 h 32 m 49 s -46. It follows that the clock is too fast,
and that the time which the clock indicates should receive
the correction of i s 'g6 in order to show the true time.
The rate of the clock may be determined by observing the
error which it has at any subsequent period ; for of course
any alteration in the error of the clock can only be due
to the rate.
When the right ascensions of objects are about to be
determined by the transit instrument, the observer com-
mences by ascertaining the errors of his instrument ; and
taking one or two standard stars, he then observes the
unknown objects, and after suitably correcting the observa-
tions for the instrumental errors, he infers the clock
time at which each of the unknown objects crosses the
meridian. During the course of these observations, and
also at their close, the observer is careful to observe a
few additional standard stars ; so that, as he knows accurately
the error of his clock at the commencement of the obser-
176
Astronomy.
vations, and also at their close, and perhaps in some inter-
mediate points, he is then able to determine with great
accuracy the clock error which existed at the moment when
each of the unknown objects was crossing the meridian.
By applying this correction to the observed time, the true
sidereal time of transit is obtained, or, in other words, the
right ascension.
It is generally convenient to express right ascensions
in hours, minutes, and seconds of sidereal time. It can,
however, easily be transformed, when necessary, into degrees,
minutes, and seconds of arc, by remembering that fifteen
degrees of arc correspond to one hour of time.
63. Celestial Latitude and Longitude. When the right
ascension and declination of a celestial body are known,
then the position of the body on the celestial sphere is fully
determined. It will, however, be readily understood that
for the purpose of indicating the position of a celestial body,
other methods are possible besides that of giving its right
ascension and declination. The celestial pole and the celes-
tial equator are the fixed objects of the celestial sphere by
which right ascensions and declinations are measured. In
the same way the ecliptic
and the pole of the ecliptic
can be used for the pur-
pose of measuring what
is called the latitude and
longitude.
Let the circle A B c D
I E (Fig. 81) be the ecliptic,
and A E c E be the equator.
Let P be the pole of the
equator, and K that of
the ecliptic, while e is the
position of a body on the
celestial sphere. Then a great circle P/?, drawn from P
through e, cuts the equator in a point a, and the arc A a is
Apparent Motion of the Sun. 177
the right ascension of e, while e a is its declination. If,
instead of taking p. the pole of the equator, we took K, the
pole of the ecliptic, and drew the arc K , which cuts the
circle A B in b, then the position of the point e could be
completely specified by knowing the length of the arc A $,
measured along the ecliptic from the equinox, and also the
arc b , measured perpendicularly to the ecliptic. These
quantities are known as the longitude and the latitude
respectively. The latitude and longtitude of a celestial
body bear to the ecliptic precisely the same relations which
the declination and right ascension bear to the equator.
The longitudes are measured round the ecliptic from
o to 360 in the same direction in which the apparent
motion of the sun is performed. The latitude of a point
on the ecliptic is, therefore, zero, while its longitude is
equal to the arc intercepted on the ecliptic between the
point and the equinox. When the right ascension and
declination of a celestial object have been observed, then
its latitude and longitude can be obtained by calculation.
64. The Sun's Path in Space. What we have ascer-
tained with respect to the apparent motion of the sun
shows us that its centre moves along a great circle of the
celestial sphere. It is, however, necessary to observe that
this does not necessitate that the actual path of the sun's
centre, through space, shall be performed in a circle, of
which the earth is centre. We have, hitherto, avoided any
reference to the actual distance at which the sun may be
situated when at the various points of its path. If these
distances were always the same, then no doubt the path of
the centre of the sun would really be a circle, but the
apparent motions of the sun, so far as they have been ex-
plained up to the present, are quite consistent with the
supposition that its path is widely different from a circle.
We have shown that the centre of the sun is always to b^e
found on a great circle of the celestial sphere which is
called the ecliptic. This has been proved t>J observing the
N
178 Astronomy.
right ascension and declination of the sun at different
periods, and then plotting the observed places on the
celestial globe, or making calculations which are equivalent
thereto. But merely observing the right ascension and
decimation of an object does not define the actual position
of an object in space ; it merely points out the direction in
which the object is seen. In fact, any number of objects
situated at even enormous distances apart will have the
same right ascension and declination, provided that they all
lie upon one straight line which is directed to the earth.
All, therefore, that our observations of the sun have hitherto
shown us, is the direction in which the sun was seen on
each occasion. It therefore appears that the centre of the
sun is always to be seen in a direction which can be found
by joining the earth's centre to a point on the ecliptic. As
the ecliptic is a great circle of the celestial sphere, of which
the earth's centre is the centre, all the lines drawn from the
centre to points on the ecliptic will lie in a plane, and,
therefore, the centre of the sun must always move in the
same plane which passes through the centre of the earth. All,
therefore, that the observations hitherto described have taught
us, is that the apparent motion of the sun is performed in
this plane. The actual form of the apparent path might,
for anything we have yet proved, be any closed plane curve
which contained the earth in its interior.
To ascertain the actual shape of the curve, it is necessary
to know the distance at which the sun is situated at any
point of its path, as well as the right ascension and declina-
tion which point out its direction. We shall subsequently
explain the methods by which the actual distance of the sun
is to be determined. For the present, it will be sufficient
to point out how the relative distances of the sun at different
seasons can be ascertained.
It will of course be admitted that the actual dimensions
of the sun are constant, so that any changes in his appar-
ent dimensions, or the angle which the diameter of the sun
Apparent Motion of the Sun. 1 79
subtends at the earth, is to be attributed to a change in the
distance between the earth and the sun. At a superficial
glance the dimensions of the sun appear to be the same at all
seasons of the year ; it would, therefore, appear at first sight
as if the distance from the sun to the earth were constant,
so that consequently the apparent path of the sun must be
a circle. When, however, the apparent dimensions of the
sun are accurately measured by means of the micrometer we
have already described, it is found that though the dimen-
sions are nearly constant, yet that there is an appreciable
degree of variation, according to a regular law which is given
in the following table :
Apparent Diameter of the Sun.
Jan. i
Feb. i .
March i
April i .
May i .
June i .
It appears from this table that the apparent diameter of
the sun attains its greatest value at the end of December and
the beginning of January, its value being then 32' 36" '4.
After that date the apparent diameter begins to diminish,
and reaches its lowest value about the ist of July, being
then 31' 32 //i o ; after this it commences to increase again, so
as to regain its maximum value in the course of the next
winter. It appears from n that the apparent diameter
is inversely proportional to the distance, and hence from
this table we can conclude, with some degree of accuracy,
the distances which the sun has on the different dates.
Thus it appears that the sun is closest to the earth in mid-
winter, and most distant from the earth at midsummer, the
E wf io of the greatest and least distance being
32' 3 6//> 4
32' 3^"'4
July i . .
3i' 32"'
32 31-8
Aug. i . .
31 35-8
32 20-6
Sept. i . .
31 47-0
32 4-0
Oct. i . .
32 2-6
31 48-0
Nov. i . .
32 19-2
31 36-4
Dec. i . .
32 31-6
31' 32 //< o 1892*0
N 2
i So
Astronomy.
The distance of the sun from the earth, therefore, changes
in a year through about one-thirtieth part of its mean
value. It is thus plain that
the orbit of the sun cannot
be accurately a circle with
the earth situated at its
centre. The variation in the
distance at the different
seasons can, however, be ex-
plained to a certain extent
by the supposition that the
orbit of the sun is a circle,
if we suppose that the earth
is not situated at the centre
of the circle. Let A s B
(Fig. 82) represent the orbit of the sun on this hypothesis,
let o be the centre of the circle, and let E be the position
of the earth. If, then, the distances E A and E B be con-
nected by the relation =19^ -. the sun when at A or
EB 1892-0
at B would exhibit to an observer at E an apparent semi-
diameter conformable to what observation shows to be the
actual value ; the ratio of the distance E o to o A can be
easily found, for we have obviously
AO + EO _ 1956-4
AO EO 1892-0*
whence - = ~ very nearly.
AO 60
To test this supposition with regard to the motion of the
sun, we shall calculate the apparent diameter of the sun on
this hypothesis at an intermediate position p. We shall
take the point P so that the angle A E p is a right angle. We
have then, from a well-known proposition in geometry
= EA X EB.
Apparent Motion of the Sun. 181
If we denote the distance E A by 1956*4, then we have
E P 2 = 1956*4 X l892'O,
whence EP=i923'8.
Assuming, therefore, that the apparent motion of the sun
can be faithfully represented by supposing the orbit to be a
circle, in which the earth is situated excentrically at a
distance from the centre equal to the sixtieth part of the
radius, we must have for the apparent diameter at P the
relation
diameter at P 1956*4
diameter at A "" 1923*8,
whence we deduce the diameter at P to be i923' /t 8
=32' 3 //< 8. The sun arrives at P about three months after it
leaves A, and its diameter as given by the table on April i is
32' 4 // *o. It would therefore seem that the apparent
changes in the sun's magnitude could be fairly represented
by the suppositions we have made. It will, however, be
shown subsequently that the orbit is not quite circular, but
that it is really an ellipse which approaches so closely to a
circle that the difference cannot be satisfactorily established
by the observations we have been describing.
65. Velocity of the Sun. The rate at which the sun
performs its motion in its orbit must next engage our atten-
tion. In the course of an entire year, the sun returns to the
point of the celestial sphere from which it started, and
therefore in a little more than 365 days must have described
an arc of 360. The average daily motion of the sun must
therefore be somewhat less than one degree. But it is found
that the rate of motion is not constant The sun at certain
parts of its path is moving more rapidly than at other parts.
If we observe the angular distance through which the centre
of the sun actually moves on certain days of twenty-four
hours distributed through the year, we shall find that the
Date.
Arc described Date.
in one Day.
Jan. 30 .
. i o'53"-8
July 29
March i .
i o 9*i
Aug. 28
March 31 .
. o 59 9-6
Sept. 27
April 30 .
. o 58 ii*5
Oct. 27
May 30 .
. o 57 29-0
Nov. 26
June 29 .
. o 57 1 1 -8
Dec. 31
1 82 Astronomy.
alterations in its rates of motion are very appreciable. This
will be made clear by the following table.
Arc described
in one Day.
'. o 57' 2 3 "- 3
. o 58 07
. o 58 56-9
o 59 57'4
i o 46'6
I I IO'I
It appears from this table that the sun attains its greatest
arcual velocity about the end of the year, when it moves
over no less than i i' io' /- i in a day of twenty-four hours.
This, it will be observed, corresponds with the season at
which the apparent diameter of the sun attains its greatest
value. The smallest value of the sun's apparent arcual
velocity is on July i, when the distance moved over in one
day is 57' n"'5. This date corresponds with that at which
the apparent diameter of the sun has its smallest value.
This coincidence suggests that the sun may be moving
uniformly, and that the variations in its apparent velocity are
only due to the circumstances of the eccentric position
which the earth occupies in the orbit. It is easy to test
this supposition by the table which we have just given. If
the sun were really moving uniformly, then the apparent
velocity would be inversely proportional to its distance.
If, therefore, we assume the orbit to be that represented
in Fig. 82, we must have
E_A_ __ i i' io"-i .
E B.~" 57' n"'5 '
from this it is easy to compute that
EO I i
- =?= very nearly.
AO 30
This result is fatal to the hypothesis on which the cal-
Apparent Motion of the Sun. 1 83
dilations were commenced. If we suppose that the sun
were to move uniformly in a circle in which the earth was
placed eccentrically, then, according to the observed varia-
tions of the sun's apparent diameter, the distance of the earth,
from the centre of the circle, should be the sixtieth part of
the radius ; according, however, to the observed values of
the arcs through which the sun moves at the seasons of
greatest and least apparent velocity, the distance of the
earth from the centre of the circle should be about the
thirtieth part of the radius. These two results are so in-
consistent, that we are obliged to discard this hypothesis
with respect to the apparent motion of the sun. If the sun's
motion be uniform, it cannot be circular ; or if it be circular,
it cannot be uniform : as a matter of fact the apparent motion
of the sun is neither circular nor uniform.
The real path in which the sun appears to move, as well
as the law according to which its velocity changes in different
parts of its orbit, can be determined by what are known as
Kepler's laws. These laws were originally discovered by
observations of the planet Mars, and we shall return to their
consideration on a subsequent occasion. For our present
purpose it will be sufficient to assume
ist. That the apparent path of the sun around the earth
is a plane ellipse with the earth situated in one of the foci.
2nd. That the area described by the radius vector,
drawn from the earth to the sun, in a given time, is propor-
tional to that time.
These two laws have been so abundantly verified that
we may adopt them without the slightest hesitation. By
their aid it will be very easy to render a satisfactory account
both of the variations in the apparent diameter of the sun
and the alteration in its velocity.
Let M b N (Fig. 83) be the ellipse in which the sun moves,
let M N be the major axis of this ellipse, and let T be the
focus in which the earth is situated. When the sun is at
1 84
Astronomy.
N, its distance from the earth attains its greatest value and
the angular dimensions are a minimum. On the other
hand, when the sun is at M, the distance is a minimum, and
therefore the angular diameter is a maximum. By the
method we have already explained, we can deduce the rela-
\
\
tive magnitudes of T N and x M, and thence the ratio of o T
to o N when o is the centre of the ellipse. This is called
the eccentricity of the ellipse, and, as already explained, it is
equal to i -f- 60.
The elliptic motion can therefore explain the alterations
Apparent Motion of the Sun. 1 8 5
in the apparent diameter of the sun. It remains to
be shown how the second law, discovered by Kepler,
accounts for the changes in the velocity of the sun's
motion.
Let M' be the position of the sun when near one extremity
of the ellipse, and N' a position near the other extremity. Let
these points be so chosen that the time occupied by the sun
in moving from M to M' is equal to that required to move
from N to N'. According to Kepler's second law, the areas
swept over on each occasion by the radius vector will be
proportional to the time, and consequently the area M T M'
will be equal to N T N'. This being the case, it is obvious
that the arc M M' must be considerably longer than the
arc N N' in order that the shaded areas represented in the
figure shall be equal. It thus appears that the sun, when
in the neighbourhood of M, must move more rapidly than
when in the neighbourhood of M'. We can also bring this
easily to the test of numerical calculation. If we take the
points M' and N' so near to M and N respectively that the arcs
M M' and N N' may be practically considered as straight
lines, then from the equality of areas we have
M M' X T M = N N' X T N,
whence
T M T N
But the two first quantities denote the angles M T M' and
N T N' when these angles are both indefinitely small, and
hence
angular velocity at M __ T N 2 m
angular velocity at N T M 2 '
but we have already seen that - = ,
T M 59
and hence angular velocity at M== 16
angular velocity at N 15
1 86 Astronomy.
This closely coincides with the ratio of the greatest
and least angular velocities actually found, and it can also
be shown that the sun's angular velocity at any other points
of its path is accurately expressed by this law.
66. Changes in the Length of the Seasons. The elliptic
path of the sun lies, of course, in the plane of the ecliptic.
This plane cuts the celestial sphere in a great circle A B c D
(Fig. 83). In this figure A c is the line of equinoxes and B D
the line of solstices. These lines are accurately drawn with
regard to the ellipse, and it will be noticed that the major
axis of the ellipse is nearly coincident with the line of
solstices. When the sun is seen in the vernal equinox, it is
referred to the point a on the celestial sphere, though it
really occupies the position A. In moving from the vernal
equinox to the summer solstice the sun moves from a to b
along its real path. The duration of spring is therefore
equal to the time the sun takes to go from a to b. In the
summer the sun travels from b to c, in autumn from c to d,
and in winter from d to a.
A curious inequality in the length of the different seasons
follows from the eccentricity of the sun's orbit. It will be
noticed that during the spring and the summer the sun is
in that portion of its path where it moves least rapidly, while
during the autumn and the winter it moves most rapidly.
The changes in the lengths of the seasons which are thus
produced are not considerable, though still sufficient to be
appreciable. The true lengths of the seasons when this cir-
cumstance is attended to are :
Days Hours Min.
Spring . . . . 92 20 59
Summer . . . 93 14 13
Autumn . . . 89 1 8 35
Winter. . . . 89 o 2
The duration of spring and summer taken together is
The Structure of the Sun. 1 87
found to be 186 days n hours 12 minutes, while the dura-
tion of autumn and winter together is 178 days 18 hours
37 minutes. During spring and summer the sun is in the
northern hemisphere, while in autumn and winter he is in
the southern hemisphere. It therefore appears that in each
year the sun remains about eight days longer in the northern
hemisphere than in the southern.
CHAPTER V.
THE STRUCTURE OF THE SUN.
67. Dimensions of the Sun. The sun, though really a
globe, appears to the unaided eye in the form of a circular
disc, of which the diameter subtends at our eyes an average
angle of about 32'. The mean distance of the sun from the
earth, as concluded from various data, is between 92,200,000
and 92,700,000 miles. Adopting a mean value, it is easy to
calculate that the diameter of the sun is about 860,000
miles that is, about no times the diameter of the earth.
The volume of the sun is therefore about 1,330,000 times
as great as the volume of the earth. A distance of 447
miles on the surface of the sun subtends an angle of one
second at the earth. A spider line used in a large tele-
scope will cover a portion of the sun which may be a
quarter of a second in breadth : thus a strip of the sun's
surface over 100 miles wide is hidden behind the spider
line. The diameter of the earth subtends at the sun an
angle of about 17" '6. To subtend an angle so small as
this, a globe one foot in diameter would have to be moved
to a distance of upwards of two miles. The radius of the
earth subtends an angle of 8" '8.
1 8 8 A stronomy.
68. Sun Spots. When the sun is observed through a
telescope, proper precautions having first been taken to
diminish by means of coloured glass, or some similar con-
trivance, the intense brilliancy of its image, a remarkable
phenomenon is often noticed. The brilliant surface of the
sun is often found marked over with black spots such as are
represented in Fig. 84. The central portion of the spot is
intensely dark, and it is surrounded by a margin which, though
much darker than the general surface of the sun, is not nearly
so dark as the centre of the spot. Sometimes the spots attain
very considerable dimensions : occasionally a spot will attain
FIG. 84.
a diameter of thirty or forty seconds. It will thus be obvious
that the real dimensions of the spots are enormous, because,
as a second corresponds to a distance of 447 miles, it is
evident that a spot thirty seconds in diameter must have
a real diameter of 13,400 miles. At their first appearance
the spots are generally found on the eastern edge of the
sun ; they then pass over the surface of the sun, and in
about fourteen days they disappear on the western side.
From observations of these spots we are led to the
very remarkable conclusion that the sun is actually rota-
ting. It might at first be supposed that the spot was a
The Structure of the Sun. 1 89
body situated above the surface of the sun, and revolving
around the sun ; but this supposition is inconsistent with
the observed facts. Let s represent the sun, let T be
the position of an observer on the earth, and suppose
that a spot is caused by a body revolving around the
sun in the orbit ABC. When the object reaches A, the
observer will for the first time see the spot on the surface
of the sun, and it will continue visible
on the surface until it arrives at B. FIG 84A.
During the rest of the journey of the
object through the arc B c A it will not ^ *x
be visible on the surface of the sun. The /
object will therefore be projected against j
the sun's disc while traversing the arc \
A B, but will not be so projected while
traversing the arc B c A. Assuming, j
therefore, that the object moves with ap- \
proximate uniformity, and observing that i
the arc A B is only a small part of the
total orbit, it follows that the time during i
which the object is invisible must greatly \
exceed the time during which it is visible. ;
This, however, is not the case. Each spot \ j
is visible, projected on the sun's surface, ', j
for a period of fourteen days, and it re- \l
mains invisible for the same period. This ii
can only be explained by the supposition
that the spot is actually on the sun himself.
As the sun always appears circular, and as it rotates
upon its axis, the actual shape of the sun must, undoubtedly,
be spherical. The most careful observations have not
afforded reliable indications of any ellipticity in the figure
of the sun.
When a spot is carefully observed for some days it is
often seen to undergo changes in its form and size which
190 Astronomy.
cannot be accounted for by the foreshortening which is
due to its approach to the limb of the sun. Occasionally
a spot is seen to become smaller and smaller or, indeed, to
disappear altogether, while new spots are often formed in
places where previously no trace of a spot existed. The
changes in the form of a spot generally take place gradu-
ally, but sometimes this is not so, and marked changes have
occasionally been noted in the lapse of a few hours or less.
The apparent time of rotation of the sun on its axis, as
concluded by the reappearance of the spot, is therefore liable
to be affected by the actual motion of the spot. An accurate
determination of the periodic time of the sun's rotation is,
therefore, at best, only to be made by taking the mean re-
sult of a number of observations made with spots on
different parts of the surface. This is the more neces-
sary because spots near the sun's equator give a shorter
period of rotation than those in higher latitudes ; the equa-
torial regions appear to rotate in 25 days, those at latitude
20 in 25! days, those at latitude 30 in 26^ days.
The spots are not distributed uniformly over the surface
of the sun. They are principally found on two zones, one
on the northern hemisphere and the other on the southern.
These zones lie between about 10 and 35 of heliocentric
latitude.
The numbers of the spots on the surface of the sun
undergo regular periodic changes in amount. Schwabe, who
observed the sun regularly, from the year 1826 to 1868,
discovered that the sun spots have very well marked periods
of maxima and minima, which succeed each other at inter-
vals of about eleven years. The number of spots, after a
minimum, commences to increase rapidly, until in three and
a half years the maximum is reached. The decline to the
next minimum takes place more slowly, and a period of
seven and a half years is required. The average period is
1 1 -i years, but with frequent irregularities as to the time of
The Structure of the Sun. 191
maxima. It is a remarkable fact that the phenomena of
terrestrial magnetism are in some way connected with the
state of the sun's surface. It has been shown that certain
magnetic disturbances recur at regular intervals, and that
the period of these disturbances is equal to the period in
the frequency of sun spots, so that the maxima and minima
of these solar and terrestrial phenomena occur at the same
moments.
69. The Nature of Sun Spots. The telescope reveals
a great many interesting details on the surface of the sun.
In order to prevent the observer's eye from being injured by
the excessive glare of the solar rays some special kind of
eye piece must be used, as described above in 52. When
seen under a high magnifying power the surface of the sun
appears to consist of a somewhat fainter background dotted
over with brilliantly luminous grains or flakes, several hun-
dred miles in diameter, and of irregular shape. They are ap-
parently luminous clouds formed by condensation from the
substances which in the lower strata of the sun's body exist
in a gaseous form. Near the limb of the sun the ' photo-
sphere' or visible surface is fainter, and certain brilliant
patches or streaks called facultz are therefore more readily
seen near the limb than near the middle of the disc.
They occur most frequently in the neighbourhood of sun
spots, but are on a higher level than these, and are
therefore less obscured by the absorption of light due to
the solar atmosphere. The spots generally consist of two
well-marked portions the central part or nucleus, which
appears black by contrast with the general brilliancy of
the sun (though in reality it is brighter than a calcium
light), and the outer portion or penumbra, formed of thread-
like streaks arranged radially. Occasionally a bright bridge
spans over the nuclei of more irregularly shaped spots. The
diameter of the nucleus sometimes reaches a size six or
eight times the diameter of the earth.
Astronomy.
Sun spots are apparently cavities in the surface, filled
with gases or vapours at a lower temperature than the
neighbouring regions of the surface. In 1769 Wilson of
Glasgow observed a spot the nucleus of which was nearly
FIG. 85.
circular, while the penumbra was also very nearly a circle
concentric with the nucleus. Wilson watched this spot
as it gradually drew near to the edge of the sun by
reason of the rotation of the sun. He observed that the
penumbra soon ceased to be symmetrical, and that while
the portion of the penumbra nearest the centre of the
The Structure of the Sun. 193
sun's disc gradually diminished, that on the other side
preserved very nearly constant dimensions. When the spot,
after an interval of about a fortnight, reappeared on the
eastern limb of the sun, the series of changes were re-
peated in the inverse order, the nucleus being at first
very eccentricaKy placed, and the penumbra on the side
away from the limb growing by degrees, until when the
spot regained the centre of the disc the nucleus was
again seen to be symmetrical with respect to the penum-
bra. These observed alterations could only be attributed
FIG. SSA.
!D
I I
to the effects of perspective (as the reader
will readily see by holding a teacup with the
bottom blackened in various positions before
him), and seemed to prove that the nucleus
was the bottom of a cavity with sloping sides.
This foreshortening seems, however, when observations
of spots extending over many years are examined, to be
by no means an everyday occurrence, as the majority of
spots do not show it ; but the conclusion which was per-
haps somewhat hastily drawn from Wilson's few observa-
tions, viz., that the nuclei of sun spots are on a lower level
than the general surface of the photosphere, seems to be still
admitted by most observers. The theory of the origin of
sun spots which appears to accord best with the observed
phenomena, and which has been ably advocated by Professor
J. Norman Lockyer, assumes a spot to represent a downrush
o
194 Astronomy.
of cooler matter from the upper regions of the solar atmo-
sphere into the region of luminous clouds forming the
photosphere.
70. The Solar Spectrum. The spectroscope shows
the spectrum of the sun to be continuous, but crossed by
a great number of dark ' Fraunhofer lines ' caused by
absorption in the lower regions of the sun's atmosphere
(see Chapter I., 19). By a simple arrangement the
spectrum of any chemical element in the state of vapour
may be viewed in the same field with the sun spectrum,
whereby the coincidence of the bright lines of the vapour
with some of the dark lines of the sun reveals the ex-
istence of the vapour in question in the atmosphere. In
this way (either by visual observations or by photograph-
ing the two spectra) the existence of various elements in
the sun has been demonstrated, e.g., hydrogen, iron, cal-
cium, manganese, sodium, magnesium, and others. But a
number of elements, which on the earth are of great im-
portance, are missing, such as sulphur, phosphorus, nitro-
gen, and probably also oxygen. As suggested by Lock-
yer, these substances may, all the same, exist on the sun,
as they may not be truly 'elements,' but composite
substances which on the sun are dissociated by the
intense heat.
The atmospheric layer in which the dark absorption
lines of the spectrum originate should, of course, if
observed without the luminous background of the sun,
give a spectrum of the very same lines bright instead of
dark. This has been seen during several total eclipses
of the sun, at the moment when the moon has just covered
the whole disc of the sun but not yet the atmosphere
immediately outside the limb. The dark lines were then
seen to be suddenly reversed, i.e., changed into bright lines,
which again faded away gradually after being only visible for
about two seconds, after which this reversing layer was also,
The Structure of the Sun. 195
covered by the advancing moon. The existence of this re-
versing layer as a separate stratum is, however, doubted by
many, as the extremely short time during which the lines
have been seen reversed has not enabled the observers to
ascertain whether all the lines were reversed at the limb or
only some.
The spectrum of a sun spot shows the ordinary solar
spectrum much diminished in brightness, while some of the
dark lines are more or less widened and increased in inten-
sity, showing increased absorption by some of the substances
of which the spot is composed. It is of special interest that
most of the lines of any element are not affected in this
manner, but only a few, a circumstance which will doubtless
eventually be of great importance for the advancement of
our knowledge of the constitution of the sun. Mr. Lockyer,
who has devoted much time to observations of spot spectra,
also finds a certain connection between the periodicity in
the number of sun spots and the number of lines in their
spectra which are subjected to this widening.
In the spectrum of a spot or its immediate neighbour-
hood we occasionally see some of the lines bent or broken.
This is caused by the violent motion of the gaseous matter
of the spot in the direction to or from the observer. When
a source of light is very rapidly approaching the observer
the number of waves of light reaching him every second is
increased, and the length of these waves is therefore dimin-
ished, and the reverse takes place when the source of light
is receding from the observer. Therefore, as the wave length
is shortened the refrangibility of a certain ray in the solar
spectrum is increased when the matter emitting this ray is
moving towards us with a considerable speed, and the line
will seem to be displaced by a very minute quantity towards
the violet end of the spectrum. Similarly, if the matter
giving rise to the line is moving away from us with great
velocity, the line will become slightly displaced towards the
02
1 96 A stronomy.
red end of the spectrum (Doppler's principle). The actual
velocity of the matter can be determined by measuring the
amount of displacement, and we frequently find masses of
gas, generally about the edges of a sun spot, moving up or
down with a speed of from thirty to fifty miles a second,
while a speed of two or three hundred miles is occasionally
met with. It is deserving of notice that it sometimes hap-
pens that not all the lines due to a certain element, such as
iron, are distorted in a certain region of the sun, but only
some, and this might be readily explained if we accept
Professor Lockyer's idea that the laboratory spectrum of
iron really consists of several superposed spectra of the
constituents of what has hitherto been supposed to be an
element.
The rotational speed of the solar surface may also be
determined by measuring the displacement of lines on the
east and west limbs of the sun, as in consequence of the sun's
rotation the eastern limb is moving towards us and the
western away from us with a velocity of about i J mile a
second. The displacement is of course a very minute one,
and the observation therefore very difficult, but good results
have been found by several observers, especially by Duner.
The comparison between the rotation as measured spec-
troscopically by this observer and as obtained from sun
spots shows a good agreement, the spectroscope also bring-
ing out the variation of the velocity of rotation with the
latitude.
71. The Chromosphere and the Prominences. During
total eclipses of the sun a number of scarlet cloudlike
objects are generally seen about the edge of the sun's disc
which are invisible in full daylight owing to the overpower-
ing glare of the sun's light. They were first spectroscopi-
cally observed during the eclipse in India in 1868, when
they were found to be gaseous and chiefly composed of
hydrogen, That they would exhibit a gaseous spectrum had
The Structure of the Sun. 197
been expected for some time, and was at last found by
Lockyer immediately before the news of the eclipse observa-
tions reached Europe. One of the observers of the eclipse
(Janssen) had also succeeded in seeing the spectra of these
so-called prominences in full daylight, after the eclipse had
shown him how bright the lines were. A spectroscope of
sufficiently great dispersive power weakens the spectrum of
our own brightly illuminated atmosphere without making
the lines in the spectra of these solar appendages fainter.
If the slit of the spectroscope is opened wide, the observer
will instead of bright lines (or images of the slit) see a
number of differently coloured images of the prominences,
which in this manner may be studied at any time. The sun
is seen to be surrounded by a thin atmospheric layer (about
five to ten thousand miles thick), the so-called chromosphere
consisting chiefly of hydrogen, from which the great clouds
known as prominences often rise to heights of several
hundred thousand miles. It is particularly the eruptive
prominences which attain such heights ; they are also
remarkable by showing in their spectra a number of
metallic lines besides those of hydrogen. They occur only
in the spot zones, and generally only near active and
rapidly changing sun spots, while the quiescent or cloudlike
prominences, which are composed almost only of hydrogen
and helium, occur on all parts of the sun. The intimate
association between these eruptive prominences and the sun
spots shows that the latter must be connected with violent
disturbances at the surface of the sun. 1
In 1868 a yellow line was discovered by Prof. Lockyer
in the spectrum of the chromosphere and prominences
1 We may specially refer to Professor Lockyer's work on the
Chemistry of the Sun, in which will be found a general account of the
subject, while the fuller details of the solar work on which Professor
Lockyer has been engaged for so many years will be found in the
Phil. Trans, and Proceedings of the Royal Society.
198
Astronomy.
which indicated the presence of some substance in the sun
unknown on the earth. This sun element was appropriately
called helium. In 1895 it was discovered by Ramsay that
a certain rare mineral, cleveite, could be made to yield a
gas which, though quite unknown to terrestrial chemistry,
gave a spectral line identical with that of helium. We thus
have the unique fact in the history of science that an
element existing on the earth in many different substances,
though no doubt in small quantities, was first discovered
not by terrestrial chemists but by astronomers, who found
this element in the sun 93,000,000 miles away.
72. The Corona. The chromosphere and the pro-
minences are not the only solar appendages which become
FIG. 8".
conspicuous during a total eclipse. Even to the naked eye
the eclipsed sun is seen to be surrounded by a brilliant halo,
which is brightest along the limb of the sun, where it is of a
greenish or grey tinge, and fades away in all directions, often
with long streamers exceeding the radius of the sun in length.
Fig. 86 gives a general idea of the appearance of this
The Structure of the Sun. 199
corona as seen by Swift at Denver, Colorado, during the
total eclipse of July 29, 1878. The corona varies much
both in brightness and general appearance at different
eclipses, and observers also frequently differ much in the
drawings which they make of the phenomenon, for which
reason photographs of the corona form a safer basis on
which to build investigations of its nature. Attempts have
been made to render the corona visible outside an eclipse
by means of photography, but hitherto without success.
The spectrum of the corona consists of a continuous
spectrum, probably due to sunlight reflected from matter in
the form of dust or fog, and a bright line in the green part
of the spectrum, together with the hydrogen lines.
73. Constitution of the Sun. The low density of the
sun, only one and a quarter times that of water, as well as
the exceedingly high temperature, point to the nature of
the body of the sun being gaseous, though the intense heat
and the enormous force of gravity must render the gaseous
substances very dense and viscous, like pitch. Even the
enormous pressure to which the matter in the interior of
the sun must be subject cannot render the gases liquid, as
the temperature cannot possibly fall below the 'critical
temperature ' of the various gases, above which no amount
of pressure will change a gas into a liquid. The atmosphere
of the sun must be of very great extent, the corona repre-
senting to some extent the outermost portions of it, though
it must be chiefly caused by meteoric matter or matter
ejected from the sun and not in a gaseous state. But the
chief difficulty at present is the nature of the upper layers of
the photosphere and of the envelope which causes the dark
Fraunhofer lines. According to Mr. Lockyer's view, the
atmosphere consists of distinct strata, in the lower ones of
which only those constituents of our terrestrial ' elements '
are found which can resist the greater heat of these regions,
while the elements are in process of ultimate formation
in the upper and cooler strata, where those lines which
20O
Astronomy.
correspond to the more complex combinations are pro-
duced. The luminous ' clouds ' of the photosphere which
in our photographs appear as * rice grains ' or ( willow leaves '
are very probably (as suggested by Dr. Johnstone Stoney)
formed of carbon, a substance which is of low vapour
FIG. 86A.
density, but not capable of existing as vapour in the cooler
parts of the sun's atmosphere, while it is volatile at the high
temperature and pressure which exist at the surface of the
sun.
74. Zodiacal Light. From February to April the phe-
nomenon known as the zodiacal light may be seen in the
Motion of the Earth around the Sun. 20 1
west shortly after sunset, and in the autumn before sunrise.
The zodiacal light is a faint luminosity of a triangular shape,
shown by the shaded portion of the adjoining figure (Fig.
86 A). As the sun gradually descends lower below the
horizon, this phenomenon disappears ; it is noticed that the
direction in which the light is most extended coincides with
the ecliptic, and that consequently the sun is situated with
regard to the zodiacal light in the manner shown in the
figure. It is generally supposed that the matter whose
luminosity gives rise to the zodiacal light is in the shape of a
thin disc, and that it is a sort of appendage placed around
the sun, though possibly extending even further than the
earth's orbit. Whatever be the materials of which this ob-
ject is composed, they must be of extreme tenuity, inasmuch
as faint stars are easily visible through its entire thickness.
Probably it is made up of an immense number of minute
bodies reflecting the sunlight, as the spectrum is a faint
continuous one.
CHAPTER VI.
MOTION OF THE EARTH AROUND THE SUN.
75. Revolution of the Earth. It has been already
shown, in discussing the apparent diurnal revolution of the
heavens, that the true explanation of that motion is to be
sought in the fact that the earth revolves on its axis, and
thus produces the same effect as would be observed if the
celestial sphere actually rotated in the opposite direction.
We have now to consider whether the apparent annual motion
of the sun around the heavens is to be regarded as real, or
whether it may not also be found to arise from an actual
movement of the earth. In the first place it is to be noted
2O2 Astronomy.
that the apparent movement of the sun could be explained
by the supposition that the earth is revolving around the
sun, and not the sun around the earth ; this may be rendered
clear by an illustration. Imagine a large open circular space
to be entirely surrounded by a forest, and in the centre of
the space a single tree to remain. If you were to walk round
this tree, you would at each point of your path see the tree
projected against the trees of the forest, but the position of
the projection will be continually changing, and by the time
you have regained your original position, the tree will in
succession have appeared in line with each of the trees in
the ring bounding the open space ; if you could be uncon-
scious of your own motion, the observed facts would suggest
that the central tree was actually revolving round you. To
apply this illustration to the present case, we suppose the
central tree to be analogous to the sun, and the distant trees
of the forest to be analogous to the stars. What we actually
observe is the apparent motion of the sun among the stars,
but this is really due to the motion of the earth, of which
we are unconscious.
It will be easy to show that the apparent elliptic orbit of
the sun about the earth in one of the foci could really be
produced by an actual motion of the earth in an elliptic
orbit, with the sun in one of the foci. In considering this
subject we may overlook the effect of the earth's rotation
upon its axis, because the effect of this rotation has already
been completely examined. Let s, s', s", s'" (Fig. 87) repre-
sent the apparent orbit of the sun around the earth in the focus
T. Suppose the ellipse be rotated through two right angles
around the point x, which bisects ST, until the ellipse
assumes the position T, T', T", T"'. Then the lines T s', T s",
T s"', in the original ellipse, will be transferred to the positions
s T', s T", s T'". Since the ellipse has been turned round
through two right angles, every straight line in the figure will
also have been turned through two right angles, and con-
sequently each line in the second ellipse will be parallel to the
Motion of the Earth around the Sun. 203
corresponding line in the first ellipse. It thus appears that the
lines T s', T s", T s'" will be respectively parallel to the lines
s T', s T", s T'" ; observing that the stars are enormously
distant compared with the dimensions of the ellipses now
under consideration, then the apparent motion of the sun
among the stars can be explained by supposing either that the
sun moves in the orbit s, s', s", s'", around the earth T at rest,
or that the earth moves in the orbit T, T', T", T'", around the
sun s at rest. For example, when the sun is at s', and the earth
at T, the sun appears to have a certain position with respect
to the fixed stars ; but this position will be the same as if the
sun had been at s, and the earth at T' for as the lines T s'
FIG. 87.
and T'S are parallel, and as the celestial sphere may be re-
garded at an infinitely great distance, the two lines T s' and
T' s will really intersect the celestial sphere in the same
point. In the same way the apparent position of the sun at
s", seen from the earth at T, coincides with the position in
which the sun at s is seen from the earth at T", and simi-
larly for the other points of the orbit. It is thus equally easy
to explain the apparent movements of the sun by the hypo-
thesis that the sun is at rest in the focus, and that the earth
moves around the sun in an ellipse, or by the hypothesis that
the earth is at rest in 'the focus, and that the sun moves
round the earth in an ellipse. It is, indeed, easy to see that
2O4 Astronomy.
on either supposition the law of the description of equal areas
in equal times will be fulfilled. To decide which of these
two hypotheses we shall accept, we must introduce other
considerations.
It is in the first place to be observed that the diameter
of the sun is more than one hundred times as large as the
diameter of the earth, and that the bulk of the sun is
stupendously greater than the bulk of the earth. It there-
fore seems more natural that the earth, being a small body,
should revolve around the sun, being a large body, rather
than that the converse should take place.
There is, however, other evidence on this subject, derived
from a study of the planets. Let us take, for example, the
planet Venus. Shortly after sunset at the proper season, this
object appears like a brilliant star in the west. On sub-
sequent evenings the angular distance between Venus and
the sun gradually increases, until the planet reaches its
greatest elongation, when it is about 47 from the sun.
Venus then begins to return towards the sun, and after
some time ceases to be visible, as its light is overpowered
by the brilliancy of the sun. Ere long the planet may be
seen in the east shortly before sunrise. The time between
the rising of the planet, and the rising of the sun, gradually
increases, until Venus again reaches the greatest distance
from the sun, after which it commences to return again,
passes the sun, and may be seen at evening in the west as
before. It appears from these observations that Venus is
continually moving from one side of the sun to the other,
and is never found at a distance of more than 47 from the
sun. The question remains as to how these movements are
to be explained. It is noticed that when Venus is at its
greatest distance from the sun, its apparent movement is
much slower than when it is nearer the sun. It is further
shown by the telescope that when Venus is at its greatest
angular distance from the sun, the disk is seen to be half
illuminated, like the moon at the quarter. The planet is
Motion of the Earth around the Sun. 205
also, on very rare occasions, seen actually to pass between
the earth and the sun, the phenomenon being known as the
transit of Venus. From all these facts it is inferred that
the planet Venus is really a dark globular body, which moves
around the sun in 224 days in a certain orbit. As the sun
executes its apparent motion among the stars, the planet
seems to accompany it, alternately appearing to the east and
the west of the sun, and never more than 47 distant there-
from. Precisely similar, though on a smaller scale, are the
apparent motions of Mercury. This planet does not go so
far from the sun as Venus, its greatest elongation being only
28. The time in which Mercury revolves round the sun is
87 days.
We thus see that there are two planets, Mercury and
Venus, which certainly appear to move round the sun.
If we compare Mercury or Venus with the earth, we find
some striking points of resemblance. All three bodies
are approximately spherical, and they are all dependent
upon the sun for light. It is therefore not at all unreason-
able to enquire whether the analogy between the three
bodies may not extend farther. We have already seen that
the phenomenon of the apparent annual motion of the sun
could be explained by supposing that the sun is really at
rest, and that the earth moves round the sun. When we
combine this fact with the presumption afforded by the
analogy between the Earth and Mercury and Venus, we are
led to the belief that the Earth, Mercury, and Venus are all
bodies of the same general character, and all agree in
moving around the sun, which is the common source of
light and heat to the three bodies.
Nor are other confirmations wanting of the same impor-
tant truth. By careful observations of the fixed stars, a very
beautiful phenomenon, known as the aberration of light, has
been discovered. This receives a most satisfactory explana-
tion when the revolution of the earth around the sun is
admitted, while it would be wholly inconsistent with the
hypothesis that the sun revolves around the earth.
206 Astronomy.
The theory of universal gravitation affords so satisfactory
an explanation of many most remarkable phenomena con-
nected with the motions of the heavenly bodies, that not a
doubt can remain of its truth in the mind of any person
capable of understanding the subject. Yet the theory of
universal gravitation is indissolubly connected with and
identified with the theory that the earth revolves around the
sun.
We shall, therefore, assume that the earth really de-
scribes an elliptic orbit around the sun, though this state-
ment is indeed not absolutely accurate. Even if all the
other planets were absent, all we could say would be that
the earth and the sun each describe elliptic orbits about
their common centre of gravity. Owing to the vast pre-
ponderance of the mass of the sun on the mass of the earth,
the centre of gravity of the two bodies is comparatively
close to the centre of the sun, and may for most purposes
be regarded as absolutely identical with the centre of the
sun. The problem of the earth's motion becomes still more
complicated when the actions of the different planets upon
the earth and sun are taken into account. Owing to these
disturbances, the ellipse which the earth describes is
gradually modified both in form and position within narrow
limits. We may, however, generally suppose that the earth
revolves in an ellipse in one of the foci of which the sun is
situated.
When the earth occupies the point T (Fig. 87), it is then
nearer to the sun in the focus s than it is in any other part
of the orbit, and this point is termed perihelion. The
opposite extremity of the major axis of the ellipse is termed
the aphelion, and the earth when in that position is at its
greatest distance from the sun. The mean distance of the
earth from the sun is an arithmetical mean between the
aphelion distance and perihelion distance, and is equal to
the semiaxis major of the ellipse.
The axis of rotation of the earth is, of course, carried
Motion of the Earth around the Sun. 207
round the sun once in the year by the motion of the earth
itself. It is exceedingly important to observe that, during
the translation of the axis, the direction of the axis remains
constantly parallel to itself. This is shown in Fig. 88, which
represents the earth in four different parts of its orbit,
though it is impossible in a figure of this kind to maintain
the actual proportions of the respective sizes and distances.
The lines NS in the four different positions of the earth
denote the axes of rotation, and these four lines are parallel.
s
As the whole dimensions of the orbit of the earth are quite
insignificant compared with the distances of the stars, the
direction of the axis of rotation of the earth points always to
the same point on the celestial sphere, i.e. to the point we
have already determined as the celestial pole.
For a more detailed exposition of the circumstances
attending the revolution of the earth around the sun, we may
refer to Fig. 89, in which the position of the earth is given
for each month of the year. The positions of the earth
are also shown at the summer and winter solstices as well
as at the vernal and autumnal equinoxes. When the earth
is at the summer solstice, then all the region within the
arctic circle remains constantly on the illuminated side of
Motion of the Earth around the Sun. 209
the earth, while at the winter solstice the region within the
arctic circle is in continual darkness. At the equinoxes it
will be observed that the boundary of light and shade
passes through the pole.
76. Precession of the Equinoxes. Although we are prac-
tically correct in asserting that during the revolution of the
earth around the sun, the direction of the axis of rotatioft
remains constant, yet when the direction of this axis is
compared with the position which it occupied at a remote
interval of time, it is seen that certain well-marked alterations
in the position have taken place. These changes are
principally manifested to us by an apparent alteration in the
places of the stars. We have already explained how the
position of a star is determined by its right ascension and
declination. Both these measurements are made with re-
spect to the celestial equator. If the equator of the earth
were constantly and absolutely parallel to itself, then the
celestial equator would remain constant also ; but if the
earth's equator were in motion, then the celestial equator
would undergo corresponding alterations in its position with
reference to the fixed stars. If we were unconscious of any
motion of the earth, then the alterations in the celestial
equator would produce changes in the places of the stars.
The extent of these changes can be determined by observa-
tion, and we can thence deduce the actual changes of the
equator, and therefore of the direction of the axis about
which the earth is rotating. We shall first point out the
nature of the changes in the apparent positions of the stars
which observation has revealed to us, and which are to be
attributed to the changes in the position of the earth's axis
of rotation.
Take for example the most brilliant star in the heavens,
Sirius, and determine the right ascension of that star at
intervals of time differing by ten years. We find from
actual observations the following values :
2io Astronomy.
Mean Right Ascension of Sinus.
Hours Min. Sec
January i, 1847, 6 38 25
1857, 6 38 51
1867, 6 39 17
1877, 6 39 44
We thus see that on the four dates here referred to, the mean
right ascension of Sirius has perceptibly altered. It will
also be perceived that these changes have taken place with
considerable uniformity, the average increase of the right
ascension being about 2-65 seconds per annum. Though
this may seem to be a small quantity, yet from the circum-
stance that the change is always taking place in the same
direction, its amount soon becomes appreciable, and in the
course of centuries attains a magnitude which could hardly
be overlooked even by the rudest methods of observing.
To understand the importance of this phenomenon, it
is necessary to bear in mind that right ascension is measured
from the vernal equinox, which is one of the points of inter-
section of the ecliptic with the celestial equator. It appears
that on January i, 1847, the point on the celestial sphere
where the vernal equinox was at that time situated, crossed
the meridian 6 h 38 m 25 s before Sirius crossed the same
meridian. Thirty years later, on January i, 1877, the ver-
nal equinox crossed the meridian 6 h 39 44 s before Sirius.
This statement admits of but a single interpretation. The
angular distance between Sirius and the vernal equinox, as
measured on the celestial sphere, must be greater in 1877
than it was thirty years previously. This phenomenon has
been called the Precession of the Equinoxes, because, com-
paring the equinox with Sirius, the former came a little
earlier on the meridian in 1877 than it did in 1847. The
years we have chosen are merely for the value of illustration :
whatever two years were taken, it would be found that in the
latter of these two years, the distance of Sirius from the vernal
Motion of the Earth around the Sun. 2 1 1
equinox (measured in the same direction on the equator)
would be greater than the former.
Nor is there any special feature connected with the star
Sirius, which renders it peculiarly fitted for the exhibition of
this phenomenon. Had any other star been chosen, it
would have been found that the distance between the vernal
equinox and the star was continually changing, though it
may be with a different velocity, and in some cases even
with a different direction, to the changes we have noted in
the case of Sirius.
From these observations we are obliged to admit that
the positions of the equinoxes, and the positions of the stars
on the surface of the celestial sphere, are constantly in a
state of change. As the equinoxes are merely the intersec-
tion of the ecliptic and the equator, it becomes necessary to
admit that either the equator or the ecliptic, or both, must
have a certain motion on the heavens relatively to the stars,
or that the stars must have a motion relatively to these
circles.
The solution of the problem is much narrowed by
observing that, at any rate, there is no motion of the ecliptic
with respect to the stars at all adequate to account for
so considerable a phenomenon as the precession of the
equinoxes. Each year the sun passes through the same
constellations in its annual progress, and the path of its track
as marked out by the stars along the line is sensibly con-
stant, or at all events is not endowed with any change large
enough to be seriously considered for the present purpose.
If we were enabled to see the stars in the vicinity of the
sun (which under ordinary circumstances his bright light
overpowers,) we should find, for example, that every 23rd of
May the sun passed between the Pleiades and the Hyades ;
that every 2ist of August the sun was to be found very close
to Regulus (a Leonis), while on every i5th of October he
passed a little above Spica (a Virginis). The track of the
sun among the stars is practically invariable, and hence
p 3
212 Astronomy.
to account for the apparent motion of the equinox we must
suppose that the ecliptic is at rest, and that the equator is in
motion.
We have hitherto only referred to the changes in the
right ascensions of the stars ; before proceeding further we
must ascertain whether there are not corresponding changes
in the declinations or the polar distances of stars. It will be
found by comparing observations of the same star, made at
considerable intervals of time, that the polar distances are
changing. Thus, for the case of Sirius, we have at the
dates already given :
Mean Polar Distance of Sirius.
i8 4 7,
1 06
30'
37
1857,
106
31
24
1867,
106
3 2
ii
i877,
106
32
56
It thus appears that the angular distance of Sirius from
the pole of the celestial sphere is constantly increasing. In
the lapse of thirty years, this increase has attained to the
substantial amount of upwards of two minutes, at the uniform
rate of about 4"*6 annually. Similar observations made
with respect to other stars show, in general, an alteration of
the polar distance which will be found to be uniform in the
same stars for hundreds of years. It follows that either the
celestial pole must be moving relatively to the stars, or that
the stars must be moving relatively to the celestial pole.
Which alternative will it be the most reasonable to adopt ?
Let us remember that the configurations of the stars inter se
are constant, and that the constellations of the present day
are the same as the constellations thousands of years ago. As,
therefore, the stars do not move perceptibly when compared
together, it is much more natural to suppose that the
changes of the pole with respect to the stars are really due
Motion of the Earth around the Sun. 213
to the motion of the pole and not to any motion of the
stars.
To this conclusion we are also conducted by the
observed changes in right ascension of the stars, for if the
equator be in motion and we have seen that it is then the
pole, which is merely the point on the celestial sphere 90
from the pole, must be in motion also.
Having thus ascertained that the pole has a certain slow
movement, the next point to be considered is the exact
determination of the rate of that movement, and of the path
along which the pole moves. We shall show that the
observed facts can be explained by the supposition that the
celestial pole is moving on the surface of the celestial sphere
in a small circle with a uniform velocity. It remains to
determine the pole of this small circle, and the length of
the arc which is equal to its radius.
We have already explained how the obliquity of the
ecliptic is to be determined : it is, in fact, merely the greatest
declination of the sun at midsummer ( 54). We here
give the obliquity of the ecliptic determined by this method
in the four years already referred to.
June 21, 1847 - 2 3 2 7' 23"'56
1857 23 27 37-12
1867 . 23 27 13-85
1877 23 27 26-51
It would not be correct to say that these different
values of the obliquity are absolutely identical. Yet the
variations in its value are extremely small. In fact, the
mean of the four values just given is
2 3 2 7 ' 2 5 "'26,
and the difference between this quantity and the greatest or
least of the four observed values is only about one seven-
thousandth part of the total amount. For our present
purpose we may overlook these small discrepancies, and
214
Astronomy.
FIG. 90.
suppose that the obliquity of the ecliptic is constant. We
are thus led to the conclusion that, notwithstanding the
equator is continually in motion among the stars, it still
preserves constantly the same inclination to the plane of
the ecliptic,
Let A B c D (Fig. 90) denote the ecliptic, and let E E be
the equator. Then regarding A B c D as fixed, the equator
moves so as to occupy the
successive positions E' A' E',
E" A" E", &c., while the in-
clinations at A, A', A" remain
constant Let K be the pole
of the ecliptic, and let P be
the pole of the equator in
the position EAE, while P'
and P" are the positions of
the pole on the equator
when in the position E' E'
and E" E" respectively. The
angle between two great
circles on the sphere is equal to the angle between their
poles, hence the inclination of the ecliptic to the equator is
equal to the arc between the poles of the ecliptic and the
equator.
Thus in the three positions of the equator, represented
in Fig. 90, the angles at A, A/ A" are respectively equal to
the arcs K P, K P', K p", and as the angles at A, A', A" are all
equal, it follows that the arcs K P, K P', K P" must be all equal;
the points P, P', p" must, therefore, lie upon the circum-
ference of a small circle of which K is the pole; and hence
the pole of the equator describes a small circle about the
pole of the ecliptic, the radius of which is equal to the ob-
liquity of the ecliptic.
The effect of the precession of the equinoxes on the
position of a star is more simply seen when we refer the
place of the star to the ecliptic by its latitude and longitude.
Motion of the Earth around the Sun. 215
Thus if e be the position of a star (Fig. 90), and e b be the
arc let fall from the star, perpendicular to the ecliptic, e b is
the latitude, while A b, being the distance from the equinox
to the foot of the perpendicular, is the longitude of the star.
The effect of the precession of the equinoxes is here mani-
fested only by the change in the point from which the
longitudes are measured : thus without any real change in the
place of the star, its longitude, which was originally A b, in-
creases to A' b, and subsequently to A" b, and so on inde-
finitely. The latitude, on the other hand, remains constant.
It is further to be observed that this increase in the longi-
tude must necessarily be the same for all stars.
77. Numerical Determination of the Precession. To
determine the numerical value of the precession of the
equinoxes, it will be sufficient to have ascertained for any
one star the annual change which precession has produced
in the longitude of that star. In -making this calculation it
will be desirable to have observations of the star separated
by as long an interval of time as possible. It appears from
the observations of Hipparchus that in the year 128 B.C. the
longitude of the star Spica Virginis was about 1 74. By the
observation of Maskelyne, the longitude of this star in 1802
is 201 4' 41". The difference between these two results
is due to the alteration in the point from which the longitude
is measured, which has taken place during the interval of
1,930 years.
We may also use for this purpose two observations sepa-
rated by a comparatively small interval when those observa-
tions have been made with the accuracy attainable with
modern instruments. The annual alteration of the inter-
section of the equator with the ecliptic, measured along
the ecliptic, amounts to 50" -24. From this it is easy to
calculate that the equinox will move completely round the
ecliptic and regain its original position in a period of about
26,000 years.
It appears from these considerations that the actual path
2i6 Astronomy.
of the celestial pole among the stars is a small circle, of
which the radius is 23 27', and that the duration of the
revolution is 26,000 years.
In the course of ages the precession of the equinoxes is
calculated to produce the most marked changes upon the
relation of the pole to the constellations. At present it so
happens that the bright star, called the Pole Star, is about
i J from the pole. The movement of the pole in the small
circle which it describes about the pole of the ecliptic, is at
present diminishing the distance between the pole and the
Pole Star. The approach will continue until the year 2 1 20,
when the distance will not be much more than half a degree.
The distance will then increase until, in the lapse of 13,000
years, it will amount to about 47. Long ere this happens,
however, the pole will have become so far from the Pole
Star as to deprive the latter of the great utility which at
present it possesses.
It appears that the movement of the north pole is calcu-
lated to bring it near to the star Vega (a Lyrse) in about
12,000 years, from which star the pole is at present distant
by about 51. The distance will diminish to a minimum of
about 5, and Vega will then by its brilliancy, as well as by
its proximity to the pole, be able to fulfil many of the pur-
poses which render the present Pole Star so convenient.
78. Gradual Displacement of the Perihelion of the Earths
Orbit. Just as we have seen that the plane which contains
the orbit of the earth has a gradual slow motion in space, so
it is found that the elliptic orbit of the earth has itself a slow
motion in the plane of the orbit, so that the major axis of
the orbit occupies successively different positions.
The movements of the earth's orbit are determined by
observations of the movement of the sun, for, as we have
seen, the apparent orbit of the sun round the earth is similar
to that of the earth round the sun. If, therefore, observation
has detected a motion in the solar perigee, that really indi-
cates a movement in the major axis of the earth's orbit.
Motion of the Earth around the Sun. 217
It is found by comparing old observations with modern
observations that the longitude of the sun's perigee changes
by 6 1 " 7 2 per annum (Leverrier). If this augmentation of
the longitude of the solar perigee had been equal to 50'' -24, it
would have been completely explained by the alteration in the
equinoxial point which we have just considered. Under these
circumstances the position of the solar perigee among the stars
would have been constant. As, however, the motion of the
longitude perigee exceeds the precession of the equinoxes
by ii"-48, it follows that the position of the perigee is dis-
placed along the ecliptic to the extent of ii"'48 annually,
and that the motion is direct.
79. The Aberration of Light. The phenomenon which
is known as aberration of light is one of the most interesting
discoveries which have ever been made in astronomy. It
had long been surmised that if the earth really moved round
the sun, as was admitted in the Copernican theory, that then
certain apparent movements ought to be observed in the
places of the stars, and that from such movements the dis-
tances of the stars would be determined. With the view of
detecting the changes whose existence was thus surmised,
the celebrated astronomer Bradley commenced a series of
observations with an instrument specially arranged for the
purpose. The star which he chose was y Draconis, which
culminates very near the zenith, at the latitude of Greenwich,
and the place of which is, therefore, but little deranged by
refraction. The observations were commenced in 1725,
and continued with great assiduity at all available oppor-
tunities. Bradley soon found that certain changes were
taking place in the positions of the stars, but that these
changes were of quite a different character from those of
which he was in search. It appeared, for example, that the
star y Draconis was in March 1726 about 20" more to the
south than it was in December 1725, while from March to
the following September the same star moved towards
the north through a distance of not less than 39". In
218 Astronomy.
December 1726 the star had returned to the same position
which it had one year previously. It thus appeared that the
zenith distance of this star oscillated through a distance of
about 20" on each side of its mean value. It can, however,
be shown that these changes could not be accounted for
merely by the displacement of the earth in its orbit, and
could not, therefore, be the parallax of which Bradley was
in search. It was not until similar movements had been
detected in the case of many other stars that Bradley was
enabled by a happy conjecture to give it a satisfactory ex-
planation. The movements of the stars were found to be a
consequence of the fact that the velocity of light, though
exceedingly great, is still not incomparably greater than the
velocity with which the earth is travelling in its orbit round
the sun. The phenomenon which has been thus so happily
explained, is called the aberration of light. This discovery,
though it relates to magnitudes so small as only to be per-
ceptible in very accurate measurement, is yet of so delicate
and so beautiful a character that it must undoubtedly rank
among the very greatest discoveries which have yet been
made in practical astronomy.
The earth is moving at the rate of about eighteen miles
per second, while light is travelling with a velocity about
ten thousand times as great. It follows that while we are
observing the star, the telescope is actually being carried on-
wards with a velocity which is one ten-thousandth part of
the velocity with which the light from the star is coming
towards the earth. Let s (Fig. 91) represent a star to which
a telescope is to be directed. If the telescope is to remain
at rest while the observation is being made, then it is obvious
that the telescope should be directed along the ray x s,
which comes from the star. If, however, the telescope be
in motion, then a little consideration will make it clear that
the telescope must generally not be pointed exactly at the
star, but in a somewhat different direction. Let us suppose
that the relation between the velocity of light and the velocity
Motion of the Earth around the Sun. 219
of the telescope is such that the telescope will be carried
from the position A B to the position x Y in the same time
as the light from the star will travel through
the distance B x. Then it is plain that if
the light from the star is to reach the eye
of the observer at all, the telescope must
be pointed not directly towards the star,
but in the direction shown by A B in the
figure. It is, indeed, obvious that the star
can only be seen when the rays of light
therefrom enter the object glass of the
telescope, and pass out at the eye piece
to the eye of the observer. The telescope
must, therefore, be placed in such a posi-
tion that this condition can be fulfilled.
When the telescope has the position A B the light enters
the telescope through the object glass at B ; the motion of
the telescope is then sufficient to enable the light to pass
down the tube of the telescope without being lost against
the sides, and when the telescope reaches the position x Y
the light emerges from the eye piece at x and enters
the eye of the observer. The observer being unconscious
of his own motion and of that of the telescope, naturally
supposes that the light from the star really travels from
the direction in which the telescope is pointed ; he, there-
fore, concludes that the star is in the direction A B, while the
star really is in the direction x B. The observer will, there-
fore, judge erroneously of the position of the star on the
surface of the heavens, and the extent of the error which he
makes is represented by the angle A B x, for this is the angle
between the direction of the telescope and the direction
from which the light of the star is actually coming.
80. Velocity of Light. In the further discussion of the
phenomenon of aberration we may proceed in either of two
ways. We may either assume the velocity of light from some
of the methods by which that velocity is known, and then
22O Astronomy.
deduce the amount of the aberration, or we may determine
the quantity of aberration from observation, and then deduce
the velocity of light. We shall adopt the former method,
though it should be noted, as a striking confirmation of
Bradley's theory, that the value of the velocity of light which
can be deduced from the observed coefficient of aberration,
agrees in a most remarkable manner with the velocity of
light as it has been determined by the other methods which
are available for that purpose.
It has been already stated that the velocity of light
is about ten thousand times as great as the velocity of the
earth in its orbit. It follows that in the triangle B A x
the line B x must be about ten thousand times as long as
the line A x. The angle B A x can, therefore, under the
most favourable circumstances, never exceed the angle whose
circular measure is one ten-thousandth, i.e. about 20". It,
therefore, appears that the greatest effect which aberration is
capable of producing is to cause a star to appear in a point
on the heaven 20" distant from the point in which that star
would have appeared had the velocity of light been infinitely
great with regard to the velocity of the earth, or had the
earth been at rest. As, however, the star which is now dis-
placed 20" in one direction will, in six months, be displaced
20" in the diametrically opposite direction, the total effect
of aberration will amount to a displacement which oscillates
within an amplitude of 40".
The line A x, which indicates the movement of the
observer, is, of course, a tangent to the actual orbit of the
earth. This tangent is directed to a certain point on the
celestial sphere, which is often called the apex of the earth's
way. The maximum effect of aberration, in deranging the
place of a star, will occur when the line s x is perpendicular
to A x, the star will then be 90 from the apex of the earth's
way, and will, therefore, be situated on that great circle of
the celestial sphere, of which the apex is the pole. It is
further to be noted that the effect of aberration is to displace
Motion of the Earth around the Sun. 221
the apparent position of a star in a plane which contains the
line A x, and, therefore, passes through the apex of the
earth's way. The effect of aberration generally is, therefore,
to cause all the stars on the surface of the heavens to appear
to move from their true places slightly towards the apex of
the earth's way. A star actually situated at the apex would
experience no effect from the aberration, while all the stars
on any circle of which the apex was the pole, would aberrate
towards that apex through equal amounts.
FIG. 92.
As the apex is daily indeed, momentarily changing its
position upon the ecliptic so as to travel completely round
the ecliptic in the course of a year, it appears that the point
towards which a given star is displaced is constantly varying.
It follows from this that the effect of aberration upon the
apparent place of a. star is to make that place describe a
small ellipse on the surface of the celestial sphere of which
the centre is the mean place, while the period in which the
ellipse is described is equal to the period of the revolution
of the earth round the sun. Let s (Fig. 92) be the position
of the sun, and let T, T', T", T'" be four positions of the
earth in its orbit, which for the present we may consider to
222 Astronomy.
be circular. Let E be the position of a star as it would be
seen from the sun s. When the earth is at T, the line T A
drawn touching the circle T T' T" T'" denotes the direction
in which the earth is moving. As the star is at an enor-
mously great distance compared with the distance of the
earth from the sun, we may practically consider the line T E
as parallel to the line s E, and, therefore, s E indicates the
point on the celestial sphere in which the star would be
seen if it were not for the effect of aberration. Through
any point R on the line s E draw a line R r parallel to the
tangent T A, and bearing the same ratio to the line s R which
the velocity of the earth bears to the velocity of light ; join
s r, and produce it on to cut the plane drawn through E
parallel to the plane of the ecliptic : then the effect of aber-
ration will be to make the star appear to be at , where E e
is parallel to R r. In the same way, when the earth is at T',
the star will be seen in a direction which points to the same
point on the celestial sphere as is indicated by the line s e'.
As the lines R r, R r f are equal, it is obvious that E t and
E ^ are also equal ; and hence as the earth assumes the
successive positions T, T', T", T'", &c., the star is found in
the corresponding positions e, e', e", e"' t &c.
The curve e e? e" e'" which the star appears to describe
in the course of a year in consequence of aberration must
obviously be a circle of which the plane is parallel to the
plane of the ecliptic. The effect of this movement upon
the apparent place of the star is to be determined by pro-
jecting the circle which is actually described upon the tan-
gent to the celestial sphere. Thus the observed path of the
star due to aberration will, in general, be an ellipse, of which
the axis major is parallel to the ecliptic : the length of the
axis major of this ellipse is constant. For a star at the pole
of the ecliptic the ellipse reduces to a circle, while for a star
actually in the ecliptic the effect of aberration is merely to
cause the star to oscillate in the arc of a great circle. A star
situated at the pole of the ecliptic will always be seen at the
Motion of the Earth around the Sun. 223
constant distance of about 20" from the position in which it
could be seen were the earth stationary.
These results are shown in Fig. 93. K B s A D is the ce-
lestial sphere. A B c D is the ecliptic, of which K is the pole.
The orbit of the star due to aberration is e e' e" e!", and
the observer is at o, the centre of the celestial sphere. The
star appears to the observer to describe the ellipse / n q m y
FIG. 93.
in which the cone drawn from o to e e 1 e" e'" is cut by the
celestial sphere. The major axis m n of this ellipse is
parallel to the ecliptic, while the minor axis q p lies in the
circle of latitude K s, which passes through the centre of the
ellipse.
81. Nutation of the Earth's Axis. Although the
discovery of the aberration afforded a satisfactory explanation
of the motion of the stars which Bradley had detected, yet he
continued his observations on the zenith distances of stars
which culminated near the zenith. It then appeared that
there were certain other alterations of the zenith distances,
224 Astronomy.
of quite a different character from those of which aberration
had already afforded so satisfactory an explanation.
By making allowance for the effect of aberration, we
can ascertain the true position in which the star would be
seen if the earth was stationary. When this is done, it is
found that the places of the stars thus determined are
not constant ; but that they indicate a movement very
different from the movements of an annual nature which are
produced by aberration or by parallax. Thus, for example,
Bradley found that from the year 1727 to the year 1736,
the star y Draconis was continually advancing towards the
north pole, while, after the latter date, the star began to
withdraw from the pole : and similar movements were
observed in other stars.
Bradley found that the changes which he had observed,
in the polar distances of certain stars, could be explained
by the supposition that the pole of the celestial sphere
oscillated, through narrow limits, about its mean place.
This phenomenon he termed nutation. As it appeared from
the observations that the period of this change was about
eighteen years, it was surmised, by Bradley, that the cause
of the phenomenon was to be sought in the motion of the
moon's nodes, which complete their revolution in a little
more than eighteen years. The explanation of this depends
upon the theory of gravitation, but for the present we shall
only attempt to describe the actual character of the phe-
nomenon now called nutation.
The axis of the earth points to the celestial pole, and
any movement in the celestial pole is, therefore, to be
attributed to a change in the position of the earth's axis
of rotation. It is not to be supposed that any change
in the actual position of the earth's axis in the earth itself
is indicated either in the phenomenon of precession or
in that of nutation. So far as observation has hitherto
gone, it would appear as if the axis, about which the earth
rotates, were actually fixed in the earth ; and that in the
Motion of the Earth around the Sun. 225
FIG. 94.
phenomenon of precession and nutation the movements of
the earth are similar to what they would be, if a fixed axis
were driven through the earth, and this axis were made to
describe the movements which observation has shown in
the motion of the axis of the celestial sphere.
The nature of the movement of the axis which produces
the phenomenon of nutation is shown in Fig. 94: T is the
position of the earth in its orbit, the direction of the revo-
lution round the sun being shown by the arrow ; T K is the
perpendicular to the plane of the ecliptic, and K is the pole
of the ecliptic. Let T o
be the axis of rotation of
the earth, then, accord-
ing to the phenomenon of
precession, the line T o
revolves around T K on
the surface of the cone
made by a line which
makes a constant angle
of 23 27' with T K.
Owing, however, to the
superposition of the
small effects of nutation
upon those of preces-
sion, the actual move-
ment of the earth's axis is on the surface of a small cone,
T m nm' '; while at the same time the axis TO of this
cone moves round on the surface of the cone of revolu-
tion, of which T K is the axis. The movement of the axis
of the small cone around the large one constitutes the
phenomenon of precession, while the motion of the axis
of the earth on the surface of the small cone constitutes
the phenomenon of nutation.
The major axis mm' of the ellipse, which forms the
base of the cone of nutation, lies in the plane which passes
Q
226 Astronomy.
through the axis of the earth T o and the perpendicular to
the plane of the ecliptic T K.
The relative sizes of the cones is necessarily very much
exaggerated in the figure, for while the semi-angle, at the
vertex of the large cone, is 23 27', the axis major mm' of
the ellipse at the base of the small cone only subtends an
angle of i8"*45 at T. The minor axis ;/ n' subtends an angle
of i3 // '73- The pole describes the circumference of the
small ellipse in a period of i8f years, but its motion
during that time is not uniform. In order to ascertain the
actual position of the pole at any given epoch, describe a
circle m z m', of which the axis major of the ellipse m m' n ri
is a diameter. If the point z move uniformly round the
circle so found, and if it start from the point m at the same
epoch as the pole is coincident with m, then the position of
the pole at any other epoch will be found by letting fall a per-
pendicular from the corresponding position of z upon the axis
major of the ellipse. The point p in which this perpen-
dicular intersects the ellipse is the position of the pole.
A remarkable consequence of the nutation of the earth's
axis consists in the variations which it produces in the
obliquity of the ecliptic. The obliquity is equal to the
angle between T K and T p, and the greatest and least values
of the obliquity correspond to the epochs at which p is at
one or other extremity of the major axis of the ellipse of
nutation. These fluctuations are limited to 9" -22 on either
side of its mean value.
82. Annual Parallax of Stars. We have already
mentioned that the discovery of aberration was made by
Bradley, while in the course of a series of observations
undertaken with the object of discovering some variations
in the positions of the stars arising directly from the annual
movement of the earth. The reason that Bradley did not
find the movements of which he was in search, was that the
effects of annual parallax on the stars which he observed
were too small to be detected by the method of observing
Motion of the Earth around the Sun. 227
which he adopted. Any annual parallax which has even up
to the present been detected is an exceedingly small quan-
tity compared with the coefficient of aberration which
Bradley's observations revealed.
Let s (Fig. 95) represent the sun, and let T be the earth,
while E is a star. An
observer situated at the FlGt 95 '
sun will see the star in
the direction s E, while
an observer on the earth
will see the star in the
direction T E. The posi-
tion on the celestial
sphere to which the star
will be referred will
therefore be different,
according as the position of the observer changes by the
annual revolution of the earth around the sun.
It is easy to show that the effect thus produced on the
apparent place of a star referred to the celestial sphere is
to make the star describe a certain small ellipse ; for the
observer will always see the star in the direction T E, and
as the earth moves round the sun the line T E will describe
a cone, of which E is the vertex, while the orbit of the earth
is the base. The star will, therefore, always appear to be on
the surface of the cone. But the star must also be referred
to the surface of the celestial sphere, and hence the place of
the star will be limited to the line in which the cone just
referred to cuts the celestial sphere. As the portion of the
celestial sphere included in the cone is extremely small, the
portion of the sphere may be represented by its tangent
plane, and then we see that the orbit of the star is the
section of the cone by a certain plane ; but the section of a
cone is in this case an ellipse, and hence it appears that the
effect of annual parallax upon a star is to cause that star to
appear to describe an ellipse on the celestial sphere of which
Q2
228 Astronomy.
the mean place of the star is the centre. It is easy to see
that if the star happened to be situated at the pole of the
ecliptic the tangent plane would cut the cone in a circle
(assuming the earth's orbit to be circular), and that therefore
the apparent orbit of a star so situated would be a circle.
In other situations the ellipse would have an eccentricity
which gradually increases as we consider stars nearer to the
ecliptic, while for a star actually situated in the plane of the
ecliptic the minor axis of the ellipse would be zero, and the
changes in the position of the star would merely cause it
to oscillate to and fro in the ecliptic.
Under all circumstances the major axis of the parallactic
ellipse (as it is called) must be parallel to the ecliptic, and
the dimensions of the major axis will depend upon the
actual distance at which the star is separated from the earth.
The star when situated at one of the extremities of the
major axis of the parallactic ellipse is at the greatest distance
from its mean place. The angular magnitude of the semi-
axis major of the ellipse is equal to the greatest angle between
the lines s E and s T. Since s T, being the radius of the
earth's orbit, is always small compared with s E, being the
distance of the star, the greatest angle between s E and T E is
obviously the angle whose circular measure is ST-J-SE.
This angle is therefore the axis major of the parallactic
ellipse. The dimensions of the ellipse are thus dependent
upon the distance of the star. If the star were so exceedingly
remote that the radius of the earth's orbit was absolutely
inappreciable when compared with the distance, then the
angular value of the semi-axis major of the parallactic ellipse
would be inappreciable, and consequently no effect of
parallax could be observed. This appears to be the case
with the majority of stars so far as our present knowledge
extends. The parallactic ellipse is so minute that in the
majority of cases our ordinary methods of measurement fail
to detect any considerable alterations in the positions of the
stars which can be ascribed to this cause. Under these cir-
Motion of the Earth around the Sun. 229
cumstances we infer that the stars in question are so ex-
ceedingly distant that the radius of the earth's orbit, great,
no doubt, as that really is, is an inappreciable magnitude
compared with their distance from us.
By adopting, however, very special modes of measure-
ment, certain minute changes have been noted in the positions
of certain stars which are unquestionably the effect of annual
parallax. The nature of these observations must now be
detailed.
By the observations of right ascension and declination
made in the manner already described, it is possible to
determine the position of a star on the surface of the
celestial sphere. By repeating these observations at intervals
throughout the year, the corresponding positions of the
star at the different dates are ascertained, and we may con-
ceive that the positions are marked upon the globe, the
effect of aberration, nutation, and precession being allowed
for. If the star was sufficiently near the earth to
have a large parallax, these positions would undoubtedly
indicate with more or less accuracy the form of the paral-
lactic ellipse. The irregularities of the observations which
are unavoidable, even with the best instruments, would
prevent the observed positions from conforming exactly to
the form of the ellipse, but a sort of general arrangement of
the positions in an elliptic form would, no doubt, be traced.
Owing, however, to the extremely great distances of the
stars, the parallactic ellipse is so very minute, that its form
is entirely lost sight of in the irregularities of the observations
which, though still small, yet bear such a large proportion to
the dimensions of the ellipse that the latter cannot be dis-
cerned. In particular we may mention that, so far as our
present knowledge extends, there appears to be no star in
the northern half of the celestial sphere which has an annual
parallax exceeding about half a second of arc. Even with this
parallax the angular value of the axis major of the parallactic
ellipse is only a single second of arc, and, unless the star
230 Astronomy.
were situated at the pole of the ecliptic, the minor axis of
the ellipse must be less than that quantity. The question
then arises as to whether our present means of determining
the absolute places of stars are sufficiently exact to enable
us to detect the existence of an ellipse of such minute
dimensions by a series of observations extended over a year.
There is no prospect that the meridional determinations of
the positions of the stars can ever attain such accuracy as
to enable the form and dimensions of an ellipse of this
order of magnitude to be accurately constructed.
Not to mention other sources of irregularity, it is sufficient
to remember that the apparent declination of a star is
affected by atmospheric refraction. The larger part of this
refraction can be determined by calculation, and its effect
can be allowed for ; but even after this has been done with
every attention, there are still irregularities outstanding,
which, although too small to be material for many purposes,
are still too large to permit of the determination of the
ellipse which is the consequence of parallax. It is true that
by choosing, as Bradley did, a star which culminates near
the zenith, the irregularities of refraction are of comparatively
small importance, but there are still so many sources of small
irregularity, that even independently of refraction the method
indicated would be inapplicable.
The star a Centauri in the southern hemisphere
appears to have a parallax much larger than any star which
has yet been investigated with this object in the northern
hemisphere. In this case the parallax amounts to J of a
second, and consequently the total displacement of the star,
from one extremity of the major axis of the ellipse to the
other, amounts to about i| seconds. A displacement so
considerable as this is no doubt capable of being detected,
and even measured with some pretensions to accuracy by
meridian observations. It was, in fact, by observations
of this kind that the remarkable parallax of this star was
originally discovered.
Motion of the Earth around the Sim. 231
It is, however, possible to arrange a method of observing
by which much smaller parallaxes can be detected and
measured than can be done in the case of meridian obser-
vations. This method is founded upon the principle that,
whatever be the irregularities which have affected the
observations, we may presume that two stars which are
close together on the surface of the heavens will be affected
to nearly the same extent. Suppose, then, that there are two
stars, of which one is considerably nearer to us than the
other, while the two stars are so nearly in the same visual
ray that they appear to be close together on the heavens.
Each of the stars will, in consequence of annual parallax,
appear to describe a small ellipse on the heavens, but the
ellipse formed by the nearer of these two stars will be
larger than that described by the more distant star. The
apparent distance measured as an arc of the celestial sphere
between the two stars will therefore change, and the direction
of the arc joining the two stars will also change, and the
period of these changes will be a year. If the two stars
subtend an angle of not more than two or three minutes,
the distance between them and the position angle can be
measured by means of the micrometer. All irregularities
arising from the instrument may be presumed to affect the
two stars equally, and though the refraction will slightly
alter the distance and position, yet its effects can be accurately
computed and allowed for. By micrometric observations we
have, therefore, the means of determining the changes in the
position and the distance which occur in the course of a
year, and thus of determining the difference between the
annual parallaxes of the two stars.
An annual parallax of even one second would require
that the star should be distant from us by 206,265 times the
radius of the earth's orbit. The actual distance of the star
from the earth would therefore amount to about twenty
billions of miles (20,000,000,000,000). So far as we know
at present it appears that a sphere of which the earth
232 Astronomy.
was the centre, and of which the radius was 20,000,000,000,000
miles, would not include a single star.
The vast distances here referred to can be illustrated by
a comparison derived from the velocity of light. Light
travels at the rate of about 186,700 miles per second, and with
this velocity it would require eight minutes to come from the
sun to the earth. To travel from the nearest star to the
earth, even with this prodigious velocity, it would seem that
at least three years would be required.
There are several stars of which the parallax has been
determined (see Appendix) : thus, for example, the bright
star Vega has a parallax of only o"'i8, and the light from
this star takes a period of about 18 years to travel to the
earth.
Viewed from the distances at which the fixed stars are
situated, the earth itself would have become invisible to the
most powerful telescopes, the vast orbit in which the earth
revolves around the sun would have shrunk to a tiny object,
while, if the sun himself were visible, it would only be as a
star of no very special brilliancy or importance.
CHAPTER VII.
THE MOON.
83. Apparent Movements of the Moon. Next to the
sun, the moon naturally demands our attention as the most
conspicuous of the remaining celestial objects. It is easy
to observe that the place of the moon among the
stars is continually changing. We are not now referring to
the apparent diurnal motion of the heavens in which the
moon participates in common with all the other celestial
bodies. If the place of the moon be compared with the
The Moon. 233
stars in its neighbourhood whose brilliancy is such that they
are still visible notwithstanding the superior splendour of
the moon, it will be found that even in the course of a few
hours the position of the moon will have perceptibly
changed. This is shown in Fig. 96, which indicates
the displacement of the moon
rIG. 90.
with respect to the fixed stars.
The movement of the moon is
about thirteen times more rapid
than that of the sun.
By continued observation of
the moon it will be seen to move
completely around the celestial
sphere, and if its path be laid
down on a globe or map, it is
found that the path is a great
circle which lies close to, though
it is still distinct from, the ecliptic
in which the sun moves. The
moon is sometimes a little to the
north and sometimes a little to the south of the ecliptic,
but it never deviates much therefrom. The direction in
which the moon moves round on the surface of the heavens
also agrees with that of the sun.
84. Phases of the Moon. The sun always presents to
us a complete circular disk. The moon, on the contrary,
only shows us a complete circular disk for a few hours in
each revolution. The figure of the moon changes with
great rapidity, and in the period of twenty-nine or thirty
days, during which it completes the circuit of the heavens
and rejoins the sun, it presents to us every possible gradation
between a circular disk perfectly illuminated and perfectly
dark.
The period of revolution of the moon relatively to
that of the sun doubtless suggested to the ancients the
idea of dividing* time into months. Perhaps also the idea
234 A stronomy.
of the week had its origin in the circumstance that a
period of seven days was nearly the interval from new
moon to first quarter, or from first quarter to full moon.
It is not unlikely that the ancients had made use of the
phases of the moon as a means of measuring time before
they were actually acquainted with the cause of the phases.
A little reflection will render the cause of the moon's
phases sufficiently obvious.
To follow the phenomena presented by the moon in a
methodical manner, let us commence by selecting an evening
in which, just after the sun has set, the moon appears low
down in the west. The moon then appears to us in the
form of a narrow crescent, of which the exterior circumference
is a semi-circle, and of which the interior circumference is a
semi-ellipse of but little eccentri-
city, and the major axis of which
coincides with a diameter of the
semi-circle. The moon sets a little
after the sun, and we remark that
the luminous segment is turned
towards the sun that is to say, the
line of greatest width of the crescent
points towards the sun. The points of the crescent are
generally called the cusps, and it will be noticed that the line
joining the cusps is oblique to the horizon, and that each of
the cusps is equidistant from the sun.
From day to day the crescent enlarges, though its cusps
still remain at the extremities of a diameter, the interior
curve becomes a semi-ellipse of increasing eccentricity, the
moon sets later and illuminates a considerable part of the
night, but the line of cusps is still always inclined to the
horizon at setting, and the greatest width of the crescent
still points towards the sun.
On the seventh day the moon appears like a semi-circle
and it is visible during a great part of the night On the
following days the luminous portion continues to increase,
The Moon. 235
the interior elliptic curve takes an opposite position, but the
semi-ellipse and the semi-circle have always a common dia-
meter.
On the 1 4th or i5th day the disk of the moon is
entirely luminous. The intensity of the light is not, how-
ever, quite uniform ; there are some places especially dark,
to which the term ' seas ' has been applied. The telescope,
however, shows that this term is incorrect, because we can
perceive in the so-called ( seas ' numerous features showing
an irregular surface.
On the following day the western edge of the moon is
seen to be somewhat less sharply defined ; gradually this
part becomes more and more obscured, and the curved line
which bounds the luminous region becomes a semi-ellipse of
more and more eccentricity. On the 22nd day the moon is
again a semi-circle, and all the phenomena previously
described reappear in an inverse manner ; about the 28th
day the moon has drawn very near the sun, after which it
becomes invisible for a few days, again to reappear in the
west in the form of a narrow crescent, and to repeat the
cycle already described.
During the entire revolution of the moon, the illuminated
portion is always turned towards the sun, and the dark part
is turned away from the sun. Now it might be supposed
that half the moon was self-luminous and the other half was
dark, and that the phases in the moon were produced by a
rotation of the moon on its axis, which at new moon turned
towards the earth the dark side, at full moon the bright side,
while for the intermediate phases the hemisphere turned to-
wards the earth is partly bright and partly dark. If this
were the case, then the ' seas ' and other markings upon the
disk of the moon would not always occupy the same portion
of the visible disk of the moon, but the illuminated hemi-
sphere would always contain the same objects, and the
boundary between light and darkness would always occupy
the same position with reference to the lunar markings.
236 Astronomy.
Observation, however, shows that this is not the case.
Among the many interesting features of the moon, there is
perhaps none more remarkable than that the moon always
turns the same face to the earth. It follows that the mark-
ings on the moon always occupy the same position on the
visible disk, and the boundary between light and darkness,
so far from occupying a constant position with respect to
the lunar objects, may actually be observed creeping' along
from night to night, and illuminating one lunar mountain or
valley after another.
From these considerations it follows that the moon can-
not be self-luminous, and that therefore the light which we
receive from it must be reflected by the moon from some
other source.
As the moon is naturally dark, from what source is its
light derived? There can be but one answer to this
question. The sun is the only body in the universe suffi-
ciently brilliant to explain the brightness of the moon. This
idea is confirmed by the following simple observations.
When the moon is full it comes on the meridian at mid-
night ; but at midnight the sun is at its lower culmination,
hence the sun and the moon are then separated by about
1 80, and the sun must therefore occupy a point of the
celestial sphere nearly opposite to that occupied by the
moon. We say nearly opposite, for if the sun and the moon
were upon the same diameter of the celestial sphere of
which the earth occupies the centre, the shadow of the
earth would be thrown upon the moon, and we would have
the phenomenon of an eclipse of the moon. As the great
majority of full moons pass without an eclipse, we infer that
the declinations of the sun and moon at full moon are not
generally equal in magnitude and opposite in sign, as they
would be if the two bodies were situated upon the same
diameter of the celestial sphere, and as they are on the days
when the moon is eclipsed.
An observer who was stationed upon the moon would
The Moon. 237
perceive; phases on the earth analogous to those which we
see on the moon. When the crescent of the moon is very
narrow, either shortly before or shortly after new moon, the
earth as seen from the moon would be nearly full, and ought,
therefore, to illuminate the moon as the full moon illu-
minates the earth. Indeed, the efficiency of the earth in this
respect considerably exceeds that of the moon, for the area
of the Dearth as seen from the moon is more than thirteen
times the area of the moon as seen from the earth.
It follows that the light which the moon receives from
the earth is more than thirteen times greater than the light
which the earth receives from the moon.
It is this light reflected from the earth which often
enables us to see that part of the disk of the moon which
is not illuminated by the sun.
85. The Eccentricity of the Moon's Orbit. One of the
most simple problems in connexion with the moon is the
determination of the eccentricity of the ellipse which we
shall now assume to be the orbit of the moon. It is easily
found by observation that the angular diameter of the moon
varies considerably, and the eccentricity may be taken to be
about o'c>55.
Thus the eccentricity of the orbit of the moon is much
greater than that of the orbit of the earth around the sun,
which is 0*0168.
86. Motion of the Perigee. To determine the position of
the moon's perigee (or the point in its orbit in which the moon
is nearest the earth), it is necessary to ascertain the place of
the moon on two different days on which the apparent
diameters of the moon are equal : the place half-way between
these positions is the position of the perigee.
When the position of the moon's perigee is determined at
different periods, it is found to be in rapid motion. In fact,
it makes a complete sidereal revolution in about nine years,
or more accurately in 3232-575 days.
238 Astronomy.
87. Mean Motion of the Moon. It is of primary import-
ance to determine the value of the mean motion of the
moon. This can be simply and accurately ascertained by
the comparison of two eclipses of the moon separated by a
wide interval of time. We may suppose that the opposition
of the sun and the moon takes place at the middle of the
eclipse; this supposition cannot entail an error of more than
a few minutes. If, then, we ascertain by observation the
time of the middle of the eclipses, and the number of lunar
months or of complete revolutions which have taken place
in the interval, we shall have an approximate value of the
lunar month by dividing the total time between the two
eclipses by the number of full moons which have occurred
in the interval. It is obvious that the accuracy of the result
will increase with the number of entire revolutions.
By this means it has been ascertained that the Synodic
lunar month, or the interval between two consecutive full
moons, is 29-530589 days.
88. Figure of the Moon. As the apparent dimensions
of the moon are so considerable, it is necessary, as it was in
the case of the sun, to select a certain point on the surface
of the moon by which its position on the celestial sphere
is to be specified. This requires us to examine accu-
rately the shape of the moon's disk as it is presented to us.
By careful measurements it is found that the apparent disk
of the moon is circular, and therefore it is natural to select
the centre of that disk as the point of reference required.
Whenever, therefore, the right ascension or the declination of
the moon is referred to, we are to understand the right
ascension or declination of the centre of the moon's disk.
The centre of the moon is not indicated by any mark which
we recognise, and therefore it is impossible to observe that
point directly ; we can, however, observe the edges of the
disk of the moon, and then reduce the observations so as to
give the position of the centre. If we were able to observe
the transit of the two edges of the circular disk (or limbs),
The Moon. 239
then the mean of these observations would give the transit
of the centre. Owing, however, to the fact that only one
limb of the moon is generally illuminated, and therefore
visible, the method is not generally practicable. We are
usually only able to observe the transit of one of the moon's
limbs. To determine from a single observation of this kind
the position of the moon's centre, we obviously require to
know the angular value of the moon's radius. The difficulty
is increased by the circumstance that this radius from day
to day nay, even from hour to hour is constantly changing.
The value of the radius may, however, be ascertained at any
moment by measuring the distance from the extremity of
one cusp of the moon to the other, for the line joining the
cusps is always a diameter of the moon, and therefore half
their distance is equal to the radius. When allowance has
been made for the moon's radius, then the right ascension of
the centre is determined from the observation of the limb.
The declination may be determined by observing both cusps
of the moon with the meridian circle, the mean between the
declinations of the two cusps being the declination of the
centre. In all that follows we are, therefore, to understand
that the centre of the moon is the point to which reference
is made.
89. Parallax of the Moon. The apparent position of
the sun on the surface of the celestial sphere depends to a
certain extent upon the position of the observer on the
surface of the earth ; and in the discussion of observations
of the sun it is necessary to reduce the observed positions
to those in which the sun would have been seen, had the
observer been able to occupy a position at the centre of the
earth. The word parallax is introduced to signify the dis-
tance between the position of the sun as seen by the
observer, and as it would be seen from the centre of the
earth, while the expression horizontal parallax is used to
denote the parallax when the sun is rising or setting, or,
240 Astronomy.
what comes to the same thing, the angle which the radius of
the earth subtends at the sun.
Precisely similar language may also be employed with
reference to the moon. The angular distance between the
position of the moon as seen by the observer and the posi-
tion in which the moon would be seen by an observer at the
centre of the earth is called the parallax of the moon, and
the angle which the radius of the earth subtends at the moon
is the horizontal parallax of the moon. There is, however,
one great difference between the parallax of the sun and
the parallax of the moon. The former is so small a quantity
as only to be detected by the most careful observations,
while the latter is of very considerable amount, being, in
fact, about 400 times greater than that of the sun. It follows
that the parallax of the moon requires to be allowed for in
nearly all observations of that body.
To determine by observation the parallax of the moon, we
proceed as follows : Let o be the centre of the earth (Fig.
FJG ^ 98), and let B and c be
two points on its surface,
which for simplicity we shall
suppose to lie on the same
meridian, passing through
the pole P. Let L be the
moon, the position of which
is to be observed from the
stations B and c. The ob-
server at B determines the angular distance between his
zenith z and the moon L that is, the angle z B L. In a
similar way, and at the same moment of time, the observer
at c determines the angle L c z', which is the zenith distance
of the moon as seen from the position which he occupies.
From these observations. we can determine the angles B LO
and c L o, which are respectively the parallaxes of the moon
at B and at c The geographical latitudes of the observations
at B and c are of course known, and therefore also the angle
The Moon.
2 4 t
B o c. This angle is equal to the difference or sum of the
latitudes, according as the two stations are on the opposite sides
or on the same side of the terrestrial equator. We can then
proceed by the following graphical method. Construct an
angle equal to the angle B o c, and mark off lengths o B and
o c on the legs of this angle, which are equal to each other.
Draw through B a line B L, making the angle z B L equal to
the observed zenith distance of the moon from L. Draw
through c a line c L, making the angle L c z' equal to the
observed zenith distance of the moon at c. The intersection
of these two lines determines the point L, which, being joined
to o, determines the angle B L o and c L o, which are the
parallaxes at the points B and c.
As a matter of fact, the determination of these angles is
really effected by trigonometrical calculation, which gives
much more accurate results than could be obtained by any
graphical process. The details of the process are very much
complicated by certain circumstances which we have omitted
for the sake of simplicity. It will not, of course, happen that
the two observatories at which the observations can be made
will lie exactly, or perhaps even nearly, on the same meridian.
The effect of this difference between the meridians can,
however, be calculated and allowed for in the resulting
values of the parallax. So, too, the assumption which we
have made that the time at which the moon is observed at
one station coincides with the time at which it is observed
at the other, cannot generally be realised. The actual
motion of the moon in the interval between the observations
has therefore to be taken into account, but the nature of that
motion is so well known as to enable this to be done with
considerable precision.
As the distance of the moon from the earth is compara-
tively small, we are obliged to take account of the fact that
the figure of the earth is not identical with a sphere. In
speaking, therefore, of the horizontal parallax of the moon,
it becomes necessary to define accurately what radius of the
R
242
Astronomy.
earth is referred to. We may assume that the section of the
earth made through the equator is a circle, and therefore
that all equatorial radii of the earth are equal, and hence we
can give precision to our language by speaking of the
equatorial horizontal parallax of the moon, meaning thereby
the angle which an equatorial radius of the earth subtends at
the moon.
From observations made at the observatories of Greenwich
and the Cape of Good Hope, the value of the mean equatorial
horizontal parallax of the moon has been determined by Mr.
Stone (1866) to be
57' 2"707.
From this it follows that the mean distance from the
earth to the moon is about 60 times the earth's equatorial
radius : but the orbit of the moon is so far from being a
circle that the actual distance fluctuates between 56 and 64
times. Remembering that the radius of the sun is about
no times the radius of the earth, it appears that if
the centre of the sun coincided with the centre of the
earth, the orbit of the moon, even
at its greatest distance from the
earth, would be all contained with-
in the volume of the sun.
90. Dimensions of the Moon.
When the parallax of the moon
is known, and also the angular
diameter which the moon sub-
tends, then the actual dimensions
of the moon are ascertained. In
this way it has been found that
the diameter of the moon is
about T 3 T that of the earth. The
relative dimensions of the moon
and the earth are represented by
the white circles in Fig. 99, the larger of these circles being
FIG. 99.
The Moon.
243
taken to represent the earth ; the smaller of them represents
the moon.
91, Movements of the Moon. We have now explained
how the position of the moon is to be ascertained by
observation, and how this position is to be corrected
for the effect of the length of the moon's diameter, and for
the effect of parallax. When these corrections have been
duly applied, we obtain the position of the centre of the
moon on the celestial sphere, as it would be seen from
the centre of the earth.
These observations having been repeated, we are enabled
to mark the position of the moon on a celestial globe, and
then to ascertain the exact nature of the movements which
it makes. It will be seen that after the lapse of about twenty-
seven days, the moon has accomplished a complete revo-
lution, and has returned to the neighbourhood from whence
it started. A great circle can be drawn which coincides
very nearly with the several positions of the moon, and
this great circle may be regarded as its path. By watching
the moon through several revolutions, and drawing the
great circle which corresponds to the path of each, it is
seen that the path of the moon is not constant. In fact, the
inclination of the path to the equator is constantly changing,
and in the course of time fluctuates between 18 and 28.
The nature of these changes will be more easily understood
by referring the position of the orbit of the moon to the
ecliptic. It will then be seen that the inclination of the
moon's orbit to the ecliptic is nearly constant, never differing
much from 5, but that the node or point, in which the orbit
cuts the ecliptic, is continually changing.
In Fig. 100, E E represents the celestial equator, and
A B c D is the ecliptic. The orbit of the moon cuts the
ecliptic at the point N at an angle of about 5, and after
completing the circuit of the sphere in the neighbourhood of
the ecliptic, cuts the ecliptic again at the point N', which
is not coincident with the former point N. The actual path
244
Astronomy.
FIG. too.
of the moon is thus exceedingly complex, consisting of a
series of spirals which are all contained within the zone
extending about 5 9' on each side of the ecliptic.
It will simplify the con-
sideration of this somewhat
difficult subject, to suppose
that the actual path of the
moon is in a great circle,
but that this great circle is
itself changing its position
on the sphere. The pole of
this great circle makes a
nearly constant angle with
the pole of the ecliptic, be-
cause the inclination of the
circle to the ecliptic is
nearly constant. In this is easily found the explanation of
the changes in the inclination of the apparent orbit of the
moon to the celestial equator. The moon's orbit will some-
times be inclined at an angle of 5 9' less than the obliquity
of the ecliptic, and sometimes at an angle of 5 9' more.
Thus the actual inclination of the moon's orbit to the
equator varies between 23 27' 5 9', and 23 2 7' + 5 9'.
92. Motion of the Moon's Nodes. The points N, N', in
which the orbit of the moon intersects the plane of the
ecliptic, are termed the nodes of the moon's orbit. The
node N, through which the moon passes when entering that
hemisphere which contains the north pole, is termed the
ascending node, while the other node is the descending node.
We have already seen that the orbit of the moon is in
motion relatively to the ecliptic, and, therefore, the positions
of the nodes on the ecliptic are continually changing. Thus
the node N moves uniformly round the ecliptic in the
opposite direction to that in which the moon is going; the
direction and amount of the motion of the node is represented
by N N'. The period required by the node to travel com-
The Moon. 245
pletely round the ecliptic, so as to regain its original position
with respect to the stars, is 6798-279 days. This movement
of the nodes of the moon's orbit is analogous to the move-
ment of the equator of the earth, which forms what we have
described as the precession of the equinoxes. In each case
the obliquity as regards the ecliptic is maintained at a nearly
constant value, while the movements of the intersection with
the ecliptic are nearly uniform. There is, however, one
very conspicuous difference the revolution of the equinoxes
requires a period of 26,000 years, while that of the moon's
nodes takes but little more than 18 years.
When a close examination of the positions of the moon
at different epochs is made, it is found that the movements
cannot be entirely explained in the manner we have de-
scribed. It is seen that the inclination of the plane of the
moon's orbit to the ecliptic is not absolutely constant. The
average value of this inclination is 5 8' 42", but the actual
value fluctuates between 5 17' 35'' and 5 o' i". It is also
to be observed that the velocity with which the nodes move
is not absolutely uniform ; this movement is sometimes
accelerated and sometimes retarded. We may, therefore,
regard the actual motion of the moon's node as consisting
of two parts first, a uniform motion, and then an oscillation
to and fro about the mean position. The normal to the
plane of the moon's orbit thus has a motion round the
normal to the plane of the ecliptic, which may be likened to
the motion of the axis of the earth already explained. In
each case the motion may be considered to take place on
the surface of a small cone, of which the axis describes a
much larger cone around the normal to the plane of the
ecliptic.
93, Sidereal Revolution of the Moon. By comparing
the places of the moon on the surface of the heavens at
remote epochs, it is possible to determine the time occupied
by the moon in making a complete revolution with respect
to the stars. In this way it is found that the sidereal revo-
246 Astronomy.
lution of the moon is 27-321661 days, or very nearly 27 days
and a third. It is very remarkable that this period is not
constant, but that it is gradually diminishing, so that the
time of the sidereal revolution of the moon is less now than
it was formerly. The difference is, however, exceedingly
small, and can only be detected by comparing the results of
many centuries of observation.
94. Rotation of the Moon. The surface of the moon
possesses certain well-marked features, visible to the unaided
eye, and still more clearly discerned in a telescope. The
simplest observations suffice to show that these objects re-
main constant in position ; in other words, that the face of
the moon which is turned towards the earth is always the
same. The movement of the moon is, in fact, nearly iden-
tical with what it would be could we conceive the moon
rigidly attached to a bar, the other extremity of which was
capable of turning around the centre of the earth. From
this fact that the same face of the moon is always turned
towards the earth the very remarkable consequence follows
that the period of rotation of the moon on its axis is equal
to the period of its revolution in its orbit around the earth.
It might at first be supposed that,
FlG - I01 - as we always see the same aspect
of the moon, the moon does not
rotate upon its axis at all. A
little consideration will, however,
show that this is a mistake. Let
T (Fig. 101) be the earth, and let
L and L' be two positions of the
moon, L a is the radius of the
moon which is directed towards
the earth when the moon is in
the position L, and the point a
indicates a certain locality on the
moon's surface. If the moon did not rotate upon its axis,
then, when the revolution of the moon had carried it to
The Moon. 247
L', the line L a would still remain parallel to itself, and be
carried into the position L' b. But observation shows
that the objects seen at a when the moon is at L will be
seen at a' when the moon is at L'. It therefore follows that
while the moon has moved from L to L' through the angle
L T L' the radius L a of the moon must have moved through
the angle b L' a'. But it is plain that the angle biJ a' is
equal to the angle L T L', and therefore the moon must be
revolving around its axis with an angular velocity equal to
the angular velocity of its revolution round the sun.
95. Mountains in the Moon. As there is no other
celestial body so near to us as the moon, so there is none
which we can scrutinise so keenly with our telescopes, and
with the configuration of whose surface we are so well
acquainted. To see the details on the moon's surface to
advantage, the phase of first or last quarter should be
chosen, or at all events the time of full moon should be
avoided. The telescopic appearance of the moon shortly
before the first quarter is represented in Fig. 102. The
irregularities of the surface are most distinctly seen along
the boundaries of light and shade. The relief there given
shows that the surface of the moon is very rugged and irregu-
lar that while there are some regions which appear compara-
tively level, there are others where mountain ranges and chasms
give an appearance of rugged grandeur to which, perhaps,
we have no parallel on the surface of the earth. But the
most characteristic objects on the surface of the moon are
what appear to be craters of volcanoes, which, though once
active, now seem to be extinct. There are some hundreds
of these objects on the surface of the moon which is
turned towards us, and many of them are of truly colossal
dimensions.
The general type of the lunar objects to which we are
now referring is represented in Fig. 103. A more or less
circular plain is surrounded by a high mountainous wall, and
in the centre of the plain rises another mountain, or some-
248
Astronomy.
FIG. 102.
The Moon.
249
times more than one. This general type is modified in
many instances. The marginal range is not always com-
FIG. 103.
plete, and may indeed be broken into by other craters ; the
central mountain may be absent, and the plain may be more
or less irregular, or marked over with still smaller craters.
Still the general typical crater as here shown is sufficiently
frequent on the moon's surface as to form the most cha-
racteristic feature of lunar scenery. The surface of the
moon has been frequently mapped, and the different objects
have been carefully measured and distinguished by names.
Among the most remarkable of these craters we may mention
Tycho and Copernicus, the former of which has a diameter
of fifty- four miles, while that of the latter is forty- six miles.
As we never detect any trace of clouds over the surface
of the moon, it has been surmised that the moon is not
surrounded by any atmosphere at all comparable in extent
with that which envelopes the earth. This opinion has been
confirmed by the most careful observations. It may be
remarked in the first place that when the surface of the
moon is only partly illuminated, the boundary between light
and shade is sharply marked. If there were on the moon
any atmosphere approaching in density to that surrounding
the earth, then it would be expected that the phenomenon
of twilight, which is due to the reflection in the upper regions
of the atmosphere, would be manifested. Under these cir-
250 Astronomy.
cumstances a fringe of partial illumination would extend
into the dark portion of the moon's surface ; but as such
illumination, if it exists at all, is extremely faint, we are
justified in concluding that the phenomenon of twilight
would not be seen by an observer on the moon's surface,
and that consequently, if the moon have any atmosphere,
that atmosphere must be of great tenuity.
96. Periods connected with the Sun and the Moon. If
the nodes of the moon were fixed, then the period of revo-
lution of the sun with regard to those nodes would be simply
equal to the sidereal year. On account, however, of the
regression of the moon's nodes, the sun returns to the same
node in a period less than a single year. This period
amounts to 346-619 days. From a comparison of this
period with that of the moon itself a very remarkable result
is obtained. If the moon revolved actually in the plane of
the ecliptic, then the centre of the moon would in each
revolution pass across the centre of the sun, and the mo-
ment of this occurrence is called the time of new moon.
Owing, however, to the circumstance that the orbit of the
moon is inclined to the plane of the ecliptic, the moon will
not usually pass over the surface of the sun. It is therefore
necessary to modify the definition of new moon accordingly.
We define the time of new moon to be the moment when
the longitude of the centre of the moon is equal to the longi-
tude of the centre of the sun. The interval between two
successive new moons is termed a lunation, and it is by this
period that the successive phases of the moon are regulated.
The length of the lunation is such that 223 lunations make
6585-32 days. Thus 19 periods of the revolution of the
sun with respect to the nodes of the moon coincide very
nearly with 223 lunations. This remarkable period,
amounting to about 18 years n days, is of service in the
prediction of eclipses. It is known as the Saros.
Another very remarkable period arises from the circum-
' stance that 235 lunations form 6939-69 days, while 19
The Moon. 25 1
years of 365*25 days amount to 693975 days. We there-
fore conclude that 19 years are nearly identical with 235
lunations. This is the Cycle of Meton. If the dates of
new moon and full moon are known for a period of 19
years, they can be predicted indefinitely, for in each sub-
sequent 19 years the dates are reproduced in the same
manner. The number which each year bears in the Cycle
of Meton is called the golden number. In 1896 the golden
number is 16. In 1900 the golden number is i, being the
commencement of a new cycle.
The period called the Solar Cycle is founded upon the
recurrence of the day of the week upon the same day of the
month. Owing to the complication produced by leap year,
this period is 28 years. In the year 1896 the Solar Cycle is
said to be i. This signifies that 1896 is the first of one
of these groups of 28 years. The cycle known as the
Roman Indiction is a period of 15 years. Though this
cycle is not connected with any astronomical phenomenon,
it is still retained. Thus the year 1896 is the ninth year
of the Roman Indiction.
In the almanacs it is usual to find a certain number
stated as the Julian Period. Thus, for example, 1896 is
the 66o9th year of the Julian Period. This cycle arises
from the three numbers 19, 28, 15, which represent the
entire periods of the Cycle of Meton, the Solar Cycle, and
the Roman Indiction respectively. It appears that in a
period of 19x28x15 = 7980 consecutive years there are
not two years which have the same golden number accom-
panied with the same solar cycle and the same Roman
Indiction. There is thus a new period, called the Julian
Period, consisting of 7980 years. The first year of this
period is 4713 B.C., which has been adopted because each
of the three other cycles had the value i on that year.
This period will continue till the year A.D. 3267.
97. Eclipses. It occasionally happens that the usually
circular disc of the sun is more or less obscured by the
252 A stronomy.
passage of the moon between the earth and the sun. In
some cases the entire light from the sun is cut off, this
constituting what is known as a total eclipse of tJie sun.
More frequently, however, only a portion of the sun is
darkened, and the eclipse is then said to be partial. An
eclipse visible at some places may not be visible at others,
even though the sun be visible ; and an eclipse which is
total at some places will only be seen as partial at others.
These phenomena of course can only occur at new moon,
when the longitude of the moon is identical with that of the
sun. It does not, however, follow that there is always, or
indeed even usually, an eclipse of the sun at new moon,
for as the orbit of the moon is inclined to the ecliptic, the
moon will generally at the time of new moon be over or
under the sun, and will only be seen against the face of the
sun when it happens that the occurrence of new moon is
nearly coincident with the time of passage of the moon
through one of its nodes.
So too it sometimes happens that the usually brilliant
appearance of the moon at the time of full moon is modified
by the appearance of a shadow with a circular edge, which
passes slowly over the bright disc. It sometimes happens
that only a portion of the moon's surface is thus obscured,
and the eclipse is then said to be partial. Not unfrequently,
FIG. 104.
however, the shadow passes completely over the moon, and
the eclipse is then said to be total.
The circumstances of an eclipse of the moon will be un-
derstood from Fig. 104. s represents the sun and T the earth.
The Moon. 253
A pair of common tangents, A B and A' B', drawn to the
earth and the sun, intersect at the point o, while the second
pair of common tangents intersect at o'. When the moon,
in its revolution around the earth, enters the region c' B' o,
it is partially obscured, and a partial eclipse of the moon
will be witnessed from the earth when the moon begins to
cross B' o. If the moon becomes immersed in the region
B o B', then the light from the sun will be altogether inter-
cepted, and a total eclipse of the moon will be seen.
It is a very curious circumstance that even when the
moon is plunged entirely in the earth's shadow it still
remains visible, with a peculiar copper-coloured hue suffi-
ciently bright on some occasions to enable the spots on
the surface to be recognised. This is due to the effect of
the atmosphere surrounding the earth in refracting the sun's
light, and bending it into the cone forming the shadow.
FIG. 105.
x
-X s -- ;===
/
This is shown in Fig. 105, where A represents a point on
the surface of the earth, while the dotted circular line is the
limit of the atmosphere. If the atmosphere were absent,
then a ray of light which just grazed the earth at A would
be directed along the straight line which just touches the
earth at A. Owing, however, to the presence of the atmo-
sphere, the light is bent so that its direction forms a part of
a curve of which the concavity is turned towards the earth.
In this way the rays from the sun which pass near enough
to the earth to be refracted by its atmosphere are bent into
the cone which forms the shadow, and thus illuminate the
254 Astronomy.
moon in the manner already described. Nor will it be
difficult to explain why the moon under these circum-
stances exhibits the peculiar copper-coloured light. The
rays to which this illumination is due have passed through
an enormous thickness of the terrestrial atmosphere,
and the absorption of light by the atmosphere tends to
render the light which has passed through it of a ruddy
colour.
98. Prediction of Eclipses. An eclipse of the moon
takes place when the moon, at the time of full moon, is
near the node of its orbit on the ecliptic. Let us, for ex-
ample, suppose that the time of full moon happened to be
exactly coincident with the passage of the moon through its
node. The position of the node must then be 180 distant
from that of the sun. In the period of 18 years n days we
find that 19 complete revolutions of the sun will have taken
place with respect to the moon's nodes. It therefore follows
that in 1 8 years and n days after the date of the eclipse
the node of the moon will again be 180 distant from the
sun. But in very nearly the same period 223 lunations will
have been completed. It therefore follows that in 18 years
and 1 1 days after the moon has been full at the node the
moon will again be full at the node. An eclipse may occur,
even though the time of full moon does not exactly coincide
with the time of passing through the node, provided that
the moon is sufficiently near the node at the time of full.
The same circumstances will recur again at an interval of
1 8 years and n days, and therefore we shall find in general
that 1 8 years and n days after the occurrence of a lunar
eclipse there will be another lunar eclipse. If, therefore,
we know all the eclipses which have occurred in a period of
1 8 years and u days, we are then able to predict future
eclipses with considerable accuracy. For example, in the
year 1862 a total eclipse of the moon, visible at Greenwich,
occurred on June n. Eighteen years and n days from
that time bring us to June 22, 1880, and accordingly on
The Moon. 255
that date again there was a total eclipse of the moon. So
also the eclipse of the moon on December 5, 1862, was fol-
lowed at the same interval of 1 8 years and 1 1 days by an
eclipse which occurred on December i6 3 1880.
It should, however, be observed that the numerical rela-
tion between the Synodic revolution and the period of the
lunation is only approximate. We cannot, therefore, employ
this method of prediction with infallible accuracy. It may
sometimes happen that a small partial eclipse is not followed
by an eclipse in 18 years and n days; and also that a
partial eclipse may occasionally occur, though no eclipse
took place 18 years and n days previously. For accurate
prediction of the occurrence of eclipses at remote epochs,
as well as for an accurate account of the details of eclipses
as to the time of commencement, and the duration, with
such other particulars as are given in the Nautical Almanac
each year, careful calculations have to be made. Such
calculations depend upon our knowledge of the motions of
the moon, derived from long-continued observations.
99. Eclipses of the Sun.^NQ have already stated that
eclipses of the sun are produced at the time of New Moon
by the interposition of the dark body of the moon between
the earth and the sun. According to the varying circum-
stances under which the occurrence happens we have a
corresponding variety in the character of the eclipse. If
the moon should cross the sun in such a manner that its
centre passes over or very close to the centre of the sun,
then the eclipse assumes one or other of two very remark-
able forms. It will sometimes happen that the entire surface
of the sun is obscured, in which case the eclipse is said to
be total. This phenomenon is, however, a very rare one,
and the apparent diameter of the moon is but very little
larger than that of the sun, so that the duration of the total
eclipse is very short. In fact, the movement of the moon
will, in a very few minutes, enable the margin of the sun to
be seen again. Sometimes, however, even though the centre
256 Astronomy.
of the moon passes very close to the centre of the sun, the
eclipse will not be total, but a ring of the sun's disk is visible
around the dark edge of the moon. In this case the eclipse
is said to be annular. It may seem at first strange that the
moon, passing centrally across the sun, should sometimes
produce a total eclipse and sometimes an annular eclipse.
This arises from the fact that the apparent angular diameter
of the moon is sometimes greater and sometimes less than
the apparent angular diameter of the sun. It will be re-
membered that the orbits both of the sun and of the moon
are eccentric, and that consequently the distances of these
bodies from the earth are constantly fluctuating within
certain limits. As the angular diameter of an object varies
inversely with its distance, it of course follows that the angular
diameter of the moon and that of the sun are also constantly
fluctuating between certain limits. It happens, curiously
enough, that the mean angular diameter of the moon is nearly
identical with the mean angular diameter of the sun. The
fluctuations arising from the eccentricities of the orbits are,
no doubt, small, but they are sufficiently large to make the
moon sometimes appear larger than the sun, and sometimes
smaller than it. In the former case the central passage of
the moon across the sun produces a total eclipse ; in the
latter case it only produces an annular eclipse.
100. Frequency of Eclipses. Eclipses of the moon are not
so frequent as eclipses of the sun. This will be manifest
FIG. 106.
from the consideration of Fig. 106. s represents the sun,
and T is the earth ; the tangents A B and A' B' intersect at o.
The Moon. 257
An eclipse of the moon will occur whenever the moon enters
the cone of the earth's shadow BOB'; an eclipse of the
sun will occur whenever the moon enters the portion of
the cone which lies between the earth and the sun. The
latter portion of the cone has a much larger section than
the former : consequently in its revolutions around the
earth the moon will more frequently enter the portion of
the cone between the earth and the sun than the portion
which is formed by the shadow of the earth. For this
reason the solar eclipses are more frequent than lunar
eclipses. It must not, however, be supposed that at any
given place on the earth more solar eclipses will be seen
than lunar eclipses. An eclipse of the moon is visible to the
inhabitants of a whole hemisphere ; an eclipse of the sun, on
the other hand, is only visible to the inhabitants of a portion,
and often only a small portion, of a hemisphere. From this
it follows that, notwithstanding there are more solar eclipses
than lunar eclipses, yet at any given locality more lunar
eclipses can actually be seen than solar eclipses. This may
be shown by the consideration that the diameter of the
earth's shadow at the distance of the moon is greater than
the apparent diameter of the sun. At a given place, there-
fore, it will be more usual for the moon to enter into the
shadow than for the moon to cross the sun, i.e. it will be
more usual for an eclipse of the moon to take place than for
an eclipse of the sun.
101. Prediction of Solar Eclipses. Although it generally
happens that a solar eclipse is followed by a solar eclipse in
the period of 18 years and n days, yet we cannot predict
the recurrence of solar eclipses in so simple a manner as we
can the recurrence of lunar eclipses. It is not possible by
the mere use of this period to say whether the solar eclipse
will be visible at a given place, or what the magnitude of the
eclipse may be. The sun's eclipses and all their circum-
stances can, no doubt, be predicted with great accuracy ;
but then, such predictions are the result of considerable
s
258 Astronomy.
calculations of a more intricate character than are required
for predicting the details of the eclipses of the moon. The
parallax of the moon being so large, the character of the
solar eclipse will depend not merely upon the locality in
which the observer is stationed, but also upon the altitude
of the moon at the time. As the altitude varies during the
progress of the eclipse, so the parallactic displacement of the
moon changes ; and this displacement must be allowed for,
as well as the actual motion of the moon, when com-
puting the duration and the other circumstances attending
the eclipse.
102. Occupations of Fixed Stars. h& the moon, by pass-
ing between the earth and the sun, produces an eclipse of the
sun, so it sometimes happens that the moon passes between
the earth and a star or a planet, and thus temporarily
eclipses them from view. This phenomenon is known as
an occupation. On account of the parallax of the moon, the
position of the moon on the surface of the heavens, as com-
pared with the fixed stars, varies with the position of the
observer on the earth. It follows that the occultation of a
star may be seen in one place, while in another the star will
not be occulted, though the moon will pass close thereto.
To predict the occurrence of an occultation the situation of
the observer must be taken into account. The calculations
necessary are very similar to those which are required for
the prediction of an eclipse of the sun.
The phenomenon of an occultation is peculiarly striking
when the disappearance of the star takes place at the dark
limb of the moon. In the interval between new moon and
full moon the motion of the moon is such that the dark
limb is on the advancing side. If, therefore, the path of the
moon happens to cross any star bright enough to be con-
spicuous, notwithstanding the brilliancy of the moon, then
the star will be instantaneously obscured when the dark edge
of the moon crosses the line joining the eye and the star.
After some time, during which the star remains hidden by
The Moon. 259
the interposition of the body of the moon, it will reappear
again on the illuminated side. Between full moon and new
moon the illuminated side of the moon is advancing, and
consequently the disappearance of the star at occultation
takes place at the illuminated limb, while the reappearance
occurs at the dark limb.
As the stars are practically at an infinite distance, we
may consider the rays from them to be parallel. If, there-
'fore, a circular cylinder be drawn just enveloping the
moon, while the axis of the cylinder is parallel to the rays
from the star, then the star will be occulted by the moon
when the observer is situated in the interior of this cylinder.
The area intercepted on the earth by the cylinder is
therefore the region in which the star will appear to be
occulted. The actual area is, of course, equal to the
section of the cylinder at the moon itself, i.e. to the section
of the moon by a plane passing through its centre. As the
area of a section of the moon is but a small fraction of the
entire surface of the earth, it follows that at a given moment
a star is only occulted from observers situated on a compara-
tively small area on the earth.
103. Determination of Longitudes by the Moon. To deter-
mine the difference in longitude between two given stations
on the earth, we require to have the means of comparing
the time at one place with the time shown simultaneously at
the other. When, for example, it is said that the longitude
of Dunsink is 25 m 2 1 8 west of Greenwich, the statement may
be interpreted in two different ways, both of which are
correct. It may mean that an interval of 25 21" of sidereal
time will elapse between the transit of a fixed star across the
meridian of Greenwich and the transit of the same star
across the meridian of Dunsink ; or it may equally mean
that an interval of 25 21" of mean solar time will elapse
between the transit of the mean sun across the meridian of
Greenwich and the transit of the mean sun across the
meridian of Dunsink. The actual angle formed at the pole
S 2
2 60 A stronomy.
by the meridian passing through Greenwich and Dunsink
bears to 360 the same proportion which 25 2i 8 bears to 24
hours. This angle is 6 20' 15".
The sidereal clock in the observatory at Dunsink should
therefore be always 25 21" slower than the sidereal clock
at Greenwich, when the two clocks are correct. So, too, the
mean time clock at Dunsink should also be slower than the
mean time clock at Greenwich by the same amount. To
determine, therefore, the difference between the longitude
of Dunsink and that of Greenwich, it is only necessary to
have the two clocks at each place correct, and to note their
difference. The difficulty in the process is entirely due to
the distance between the two stations, which makes the
accurate comparison between the two clocks a matter of
difficulty. The method formerly adopted was to compare
chronometers with the clock at one station and then to carry
these chronometers to the second station. This method has
been superseded in the case where telegraphic communica-
tion exists between the two stations. As the telegraphic
signal is practically instantaneous, it can be arranged that at
a given signal from one station to the other the time shown
by the clocks is to be noted ; and if the clocks are correct,
or, what comes to the same thing, it ttyeir errors are known,
the difference between the two clocks, and, therefore, the
difference in longitude, is ascertained. This method is by far
the most accurate, and it is always employed when great pre-
cision is required, if the telegraphic communication exists.
To determine the longitude at sea or under other cir-
cumstances when either of the methods we have suggested
are inapplicable, resort may be had to the method of lunar
distances, now about to be described. It is to be remembered
that when we know the time at the station where we are
situated, it is only necessary to know the simultaneous time
at Greenwich in order to know the longitude. If, therefore,
there were a clock in the heavens, the hands of which always
indicated true Greenwich time, and if this clock were visible
The Moon. 261
from all parts of the earth, then the determination of longi-
tude would be a comparatively simple matter. The motions
of the moon on the surface of the heavens do actually
provide us with such a clock. The fixed stars are the
numbers on the clock, while the moon is the hand by which
the time is indicated. To interpret this clock, and deduce
from it the Greenwich time, use is made of the tables of the
moon, by which the place of the moon can be predicted
with considerable accuracy for many years in the future.
From these tables we can deduce the angular distances at
which the moon will be separated from the bright stars
which lie along its path at stated intervals. These distances
are recorded in the Nautical Almanac for intervals of three
hours daily. For example, on June 30, 1879, the distance of
the moon from the star Regulus at noon, Greenwich time,
was 83 54' 1 8" ; at III. hours the distance was 85 43' 45'' ; at
VI. hours it was 87 33' if, and at IX. hours 89 22' 52".
If, therefore, the actual distance of the moon from the star
Regulus be measured, and if the distance coincides with any
of those above specified, then the corresponding Greenwich
time is at once discovered. It will, of course, generally
happen that the observed distance will not coincide with
any of the actually recorded distances. A simple interpola-
tion will, however, enable the corresponding mean time to
be determined.
In the application of this method it is necessary to allow
for the effect of parallax in deranging the position of the
moon, while the effect of refraction both on the moon and
the star must be taken account of also.
The mode of doing this is shown in the adjoining figure.
Let o represent the position of the observer, while z is his
zenith, E is the observed position of the star, and L is the
observed position of the moon. With the sextant the
observer measures the apparent angular distance between E
and L that is, the angle E o L. He also at the same time
measures the zenith distances, z E and z L. The effect of
262
A stronomy.
refraction upon the star is to make the star appear at E,
while, if refraction were absent, the star would really be
found at E'. In the same way, if the apparent place of the
moon is at L, its true place is at L' so far as refraction is
concerned. If, however, the observer were stationed at the
centre of the earth, the moon would be thrown up by
parallax from L' towards the zenith, and would therefore be
found in the position L". The corrected distance, which is
to be employed, is therefore E' L". This can be calculated
from the spherical triangle z E' L". For since the distances
z E, z L, and also the distance E L, are determined by ob-
FIG. 107.
servation, the angle E z L is known. Also, since the effects
of refraction and parallax on the zenith distances can be
computed and allowed for, the corrected zenith distances
z E' and z L" may be regarded as known. In the spherical
triangle E' z L" we therefore know the two sides and the
angle included at z ; the base E' L" is therefore also known.
The accuracy of the method of lunar distances as we have
here described it is, of course, affected by any irregularities in
the tables of the moon's motion, as well as by the actual
errors which may arise in the observations.
The occultation of a bright star by the moon affords a
method by which the longitude may be determined with
The Planets. 263
very considerable accuracy. If the time of the occultation
be noted at each of two places, and if the suitable allowance
be made for the effect of parallax, then a comparison of the
observations will show the difference between the local times
at the moment of occultation as seen from the earth's centre.
This difference is, of course, the longitude. This method pos-
sesses the advantage of being but little affected by the errors
of the tables of the moon. The occultation of a sufficiently
bright star is, however, a comparatively rare occurrence.
CHAPTER VIII.
THE PLANETS.
104. Determination of the Planets. The planets of our
system which were known to the ancients are Mercury,
Venus, Mars, Jupiter, and Saturn. These objects, in a
superficial view, resemble somewhat brilliant stars, but a
little attention is sufficient to point out that they are of a
very different character. If we note the position of one of
these bodies with reference to stars which lie in its vicinity,
and if we repeat the observation after the interval of a few
days, it will be found that, though the stars have retained
their relative positions, the position of the planet with respect
to the stars has altered. This remarkable feature of the
planets attracted attention in the earliest times.
To distinguish a planet we may make use of a celestial
globe. If, in comparing the constellations marked on the
globe with the constellations in the heavens, a conspicuous
starl ike object is seen in the heavens which is not to be
264 Astronomy.
found on the maps, we may conclude with considerable
certainty that the object is one of the five planets Mercury,
Venus, Mars, Jupiter, or Saturn. If we wish to solve the
common problem of identifying a given planet in the sky,
we must then make use of the Nautical Almanac, or some
similar work, in which the right ascensions and declinations
of the planets are recorded daily or at frequent intervals
throughout the year. Thus, for example, if we wish to find
out the planet Jupiter on June 23, 1879, we turn to the
Nautical Almanac for 1879, an ^ on p. 253 we see that the
right ascension of Jupiter is 22 h 57 m 3 3 s '5 9, while its south
declination is 7 53' i$"'i. With the aid of a telescope
mounted equatorially and provided with graduated circles,
it is only necessary to set the telescope to the required
declination, and then turn the instrument round the polar
axis until the hour angle is equal to the difference between
the sidereal time at the moment and the right ascension of
Jupiter. The planet will then be seen in the field of view.
But a telescope is not necessary when the object is merely
to identify the planet and distinguish it from the stars. By
referring to a celestial map or globe it will be easy, from the
known right ascension and declination, to determine the
position of Jupiter on the celestial sphere. It will be found
to lie in the constellation Aquarius at the date under con-
sideration. If, therefore, the observer looks at that part of
the heavens where Aquarius is situated, he will at once
recognise Jupiter as the very brilliant object there situated.
This he will confirm by noticing that there is no star marked
on the globe in the position in which he sees Jupiter. It
will be of great interest for the beginner, having once recog-
nised Jupiter by either of the methods we have described, to
note the changes in position which it undergoes with refe-
rence to the stars in its vicinity. If he be provided with a
telescope, then from one night to the next, or even in the
course of a single night, he will be able to detect the move-
ments of Jupiter by carefully comparing his position with
The Planets. 265
the stars in the neighbourhood. Even without the aid of a
telescope careful observation by alignment with the stars
will in a few weeks reveal the motion of the planet.
All the movements of the planets which are visible to
the unaided eye, including Mercury, Venus, Mars, Jupiter,
and Saturn, are performed in orbits which never deviate
much from the plane of the ecliptic. It follows that these
planets are always seen in a portion of the heavens near the
ecliptic. This consideration considerably simplifies the
operation of finding out the planets. For example, to take
the case of Jupiter in June 1879. Suppose that it is known
that this planet crosses the meridian about 23 hours of
sidereal time. The place of the planet in the heavens can
then be easily found by the globe. On the great circle of
the globe which represents the equator the hours of right
ascension are marked. Draw from the pole a great circle to
the point marked XXIII. ; produce this on to cut the ecliptic :
then Jupiter must be very close to this intersection, because
it is known to be close to the ecliptic, and it is also known
to have a right ascension of 23 h . This method will be
quite sufficient for the purpose of identifying a planet.
105. The Zodiac. As the planets which are now under
consideration never depart very widely from the ecliptic, it
is possible to mark out a certain zone in the heavens, on the
interior of which the planets are always to be found. This
zone extends to 8 on each side of the ecliptic, and it is
termed the zodiac. If we divide the ecliptic into twelve
equal portions, and then draw through each of the points of
division great circles perpendicular to the ecliptic, these
great circles will subdivide the zodiac into twelve equal
portions. Each of these portions is represented by a certain
name, which is also borne by the constellation which each
portion contains.
106, Kepler's Laws. By the aid of the meridian circle it
is possible to determine a series of positions of a planet at
different times, and thus to mark these positions on the
266 Astronomy.
celestial sphere with precision. When this is done, it is
found that although the general features of the motions of
the planets are consistent with the supposition that the
orbits are perfect circles, yet that when a more minute com-
parison is instituted between the results of this supposition
and the results of actual observation, certain discrepancies
are brought to light which are too large and too systematic to
admit of being explained away as merely errors of observation.
The first of the three discoveries which bear the name of
Kepler may be thus enumerated :
The path of a planet round the sun is an ellipse, in one
focus of which the centre of the sun
is situated.
Thus, let s (Fig. 108) represent
the centre of the sun ; then the
ellipse A B p Q denotes the path of
the planet. In none of the prin -
cipal planets is the deviation from
a circle so great as it is repre-
sented in the figure, which has been designedly exaggerated.
It is approximately correct to say that the planets move
with uniform velocity in these orbits round the sun. When,
however, this question comes to be tested by careful obser-
vations, it is found that the movements are not quite uni-
form. The planet is found to be moving more rapidly at
some parts of its path than it is at others. The law by
which these variations in the velocity of a planet are con-
trolled was also discovered by Kepler, and is expressed by
his second law, which is thus stated:
In the motion of a planet round the sun, the radius vector,
drawn from the centre of the sun to the planet, sweeps over
equal areas in equal times.
Thus, for example, in Fig 108, when the planet moves
from A to B, its radius vector sweeps out the area A s B, and
in moving from p to Q the radius vector sweeps out the area
p s Q. Kepler's second law asserts that if the area A s B be
The Planets. 267
equal to the area p s Q, then the time taken by the planet in
moving from A to B is equal to the time taken by the planet
in moving from P to Q.
It is easy to show how, when the planet moves in obe-
dience to this law, the observed changes in the velocity of
the planet can be completely accounted for. Since the
planet must move from p to Q in the same time as it takes
to move from A to B, and since the distance P Q is very
much larger than the distance A B, it follows that the velocity
of the planet must be greater when it is moving through p Q
than when it is moving through A B. We hence see that
the planet must be moving with greater velocity according
as its distance from the sun is less.
In the two laws of Kepler, which have been already
discussed, we have only been considering the motion of one
planet. We have now to consider the very remarkable law,
also discovered by Kepler, which relates to a comparison
between two planets. This law, known as Kepler's third
law, is thus stated :
The squares of the periodic times of two planets have the
same ratio as the cubes of their mean distances from the sun.
To explain this, it must first be observed that by the
mean distance of the planet from the sun is to be understood
a length which is equal to the semiaxis major of the ellipse,
while the periodic time is understood to be the actual
number of days and fractions of a day, in which the planet,
as seen from the sun, makes a complete revolution round
the heavens.
To illustrate the application of Kepler's third law we
may take the cases of Venus and the Earth. The periodic
times of Venus and the Earth are respectively 365-3 days
and 2247 days, while the mean distance of Venus is 07233
if we take the mean distance of the earth as unity. We
have for the square of the ratio of the periodic times
1
2247
268 Astronomy.
while for the cube of the ratio of the mean distances
which verifies the law.
Kepler's three laws are found to be borne out com-
pletely, even to their minutest details, when proper allow-
ance has been made for every disturbing element.
107. The Planet Venus. With the exception of Mercury,
and possibly also of some one or more other planets which
may be still closer to the sun, Venus is the nearest of all
the planets to the great centre of our system. The actual
path of Venus differs but little from a circle of which the sun
is the centre, and of which the radius is 67,500,000 miles.
Owing, however, to the ellipticity of the orbit, the exact
distance fluctuates a little on either side of its average value,
but it is never less than 67,000,000 miles, or more than
68,000,000 miles. The planet Venus, therefore, describes
around the sun an orbit of about 135,000,000 miles in
diameter. This, though no doubt an orbit of majestic pro-
portions, is still considerably smaller than the orbit which is
described by the earth, and it is very much smaller than the
paths described by the more distant planets. Round her
path Venus sweeps in a period of 224 days 15 hours, and
though this may seem a considerable time for the journey
round the sun to be accomplished, yet the length of that
journey is such that the planet has to move at an average
rate of twenty-two miles per second, in order to accomplish
it in the time. The actual velocity with which Venus moves
is not absolutely uniform, but it is never greater than twenty-
two and a half miles per second, or less than twenty-one and
a half miles. It is instructive to contrast the velocity of
Venus with the velocity of the earth, for as the latter is
eighteen and a half miles per second, we have an illustration
of the general truth that those planets, which are near the
sun, move more quickly than those which are farther off.
The Platiets. 269
In order to consider the circumstances under which
Venus appears alternately as a morning or evening star, it is
necessary to observe that the relative positions of the sun
and of Venus, as seen from the earth, are the same as if the
earth and the sun remained fixed, and if Venus turned around
the sun in a period of 584 days. We have thus a cycle of
phenomena which run through their course in a period of
584 days and then begin again. We shall briefly describe
the course of the changes in the appearance of Venus in
one of these cycles, and we shall take for example the cycle
which commenced on May 6, 1877. Venus was then in
what is called superior conjunction with the sun ; in other
words, Venus was so placed that the sun lay between the
planet and the earth. It would not, however, be correct to
say that Venus was actually behind the sun, for although this
sometimes happens, yet its occurrence is very rare, because
of the inclination of the orbit of Venus to the ecliptic. At
the date we have mentioned Venus was south of the sun
by a distance equal to more than three of the diameters of
the sun. (We refer, of course, to the apparent diameters
projected on the surface of the celestial sphere.) It is
obvious that when Venus is in superior conjunction, very
nearly the entire illuminated surface is turned towards the
earth, but the distance from the earth to the planet is then
so great, that the brilliancy does not amount to the fourth
part of what it will ultimately become.
After passing through the position of superior conjunction,
Venus begins to move to the east of the sun, and thus to set
after the sun. It was thus that late in the autumn of 1877
Venus began to be seen in the west after sunset, gradually
increasing in brilliancy as well as in the apparent distance
by which it was separated from the sun. The successive
changes in the situation of Venus at this time are shown in
Fig. 109, which exhibits the actual position of the apparent
orbit of Venus about the sun during the cycle referred to.
For convenience the sun is represented on the horizon at
270 A stronomy.
the moment of setting. The angular distance between the
sun and Venus gradually increased until it attained a
maximum on December ir, 1877, the planet being then at
its greatest elongation east. The angular distance between
the sun and Venus was then 47. We thus come to the
first critical epoch of the cycle, 219 days after its commence-
ment. The brilliancy of the planet has also been increasing,
and at the time of its greatest elongation the brilliancy has
attained three quarters of its greatest value. If looked at
through a telescope during its movement, the phases of the
planet can be seen exactly resembling in miniature the
FIG. 109.
phases of the moon. Thus in superior conjunction the
planet appeared full, but gradually changed its form, until at
greatest elongation the planet resembled the moon at first
quarter. After passing the point of greatest elongation,
Venus commences to assume a crescent form, but its
brilliancy is still increasing, because the continual diminution
of the distance between the earth and the planet more than
compensates for the gradual diminution of the portion of the
illuminated hemisphere which is turned towards the earth.
Each day the shape of the crescent becomes more slender,
but each day the apparent diameter of the crescent measured
from one horn to the other gradually increases, so that the
The Planets. 271
apparent area of the crescent on which its brightness depends
gradually increased until January 16, 1879. On this date,
or 256 days after the commencement of the cycle, the
brilliancy of the planet attained its maximum. It is thus on
one occasion during each cycle, or on an average once
every 584 days, that Venus attains its greatest brilliancy as
an evening star. The next occasion on which Venus was
brightest in the evening occurred on August 18, 1879: the
exact interval between these dates is 579 days. The
difference of 5 days between this period and that of the
average lengths of the cycle, i.e. 584 days, is principally due
to the circumstance that the orbit of Venus, though nearly
a circle, is still slightly different therefrom. The average
of a large number of intervals between two successive
recurrences of Venus at its brightest in the evening will
be found to equal 584 days, and the differences will never
amount to more than a few days on one side or the other of
its average value.
After the position of greatest brilliancy has been passed,
the crescent formed by Venus becomes more and more
slender, though the circle of which the crescent is a part has
a diameter which is gradually increasing. The planet is
now drawing in again towards the sun. In fact, the elonga-
tion or the angular distance between the planet and the sun,
which at the time of greatest elongation was equal to 47,
has already diminished to 40 at the time of greatest
brilliancy. As the planet approaches the sun, the crescent
becomes gradually attenuated to a thin line of light, still a
beautiful object in the telescope, though of course, as the
planet is now so close to the sun and sets very soon after it,
it will become necessary to search for the planet in the day
time. On February 20 Venus had approached as nearly as
possible between the earth and the sun into the position
called inferior conjunction. This occurs 292 days after
superior conjunction, and thus half the cycle of 584 days
has been accomplished.
272 Astronomy.
Owing, however, to the inclination of the orbit of Venus
to the plane of the ecliptic, the planet did not actually come
between the earth and the sun at this conjunction. After
passing through inferior conjunction, Venus moves towards
the west of the sun, and, therefore, rises before the sun,
and is called a morning star. The actual orbit which Venus
describes, relatively to the sun at sunrise, is shown in
Fig. no. From this figure it will be seen that Venus then
performed the second half of the cycle of changes in a
similar manner to the first half, only with the order reversed.
FIG. no.
The planet then moved further from the sun, increasing in
brilliancy at the same time, until March 29, when, after an
interval of 329 days from the commencement of the cycle of
changes, the position of greatest brilliancy is again attained.
Thus in each cycle of changes we have two epochs of
greatest brilliancy, and the interval between these epochs
averages 73 days. On the first of these occasions Venus is
always an evening star, and on the second a morning star.
The angular distance from the sun gradually increases until
May i, when the elongation is 46. This is the last re-
markable phase in the cycle of changes, and occurs on the
3651!! day. During the remaining 219 days Venus is moving
slowly through the remote part of its orbit back to the
The Planets.
273
position of inferior conjunction, from which we have supposed
it to start.
When Venus is in the neighbourhood of superior conjunc-
tion that is, when it is most remote from the earth its
apparent diameter is about ten seconds of arc, but when the
planet is in the neighbourhood of inferior conjunction it
becomes a much more imposing object ; for, owing to our
diminished distance, the apparent diameter is augmented to
about sixty seconds. It will thus be readily understood
that the best time to see Venus during each cycle of 584
days is during the period of about four months, when the
planet is passing from the greatest elongation east to the
greatest elongation west.
It is easy to show how all these changes in the appear-
ance of Venus can be explained by the actual motion of
Venus around the sun. Let T (Fig. in) be the earth, and
T
274 Astronomy.
let s be the sun, while v denotes Venus. Then the circle
described about the sun's centre represents the orbit of
Venus. When Venus is at the position A, its entire illumi-
nated hemisphere is turned towards the earth, but its dis-
tance is so great that the apparent angular diameter is very
small, and the actual size of Venus is represented at A (Fig.
112). When Venus moves to B, a portion of the dark hemi-
sphere is directed towards the earth, and, consequently, the
planet appears as represented in B (Fig. 112), the apparent
diameter of the planet having increased, owing to the
diminished distance from the earth. When Venus arrives at
c it is in the position of greatest elongation ; the planet then
appears with half its disk illuminated, as shown in c (Fig. 112).
FIG. 112.
D
After passing this position, Venus moves on till, in the position
D, when it has come comparatively close to the earth, it
assumes the crescent form shown in D (Fig. 112). It may
be observed that two points, D and B, have been chosen,
which lie in the same straight line through T. It follows
that the angular distance between the sun and Venus in
either of the positions B and D are equal ; yet how different
is the actual appearance of the planet in the two cases ; in the
one it is shown in B, and in the other in D (Fig. 112). After
leaving D the planet moves on to E, where almost the entire
dark surface of the planet is directed towards the earth.
The Planets. 275
The actual size of the disc of Venus in this case is repre-
sented at E (Fig. 112).
From the observation of certain markings upon the
surface of Venus it has been shown that this planet revolves
upon its axis in the same direction as the planet revolves
round the sun. The markings are, however, so exceed-
ingly difficult to see that there is a great deal of uncer-
tainty as to the length of the period of rotation, some
observers maintaining that Venus rotates in about 23 hours,
others believing with Schiaparelli that Venus always turns
the same face to the sun, as the moon does to the earth.
Venus appears to be surrounded by an atmosphere the
existence of which is rendered manifest by a twilight
analogous to the same phenomenon on the earth. The
hemisphere of the planet which is turned away from the
sun is not entirely dark, but it is illuminated for a short
distance within the boundary by light which is reflected
from the atmosphere. The density of this atmosphere
appears to be comparable with that surrounding the earth ;
for it would appear from the observations of Madler that
the horizontal refraction at Venus is 44', while in our
atmosphere the horizontal refraction is 33'. The line of
separation between the shadow and the illuminated portion
of Venus is sometimes irregularly notched and indented,
and the cusps or horns of the crescent are occasionally
seen truncated. This appears to be due to the moun-
tains and asperities upon the surface of Venus.
On those rare occasions in which a transit of Venus takes
place, the planet is seen to form a black circular disc pro-
jected against the surface of the sun. The measures which
have been taken of this disc do not indicate the existence of
any ellipticity. It is, however, not impossible that the globe
of Venus may have an ellipticity comparable with that of the
earth ; for even the ellipticity of the earth itself would not
be recognisable if it were viewed from the distance at which
Venus is separated from the earth.
T3
276 Astronomy.
The apparent diameter of Venus, or rather the angle
which its diameter subtends at the eye, varies of course
with its distance. According to Hartwig (1879) the dia-
meter of Venus, when at a distance equal to that of the
earth from the sun, is 17 "'6 7. From this we conclude that
the radius of Venus is nearly equal to the radius of the
earth.
108. Mercury. The movements of Mercury are to a
certain extent analogous to those of Venus. The planet
oscillates from one side of the sun to the other, as Venus
does, and is thus occasionally to be seen as a morning star,
and occasionally as an evening star. The movements of
Mercury are, however, not nearly so regular as those of
Venus, owing to the much greater eccentricity of the orbit
of Mercury.
Though Mercury is sometimes very easily visible with
the unaided eye, it is not very often seen, on account of the
planet being always in the proximity of the sun. Mercury
is also usually too near the horizon, when visible at all, to
be seen to much advantage. It is, therefore, not surprising
to find that many persons who are familiar with the four
greater planets of our system viz. Venus, Mars, Jupiter,
and Saturn have never yet seen the planet which, so far as
we certainly know at present, is the nearest of all to the
sun.
The planet Mercury has a diameter of about 3,000
miles. It is therefore much smaller than the earth, of which
the diameter is about 8,000 miles. The only one of the
principal planets which at all approaches Mercury in bulk is
Mars, of which the diameter is 4,000 miles. The diameter
of Jupiter is more than thirty times as great as the diameter
of Mercury, yet the brilliancy of Mercury on some occasions
(e.g. February 1868) rivals that of Jupiter in splendour.
This arises from two causes. In the first place Mercury is
only distant from the sun by about ^ th part of the distance
The Planets. 277
by which Jupiter is separated from the sun. It follows
that the brilliancy with which the surface of Mercury is
illuminated by the sun's rays must be much greater than
the brilliancy of the illumination of Jupiter. When this
is combined with the circumstance that the earth is much
nearer to Mercury than it is to Jupiter, it will be under-
stood how, notwithstanding the small size of Mercury, it
may sometimes be nearly, if not quite, as splendid as
Jupiter.
The eccentricity of the orbit of Mercury is much
more considerable than that of any other of the principal
planets of our system. In fact, the greatest and the
least distances of Mercury from the sun are respectively
43,000,000 miles and 28,000,000 miles, or very nearly in
the ratio of 3 to 2. Mercury accomplishes one complete
revolution around the sun in about 88 days. Owing to the
revolution of the earth around the sun in 365 days, the
apparent time of one revolution of Mercury relatively to the
earth is 116 days, and this is the average duration of the
cycle which includes a complete series of the changes in the
relative positions of Mercury and the sun. Once in each
period of 116 days Mercury appears at its greatest elonga-
tion to the east of the sun, and then in about 48 days after-
wards the planet has moved to its greatest elongation west
of the sun.
The actual angular value of the greatest elongation is not
constant, for it depends upon the relative distances of the
earth and Mercury from the sun. The distance of the earth
is very nearly constant, but the distance of Mercury fluc-
tuates between the wide limits already specified. Under
the most favourable circumstances, at the greatest distance
of Mercury from the sun, combined with the least distance
of the earth from the sun, the elongation might amount
to upwards of 28. On the other hand, if Mercury hap-
pened to be at its least distance from the sun at the time
278 Astronomy.
of greatest elongation, while at the same time the earth was
at its greatest distance, the elongation would only amount to
16 or 17.
As, however, we pointed out in the case of Venus, it
does not follow that a planet is brightest at the time of
greatest elongation. No doubt, if a planet were situated at
the distance of 41,000,000 miles from the sun, it would
appear brightest at the time of the greatest elongation, and
the appearance of the planet in the telescope would then
resemble that of the moon at first quarter. If the distance
of the planet from the sun be greater or less than 41,000,000
miles, then the maximum brightness will not occur at the
time of greatest elongation. There is, however, an import-
ant distinction to be observed. If the distance of the planet
exceed 41,000,000 miles, as is always the case with Venus,
but rarely the case with Mercury, then the greatest bright-
ness occurs after the greatest elongation east, or before the
greatest elongation west ; in either case when the planet
appears somewhat crescent-shaped in the telescope. If the
distance of the planet from the sun at the time of greatest
elongation be less than 41,000,000 miles, as is generally the
case with Mercury, then the greatest brightness occurs a few
days before the greatest elongation east, or a few days after
the greatest elongation west ; in either case when the planet
shows more than half its disc illuminated.
Mercury, when visible at all, must be sought for low
down in the west shortly after sunset, or low in the east
shortly before sunrise, according as the planet is at its east
or west elongation. It is not usually a very striking object
in the telescope, but its phases, resembling those of a minia-
ture moon, are readily seen. There is the same diffi-
culty in determining the period of rotation as in the case
of Venus. Schroter concluded from some minute irregu-
larities in the shapes of the horns that Mercury rotates
in 24 hours, but Schiaparelli maintains that some very
The Planets. 279
faint surface markings prove the mercurial day to be 88
days, equal to the period of revolution round the sun.
109. The Superior Planets. The inferior planets,
Mercury and Venus, are, as we have seen, always to be
found in the neighbourhood of the sun. The case is very
different with the planets Mars, Jupiter, and Saturn, now to
be considered. These planets are, it is true, always found
in or near the ecliptic, but so far from being limited to that
part of the ecliptic which is near the sun, they may occupy
any position with respect to the sun, and are sometimes
even 180 distant from the sun on the opposite side of the
circle.
110. The Planet Mars. The nearest of the superior
planets to the earth is Mars, and we shall therefore com-
mence the study of the exterior planets by an examination
of his movements. Let us imagine for a moment that the
earth and Mars are each revolving around the sun in circles
of which the sun occupies the centre. The motion of the
earth is of course completed in 365 days, but the motion of
Mars requires the longer period of 687 days. It follows
that, as the earth moves more rapidly than Mars, it must
occasionally overtake him, and pass between him and the
sun. This phenomenon is known as an opposition of Mars,
and it occurs once in every 780 days. When this is the
case, Mars is 1 80 distant from the sun, and he consequently
comes on the meridian at midnight. A moment's conside-
ration will also show that when Mars is in opposition he is
nearer to the earth than he is when he occupies any other
position. If we take the mean distance of the earth from
the sun to be 92,000,000 miles, then the mean distance of
Mars from the sun is 140,000,000 miles. It is therefore
plain that when Mars is in opposition, the distance by which
he is separated from the earth is 48,000,000 miles. This,
therefore, is the distance at which we would see Mars at
every opposition ; and supposing the orbits of the earth and
280 Astronomy.
Mars were exact circles, then this distance would be the
same at every opposition.
But the orbits are not exact circles. The orbit of the
earth is an ellipse, which, indeed, has such a small eccentri-
city that it differs but little from a circle. But the orbit of
Mars differs a good deal from a circle, and hence it follows
that at some oppositions Mars is nearer to the earth than he
is at others. To state the matter accurately, we find that
though the average distance between the earth and the sun
is 92,000,000 miles, yet that the real distance is sometimes
as great as 93,500,000 miles, and sometimes as small as
90.500,000. Similarly it is shown by observations of Mars
that the distance at which he is separated from the sun
ranges between 153,000,000 miles and 127,000,000 miles.
If it should happen that at the time of opposition Mars was
at its greatest distance from the sun, and the earth at its
least distance, then the actual distance between the earth
and Mars at such an opposition could not be less than
62,500,000 miles. But if at the time of opposition Mars
was found at its least distance from the sun, while the earth
happened to be at its greatest distance, then the actual
distance between the earth and Mars would be only
33,500,000 miles. We learn from these considerations that
at the time of opposition the distance between Mars and
the earth cannot possibly be greater than 62,500,000 miles,
or less than 33,500,000 miles.
Mars is of course most favourably situated for
observation when he is in opposition. He then comes
on the meridian at midnight, and his distance from
the earth is at its minimum value. The figures we have
just given show, however, that some oppositions may be
much more favourable than others. The distance at the
time of opposition, when the planet is most favourably
situated, is scarcely more than half what that distance is under
the least favourable circumstances. The advantage with
The Planets. 281
which a distant object may be scrutinised varies inversely as
the square of the distance. We therefore find that some
oppositions may be nearly four times as favourable as others
for the purposes of the astronomer.
At the great majority of oppositions, of which one occurs
about every two years, the distance between the earth and
Mars lies well between the limits we have mentioned. But
in the opposition of September 1877 a combination of
favourable circumstances brought the distance of Mars
from the earth to very nearly as low a point as that distance
is capable of attaining. On September 2, 1877, Mars ap-
proached the earth to a distance of 34,700,000 miles, which
is very close to the lowest limit It was on August 17 in that
year that the inner of the two satellites of Mars was disco-
vered by Professor Hall, at Washington, the distance of the
planet from the earth being then only 36,300,000 miles. It
is necessary to go back to the year 1845 m order to find an
opposition at which Mars approached the earth so closely
as it did in September 1877. It appears that on August
1 8, 1845, the distance between the earth and Mars was
34,300,000 miles. On this occasion, therefore, Mars was
nearly half a million miles nearer the earth than it was in
1877. The next nearest approach was in the year 1860,
when on July 2 the distance of Mars was 36,000,000 miles.
It may be observed that although this approach is not
so close as that witnessed in the opposition of 1877, yet
Mars was actually closer to the earth then than he was
at the time when the two satellites were first discovered.
The last close approach of Mars was on August 6, 1892,
when the distance was only 64,000 miles greater than in
September 1877.
Another past opposition may be noted for the greatness
of the distance between the earth and Mars, even when they
were closest. On February 13, 1869, the distance from the
earth to the planet then in opposition was 62,300,000 miles.
282 Astronomy.
This, it will be observed, approaches very closely to the
maximum value of the distance at opposition between the
earth and the planet.
Assuming, as we may for our present purpose, that the
orbit of the earth is circular, there is another mode of
viewing the subject which may perhaps tend to make it
clearer. It has been found that Mars completes his revo-
lution round the sun in a period of 687 days. In the course
of this period the distance of Mars from the sun goes through
all its changes, increasing from 127,000,000 miles up to
153,000,000, and then again decreasing to the same limit.
If we conceive an observer stationed at the sun, then the
direction in which he will see Mars when that planet is
closest to the sun is the same for every revolution. This, in
fact, amounts to the statement that the direction of the
major axis of the orbit of Mars is practically constant, for
we may overlook for the present purpose the small and slow
changes of that direction which arise from the action of the
other planets. This line produced backwards will point to
that part of the heavens in which Mars is always to be found
when he is at the greatest distance from the sun. Twice
every year the earth in its annual motion crosses or passes
extremely close to this line. On August 26 each year the
earth passes between the sun and that point of the heavens
in which Mars must be situated when he is nearest to the
sun. Similarly on February 2 2 in each year the earth passes
between the sun and that point of the heavens in which
Mars must be situated when he is at the greatest distance
from the sun.
We can now understand the circumstances under which
an opposition is favourable for the purpose of observing
Mars. If it so happened that an opposition occurred on
August 26 in any year, Mars would be as near as possible
to the sun, and therefore as near as possible to the earth,
because the earth is then situated exactly between Mars and
the sun. If, on the other hand, an opposition occurred on
The Planets. 283
February 22, then matters would be as unfavourable as pos-
sible, because for an opposition at any other date the earth and
the planet would be nearer together. We have, therefore,
in the date alone a very simple test as to the excellence of
an opposition of Mars for astronomical purposes. The
nearer that date is to August 26, the better it is, and the
nearer that date is to February 22, the worse it is. These con-
siderations are illustrated by the opposition of 1877, which
occurred on September 5, or only ten days after the best
date possible. In 1845 the opposition took place eight days
before the critical date, and therefore, as we have already
mentioned, it was somewhat more favourable than the op-
position of 1877. On the other hand, a very unfavourable
opposition occurred on February 13, 1869, the day of the
year being not far from that on which an opposition would
be least favourable.
It is worth noticing that the revolution of Mars round
the sun, and the revolution of the earth around the sun, are
so related that Mars accomplishes 17 revolutions in very
nearly 32 years, or, with still greater accuracy, 25 revolutions
in 47 years. From the last-mentioned numbers it appears
that if the earth and Mars occupy a certain position at a
given date, they will in 47 years be again found in the same
relative position, Mars having in the interval performed 25
revolutions. It therefore appears that a favourable opposi-
tion of Mars will be followed in 32 years, and also in 47 years,
by favourable oppositions. For example, we have mentioned
that 32 years before the opposition in 1877 a favourable
opposition occurred in 1845. We therefore infer that 47
years after this date, i.e. in 1892, a favourable opposition
may be looked for.
The accompanying diagram (Fig. 113), which is drawn
to scale, exhibits the orbit of the earth and the orbit
of Mars. E E' E" represents the orbit of the earth, and
M M' M" the orbit of Mars. The axis major of the earth's
orbit is M L, that of Mars's orbit is P Q. A favourable
284
Astronomy.
opposition obviously occurs whenever Mars is near p while
the earth is near A, while the most unfavourable opposition
takes place whenever Mars is near Q while the earth is near
B. It was on August u, 1877, when the earth and Mars
had the position represented by E and M, that the first satellite
FIG. 113.
of Mars was discovered. The actual closest approach of
the planet to the earth took place on the following September
2, when the relative positions of the two bodies are shown
by E and M'. At the opposition which occurred in Novem-
ber 1879 the closest approach of the planet to the earth
took place on the 4th, when the planet and the earth had
the position represented by E" and M".
The movement of Mars among the stars appears some-
times to be direct, i.e. in the same direction as that in
which the sun or the rnoon move, and sometimes to be re-
The Planets.
285
FIG. 114.
trograde, i.e. in the opposite direction. It will be easy to
render an explanation of these features of the movements
from what we have already seen.
Let the outer of the two circles (Fig. 114) represent the
orbit of Mars, while the inner arc is the orbit of the earth, s
being the sun in the centre. As we are
only considering the apparent move-
ments of Mars, we may suppose that
Mars is at rest at M, while the earth is
moving with a corresponding slower
motion. Let us first suppose the
earth to be at x ; then Mars, which is
situated at M, will be seen in the direc-
tion x M, and will be referred to the
stars in the position P. As the earth
moves on in the direction towards
c, Mars appears to move towards
H, but this motion will gradually be-
come more slow, until at the moment when the earth
reaches B, which is the point of contact of the tangent
drawn from M, the motion of Mars will apparently cease.
As the earth passes from B towards Y Mars will begin to
move backwards, so that when the earth arrives at Y Mars
will have returned to Q. As the earth approaches A Mars
will move gradually towards K, so that when the earth
reaches A Mars will have reached K, after which it will
gradually return again towards H. It will thus be seen that
the retrograde movement of Mars occurs about the time of
opposition.
111, Appearance of Mars. From observations of
certain spots or markings upon the surface of Mars it has
been concluded that that planet, like Venus and the earth,
revolves on its axis. The actual duration of this period has
been estimated by various astronomers. By comparing the
observations of Hooke in 1666 with those of Sir W. Herschel
in 1783 and of Dawes in 1856-1867, Proctor found that
286 Astronomy.
the duration of one revolution of Mars on its axis is 24 h 37
22 9 735. The equator of Mars is inclined to the plane of
its orbit at an angle of about 28. The angular diameter
of Mars when viewed from the mean distance of the earth
is about $"'4. The ellipticity of its disc is practically in-
sensible.
112. Satellites of Mars. Although many astronomers
had carefully examined Mars with the view of finding
whether he was attended with any satellites, yet it was not
until the opposition of 1877 that the two satellites which
attend Mars were really found. This very interesting dis-
covery was made by Mr. Asaph Hall, with the great object-
glass of the observatory at Washington. The following is
the account of the discovery in his own words :
'My search for a satellite was begun early in August, as
soon as the geocentric motion of the planet made the de-
tection of a satellite easy. At first my attention was directed
to faint objects at some distance from the planet, but all
these proving to be fixed stars, on August 10 I began to
examine the region close to the planet, and within the glare
of light that surrounded it. This was done by sliding the
eye piece so as to keep the planet just outside the field of
view, and then turning the eye piece in order to pass com-
pletely around the planet. On this night I found nothing.
The image of the planet was very blazing and unsteady, and
the satellites being at that time near the planet, I did not see
them. The sweep around the planet was repeated several
times on the night of the nth, and at half-past two o'clock
I found a faint object on the following side and a little north
of the planet, which afterwards proved to be the outer
satellite. I had hardly time to secure an observation of its
position when fog from the Potomac river stopped the work.
Cloudy weather intervened for several days. On the night
of August 15 the sky cleared up at eleven o'clock, and the
search was resumed ; but the atmosphere was in a very bad
, condition, and nothing was seen of the object, which we now
The Planets. 287
know was at that time so near the planet as to be invisible.
On August 1 6 the object was found again on the following
side of the planet, and the observations of that night showed
that it was moving with the planet, and, if a satellite, was
near one of its elongations. On August 17, while waiting
and watching for the outer satellite, I discovered the inner
one. The observations of the iyth and i8th put beyond
doubt the character of these objects, and the discovery was
publicly announced by Admiral Rodgers. Still, for several
days the inner moon was a puzzle. It would appear on
different sides of the planet in the same night, and at first I
thought there were two or three inner moons, since it seemed
to me at that time very improbable that a satellite should
revolve around its primary in less time than that in which
the primary rotates. To decide this point I watched this
moon throughout the nights of August 20 and 21, and saw
that there was in fact but one inner moon, which made its
revolution around the primary in less than one- third the
time of the primary's rotation, a case unique in our solar
system.'
The names ! which have been chosen for the satellites
are
Deimos for the outer satellite,
Phobos for the inner satellite.
From the observations made in 1877 and 1879 the following
values of the times of revolution have been found by the
discoverer :
Deimos 3o h i7 m 54 S< 377 ;
Phobos 7 37 13*938.
The planes of the orbits of both the satellites are very
1 AeTjuos and 4><$$os are the sons of Mars whom he summons to yoke
his steeds. See //., xv. 119. I am indebted to Professor Tyrrell for
the following version of the lines referred to :
' He spake ; and called Dismay and Rout to yoke
His steeds ; and he did on his harness sheen,'
288 Astronomy.
nearly coincident with the plane of the equator of Mars.
The orbit of Deimos is practically circular, but that of
Phobos had a certain small eccentricity.
As the hourly motion of Phobos is about 47 round the
centre of Mars, and as it is so near to the surface of the
planet, this satellite will present a very singular appearance
to an observer situated on Mars. Phobos will rise in the
west and set in the east about 5^ hours after, and it will
meet and pass Deimos, whose hourly motion is only 1 1-882.
On the other hand, Deimos will remain above the horizon
nearly 66 hours. The distances of the satellites from the
centre of the planet are for Deimos 14,500 miles and for
Phobos 5,800 miles. The semidiameter of Mars being
2,100 miles, the horizontal parallaxes of the satellites are
very large, amounting to 21 for Phobos. The sizes of the
satellites have not been satisfactorily ascertained. All
that is certainly known is that they must be very small, not
having a diameter of more than ten to twenty miles. 1
1 In connection with this discovery it is curious to note the following
letter of Kepler, written to one of his friends soon after the discovery
by Galileo in 1610 of the four satellites of Jupiter, and when doubts
had been expressed as to the reality of this discovery. The news of
the discovery was communicated to him by his friend Wachenfels, and
Kepler says, ' Such a fit of wonder seized me at a report which seemed
to be so very absurd, and I was thrown into such agitation at seeing
an old dispute between us decided in this way, that between his joy,
my colouring, and the laughter of both, confounded as we were by
such a novelty, we were hardly capable he of speaking or I of
listening. On our parting I immediately began to think how there
could be any addition to the number of the planets without overturning
my " cosmographic mystery," according to which Euclid's five regular
solids do not allow more than six planets round the sun. ... I am so
far from disbelieving the existence of the four circumjovial planets
that I long for a telescope to anticipate you, if possible, in discovering
two round Mars, as the proportion seems to require, six or eight round
Saturn, and perhaps one each round Mercury and Venus.' The an-
ticipations of Kepler with respect to Mercury and Venus have not yet
been realised.
The Planets. 289
113. Jupiter. Although Jupiter is much more distant
from the earth than Mars, yet the magnitude of the disc is
so great that it appears to the unaided eye as one of the
most brilliant stars, nearly equal to Venus in brightness,
while it is a very remarkable object in the telescope. The
equatorial and polar radii are respectively equal to in6 and
10-51 times the radius of the earth, the ellipticity amount-
ing to about one-seventeenth. This is caused by the rapid
rotation of Jupiter on his axis in a period of about 9 h 55.
The mean distance from the sun is 483,000,000 miles,
and the period of revolution is ii'86 years. The mass of
Jupiter is -^-g of the mass of the sun, while its density is
0-24 of that of the earth, or almost exactly equal to that of
the sun.
The most striking feature of Jupiter's disc is the presence
of markings, generally in the shape of bands parallel to the
equator of the planet, and frequently changing their appear-
ance. It is certain that the surface we see is not the actual
surface of the planet, but merely strata of clouds or vapours
in which Jupiter is enveloped, and as the rapid changes in
these cannot be caused by the small amount of heat received
from the sun, it seems certain that Jupiter is still very hot
and not yet a solid body. The equatorial regions rotate
somewhat taster than those in higher latitudes, as we have
seen is also the case on the sun. When Jupiter is viewed
through a telescope, even of quite moderate power, certain
small points of light are seen in his neighbourhood, which
are constantly changing their relative positions, though
always accompanying Jupiter in his movement round the
heavens. These small objects are four satellites, or moons,
of Jupiter, which were discovered by Galileo and were one
of the firstfruits of the invention of the telescope.
Observation shows that the movements of the satellites
of Jupiter around the planet obey Kepler's laws, just as the
planets do around the sun. The following table gives the
u
290 Astronomy.
mean distances of the satellites from Jupiter in terms of the
radii of Jupiter (Laplace) :
Mean Distances. Periodic Times.
ist satellite 5*698 177 days.
2nd 9-067 3-55
3rd 14-462 7-15
4th 25-436 16-69
The eccentricities of the orbits of the first and second
satellites are insensible, and those of the third and fourth are
very small ; the planes of the orbits of the satellites are very
close to the plane of Jupiter's equator.
The orbits of the four satellites of Jupiter are represented
in Fig. 115, in which the relative proportions of the orbits,
as well to each other as to the bulk of Jupiter, are shown.
Jupiter projects from the side which is turned away from
the sun a cone of shadow, into which the satellites every
now and then enter, and undergo an eclipse, which resembles
an eclipse of our moon. As Jupiter is much larger than the
earth, and as it is much farther away from the. sun, it is easy
to see that the length of the cone which forms the shadow
of Jupiter greatly exceeds the length of the cone which is
formed by the shadow of the earth. It follows that the
dimensions of the section of the cone of Jupiter's shadow,
even at the distance of the outermost satellite, is very nearly
as large as the section of Jupiter himself. The eclipses of
the satellites of Jupiter are consequently much more fre-
quent than the eclipses of the moon. The three first
satellites enter the cone of Jupiter's shadow once during
each revolution. The fourth satellite alone sometimes
passes above or below the shadow, so as to escape being
eclipsed.
As the eclipses of. the satellites are capable of being
observed simultaneously at different places, these pheno-
mena are sometimes employed for the purpose of deter-
mining longitudes. The method, however, is not a very
The Planets.
291
accurate one. Independently of other difficulties, the
eclipse of a satellite is not an instantaneous phenomenon ;
the illumination of the satellite is at first enfeebled by being
plunged in the penumbra before entering the cone of total
darkness, and the disc of the satellite, being of appreciable
dimensions, does not cross the boundary instantaneously.
For both these reasons, the decrease in the light of the
FIG. 115.
satellite is not instantaneous, and consequently the time
when the satellite ceases to be visible will depend upon the
power of the telescope which is employed. The eclipse,
therefore, wants the precision and definiteness which render
it a suitable signal for observers at the different stations to
! note their local times, and then by comparison find out the
difference between their longitudes.
u 2
292 Astronomy.
The eclipse of a satellite of Jupiter must be carefully
distinguished from an analogous phenomenon which is often
witnessed, i.e. the occultation of a satellite by the disc of the
planet. In the case of an eclipse the satellite ceases to be
visible because the mass of Jupiter is interposed between
the satellite and the sun, and thus cuts off the sun's light
from the satellite, which ceases to be luminous and is there-
fore invisible. But in the case of the occultation of a
satellite, what really happens is that the satellite actually
goes into such a position that the body of Jupiter is inter-
posed between the satellite and the earth, thus rendering the
satellite invisible.
It will often happen that a satellite is seen in transit
across the face of Jupiter. The shadow thrown by the
satellite then forms a circular dark spot on the face of
Jupiter, which can be seen in the telescope. An observer
who was stationed on the interior of that spot would find the
satellite interposed between himself and the sun, and that
consequently the sun was in a state of total eclipse.
In addition to the four conspicuous satellites, Jupiter is
attended by a very minute fifth satellite, discovered by
Barnard at the Lick Observatory on September 9, 1892. Its
orbit lies between Jupiter and the orbit of the * first ' satellite,
and the period of revolution is only n h 57 22 8 *6.
114. Saturn. When Galileo directed his newly-dis-
covered telescope to Saturn, he saw at once that the planet
was not a simple disc like Mars, or like Jupiter, but that it
had Appendages which caused Saturn to present a peculiar
appearance, the nature of which he was not able to under-
stand. By careful observation it was shown by Huyghens
that the appearance which had puzzled Galileo was really
due to a remarkable circular ring, or rather series of thin
flat rings, which completely surround Saturn without touch-
ing it. The appearance of Saturn is shown in Fig. 116, in
which we see a portion of the ring in front, while another
portion is hidden behind the globe of the planet. The pro-
The Planets.
293
jecting portions on each side of the globe are often called
the ansce. In the revolution of the planet round the sun
the plane of the ring remains constantly parallel to itself.
FIG. 116.
This is shown in Fig 117, where the point s represents the
sun, and where T is the position of the earth in its orbit
round the sun. It is obvious that an observer stationed on
T can only see the ring obliquely. Thus, though the actual
contour of the ring is a circle, yet as we only see the pro-
jection of that circle, it appears to us like an ellipse.
FIG. 117.
The mean distance of Saturn from the sun is 9*54 times
the mean distance of the earth, or 886,000,000 miles, and
the period of revolution is 29^ years. The equatorial
diameter of the planet is about 75,000 miles, or more than
294 Astronomy
nine times that of the earth. When seen in a telescope the
globe of Saturn exhibits belts somewhat similar to those of
Jupiter, but fainter and not so full of well-defined markings,
so that the rotation period, io h 14'", is difficult to determine.
The ellipticity is about one-tenth. The density of Saturn
is remarkably low, being only about five-sevenths of that of
water.
The rings of Saturn consist of separate particles like
meteorites, revolving independently round the planet in
accordance with Keple.'s laws. This has recently been
verified spectroscopically by Keeler. See Chapter XII.,
where particulars about the eight satellites of Saturn will
also be found.
115. Law of Bode. There exists a very remarkable
law which connects together the approximate distances of
the planets from the sun. This law is generally known by
the name of Bode's Law. Attention was drawn to it in
1778 by the astronomer Bode, but he was not really the
author of the law.
To express this law we write the following numbers :
o, 3, 6, 12, 24, 48, 96.
This series is easily remembered by the circumstance that
with the exception of the first and second each number is
double the one which precedes it. If we add 4 to each of
these numbers, the series becomes
4, 7, 10, 16, 28, 52, 100,
which series was known to Kepler. These numbers are,
with the exception of 28, sensibly proportional to the dis-
tances at which the principal planets are separated from the
sun. In fact, the actual distances are represented as follows :
Mercury. Venus. Earth. Mars. Jupiter. Saturn.
3-9 7-2 10 15-2 52-9 95-4
The Planets. 295
These numbers agree tolerably well with those indicated by
Bode's law. It is to be observed that this law does not ap-
pear to have any theoretical foundation, and for that reason
stands in quite a different category from the laws of Kepler.
116. Discovery of New Planets. Including the earth
itself, the number of planets known to the ancients was but
six. The invention of the telescope has, however, revealed
to us the existence of numerous other planets ; so that the
number of these bodies at present recognised is about 200,
and frequent additions are being made to the list by new
discoveries.
On March 13, 1781, William Herschel was examining
the stars in the constellation Gemini with a telescope
of considerable magnifying power, when he perceived
an object which was not a luminous point, as ordinary
stars are, but which had a diameter of appreciable dimen-
sions. By continued observation of the same object he
noticed that it also differed from the stars in another im-
portant respect, for while the stars remained fixed in their
relative positions, this new object was in motion. It was
soon after recognised that this new object was really a planet
moving like the other planets in a nearly circular orbit round
the sun, and in a plane but little inclined to the plane of the
ecliptic. This planet has received the name of Uranus^ and
it is attended by four satellites.
Adopting the distance of the earth from the sun as unity,
the distance of Uranus from the sun is 19-18. Thus the
orbit of Uranus lies considerably outside that of Saturn,
and its radius is very neary double that of Saturn. The
law of Bode is also fulfilled approximately in the case of
Uranus. The distance which that law assigns for the planet
immediately outside Saturn is 196, which does not differ
much from 191-8, which is found by multiplying the distance
of Uranus, expressed in terms of the mean radius of the
earth's orbit, from the sun by 10.
The astronomer Bouvard, when publishing in 1821 the
296 Astronomy.
tables of Uranus, by which the position of the planet at
different epochs could be found, pointed out that the calcu-
lated positions of the planet could not be reconciled with
the observed positions. The discrepancies could, he sug-
gested, be reconciled by supposing that they arose from
some extraneous and unknown influence disturbing the
movements of Uranus. Bouvard even suggested that this
extraneous influence might be due to a planet which circu-
lated in an orbit exterior to that of Uranus.
The research for this unknown planet was taken up
independently by M. Leverrier in France, and by Mr.
Adams in England. It was shown that when every allow-
ance was made for the action of Jupiter and Saturn upon
Uranus, there were still outstanding discrepancies. Le-
verrier showed that these discrepancies could be reconciled
by the existence of an exterior planet, and he predicted the
situation of the planet so accurately that on the night of
September 23, 1846, Neptune was actually found by Dr.
Galle, at Berlin, in the place indicated. Professor Challis, at
Cambridge, had previously commenced a search in accord-
ance with the indications of Adams, and he had actually
observed the planet on August 4 and 12, 1846. There can
be no doubt that when these observations were compared
he would have recognised the planetary nature of the object.
The merit of this brilliant discovery must therefore be shared
between Leverrier and Adams.
Neptune is not visible to the unaided eye. Viewed in a
telescope of inconsiderable magnifying power, this planet
seems like a star of the eighth magnitude. When the mag-
nifying power of the instrument is increased, the dimensions
of the planet become more considerable, and its circular
disc can be perceived. The apparent angular diameter of
Neptune is 2"'o. The actual diameter of Neptune is about
4 times the diameter of the earth. Neptune is accompanied
by a single satellite.
Neptune is, so far as we know at present, the outermost
The Planets. 297
planet of the solar system. The law of Bode is, in the case
of this planet, very much astray. It would indicate 388 as
the distance of the planet immediately outside Uranus, while
the actual distance of Neptune is only 300^4
117. The Minor Planets. According to the indica-
tions of Bode's law there ought to be a planet situated in
the interval between Mars and Jupiter at a distance repre-
sented by 28. This has been abundantly confirmed by the
discovery within the present century of a great number of
planets which circulate round the sun at about the distance
which was indicated by Bode's law. These planets are all
small objects, requiring telescopic power; they now number
more than 400. The following are a few of the more remark-
able of these bodies, with the names and dates of their
discoveries.
1. Ceres ) discovered by Piazzi at Palermo on January i,
1 80 1. The distance of this planet from the sun is 277.
Multiply this by 10 ; we obtain 277 instead of 28, as indicated
by Bode's law.
2. Pallas, discovered by Olbers at Bremen on March 28,
1802. Its distance from the sun is 277.
3. Juno, discovered by Harding at Gottingen Septem-
ber i, 1804. Its distance from the sun is 2*67.
4. Vesta, discovered by Olbers at Bremen March 29,
1807. Its distance from the sun is 2-36.
The search for minor planets is a work now carried
on in several observatories. For this purpose maps
have been prepared, on which the stars are recorded with
great accuracy and minuteness. These maps need not
extend to the whole surface of the heavens, as the planets
are generally found in or near the ecliptic, and therefore it
is only the regions of the sky in or near the ecliptic which
require to be mapped for this purpose. The astronomer
compares the stars which he sees through his telescope with
the stars which he sees recorded on the map. If he detects
an object in the heavens which is not represented on the
298 Astronomy.
map, then the question arises as to what the object may be.
If it be very small, it may possibly be a star which has
escaped the attention of the astronomer by whose observa-
tions the maps were constructed. It may even be a star
which, by reason of variability in its brightness, was not
noticed when the maps were made, but which has become
conspicuous when the comparison of the maps with the
heavens is made in the manner we are now supposing. The
first test to apply to an object of this kind is to ascertain
whether its position is constant or whether it has a move-
ment relatively to the stars. If in the course of a few nights
the object remains sensibly in the same position as compared
with the stars in its vicinity, we are then justified in sup-
posing that the object is really a star which from one cause
or another previously escaped notice. If, however, the star
really has changed its place in the course of a night or two,
or if, as sometimes happens, the observations of a single
night are sufficien to show marked changes in the position,
then we may infer that the unknown object is really a planet
or a comet. If it be a minute body resembling a star, we
may assume that the object is a planet ; but if it be a diffused
mass of luminous matter, we may generally assume that it is
a comet. The question will then remain as to whether the
object thus revealed to us is new or whether it has been
previously observed. In the case of the majority of the
comets their orbits are such that they only visit the neigh-
bourhood of the earth so as to become visible once for a few
weeks or months, and then again retreat to the depths of
space from which they have come. The case of the minor
planets is, however, different. They revolve in nearly circular
orbits around the sun, the periods of such revolutions being
only a few years. It is, therefore, quite possible that the
planet which has been observed has been already seen on
previous occasions. To ascertain this point, reference must
be made to an ephemeris in which the orbits of all the
The Planets. 299
planets which are known are given, and in which will be
found predictions of the places of the planets. The ephe-
meris for this purpose is contained in the ' Berliner Jahr-
buch.' Here will be found the position of each minor
planet at intervals of 20 days throughout the year, while the
place is given for each day in the case of the passage of
a planet through opposition. If, therefore, the observer
detects a planet, he first refers to the ' Berliner Jahrbuch/ to
find whether any of the planets already discovered may not
be situated in the position in which the new object appears.
During the last few years photography has been exten-
sively used in the discovery of minor planets. A plate is
exposed to a certain region in the sky for a few hours, great
care being taken that the clock driving the telescope keeps
pace accurately with the rotation of the earth, so that fixed
stars appear on the plate as sharp points. If on developing
the plate a star is found to have left a trail on the plate, it
must be a planet. In this way Wolf of Heidelberg has
discovered 36 new minor planets in the years 1892-95,
using two 6-inch portrait lenses.
118. Elements of the Movements of a Planet. Observa-
tions of the minor planets show that they also obey the three
laws of Kepler. Each of the planets revolves in an ellipse
of which the sun occupies one of the foci; each of the
planets sweeps over equal areas in equal times, and the
squares of the periodic times are proportional to the cubes
of the mean distances.
In order to define completely the nature of the orbit of
a planet, it is necessary to specify certain quantities with
regard to that orbit which are called its elements. In the
first place we must have the shape and size of the ellipse
specified. This will involve two quantities namely, the
length of the semi-axis major and the eccentricity of the
ellipse. From Kepler's third law it appears that the period
of revolution is known when the length of the semi-axis
3 oo A sir 01 winy.
major of the ellipse is known, and therefore this element is
really included in the t\vo already specified. But besides
knowing the shape and size of the ellipse, certain other
elements are necessary in order to specify the orbit. We
require to know the plane in which the ellipse lies, as well as
the actual position of the ellipse in its plane. The position
of the plane of the orbit is specified by its line of nodes that
is, by the line in which it intersects the plane of the ecliptic
and by the inclination at which the plane of the orbit is in-
clined to the plane of the ecliptic. Still one more quantity is
required to determine the ellipse. We know that the focus cf
the ellipse is situated at the sun, but the direction of the
axis major of the ellipse is still undetermined. This
may be defined by the longitude of the perihelion, which is
the sum of the longitudes of the ascending node and the
angular distance (measured in the direction of the motion)
of the perihelion from the node. Finally, we require to
know the date at which the planet occupied a certain
specific point of its orbit. When this and the other
elements of the orbit are known, the place of the planet
at any time can be predicted.
To determine the six elements of the orbit of a planet, it
is necessary to have three observations of the planet both in
right ascension and declination. The computation of the
actual shape and position of the orbit from these observa-
tions is a matter of no little complexity. It is, however, easy
to render a general account of the method so far as to show
that three observations will be adequate for the purpose.
When the right ascension and the declination of a
celestial body are known, all that we really infer is that at
the time when the observation was made the body was seen
in a certain direction. The position of the observer has to
be taken account of, because that position is constantly
changing in consequence of the annual motion of the earth
around the sun (we may for the present overlook the diurnal
The Planets. 301
rotation of the earth). The date of the observation being
known, the precise position of the observer on the ecliptic at
that date is also known ; and as the direction of the planet is
determined by the observation, it follows that at the moment
of the observation the planet must have been situated upon
a straight line of which the position in space was actually
known. The same takes place at the two other observa-
tions, and consequently the result of the three observations
is, that, on dates which are given, the planet was situated
respectively on three lines of which the positions in space
are given.
The problem which has now to be solved may be thus
stated. To describe an ellipse of which the sun is at the
focus, which shall intersect three given straight lines in
space. Draw any plane through the sun ; this will cut the
three lines in three points, and a conic section can be drawn
to pass through these points, and so that the sun shall be
situated in the focus. Unless, however, the plane be
properly chosen this conic will not be the ellipse which the
planet is describing. In accordance with Kepler's laws
the area swept over by the radius vector to a planet is pro-
portional to the time, and, consequently, as we know the
dates of the observations, the area swept over by the radius
vector between the first and second observations, and also
between the first and the third, are also known. The plane
must therefore be so drawn through the sun, that the conic
passing through the three points shall be an ellipse, and that
the areas subtended by the two arcs of the ellipse at the
focus shall be given. We thus have two conditions imposed
on the plane, and these two conditions will be sufficient to
determine the plane, for it will be remembered that, when a
plane is drawn through a given point, two other elements are
sufficient to fix the position of the plane. These two elements
may conveniently be taken as two of the direction angles of
the normal to the plane. In this way we have shown that
3O2 Astronomy.
three complete observations of a planet are adequate for the
determination of its orbit.
119. The Parallax of the Sim. There are several
distinct methods by which the distance of the sun from the
earth may be ascertained. The best known of these methods,
even if not the most trustworthy, is that which is afforded by
the rare occurrence of the phenomenon which is known as
the transit of Venus.
Owing to the inclination of the orbit of Venus to the
orbit of the earth, it usually happens that when in conjunc-
tion Venus passes over the sun or under the sun. ]f,
however, the conjunction occur when Venus is near the
node, then Venus will pass actually between the earth and
the sun, and will be seen like a dark spot upon the face of
the sun. Thus, suppose the circle CAB (Fig. 118) to repre-
sent the apparent disc of the sun, the planet Venus appears
to enter on the disc of the sun at A, and then moving across
the sun in a direction which is indicated FIG. us.
by the dotted line A B, leaves the sun
atB.
In discussing this question no little
complexity arises from the inclination
of the orbit of Venus to that of the
earth. We shall therefore simplify the
subject by supposing that the orbit of
Venus coincides with the ecliptic, as the
principle of the method will not be affected. We may also
suppose that the orbits of the earth and of Venus are circles.
Under the circumstances we have supposed the path of
Venus across the disc of the sun would pass very near the
centre of the sun when seen from any point on the earth.
When the planet has just entered completely upon the disc
of the sun, as at A (Fig. 118), the phenomenon is said to be
first internal contact. After passing across the face of the
sun the planet reaches B, and when the circular edge of the
The Planets. 303
planet just touches the circular edge of the sun, the phase
called last internal contact is reached. Observations of the
transit of Venus are mainly devoted to the accurate deter-
mination of the time at which first internal contact and last
internal contact occur. It is from these observations, made
at different parts of the earth, that the parallax of the sun is
to be concluded. We shall not enter into any detail in the
matter, but merely point out how such observations will
enable the parallax of the sun to be ascertained. Let P Q T
(Fig. 119) denote the sun, of which s is the centre. Let A B
represent the earth. Draw A T a common tangent to the
sun and the earth, and also the common tangent B T, which
touches the earth at B and the sun in a point so close to T
as to be undistinguishable therefrom. The circle through
A B denotes the orbit of the earth, and the circle through x Y
denotes the orbit of Venus, and th<* arrows indicate the
direction in which the earth and Venus are moving. As
Venus is moving faster than the earth, it follows that Venus
will overtake the earth, and thus at a certain time will arrive
FIG. 119.
a
A
Q~
at the position x. Remembering that we have assumed
that the orbit of Venus lies in the same plane as that of the
earth, it follows that an observer stationed at A will just see
304 Astronomy
Venus at first internal contact, and, having previously regu-
lated his clock accurately, he will be able to note the moment
when Venus occupies the position x.
Venus, however, is moving around the sun with a greater
angular velocity than that which the earth has round the
sun : it follows that after a certain interval of time Venus will
have attained the position represented by Y, where it touches
the second common tangent drawn to the earth and the sun.
An observer at the point on the earth's surface denoted by E
will therefore now see Venus at first internal contact. It is
therefore clear that A is the spot on the earth at which the
internal contact is first seen, and that B is the spot where the
internal contact is last seen. A correction will have to be
made here on account of the rotation of the earth on its axis,
for during the time occupied by Venus in passing from x to
Y the earth will have turned through an angle which is quite
appreciable. Consequently the real point B on the earth's
surface, where the internal contact is last seen, is different
from what it would have been had the earth not rotated on
its axis after the first internal contact was observed from A.
Astronomers, however, know how to allow for this difference,
and we shall not here consider it further.
We shall, therefore, suppose that expeditions are sent to
the two stations A and B (of course, as a matter of fact, they
can only be sent to the places nearest A and B which are
suitable from geographical considerations), and that at each
of these two stations the moment of first internal contact is
observed. We may also suppose that a telegraph wire is
kid from A to B, so that at the instant of contact as seen
from A a telegraphic signal is despatched to B. The observer
at B then notes the arrival of this signal by his clock, and
when he himself sees the internal contact at a time also
marked by his own clock he is able with the greatest pre-
cision to determine the interval of time between the two
contacts. We thus learn from these observations the
Astronomy. 305
actual time which Venus takes to pass from the position
x to the position Y. But we also know that the entire time
which Venus requires for performing a revolution around
the sun relatively to the earth is 584 days. Hence, if we
assume that Venus moves uniformly, we can, by a simple
proportion, find the angle x s Y. The radius T s is small
compared with the distance s x ; we may therefore, with
sufficient accuracy for our present purpose, suppose that the
angle x T Y is equal to the angle x s Y. We can now con-
sider the problem to be solved, for the distance A B, being
very nearly equal to the diameter of the earth, is therefore
known, also the angle A T B is known, and therefore the
distance A T from the sun to the earth is known.
From the transit of Venus which occurred in 1874, Sir
George Airy, after a discussion of the results obtained by the
expeditions sent by the British Government, concluded that
the equatorial or horizontal parallax of the sun is 8" 7 60.
This corresponds to a distance of the sun from the earth
equal to 93,300,000 miles. 1 Airy's value of the parallax
is smaller than any which has been deduced by this or
other methods during the last twenty years, and other
astronomers have found different values from the same
transit of Venus. This is due to the difficulty of deter-
mining accurately the moment when Venus enters or leaves
the sun's disc (owing to irradiation and to some extent to
the atmosphere of Venus), and the accounts of what the
different observers saw may be interpreted differently by
different computers. The transit of Venus on December 6,
1882, was also extensively observed. The next transit will
not occur till the year 2004.
The astronomical importance of an accurate knowledge
of the sun's distance can hardly be over-estimated. With a
single exception it is the unit in which the distances of the
1 Report ordered to be printed by the House of Commons, July 6,
1877. (For other values of the solar parallax, see Chapter XII.)
X
306 Astronomy.
heavenly bodies are invariably expressed. The exception
to which we refer is the moon, the distance of which is
directly determined by observations of the zenith distance
of the moon in the way already described. Once, however,
the distance of the sun from the earth is found, then from
Kepler's third law the distances of all the planets are
found. From this will follow the dimensions of the planets
and of the orbits of their satellites. Thus, to determine
the scale of the whole solar system, it is only necessary to
determine the distance of the sun from the earth. So also
when we seek to determine the distances of the fixed stars
from the earth, the quantity which the observations give
is the angle which the radius of the earth's orbit subtends
at the star. The determination of the distance of the star
is therefore expressed in terms of the radius of the earth's
orbit.
There are many other methods by which the distance of
the sun from the earth can be found, besides that which is
afforded by the transit of Venus. One of the best of these
methods is by the observations of the parallax of a planet as
seen from different places on the earth's surface. In the
application of this method, either Mars or a small planet is
chosen, and its apparent position relatively to the fixed stars
in its neighbourhood is measured from two stations on the
earth. If the planet were as far off as the stars, then no
apparent difference would be seen in the places afforded by
the two different sets of observations ; but as the planet is
comparatively near the earth, the distance between the two
stations is sufficiently great to cause an appreciable change
in the place of the planet when viewed from the two places.
In this way the distance of the planet can be found, and
thus the scale of the solar system, and the distance of the
sun itself, is ascertained.
A still more simple method, and one which has much to
recommend it, is a modification of that which has just been
Comets and Meteors. 307
described. Owing to the rotation of the earth, the position
of the observer himself is in constant motion. If, therefore,
the planet be observed with reference to the stars in its
neighbourhood, and if the observer repeat these observations
some hours later, he will find that the apparent place of the
planet has changed. The alterations in the place of the
planet are due to three causes ist, to the actual motion of
the planet itself ; 2nd, to the displacement of the observer
due to the revolution of the earth around the sun ; 3rd, to
the displacement of the observer due to the rotation of the
earth on its axis. By suitable discussion of the observations
it is possible to distinguish the amount of displacement
arising from the last-mentioned cause, and thence to deter-
mine the ratio of the distance of the planet to the diameter
of the earth. For the application of this method, it is
obviously desirable to have the planet as close to the earth
as possible.
CHAPTER IX.
COMETS AND METEORS.
120. Comets. Besides the planets, there are certain
other bodies belonging to the solar system which are some-
times seen moving among the constellations. These bodies
are called comets. A comet usually consists of a more
or less brilliant nucleus surrounded with a nebulosity
which is often extended in one direction so as to form a tail
(Fig. 120). Frequently, however, comets are seen which do
not appear to have any conspicuous tail, and sometimes
they have more than one. Sometimes also the nucleus
is very minute, or entirely wanting. The actual dimen-
sion to which a comet extends is often enormously great.
X 2
308 Astronomy.
Thus, in the month of March 1843, a comet appeared
of which the tail extended to a length of 40. The tail
of the comet of 1680 had a length of 90, and that
FlG< I20> of 1618 was stretched
across the sky, through
an arc not less than 104.
The comet of 1811 had
a tail 23 long, and in
1744 a comet appeared
with six tails. The most
recent great comet which
was well seen is that of
1882. The examples
which we have alluded to
are those of comets
which, from their splen-
dour, were exceedingly
conspicuous objects. The ordinary comets are much
smaller, and indeed the great majority of these bodies
are faint telescopic objects, of which a few are usually
found every year. The spectrum of a comet consists of a
faint continuous spectrum, due to reflected sunlight, and
certain bright bands showing that the comet consists at least
partly of hydrocarbon gas.
A comet is only visible in the heavens for a limited
period. It first appears in some region of the heavens
where nothing of the kind had been seen a few days pre-
viously ; from day to day the comet changes its position and
its brightness, and even its shape. It will remain visible
for some weeks, or perhaps months. Occasionally it be-
comes lost to view from having gone too close to the sun,
and then again the comet is seen on the other side of
the sun, when, after remaining visible for some time, it
gradually recedes, becomes fainter, and is finally lost to
sight.
It was Newton who first explained the real motion of
Comets and Meteors. 309
comets. He discovered that comets really move in conic
sections with the sun in one of the foci Many of these
orbits appear to be parabolic, but the majority are perhaps
very elongated ellipses, and the path of the comet in the
vicinity of the sun, when alone we see it, is in this case
hardly to be distinguished from a parabola.
When a comet appears, its right ascension and declina-
tion are determined, and from three such observations
the orbit of the comet can be completely ascertained. To
accurately describe this orbit its elements must be ascertained.
The elements of the orbit of a comet are ist, the inclination
of the plane of the orbit to the plane of the ecliptic ; 2nd,
the longitude of the ascending node of the orbit, that is, the
angle which the line of intersection of the comet's orbit on the
ecliptic makes with a line drawn through the sun parallel to
the line of the equinoxes; 3rd, the longitude of the perihelion >
which is in the case of direct motion the sum of the longitude
of the ascending node and the angular distance (measured
in the direction of the motion) of the perihelion from this
node ; 4th, the perihelion distance^ that is to say, the
shortest distance of the parabola from the centre of the
sun, the radius of the earth's orbit being taken as unity ;
5th, the epoch, or the time at which the comet has passed
through its perihelion ; 6th, the direction of the motion which
is direct from west to east like the sun, or retrograde from
east to west.
121. Periodic Comets. If the orbit of a comet were
really parabolic, then, after once passing round the sun, the
comet would retreat to the depths of space from whence it
came, and would never again become visible. If, however,
the orbit be elliptic, then after a greater or less time, de-
pending upon the length of the axis major of the ellipse,
the comet would return, and thus form what is known as a
periodic comet.
When a comet appears, the question arises as to whether
this comet is to be regarded as parabolic, or whether it is
3io Astronomy.
not one of the periodic comets. This question cannot be
decided by the appearance of the comet. The actual shape
and dimensions of a comet vary so much, even in the course
of a single apparition, that it is quite hopeless to expect
that the identity of the comet at future returns can be de-
tected from its resemblance to comets previously seen. The
only method of determining the identity of a comet is, to
ascertain the elements of its orbit, and then seek in the
record of previous comets for a comet which has an orbit
of a similar character.
122. Halley's Comet. To illustrate this subject, we
shall take the case of the comet which appeared in 1682,
and which is generally known as Halley's comet. From
the observations made by Lahire, Picard, Hevelius, and
Flamsteed, the following elements were found for the orbit
of the comet during the apparition of 1682 :
Inclination. Longitude of Longitude of Perihelion Direction
Node. Perihelion. Distance, of Motion.
17 44' 45" 5i Li' 18" 3oi 55' 37" '58 Retrograde.
But from the observations of Kepler and Longomontanus
it appeared that a great comet, observed in 1607, had the
elements
Inclination. Longitude of Longitude of Perihelion Direction
Node. Perihelion. Distance, of Motion.
17 6' if 48 14' 9 ' 300 46 59" 0-58 Retrograde.
From the close resemblance between these elements and
those of the comet of 1682, Halley concluded that the
comet of 1682 and that of 1607 were really the same object,
and that the period of its revolution about the sun was 75
years. It further appeared that the comet observed by
Apian in 1531, i.e. 76 years before 1607, had an orbit with
the following elements :
Inclination. Longitude of Longitude of Perihelion Direction
Node. Perihelion. Distance, of Motion.
17 o' 45 30' 301 12' 0-58 Retrograde.
Comets and Meteors. 3 1 1
The identity of these elements with those found for the
comets of 1607 and 1682 left no doubt as to the identity of
the objects. If this were true, then Halley predicted that
the comet would reappear in 1758. The influence of the
planets in perturbing the motion of this comet is very con-
siderable. Clairaut computed that by the action of Jupiter
the comet would be retarded 528 days, and 200 days by that
of Saturn. He therefore predicted that the comet would
return to perihelion about the middle of April 1759, but
that, owing to the calculations being only approximate, an
error of 30 days on one side or the other was possible. The
comet did actually return very close to the predicted time,
and passed the perihelion on March 12, 1/59. The following
elements were deduced from the observations then made :
Inclination. Longitude of Longitude of Perihelion Direction
Node. Perihelion. instance, of Motion.
i? 36' 52" 53 5' 2 7" 303 10' 28" 0-58 Retrograde.
Observing that the period of the comet is about 75 years,
another return was expected in the year 1835, and, by ac-
curate calculation of the perturbation, the date of the peri-
helion passage was fixed for November 13. The perihelion
passage actually did take place on November 16.
As we know the periodic time of the comet, we are
enabled, by means of Kepler's third law, to find the mean
distance of the comet from the sun. Representing the
mean distance of the earth by unity, the mean distance of
Halley's comet is 3 5 '9. The actual shape and dimension
of the orbit of Halley's comet, as compared with the planets,
is shown in Fig. 121, where it will be seen that the orbit of
the comet passes a little outside that of Neptune. 1
123. Distinction between Planets and Comets. As
both planets and comets revolve round the sun in orbits
which are described in accordance with the laws of Kepler,
it is necessary to specify the wide differences in their
1 A list of periodic comets will be found in Chapter XII,
3 I2
Astronomy.
FIG. 121.
movements which separate the class of bodies we call
planets from the class of badies we call comets.
The planets all move
round the sun in the same
direction, from west to east,
and, if we except a few of
the minor planets, their
orbits are but very little
inclined to each other. The
eccentricities of the orbits
of planets are but small, so
that the ellipses which they
describe differ but little
from circles. Comets, on
the other hand, move in
orbits whose planes are in-
clined at all possible angles
to the plane of the ecliptic ;
some have a direct motion,
while that of others is retro-
grade. Most of them de-
scribe orbits of such great
eccentricity that, while they
are visible, the orbit cannot
be distinguished from a
parabola.
124. Shooting Stars.
In addition to the planets
and their satellites, and the
vast host of comets, there
are numerous other small
bodies generally recognised
as belonging to the solar
system. The study of these
small bodies is a branch of
astronomy in which the telescope is of but little use. We
Comets and Meteors.
313
do not see these bodies under ordinary circumstances with
the telescope, but we become aware of their existence in
other ways. We sometimes find them actually tumbling
down upon the earth : we can then take them in our hands,
weigh them, and analyse them ; they are the bodies which
we call Meteorites- Collections of these objects are to be
seen in the British Museum and elsewhere.
But there is another very different way by which we
become aware of the existence of these small bodies. The
descent of a meteorite is a comparatively rare, and at all
times very noteworthy, phenomenon ; yet everyone is fa-
miliar with what are called 'shooting stars,' while oc-
casionally the somewhat more imposing phenomena which
are known as fire-balls are witnessed. We have the best
reasons for knowing that what we call shooting stars are
really small objects which dash into our atmosphere from
external regions. Thus meteorites and shooting stars are
the evidences which we possess of the existence of compara-
tively minute bodies in space, which are external to the earth
and to our atmosphere.
As an illustration on a somewhat imposing scale of
the circumstances under which these external bodies (often
called meteors] enter our atmosphere and thus become
manifest, we may take a very remarkable fire-ball which
occurred on November 6, 1869. This fire-ball was very
extensively seen from different parts of England, and by
combining and comparing these observations very accurate
information has been obtained as to the height of this object
and the velocity with which it travelled.
Let us suppose that an object many miles up in the air
is seen simultaneously by two observers stationed at a con-
siderable distance apart, and that each observer has noted
carefully the direction in which he saw the object ; then
the height of the object can be determined. For, take a
map on any convenient scale, and at the two stations of the
observers insert straight wires projecting from the map in the
314 Astronomy.
directions in which the object was seen from each of the
stations. These two wires must, of course, intersect at the
FIG. 122.
true position of the object. Letting fall a perpendicular
Comets and Meteors. 2 1 5
from their intersection upon the plane of the map, the height
of the object is found on the same scale as that of the map.
It is in this manner that the point of appearance and dis-
appearance of a meteor can be ascertained, and thus the
entire track of the meteor becomes known. By observations
of this kind the path of the fire-ball under consideration
was determined, and it is represented in Fig. 122.* It ap-
pears that this meteor commenced to be visible at a point
90 miles above Frome, in Somersetshire, that it then moved
in the manner shown in the diagram, until it disappeared at
a point 2j miles over the sea near St. Ives, in Cornwall.
The whole length of its course was about 1 70 miles, which
was performed in a period of 5 seconds, thus giving an
average velocity of 34 miles per second. A very remarkable
part of the appearance which the fire-ball presented was the
persistent streak about fifty miles long and four miles wide
which remained in sight for fully fifty minutes.
We have in this example an illustration of the chief
features of the phenomenon of a shooting star presented on
a very grand scale. This consists of a brilliant object
moving with a very high velocity and leaving after it a per-
sistent streak of light. It is true that the persistent luminous
streak is not a universal, nor indeed a very common, feature
of a shooting star. These phenomena admit of a tolerably
simple explanation. The velocity of 34 miles per second,
with which the body, whatever it may have been, entered
our atmosphere, altogether transcends the velocities with
which we are accustomed to deal on the surface of the earth.
It is more than a hundred times as great as the swiftest shot
that was ever fired from a cannon. It is in this high velocity
that the explanation of the light and the streak are to be
sought. The friction against the atmosphere develops heat
sufficient to render the body red hot, white hot, and even in
1 This figure, ns well as the accompanying particulars, have been
taken from the British Association Reports, Liverpool, 1870, p. 80.
3 1 6 A stronomy.
many cases (perhaps in most) entirely to dissipate the body
into vapour.
One of the most remarkable features connected with the
phenomena of shooting stars is their periodic recurrence in
what are called star showers. On some occasions, as, for
example, on the night of November 13-14, 1866, the display
of shooting stars has produced a spectacle of the most sublime
character. Less splendid, though perhaps quite as interesting,
was the shower which took place on November 27-28, 1872.
We shall select this shower for discussion, as it was the last
important one which occurred.
We shall suppose that the observer is provided with a
chart of the fixed stars in that part of the heavens in which
the shower of shooting stars appeared. He fixes his attention
on one particular shooting star, and carefully observes its
path with respect to the fixed stars in its vicinity. He then
draws a line upon his chart in the direction in which the
shooting star moved, and he repeats this process for as many
stars as possible during the shower.
The most casual glance at this chart will show that the
tracks of nearly all the shooting stars marked thereon
diverge from one point or region. In some of the ordinary
showers the tracks almost all diverge from a single point,
which is called the radiant. In the case of the shower now
under consideration, the tracks are not actually directed from
a single point, but they all diverge from a clearly defined ra-
diant area, and as this area was situated in the constellation
Andromeda, the shower is often called the ' Andromedes?
Astronomers have often to discriminate motions which
are only apparent from those which are real, and it will be
necessary to exercise that discrimination here. It certainly
looks at first sight as if all the shooting stars did actually
dart from the region we have been considering, but this is
not exactly the case. Those who make use of the principles
of perspective often draw a set of lines intersecting in a point
in order to represent a set of parallel lines in the object
which is being copied. When we are looking at the shoot-
Comets and Meteors. 3 1 7
ing stars we really only see the projections of their paths
upon the surface of the heavens. But we have shown that
all these projections pass nearly through the same point, and
therefore we infer that the shooting stars belonging to the
same shower are moving in nearly parallel lines. It is not
of course meant that throughout all space the paths of the
meteors producing the shooting stars are a group of parallel
straight lines. We refer only at present to the very short
portions of those paths which are described by the meteors
when we see them as shooting stars just at the moment of
their dissolution.
We are now able to ascertain the actual direction in
which the shooting stars of a shower are moving ; in fact, a
line drawn from the eye of the observer to the radiant must
be parallel to the straight lines along which the shooting
stars move relatively to the earth.
It will next be necessary to consider the true significance
of the special day of the year on which the shower of the
Andromedes was witnessed. The following table gives the
names of the three principal showers of shooting stars, as
well as the days of the year on which they may be looked
for:
Name of shower. Date of appearance.
Perseids . . . August 9 to 1 1
Leonids . . . . November 12 to 14
Andromedes . ... November 27 to 29
As the earth moves round the sun once in a year, the
earth is on each day of the year in the same part of its orbit
as it was on the same day of the preceding year. We are
therefore led to connect the annual recurrence of the shoot-
ing star showers with the position of the earth in its orbit
round the sun. Thus, when the earth is in one part of its
orbit it is likely to meet the Leonids, when it is in another
it is likely to meet the Perseids, and so on. We therefore
infer with certainty that the stream of meteors which form
the Andromedes, when they enter our atmosphere as shoot-
Astronomy.
ing stars, must pass through that part of the earth's orbit in
which the earth is situated at the end of November.
The question has now assumed a geometrical form of
considerable interest Let E (Fig. 123) denote the position
FIG. 123.
of the earth at the time of the occurrence of a shower, and
let the line E R, drawn through E, denote the direction of the
radiant, after allowing for the motion of the earth. Then
the line E R must be a tangent to the orbit of the meteors,
and of course the sun is a focus of that orbit The position
of the other focus is, however, indeterminate. All that we
know at present is that, from a property of the ellipse, the
second focus must lie oivthe line E F,, which is drawn through
E so as to make with the tangent the same angle as E s
makes with the tangent. To determine the position of this
second focus some additional datum is indispensable ; the
most suitable datum is the time of revolution of the meteors.
Comets and Meteors. 319
In the figure we have shown orbits corresponding to periods
of six months, one year, two years, and three years, all drawn
to scale. As a matter of fact, it would be impossible to draw
on this scale the actual orbits of any of the meteor showers,
as the periods are all much longer than those here referred
to. When, however, the periodic time is known, then, from
Kepler's third law, the axis major of the ellipse is known,
and therefore the position of the focus is determined.
All, therefore, that is necessary to determine the orbit of a
swarm of meteors is given, when we know the day on which
the shower takes place, the position of the radiant, and the
periodic time of the swarm.
Pausing for a little in our consideration of the Andro-
medes, let us turn to the periodic comet which was dis-
covered more than a century ago, and which is now known
by the name of Biela's comet. It must be regarded as a
very remarkable circumstance that the path of Biela's comet
actually crosses the path of the earth. This is of importance
in connection with the Andromedes, because the point of
the earth's orbit, where it is crossed by the orbit of Biela's
comet, is precisely that spot which is occupied by the earth
on November 27 in each year. It surely is a remarkable
coincidence that the earth should encounter the Andromedes
at the very moment when it is crossing the track of Biela's
comet. We are at once tempted to make the inference that
the comet and the meteors are in some way connected, and
the justice of this inference is corroborated in the most
astonishing manner by three additional circumstances :
1. We have already explained how the direction from
which the Andromedes come is to be found, and we can
also find the direction from which Biela's comet comes.
These two directions are identical.
2. Biela's comet sweeps around the sun in an elliptic
orbit, with a period of 6 '6 years. Thus, after coming into
the vicinity of the earth and being occasionally visible, the
comet again withdraws to a vast distance, to return again in
about 6], years more. Now it so happens that at the end
320 Astronomy.
of 1872 the time had arrived for the return of Biela's comet,
and thus the occurrence of the great shower of the
Andromedes took place at the time when we knew that
Biela's comet must, comparatively speaking, have been in
the vicinity of the earth, though it had not yet been observed.
Another great shower occurred in November 1885, when
the earth crossed the path of the comet.
3. Professor Klinkerfues ingeniously argued that if a
comet, coming from the radiant of the Andromedes, actually
brushed past the earth on the night of November 27, 1872,
the comet ought to be found immediately afterwards in that
region of the heavens which is diametrically opposite to the
radiant of the Andromedes. He therefore telegraphed to
Mr. Pogson at Madras, requesting him to search in the region
thus indicated. The search was made, and the comet (or a
comet) was found. Unfortunately, bad weather prevented
sufficient observations of the comet being made, but there can
be little doubt that it was connected with the Andromedes.
This connection between comets and shooting stars has
been found to exist in several other cases, especially in the
great showers of the Leonids and the Perseids. The orbit
of the Perseids was the first orbit of a swarm determined
by Schiaparelli (to whom the modern development of
meteoric astronomy is chiefly due) in 1866. The period
of revolution was unknown, but from the rate of increase
of the number of shooting stars seen during every hour
of the night, reaching a maximum at 6 A.M. (when the
point of the heavens towards which the earth is moving is
on the meridian), Schiaparelli found that the orbital velocity
of the shooting stars was equal to that of the motion in a
parabola at a distance from the focus equal to the radius of
the earth's orbit. This, in connection with the position of
the radiant, gave him .the means of computing the orbit of
the Perseids, and it turned out to be the same as that in
which the third comet of the year 1862 moves.
Out of the thousands of comets there are but com-
paratively few of which the orbits cross the earth's orbit ;
Comets and Meteors. 321
consequently, supposing that comets are often accompanied
by meteor streams, we are led to the conclusion that there
are many comet-meteor streams in the solar system which
we never see. The streams of cometary meteors have, of
course, an existence quite independent of the earth, and it is
a merely accidental circumstance that the earth's orbit
intersects a few of the comet -meteor orbits, and thus enables
us to become aware of the existence of the meteors when
they enter our atmosphere as shooting stars.
FIG. 124.
Meteor?
Although the great showers only recur at distant
intervals of time, yet it frequently happens that, even in
ordinary years when no large shower is seen, a number of
shooting stars are observed when the earth crosses the track
of one of the great meteor currents. Thus, for example,
though the great showers of the Leonids only recur at
intervals of 33^ years, yet it generally happens that from
November 12 to November 14 some meteors are seen which
diverge from the well-known region in the constellation Leo,
and are undoubtedly moving in the orbit of the Leonids. 1
The cause of this may be explained by Fig. 124, which
1 For further particulars about the orbit of the Leonids see Chap. XII.
Y
322 Astronomy.
shows the orbit in which these meteors and the first comet
of 1866 are moving.
If we suppose that the several meteors of the shoal
describe similar ellipses, then those which are moving on
the larger ellipses will have a larger periodic time than those
which are moving in the smaller ellipses. The consequence
is that the shoal iiadually lengthens out until the more
erratic members become dispersed round the entire orbit.
It is these meteors, thus distributed, which the earth meets
in ordinary years, while when the earth encounters the
main shoal, a grand display is witnessed.
CHAPTER X.
UNIVERSAL GRAVITATION.
125. The Law of Gravitation. When Kepler's laws of
the motion of the planets were announced, they were merely
empirical results deduced from actual observations. It was
Newton who showed that Kepler's laws are really only the
consequences of the grand law of nature which is called the
law of gravitation.
We know from \hzfirst law of motion, that when a body
is not acted upon by any force it moves with uniform
velocity in a straight line, but that if the body be moving in
a curved path, or if its velocity be not uniform, then force
must be acting upon that body. Kepler's laws state that
planets move in ellipses and not in straight lines, and also
that the velocities of the planets do not remain constant. We
are, therefore, forced to admit that some force must con-
stantly act upon the planets. It remains to discover at each
moment the direction and intensity of this force.
We can first prove that the direction of the force
which acts upon the planet passes constantly through the
sun. This was shown by Newton to be a consequence of
the law discovered by Kepler that equal areas are described
in equal times by the radius vector, drawn from the sun to
Universal Gravitation.
323
the planet. The orbit of the planet, although really a curve,
may be considered to form a polygon of an indefinitely
large number of sides. We may further suppose that the
length of each side of the polygon is proportional to the
velocity with which the planet is moving on that side, so that
equal time is occupied in describing each of the sides. The
actual force which acts upon the planet may be conceived to
be an instantaneous impulse which the planet receives at
each of the corners of the polygon, while during the passage
from one corner to the next no force is in action. As the
time taken to describe a side of the polygon is constant, the
property of equal areas in equal times amounts to the
assertion that the areas subtended by the sides of the
polygon at the centre of the sun are all equal.
From the second law of motion it appears that if a body
FIG. 125. FIG. 126.
have a velocity which is represented
both in magnitude and direction by
the line A p (Fig. 125), and if by the
sudden application of a force the
direction and magnitude of the
velocity are changed into A Q, then
the force which has produced this
effect will be parallel to p Q. Let
ABC (Fig. 126) be three consecutive corners of the polygon
described by the planet. Produce A B until B D is equal
to AB. Then BD will represent the velocity both in
direction and magnitude which the planet has while describ-
ing A B, and B c represents both in magnitude and direction
the velocity which the planet has along the side B c. From
the principle just explained, the instantaneous force which
acted upon the planet at B, must have been parallel to the
Y 2
324 Astronomy.
line D c. But as A B is equal to D B, the area of the triangle
s B A is equal to the area of the triangle s B D, and conse-
quently the area of s B D must be equal to that of s B c. It
hence follows that the line D c is parallel to B s, and there-
fore the impulsive force which acted upon the planet at B
must be parallel to the line B s.
We therefore see that the direction of the impulsive force
which acts at each corner of the polygon points towards the
centre of the sun. Let the number of sides of the polygon
be increased indefinitely, and we see that the planet will at
each position be acted upon by a force which is directed
towards the centre of the sun.
Thus Kepler's discovery of the law of equal areas in equal
times shows that the force which acts upon the planets must
be directed towards the sun. It can also be shown con-
versely that, when the motion of a body takes place under
the action of a force directed towards a fixed point, then
the body describes equal areas in equal times.
All that the second law of Kepler has shown us, is the
direction of the force which acts upon the planets : it has told
us nothing of the law according to which the intensity of
that force varies. To solve this question we must have re-
course to the two remaining laws.
The third law asserts that the squares of the periodic
times are in the same ratio as the cubes of the mean
distances, and as there is no reference made to the eccen-
tricities, we may, for the purpose of considering this law,
assume the hypothetical case of planets which revolve in
circular orbits around the sun in the centre. This supposi-
tion is not excluded by the first law, which states that the
orbit of a planet is an ellipse ; for there are ellipses of every
degree of eccentricity, including the circle as an extreme
case. In the case of a planet revolving in a circular orbit,
the second law of motion, which asserts the description of
equal areas in equal times, requires that the velocity shall
be uniform.
Universal Gravitation. 325
Let us, then, suppose the case of two planets moving in
circular orbits and with uniform velocities around the sun.
Let the radii of the circles be R t and R 2 , and the times of
revolution be T t and T 2 ; then Kepler's third law asserts the
proportion
But we know from the principles of mechanics that when a
body is revolving in a circle with uniform velocity, the body
must be constantly acted upon by a force which is directed
towards the centre of the circle, and that the magnitude of
that force is proportional to
47r 2 R t
where, as before, R! is the radius of the circle, and T l is the
periodic time.
If, therefore, we denote by F I and F 2 the intensities of the
two forces, we must have the proportion :
F. TJi 1 2 .
i * a " * 2 * 2 '
but, from what we have already seen
R . R. .. i i
and hence we have
From this we deduce the very important result that in
the case of two planets revolving around the sun in circles,
the intensities of the forces vary inversely as the square of
the distances. We may state this result with increased
generality as follows :
Each planet is acted upon by a force directed towards the
326 Astronomy.
sun, and varying inversely as the square of the distance from
the sun.
Assuming this law to be true, Newton discovered that the
orbit of a planet would be a conic section of which the sun
was situated in one of the foci, thus explaining in the most
simple manner the first of Kepler's laws.
In the same way as the planets describe ellipses in con-
sequence of their attraction to the sun, so the moon de-
scribes an ellipse around the earth, and the satellites
describe ellipses around their primaries. More generally
it is believed that every body in the universe attracts
every other body, and this is termed the law of universal
gravitation.
It remains to explain how the magnitude of the gravita-
tion between two bodies is affected by the masses of those
bodies. If the mass of either body be doubled, the intensity
of the attraction is doubled. It therefore appears that the
intensity of gravitation must vary proportionally to the pro-
duct of the masses. The exact expression for the gravi-
tation of two masses m and m', separated by a distance
r, is
c mm' -r- r 2 ,
where c is a certain constant depending upon the nature of
gravitation itself, and is equal to the number of units of force
in the gravitation between two units of mass when placed
at the unit of distance apart.
A very remarkable circumstance connected with the
force of gravitation must be here adverted to. We have
stated that the intensity of the force is proportional to the
product of the masses, but it appears to be quite independent
of the nature of those masses. For example, two masses of
lead placed at a certain distance are attracted by the same
force, as two equal masses of iron would be when separated
by the same distance. The attraction of gravitation is there-
fore a very different force from that kind of attraction called
Universal Gravitation.
327
magnetic attraction, where the character of the masses is of
the utmost importance.
It is not difficult to show that the force by which the
moon is retained in its orbit around the earth is really
produced by the same attraction of the earth which causes
a body to fall at the earth's surface.
A body falling freely near the surface of the earth will in
one second move over a distance of 16-1 feet. Remembering
that the distance of the moon from the centre of the earth is
about 60 radii of the earth, and that the intensity of gravity
varies inversely as the square of the distance, it appears
that, at the distance of the moon, a body let fall would in one
second move towards the earth through a distance i6 - i-4-
3600 feet=o*o53 inch very nearly. The moon is moving in
an orbit which for our present purpose we may regard as a
circle, of which the earth is the centre (Fig. 127). If the
attraction of the earth were
suspended, then the moon
would move in a straight line,
and we shall suppose that in
one second the moon at M
would move along the tangent
to its orbit at M to a distance
M P. Owing, however, to the
attraction of the earth, the
moon, instead of being found at
p, is really at Q, and as P is very
close to M, we may consider
the line P Q as parallel to M E. The moon, therefore, has in
one second fallen in towards the earth through a distance
PQ. It remains to calculate the length of this line PQ.
Produce M E to intersect the circle at A, and let fall Q R per-
pendicular on A M, then it is easy to show that the triangles
M Q R and M A Q are similar, and that consequently
M R : M Q : : M Q : M A,
3 2 8 Astronomy.
whence
P Q = M R=M Q 2 -f-M A.
As the sidereal revolution of the moon occupies 27*32 days,
and as the radius of the moon's orbit is about sixty times
the radius of the earth, it is easy to compute that the
distance M Q through which the moon moves in one second
is about 40, 120 inches. The diameter of the moon's orbit is
approximately 30,130,000,000 inches.
Whence we have
P Q=4O,I2O 2 -r-3O,I3O,OOO,OOO = O < O53.
The identity between the actual value thus found for p Q
and the distance through which a body ought to fall in one
second when at a distance from the earth equal to the
radius of the earth's orbit, places it beyond any doubt that
the motion of the moon is controlled by precisely the same
force as that which causes a stone to fall at the surface of the
earth.
126, Perturbations of the Planets. The movements of
the planets around the sun are not quite so simple as would
be the case if the laws of Kepler were accurately fulfilled.
The vast mass of the sun, which so enormously exceeds that
of all the planets taken together, no doubt subordinates the
planets, so that, as a first approximation, we may suppose that
the movements of the planets are entirely and solely con-
trolled by the sun. When, however, a nicer calculation is
made, it is found that while Kepler's laws are very nearly
fulfilled, there are still well-marked divergencies therefrom.
The orbits do not constantly remain in the same plane; they
are not accurately ellipses, nor is the law of the description of
equal areas in equal times accurately fulfilled. The theory
of universal gravitation has, however, rendered a most
satisfactory account of these irregularities. According to
that theory, not only must the sun attract the planets, but
the planets must attract the sun, and also each other, and it
Universal Gravitation. 329
is in the mutual attractions of the planets-, that the explana-
tion is found of the irregularities to which we have referred
The complete account which theory thus gives of these
irregularities is a most wonderful confirmation of the truth
of the law of universal gravitation. Conceive a fictitious
planet moving exactly according to Kepler's laws in an orbit
of which the elements are changing slowly and continuously.
The motion of this fictitious planet can be so chosen, that it
shall represent closely the actual motion of the real planet.
The position of the real planet will sometimes be in advance
of, and sometimes behind, the fictitious planet, and these
oscillations are usually called the periodic variations. The
changes in the elements of the orbit of the fictitious planet,
which are found necessary to keep that planet in the vicinity
of the real planet, are termed the secular variations of the
orbits.
By the theoretical study of the secular variations, certain
very remarkable propositions have been discovered, some of
which shall be here considered. For simplicity we shall
suppose that only two planets are under consideration, and
we shall consider the derangement produced in the orbit of
each planet by the action of the other planet. It has been
demonstrated that, notwithstanding the changes which all the
other elements of each orbit undergo, the length of the axis
major of each ellipse, or the mean distance of each planet
from the sun, remains constant. The importance of this
conclusion will be manifest, when it is remembered that the
time of revolution of a planet round the sun is, by Kepler's
third law, solely dependent upon the axis major of the
elliptic orbit. From the constancy of the length of this axis
major, we can therefore infer that, notwithstanding the
perturbations, the periodic time of each planet remains
constant.
The eccentricities of the orbits of the disturbed planets
undergo certain secular changes. Yet these changes are
confined within such narrow limits, that no considerable
33O Astronomy.
alteration in the configuration of the solar system can arise
from this cause. When two planets moving in the same
direction are mutually disturbed, the sum of the squares of
their eccentricities, each multiplied by a certain numerical
factor, remains constant. As the eccentricities are at
present small, the constant is small, but if the sum of two
positive quantities be small, then each of the quantities
must be small: hence it follows that the eccentricities of the
disturbed orbits must for ever remain small. A similar
proposition holds good for the inclinations of the orbits to
the plane of the ecliptic, so that, though the inclination may
change, yet it never can change to any large extent.
The propositions we have just referred to, relative to the
major axis, the eccentricities, and the inclinations of the
orbits of the planets, indicate the stability of the planetary
system, as at present constituted. We thus see that the
orbits of the planets must preserve very nearly the same
relations as they have at present.
127. Masses of the Planets. By the aid of the theory
of gravitation, we are enabled to solve the very important
problem of determining the masses of the different bodies in
the solar system. In the first place, we shall show how the
relative values of the masses of the earth and the sun are to
be obtained. If we had the means of determining the
attraction exerted by the sun and the attraction exerted by
the earth on an object at an equal distance from the two
bodies, then, since the ratio of these attractions would be equal
to the ratio of the masses of the sun and the earth, we could
determine the latter ratio. Now we have by the motion of
the earth itself a means of making this calculation. The
attraction of the earth would make a body at its surface
fall 1 6- 1 feet in one second. As the distance of the
sun is about 23,300 radii of the earth, the attraction of
the earth on a body situated at the distance of the sun is
such as to make the body fall in one second through
a distance 16*1-7-23,300x23,300. From the motion of
the earth around the sun we can find the distance through
Universal Gravitation. 331
which the earth falls in one second towards the sun (see
120). We hence deduce that the mass of the sun is
324,000 times that of the earth, or, taking the mass of the
sun as unity, we have for the mass of the earth 1-7-324,000.
There is but little difficulty in finding the mass of a
planet which, like Mars, Jupiter, Saturn, Uranus, or Neptune,
is attended by one or more satellites. From the observa-
tions of the motions of the satellite, the distance a body
falls through in one second towards the planet can be com-
puted, and, from the motion of the planet round the sun, the
distance the planet falls in towards the sun in one second is
found, whence we can deduce the ratio of the mass of the
planet to the mass of the sun.
In the case of planets which, like Venus and Mercury, are
not attended by visible satellites, the determination of the
masses constitutes a more difficult problem. We are then
obliged to resort to the perturbations which those planets
produce in the movements of other bodies belonging to the
solar system. The theoretical expressions of these perturba-
tions involve the mass of the disturbing body, and as the
actual amounts of the perturbations are determined from the
observations, it is possible by a comparison between theory
and observation to obtain the value of the unknown mass.
Although this method may seem very recondite, yet such is
the perfection of the theory of perturbation, that it is possible
by these means to obtain the masses of certain planets
with considerable accuracy. This was very remarkably con-
firmed in the case of the planet Mars, for, until the discovery
of the satellites in 1877 placed a more accurate means of
finding the mass of the planet within our reach, our know-
ledge of the mass of Mars was solely deduced from the
perturbations which it produces. Yet the value of the mass
which was arrived at from the observations of the satellites
merely confirmed, with a slight correction, the value of the
mass which had been determined from the perturbations.
The masses of comets have also been estimated.
33 2 Astronomy.
The orbits of the comets are so irregularly placed with
regard to the planets, that it has frequently happened that a
comet passes so close to a planet as to be very greatly
deranged by the attraction of the planet. Yet in such cases
it has appeared that the action of the comet upon the planet
is inappreciable, and thus it follows that the mass of the
comet must be very small.
128. Gravitation at the Surface of the Celestial Bodies.
The gravitation at the surface of a celestial body, which
may be regarded as spherical, depends partly upon the mass
of the body and partly upon its radius. When we know the
mass and also the radius we are enabled to compute the
gravitation. Thus in the case of the sun, it appears that
the actual intensity of gravitation at his surface is about
twenty-seven times greater than the intensity of gravitation
at the surface of the earth. By this it is meant that a mass
of one pound would require as much to support it at
the surface of the sun, as would be adequate to support
a mass of twenty-seven pounds at the surface of the
earth. In the case of Jupiter the gravitation at the surface
is about two and a half times as great as the gravitation at
the earth. On the other hand, owing principally to the
small mass of the moon, the gravitation at the surface of the
moon is about one-sixth part of what it is on the earth. A
man on the surface of the moon would be able to raise a
load containing six times as much matter as he would be
able to lift on the earth.
129. Perturbations of the Moon. According to Kepler's
laws, the moon should accurately describe an ellipse about
the centre of the earth as one of the foci. It is, however, very
easily shown by observation that the movements of the moon
are not by any means of so simple a character as those which
Kepler's laws would prescribe. The orbit of the moon is
not exactly an ellipse, nor does the plane of the orbit remain
constant. The moon is, in fact, perturbed just as we have
already seen that the planets are perturbed by their mutual
actions.
Universal Gravitation, 333
The perturbations of the moon arise, however, from a
very different cause from those of the planets. The moon is
an appendage to the earth, and it is by the gravitation of
the moon towards the earth that the motion of the moon is
mainly controlled. The disturbing body in the case of
the moon is really the sun. The earth and the moon are of
course both attracted by the sun, but the moon is sometimes
nearer to the sun (for example, at or near new moon) than it
is on other occasions (for example, at or near full moon).
Under these circumstances the moon is therefore more
powerfully attracted by the sun at some parts of its path
than it is at others, and this irregularity in the intensity of
the sun's attraction is the cause of the lunar perturbations.
At the time of new moon, the moon, being nearer the
sun, is more powerfully attracted by the sun than the earth
is attracted by the sun, and consequently the distance from
the earth to the moon is augmented. At full moon the
attraction of the sun is more powerful on the earth than it is
on the moon, and consequently the earth is more drawn in
to the sun than the moon, the effect of which is also to
increase the distance between the earth and the moon. At
the time of first and last quarter, the earth and the moon are
practically at the same distance from the sun, and as the
distance of the sun is so great, the earth and moon may be
considered to be displaced along parallel lines through equal
distances, and therefore the distance of the earth and the
moon is unaltered. As, however, the distance of the earth
from the moon is generally increased by the disturbing effect
of the sun, we may assert, as one consequence of the dis-
turbance of the sun, that the orbit of the moon is larger than
it would be were that source of disturbance absent. The
efficiency of the sun in producing this disturbance increases
when the earth is near perihelion ; for then, the distance of
the sun from the earth and moon being diminished, the
difference of its effects upon the earth and moon becomes
more manifest. The orbit of the moon, therefore, varies in
334 Astronomy.
size with the different positions of the earth in its annual
revolution : according to Kepler's third law the time of
revolution of the moon increases when the size of the orbit
increases ; and hence it appears that when the earth is in
perihelion the periodic time of the moon is a maximum, and
when the earth is in aphelion, the periodic time of the moon
is a minimum. The effect of this upon the apparent place
of the moon is to produce a certain derangement called the
annual equation. This inequality of the moon was dis-
covered by Tycho Brahe by observation, long before the ex-
planation of it was known.
130. The Secular Acceleration. Were the eccentricity
of the earth's orbit constant, then the motion of the moon at
the end of the year would be the same as it was at the
commencement, so far as the annual equation is concerned.
Owing, however, to the secular alterations of. the earth's
orbit, which are produced by the perturbations of the
planets, the eccentricity is changing, and consequently there
is a gradual alteration in the orbit of the moon. As the
axis major of the earth's orbit remains constant, it can
be shown that the sun causes the orbit of the moon to
be larger, the greater is the eccentricity of the orbit. At
present the eccentricity of the earth's orbit from one century
to another is gradually decreasing, and consequently there
is a gradual decrease in the size of the moon's orbit, and
therefore a gradual decrease in the periodic time of the
revolution of the moon. About one half of the observed
value of the acceleration of the moon's motion can be ex-
plained in this manner.
The gradual diminution of the eccentricity of the earth's
orbit will not continue indefinitely. All the secular in-
equalities of the planet's orbits are really periodic, though
usually requiring vast durations of time to run through their
changes. The time will, however, come, when the diminution
of the eccentricity of the earth's orbit will be turned into an
increase. The acceleration of the moon now in progress
Universal Gravitation. 335
will then, so far as it is due to this cause, be turned into a
retardation. This again after the lapse of ages will be
turned into an acceleration, and so on indefinitely.
. 131. Cause of the Precession of the Equinoxes. The
diurnal rotation of the earth about its polar axis is subject
to a very remarkable disturbance which gives rise to the
phenomena of the precession of the equinoxes and nutation.
The disturbance is due to the attraction of the sun and the
moon upon the protuberant portions at the earth's equator.
To explain this we have to make use of a theorem in
dynamics which we cannot demonstrate in this volume. If
the earth be rotating around its polar axis, then that rotation
will not be disturbed by any force which passes through the
centre of gravity of the earth. In fact, so far as the mere
rotation of the earth upon its axis is concerned, we might
regard the centre of gravity as a fixed point, and then the
force which passed through the centre of gravity could be
neutralised by the reaction of the fixed point.
If the earth were a perfect homogeneous sphere, the
attraction of the sun or the moon would be a force passing
through the centre of the sphere, and would leave the rota-
tion unaffected. Even though the earth were not a perfect
sphere, or not homogeneous, still if the attracting body were
so far off that all points of the earth might be considered
practically at the same distance from the attracting body,
the attraction would be a force passing through the
centre of gravity of the earth. The sun and the moon,
however, are both so comparatively near the earth that
we are not entitled to make this supposition, and con-
sequently neither the attraction of the sun or of the moon
passes through the earth's centre. To this is due the
phenomenon of the precession of the equinoxes.
Let PQ (Fig. 128) represent the axis of the earth, and let
s be the position of the attracting body ; then, since the
attraction varies inversely as the square of the distance, it
follows that the portion of the earth turned towards that
Astronomy.
attracting body will be acted upon by a greater force than
the portion towards the remote side, and consequently the
FlG I2g total attraction will be
directed along the line
H s, which passes above
the centre of gravity of
tne eartn c - Let H T
Y represent the magnitude
of this force both in
intensity and direction.
Through the centre c draw a line x Y parallel to
H T, and let us suppose that equal and opposite forces are
applied at the centre c, each of these forces being equal to
H T. The force c Y may now be left out of view, for as it
acts through the centre of gravity it can have no effect upon
the rotation of the earth around its axis. Thus the effect of
the attracting body upon the earth may, so far as the rotation
of the earth is concerned, be represented by the pair of equal
parallel and opposite forces H T and c x. Such a pair form
what is known in mechanics as a couple.
It would seem as if the immediate effect of this couple
would be to turn the earth so as to bring its polar axis c P
perpendicular to the line c s, or (supposing the sun to be
the attracting body under consideration) to bring the plane
of the equator to coincide with the plane of the ecliptic.
The effect of the couple is, however, so entirely modified by
the fact that the earth is in a state of rapid rotation, that,
paradoxical as it may appear, the real effect of the couple
is not to move c P in the plane of the paper, but to make
c P move perpendicular to the plane of the paper.
In explanation of this apparent paradox, we may remark
that, in a miniature form, every schoolboy is already
acquainted with a precisely analogous phenomenon in the
motion of a common peg-top. In Fig. 129 the line P z is
vertical, P c is the axis of the peg-top; and c is the centre of
gravity of the peg-top. If the peg-top, when not spinning,
Universal Gravitation.
337
FIG. 129.
were placed in the position represented in the figure, the
force of gravity acting along c H would immediately cause
it to tumble over, the line c P moving
in the plane of the paper. But when the
peg-top is in a state of very rapid rotation,
the circumstances are entirely different.
Everyone has observed that the axis c P,
so far from falling in the plane of the
paper, commences to move perpendicu-
larly to the plane of the paper, and will,
in fact, describe a right circular cone
around P z as an axis. It is undoubt-
edly true that after a time the angle z P c
begins to increase, and that before long
the peg-top really does tumble down, but this is solely due
to the influence of disturbing forces viz. friction at the
point, and the resistance of the air and if these forces could
be evaded the speed with which the peg-top spins would be
undiminished, and so long as that speed remained unaltered,
so long would the axis of the peg-top continue to describe
the right circular cone around the line P z.
Assuming that what holds good in the case of the peg-top
holds good in the colossal case of the earth itself, we should
expect to find that the axis P c (Fig. 128), instead of moving
towards s, and thus diminishing the obliquity of the ecliptic,
would commence to move perpendicularly to the plane of the
paper and thus not alter the obliquity of the ecliptic at all.
The axis of the earth would thus describe a right circular
cone, of which the axis is perpendicular to the plane of the
ecliptic, and this is actually the motion which the precession
of the equinoxes requires.
The precession of the equinoxes is due to the action of
both the sun and the moon. Owing, however, to the proxi-
mity of the moon, its effect is greater than that of the sun.
In fact, of the total amount, about one-third is due to the
sun and the remainder to the moon.
z
338 Astronomy.
132. Nutation. The efficiency of the moon in the pro-
duction of the phenomenon just considered depends upon the
position of the orbit of the moon with respect to the ecliptic,
and as this is changing, so the efficiency of the moon will
undergo certain changes, the period of which is equal to
that of the revolution of the moon's nodes. The effect of
this is that the phenomenon of precession is not so simple as
it would be were the moon actually in the plane of the
ecliptic. Thus the true position of the pole oscillates about
its mean place as determined by precession, and this oscilla-
tion is the nutation.
CHAPTER XL
SPARS AND NEBULAE.
133. Star Clusters. The stars are very irregularly dis-
tributed over the surface of the heavens. This is, indeed,
sufficiently obvious to the unaided eye, and it is confirmed
by the telescope. In certain places we have a dense aggre-
gation of stars of so marked a character as to make it almost
certain that the group must be in some way connected
together, and that, consequently, the aggregation is real, and
not only apparent, as it might be if the stars were really only
accidentally near to the same line of sight, and, con-
sequently, appeared to be densely crowded together, when,
in reality, they might be at vast distances apart.
Of such a group we have a very well known example in
the group called the Pleiades, which we have already men-
tioned ( 25). Most .persons can see six stars in the Pleiades
without difficulty, but with unusually acute vision more can
be detected. With the slightest instrumental aid, however,
Stars and Nebulce. 339
the number is very greatly increased, and photography shows
that the group consists of perhaps 2,000 stars.
Another illustration of such a group is an object in the
constellation Cancer known as the Praesepe, or the Beehive.
To the unaided eye this is merely a dullish spot on the sky,
not well seen unless the night is very clear. A telescope
shows, however, that this dullish spot is really an aggregation
of many small stars.
By far the most splendid object of this kind in the
northern hemisphere is the cluster in the Sword-handle of
Perseus. We have here two groups of stars close together,
and, when seen in a good telescope, the multitudes of these
stars, and their intrinsic brightness, form a most superb
spectacle.
The objects known as star clusters are exceedingly nu-
merous. Among them are several which are remarkable
telescopic objects, not for the brightness (even in the
telescope) of the individual stars composing the star cluster,
but for the vast numbers in which the stars are present, and
for the closeness in which they lie together. These objects
are often known as globular clusters, because the stars
forming them seem to lie within a globular portion of space,
and they frequently appear to be much more densely
compacted together towards the centre of the globe. In
fact, at the centre of one of these splendid objects it is in
some cases almost impossible to discriminate the individual
stars, so closely is their light blended. One of the most
remarkable of these objects in the northern hemisphere is
the globular cluster in Hercules. Most of these objects
are situated in the neighbourhood of the Milky Way> an
immense stream of faint stars spanning the whole heavens.
For more than a third of its extent the Milky Way is
split into two streams running at a short distance from
each other, and of an exceedingly irregular structure. As
our telescope in sweeping over the heavens approaches
the Milky Way, the stars are seen rapidly to increase in
Z2
340 Astronomy.
number. According to a theory originally proposed by
Thomas Wright in 1750 and adopted for some time by
W. Herschel, the stars of the Milky Way were supposed to
be arranged in the shape of a huge disc (like a grinding-
stone), near the centre of which our solar system was
situated, by which the comparatively small number of stars
near the poles of the Milky Way was readily explained.
But the complicated structure of the Milky Way, the dark
holes in it and the branching streamers of stars projecting
from it, as well as the fact that even the bright stars con-
gregate towards it, render it far more probable that the
Milky Way really is a stream of stars encircling the heavens
like a ring at a great distance from us.
134. Spectra of Stars. While the spectra of the
planets are little else than faint reproductions of the solar
spectrum (with some additional dark lines or bands arising
from absorption in the planet's atmosphere), many of the
fixed stars show a totally different spectrum. The simplest
classification of stellar spectra is that of Secchi, who
divided them into the following four types :
Type I. The spectrum contains very few absorption lines
except those of hydrogen, which are very strongly marked.
The stars are white or blue in colour, like Sirius or Vega.
Type II. The spectrum is essentially the same as that
of our sun, showing numerous dark lines. Arcturus and
Capella are examples. The stars of these two types include
about ninety per cent, of those spectroscopically examined.
Type III. Most of the red or variable stars have spectra
crossed by dark bands or flutings instead of lines, sharply
defined towards the blue and shading off gradually towards
the red end of the spectrum, apparently due to carbon.
a Orionis and o Ceti are examples.
Type IV. includes a small number of red and faint stars
with spectra like those of Type III., except that the bands
are shaded towards the blue and sharp towards the red end
of the spectrum.
Stars and Nebula. 341
Some stars also exhibit a few bright lines in addition to
the dark ones, such as the lines of hydrogen and helium.
135. Telescopic Appearance of a Star. The appearance
of a star in a telescope differs in a most marked manner
from the appearance of one of the larger planets. In the
case of the planet we can see what is called the ' disc ' : we
can actually observe that the planet appears circular, and
that it is presumably a globe with an appreciable diameter.
By increasing the magnifying power of the telescope the
size of the disc can be increased, though, of course, at the
expense of its intrinsic brightness.
Widely different, however, is the telescopic appearance
of a fixed star. Even the most powerful telescope only
shows a star as a little point of light. By increasing the
optical power of the telescope, the brilliancy of the radiation
from this point can be increased, but no augmentation of
the magnifying power has hitherto sufficed to show any
appreciable ' disc ' in any of the fixed stars which have been
examined. 1 How is this to be explained ? The answer is
to be sought not in the real minuteness of the stars, but in
the vast distances at which they are situated. In order to
form some estimate of the real diameter which the stars do
subtend at the eye, let us suppose that our sun were to be
moved away from us to a distance comparable with that by
which we are separated from those stars which are nearest
to us.
For this purpose the sun would have to be transferred
to a distance not less than
200,000 times as far as his
present distance from the earth.
Let A B (Fig. 130) denote the
diameter of the sun, and let E
be the position of the earth. Then, as we have already
1 In a stellar spectroscope it is therefore necessary to place a cylin-
drical lens in the eye piece to widen the spectrum into a band. Other-
wise it would be a mere line and would not show the absorption lines.
342 Astronomy.
seen ( n), the circular measure of the angle which the sun
subtends at the earth is practically equal to A B-T-E B. Now
suppose the sun be transferred to the position indicated by
A' B', then the angle which he would subtend in the new
position is A' B'-T-E B'.
Hence the ratio of the angles which the apparent
diameter of the sun subtends at the eye at the two different
distances is
A B ^ A' B' .
E B " E B' '
but as the real diameter of the sun is the same in both cases,
we must have
A B=A' B',
and hence the ratio just written becomes
EB'
E B*
Hence we infer that the angle which the sun's diameter
subtends at the eye varies inversely as his distance from the
observer.
If, therefore, the sun were to be carried away from us to
a distance 200,000 times greater than his present distance,
the angle which his diameter at present subtends would be
diminished to the 2oo,oooth part of what it is at present.
Assumin g, as we may do for rough purposes, that the sun's
apparent diameter is half a degree, it follows that the
apparent diameter when translated to the distance of a star
would be expressed in seconds by the fraction
1800 =o"-oo 9 .
2OOOOO
In other words, the sun's diameter would then subtend an
angle less than the hundredth part of a single second.
It is at present, at all events, quite out of the question to
suppose that a quantity so minute as this could be detected
by our instruments. Even were it ten times as great it
Stars and Nebula. 343
would be barely appreciable, nor unless it were at least fifty
times as great would we be able to measure it with any
approach to precision.
It is, therefore, clear that we cannot infer the actual
dimensions of the stars from their minute apparent size in
the telescope.
136. Stellar Photometry. We have already ( 25)
mentioned the mode of classifying stars by their magnitude.
Measures of the apparent brightness of stars were formerly
only eye-estimations, but of late years several instruments
have been designed by means of which more accurate
measures can be made. We shall here only describe the
principles of two of them.
Pritchard's wedge photometer consists of an eye piece
with a wedge of neutral-tinted dark glass, which the observer
slides to and fro until the star under observation just dis-
appears, after which the position of the wedge is read off on
a graduated scale. As it has been beforehand determined
what displacement of the wedge corresponds to a change of
one magnitude, this observation will furnish the actual
magnitude of a star. In this manner Professor Pritchard's
' Uranometria Oxoniensis ' was compiled, giving the mag-
nitudes of all the stars visible to the naked eye between the
North Pole and 10 south declination.
Pickering's meridian photometer compares the light of a
star directly with that of a standard star, most conveniently
the Pole Star. The rays from the two stars are sent through
two separate object glasses and through a double-image
prism. Two of the four pencils emerging from this are
intercepted by a screen, the two others (the ordinary pencil
from one star and the extraordinary pencil from the other)
are received by a Nicol prism, and being polarised at right
angles to each other, one will increase and the other de-
crease in brightness as the Nicol is turned. In this way
the two images may be made equal in brightness, and the
angle through which the Nicol is turned gives the difference
344 Astronomy.
of magnitude. The magnitudes of the ' Harvard Photo-
metry ' agree well with Pritchard's.
137. Variable Stars. Some stars are called variable
stars, inasmuch as their brightness is not constant, as that
of the majority of stars appears to be. There are some
hundreds of stars in the heavens the brightness of which is
now known to change. It would be difficult here to de-
scribe in detail the different classes of the variable stars, so
we shall merely give a brief account of one or two of the
most remarkable.
In the constellation Perseus is a bright star, Algol (right
ascension, 3 h o m ; declination, -f 40 27'). Owing to the
convenient situation of this star, it may be seen every night
in the northern hemisphere. Algol is usually of the second
magnitude, but in a period of between two and three days,
or more accurately in a period of 2 d 2o h 48 55 s , it goes
through a most remarkable cycle of changes. These
changes commence by a gradual diminution of the bright-
ness of the star from the second magnitude down to the
fourth in a period of four and a half hours. At the fourth
magnitude the star remains for twenty minutes, and then be-
gins to increase in brightness again until, after an interval
of three and a half hours, it regains the second magnitude.
Algol continues at the second magnitude for about 2' 1 i2 h ,
when the same series of changes commences anew. The
variability of stars of the Algol type seems to be caused by
a dark companion revolving round the star and causing a
partial eclipse whenever it comes between us and the star.
Spectroscopic observations confirm this theory (see below,
140).
Another very remarkable star belonging to the class of
variables is o Ceti or Mira (right ascension, 2 h i3 m ; decli-
nation, 3 34'). The period of the changes of this star
is 33 1 d 8 h . For about five months of this time the star
is very faint ; it then gradually increases in brightness
until it becomes nearly of the second magnitude. After
Stars and Nebulce. 345
remaining at its greatest brightness for some time it again
gradually sinks to the ninth magnitude. Mr. Lockyer suggests
that a variable of this class may not be a star in the usual
meaning of the word, but a dense and much extended
swarm of meteorites, with another smaller swarm revolving
round it in a very eccentric orbit, so that the smaller swarm
at perihelion passage has to pass through part of the larger
one, and increases its brightness by the collisions between
the members of the two swarms.
The so-called temporary stars are probably also caused
by a collision of some sort. The most remarkable star of
this kind appeared suddenly in Cassiopeia in November 1572,
and was when first seen as bright as Venus when this planet
is brightest. It then gradually faded, and disappeared to the
naked eye about the end of March 1 5 74. Several stars of
this kind have appeared in our own time, the most recent
one of interest being one in Auriga. It was discovered by
an amateur, Dr. Anderson of Edinburgh, on January 24, 1892,
as a star of the fifth magnitude, but it was afterwards found,
from photographs which had been taken of the region where
it appeared at various observatories, that it must have flashed
out between December 8 and 10, 1891 ; on the latter day
it was already nearly of the fifth magnitude. After fluctu-
ating somewhat in brightness for some weeks, it declined
rapidly, and ceased to be visible about the end of April
1892, but in the following autumn it rose again for a while
to the tenth magnitude. Temporary stars generally show
a spectrum with both dark absorption lines and bright lines.
138. Proper Motion of Stars. We have hitherto
frequently used the expression fixed stars ; ' we have now
to introduce a qualification which must be made as to the
use of the word fixed with reference to the stars. Com-
pared with the planets, the places of which are continually
changing upon the surface of the celestial sphere, the stars
may, no doubt, be termed fixed ; but when accurate obser-
vations of the places of the stars made at widely distant
346 ' Astronomy.
intervals of time are compared together, it is found that to
some of the stars the adjective fixed cannot be literally
applied, as it is undoubtedly true that they are moving.
It is true that the great majority of what are called fixed
stars do not appear to have any discernible motion, and
even those which move most rapidly, when viewed from
the vast distances by which they are separated from the
earth, only traverse but a very minute arc of the heavens in
the course of a year. The most rapidly moving star moves
over an arc on the celestial sphere of 7" per annum. A
motion so slow as this is inappreciable without very refined
observations. The moon has a diameter which subtends
at the eye an angle which we may roughly estimate at half
a degree, and to move over a space equal to the diameter
of the moon on the surface of the heavens would require a
couple of centuries even for the most rapidly moving star.
We have already had frequent occasion to discriminate
between real motion and apparent motion, and are there-
fore naturally tempted to inquire whether the motions of
the stars which we have been considering are real, or
whether they can be explained as merely apparent motions.
Now where must we look for the cause of the apparent
motion ? It is manifest that the annual motion of the earth
around the sun could not possibly explain the appearances
ivhich have been observed. The annual motion of the
earth around the sun would have an effect which must be
clearly periodic in its nature. In fact, it would be merely
the annual parallax which we have already considered.
The motions which we have to explain are not (so far as we
know at present) of a periodical character ; for the stars
which possess this motion usually appear to move con-
tinually along great circles.
1 139. Motion of the Sun through Space. It was first
suggested by Sir W. Herschel that a portion of the proper
motions of the stars could be explained by the supposition
that the sun, carrying also the retinue of planets, and all
Stars and Nebula. 347
the other bodies forming the solar system, was actually
moving in space. On this supposition, it is clear that those
stars which were sufficiently near to us must have an appa-
rent proper motion. If the motion of the sun were directed
along a straight line towards a certain point of the heavens,
then the apparent place of a star at that point would be un-
affected by the motion of the sun ; but all other stars would
spread away from that point, just as when you are travelling
along a straight road the objects on each side of the road
appear to spread away, as it were, from the point towards
which your journey was directed.
It was found by Sir W. Herschel that a considerable
portion of the observed proper motions of the stars could
be explained by the supposition that the sun was moving
towards a point in the heavens near to the star X Herculis.
The investigations of other astronomers have confirmed
this very remarkable deduction as to the sun's motion in
space, and have led them to conclude that the sun is
moving towards a point in the heavens which (considering
the difficulty of the investigation) is near the point deter-
mined by Sir W. Herschel. The right ascension of the
point thus determined is 2 66 7 and its declination is + 31
(L. Struye and others).
Not only has the direction in which the sun moves been
determined, but the observations also give us some idea of
the velocity of the motion. It is found that in one year the
sun probably moves through an arc of o"'4i as seen from
the distance of a star of the first magnitude.
We thus see that the real motion of the earth in space is
of a very complicated character ; for though it describes an
ellipse about the sun in the focus, yet the sun is itself in
constant motion, and consequently the real motion of the
earth is a composite movement, partly arising from its own
proper motion around the sun, and partly arising from the
fact that, as a member of the solar system, the earth partakes
of the motion of the solar system in space.
348 A stronomy.
140. Real Proper Motion of the Stars.~lt should,
however, be observed that after every possible allowance has
been made for the effect of the motion of the solar system,
there remain still outstanding certain portions of the proper
motions of the stars, which are only to be explained by the
fact that the stars in question really are in actual movement.
Nor, if we reflect for a moment, is there much in the last
conclusion to cause surprise. The first law of motion com-
bined with the most elementary notions of probabilities
will show us how exceedingly improbable rest really is.
Among all the possible kinds of motion, infinitely various
both in regard to velocity and in regard to direction, there
is no one which is not a priori just as probable as another ;
there is no one which is not a priori just as probable as rest.
Hence, even if there were no causes tending to produce
change from an initial state of things, it would be infinitely
improbable that any body in the universe was absolutely at
rest. But even if a body were originally at rest it could
not remain so. Distant as the stars are from the sun, and
from each other, they must still, so far as we know at present,
act upon each other. It is true that these forces acting
across such vast distances may be slender, but, great or
small, they are incompatible with rest, and hence we may
be assured that every particle in the universe (with, it is
conceivable, one exception) is in motion.
We are thus led to believe that the fact that proper
motion has only been detected in comparatively few stars is
to be attributed, not to the actual absence of proper motion,
but rather to the circumstance that the stars are so exceed-
ingly far off that, viewed -from this distance, the motions
appear so small that they have not hitherto been detected.
It can hardly be doubted that, could we compare the places
of stars now with the places of the same stars 1,000 years
ago, most of them would be found to have changed. Un-
fortunately, however, the birth of accurate astronomical
observation is so recent that we have only imperfect means
Stars and Nebulas. 349
of making this comparison, for the ancient observations
which have been handed down to us are not sufficiently
accurate to afford trustworthy results.
It is easy to see that meridian or micrometer obser-
vations do not enable us to find the true proper motion
of a star, but only the projection of this motion on the
celestial vault, or, in other words, the component of the
proper motion perpendicular to the line of sight. We can,
however, in many cases form an idea of the component
of the motion in the line of sight. In the chapter on
the sun we have already shown how this may be done
by observing displacements of spectral lines by Doppler's
principle. The lines in the spectra of stars being vastly
fainter than those in the solar spectrum and not so sharply
defined, these observations, which were first made by
Huggins in 1868, and have since been continued at the
Greenwich Observatory, are extremely difficult, and the
results often contradictory. Generally a certain line (e.g.
one of the hydrogen lines) in the star spectrum is directly
compared with the corresponding line in the spectrum of
the chemical element. More recently photography has been
used with better success at the Potsdam and Harvard
Observatories. In this way a brilliant confirmation of the
eclipse theory of the variable star Algol ( 137) has been
obtained. It has been found at Potsdam that Algol moves
with a velocity of about 26 miles a second round the com-
mon centre of gravity of itself and a dark companion. The
latter must be slightly smaller than our sun, 830,000 miles
in diameter, while the diameter of the bright star is about
1,061,000 miles, assuming that at central transit the com-
panion is altogether projected on the bright star.
141. Double Stars. We have already alluded to the
occasional close proximity in which stars are found on the
celestial sphere. In many cases we have the phenomenon
which is known as a double star. Two stars are frequently
found which appear to be s6 exceedingly close together that
3 SO Astronomy.
the angular distance by which the stars are separated is less
than one second of arc, and an exceedingly good telescope
is required to 'divide ' such an object, which, when viewed
in an inferior instrument, would appear to consist only of a
single star. The great majority of double stars known at
present are, however, not nearly so close together. About
10,000 objects have now been discovered which are included
under the term double stars, though it must be added that
the components of many of these are at a considerable
distance apart.
We shall here describe briefly a few of the most remark-
able of these very interesting objects.
142. The Double Star Castor. One of the finest
double stars in the heavens is Castor ( Geminorum).
(Right ascension, 7 h 26; declination, + 32 17'.) Viewed
by the unaided eye, the two stars together resemble but a
single star, but in a moderately good telescope it is seen
that what appears like one star is really two separate stars.
The angular distance at which these two stars are separated
is about five seconds. One of the stars is of the third
magnitude, and the other is somewhat less. The reason
why the unaided eye cannot distinguish the separate com-
ponents is their great proximity. The angular distance of
the components is the same angle as that which is sub-
tended by a length of one inch at a distance of 1,146 yards,
and is therefore quite inappreciable without instrumental aid.
The question now arises whether the propinquity of the two
stars forming Castor is apparent or real. This propinquity
might be explained by the supposition that the two stars
were really close together, compared with the distance i>y
which they are separated from us. Or it could equally be
explained by supposing that the two stars, though really
far apart, yet appeared so nearly in the same line of vision
that, when projected on the surface of the heavens, they
seemed to be close together. In the case of many of the
double stars, especially those in which the components
Stars and Nebula. 3 5 I
appear tolerably distant, the propinquity is only apparent,
and arises from the two stars being near the same line
of vision. But it is also undoubtedly true that, in the
case of very many of the double stars, especially among
those belonging to the class which includes Castor, the
two stars are really close together.
Many double stars of this description exhibit a pheno-
menon of the greatest possible interest. If we imagine a
great circle to be drawn from one of the two component stars
to the north pole of the celestial sphere, then the angle
between this great circle and the great circle which joins the
two stars is termed the position angle of the double star. By
the ingenious instrument called the micrometer ( 48), which is
attached to the eye end of a telescope mounted equatorially,
it is possible to measure both the position angle of the two
components of a double star, and also the distance of the
two stars expressed in seconds of arc. When observations
made in this way are compared with similar observations of
the same double star, made after an interval of some years,
it is found in many cases that there is a decided change both
in the distance and in the position angle. In the case of
the double star Castor, at present under consideration, it is
true that the movement is very slow. It is, however, un-
doubted that in the course of some centuries * one of the
components will revolve completely around the other.
143. Motion of a Binary Star. The theory of gravita-
tion affords us the explanation of these changes. We have
seen how, in the case of the sun and the planets, each
planet describes around the sun an orbit of which the figure is
an ellipse, with the sun in one focus, while the law according
to which the velocity changes is defined by the fact that
equal areas must be swept out in equal times. The circum-
stances presented by the sun and a planet (the earth, for
example) are somewhat peculiar, and Kepler's law must be
stated somewhat differently before they can be applied with
1 The period assigned for the time of revolution of Castor is 996 years
(Thiele).
352 A stronomy.
strict generality to the motion of a binary star (as one of the
revolving double stars is termed). In the case of the sun and
the earth we have a comparatively minute body moving
around a very large body. In fact, as the mass of the sun
is more than 300,000 times greater than the mass of the
earth, we may neglect the mass of the earth in comparison
with the mass of the sun. Thus, in speaking of Kepler's
laws as applied to the motion of a planet around the sun,
we often regard the centre of the sun as a fixed point, and
attribute all the motion which is observed to the planet.
It is manifest, however, that some modification of
Kepler's laws is necessary before we can apply them to the
case of most of the binary stars. In the case of Castor,
though the two components are not exactly equal, yet they
are so nearly so that it would obviously be absurd to regard
even the larger of them as a fixed point while the whole
orbital motion was performed round it by the other. The
fact of the matter is that both the components are in motion,
each under the influence of the attraction of the other, and
that what we actually observe and measure is only the
relative motion of the components.
It would lead us beyond the limits of this book to
endeavour to prove the more generalised conception of
Kepler's laws which we shall now enunciate. Let us suppose
the case of a binary star so far removed from the influence
of other stars or celestial bodies that their attraction may be
regarded as insensible. Then each of the two components
of the binary star is acted upon by the attraction of the
other component, but by no other force. We suppose a
straight line A B to be drawn connecting the centres of the
stars, and we divide this line into two parts, A G and B G, in
the proportions of the masses of the two stars, so that the
point of division G lies between the two stars and nearer to
that star, A, which has the greater mass. The point G thus
determined is the centre of inertia of the two stars. It
can be proved that, however the stars A and B may move in
Stars and Nebula. 353
consequence of their mutual attractions, the point G will
either remain at rest or will move uniformly in a straight
line. It can be shown that each of the stars A and B will
move in an elliptic orbit around the point G as the focus,
and that each star will describe equal areas in equal times.
It can also be shown that, although both of the stars
are in motion, yet the relative motion of one star about the
other i.e. the motion of the star B about the star A as it
would be seen by an observer who was stationed on A is
precisely the same as if the mass of the star A were aug-
mented by the mass of the star B, and as if A were then at
rest and B moved round it just as a planet does around the
sun. To this apparent motion of B around A, Kepler's laws
will strictly apply. The orbit of B is an ellipse of which A is
one of the foci, and the radius vector drawn from A to B will
sweep out equal areas in equal times.
It is natural to inquire whether these theoretical anticipa-
tions with respect to the motions of the binary stars are
borne out by observation. We have no reason to expect
that we shall actually see motions of the simple character
which we have described. It is to be recollected that the
plane in which the orbit is described may be inclined in any
way to the surface of the celestial sphere. Consequently
the orbit which we shall see may only be the projection of
the real orbit upon a plane which is perpendicular to the
line joining the binary star to the eye. We have therefore
to consider what modifications the orbit may undergo by
projection. It can be shown that if the original orbit be
elliptic, the projected orbit will be elliptic also ; but it also
appears that though the star A was the focus of the original
orbit, it would, generally, not be the focus of the projected
orbit. The law of the description of equal areas in equal
times would hold equally true both in the original orbit and
in the projected orbit.
By a comparison of observations made at different times
it is possible to plot down the actual position of the star B
A A
354 Astronomy.
with respect to the star A, at the corresponding dates. It is
found that in the case of several binary stars the orbit thus
formed is elliptic, and it is possible, by a consideration of
the position of the point A in this ellipse, to determine the
position of the true orbit with reference to the celestial sphere
and the various circumstances connected with the motion.
In this way the true orbits of several of the most re-
markable among the binary stars have been determined.
One of the most rapidly revolving double stars appears to
be 42 Comae Berenices, which accomplishes its revolution in
a period of 257 years. The two components of this star
are exceedingly close together, the greatest distance being
about one second of arc. There is very great difficulty in
making accurate measurements of a double star so close as
this one. Consequently more reliance may be placed upon
the determination of the orbits of other binary stars, the
components of which are farther apart than those of 42
Comae Berenices. Among these we may mention a very
remarkable binary star, Ursae Majoris. The distance of
the two components of this star varies from one second of
arc to three seconds. The first recorded observation of the
distance and position angle of this star was by Sir W.
Herschelin 1781, and since that date it has been repeatedly
observed. From a comparison of all the measurements
which have been made it appears that the periodic time of
the revolution of one component of Ursse about the other
is 60 years, and it is exceedingly improbable that this could
be erroneous to the extent of a single year. Thus this star
has been observed through more than one entire revolution.
144. Dimensions of the Orbit of a Binary Star. In
the determination of the size of the orbit of a binary star all
we can generally ascertain is, of course, the diameter of the
orbit measured in seconds of arc. Actually to determine
the number of miles in the diameter of the orbit it would be
further necessary for us to know the distance at which the
binary star is separated from the earth. This distance is in
Stars and Nebulce. 355
the great majority of cases entirely unknown to us at present.
There are, however, one or two exceptions. Of these we
shall mention Sirius. Early in the present century the
proper motion of this star was found to be affected by an
irregularity which showed that an unseen body must be
moving around it and disturbing its motion by its attraction.
After a hundred years of observation the orbit of this body
was calculated, and it was shown that the irregular motion
of Sirius could be accounted for by supposing that the
disturbing satellite had a period of about fifty years. The
satellite was actually discovered by Alvan Clark in 1862,
and was found to be moving around Sirius at a mean
angular distance of about seven seconds. The annual
parallax of Sirius is found to be o"'2$ that is to say, the
radius of the earth's orbit, viewed from the distance of
Sirius, subtends an angle of o"'2^. It therefore follows that
the real distance of the companion of Sirius must exceed the
distance of the earth from the sun in the ratio that 7"
exceeds o"'2$ that is, it is 28 times as great.
145. Determination of the Mass of a Binary Star.
When we know the diameter of the orbit of a binary star
and its periodic time, we are able to compute the sum of the
masses of the two component stars. This is an exceedingly
interesting subject, inasmuch as it affords us a method of
comparing the importance of our sun to the other stars as
far as mass is concerned.
Let us first consider what the periodic time of a planet
would be if it revolved round the sun in an orbit of which
the radius were twenty-eight times that of the earth's orbit.
According to Kepler's third law, the square of the periodic
time is proportional to the cube of the distance. Conse-
quently, since the earth revolves around the sun in one year,
it follows that a planet such as we have supposed would
revolve around the sun in a period of time which was equal
to the square root of the cube of 28, i.e. to 148 years very
nearly. According to the latest results it would appear that
A A 2
356 Astronomy.
the periodic time of the revolution of the satellite of Sirius is
49'4 years, i.e. the velocity with which the motion takes
place is greater than it would be if the mass of Sirius only
equalled the mass of the sun.
The ratio which the mass of the sun (augmented, it
should in strictness be said, by the mass of the earth) bears to
that of Sirius and its satellite taken together can be ascer-
tained. For this we require the following principle, which
for the present we shall take for granted.
If two bodies, A and B, are revolving in consequence of
their mutual attraction, then the sum of the masses is
inversely proportional to the square of the periodic time,
supposing the mean distance of A and B to remain unaltered.
It therefore appears that the following proportion is true :
Mass of Sun and Earth _ /'49
Mass of Sirius and Satellite \i
It follows from this that the mass of Sirius and its
satellite taken together are about nine times the mass of the
sun.
Now though it is true that subsequent observations may
necessitate corrections in these results, yet we may be pretty
confident that the mass of Sirius is several times as great as
that of our sun. The most uncertain part of the data is the
annual parallax of Sirius, which has not yet been certainly
determined, and may deviate from o"*25 by a considerable
fraction of its total amount.
146. Colours of Double Stars. Among the most
pleasing and remarkable phenomena presented by double
stars are the beautiful colours which they often present.
The effect is occasionally heightened by the circumstance
that the colours of the two components are frequently not
only different, but are contrasted in a marked manner.
Conspicuous among these objects is a very beautiful double
star, y Andromeda?. The two components of this star are
orange and greenish blue. Attentive examination with a
Stars and Nebula. 357
powerful telescope shows also that the greenish blue com-
ponent consists of two exceedingly small stars close together.
While considering this subject, it should be remarked that
isolated stars of a more or less reddish hue are tolerably
common in the heavens, the catalogues containing some
four or five hundred stars of this character. Among those
visible to the naked eye perhaps the most conspicuous is the
bright star a Orionis. Stars of a greenish or bluish hue are
much less common, and it is very remarkable that, with very
few exceptions, a star of this colour is not found isolated,
but always occurs as one of the two components of a ' double
star.'
147. Nebula. There are a great number and variety
of objects in the heavens which are known under the general
term of 'Nebulae.' The great majority of these objects are
invisible to the naked eye, but with the aid of powerful
telescopes some thousands of such objects have been already
discovered. Of these objects, which for convenience are
grouped together, many are undoubtedly mere clusters of
stars such as those of which we .have already given some
account. It is, nevertheless, tolerably certain that many of
the objects termed nebulae are not to be considered as mere
clusters of stars, though their real nature has, as yet, been
only partially determined.
148. Classification of Nebula. The following analysis
of the different objects which are generally classed under
the name of nebulae and clusters has been made by Sir
William Herschel, to whom the discovery of a vast number
of nebulae is due :
1. Clusters of stars, in which the stars are clearly distin-
guishable ; these are again divided into globular and irregular
clusters.
2. Resolvable nebulae, or such as excite a suspicion that
they consist of stars, and which any increase of the optical
power of the telescope may be expected to resolve into dis
tinct stars.
358 Astronomy.
3. Nebulae, properly so called, in which there is no
appearance whatever of stars, which again have been sub-
divided into subordinate ones, according to their brightness
and size.
4. Planetary nebulae.
5. Stellar nebulae.
6. Nebulous stars.
The first of these classes is that which we have already
described ( 133). The resolvable nebulae, which form
the second class, are to be regarded as clusters of stars
which are either too remote from us or the individual stars
of which are too faint to enable them to be distinguished.
Among the most remarkable objects at present under con-
sideration are the oval nebulae. They are of all degrees of
eccentricity, some being nearly circular, while others are so
elongated as to form what have been called ' rays.' The
finest object of this class is the well-known nebula in the
girdle of Andromeda. This, object is just visible to the
naked eye as a dullish spot on the heavens. Viewed in a
powerful telescope it is seen to be a nebula about 2^ in
length and i in breadth. It thus occupies a region on the
heavens five times as long and twice as broad as the dia-
meter of the full moon. The marginal portions are faint,
but the brightness gradually increases towards the centre,
which consists of a bright nucleus. This nebula has never
actually been resolved, though it is seen to contain such a
multitude of minute stars that there can be little doubt that,
with suitable instrumental power, it would be completely
resolved.
Among the rarest, and indeed the most remarkable,
nebulae are those which are known under the name of the
'Annular Nebulae.' The most conspicuous of these is to be
found in the constellation Lyra ; it consists of a luminous
ring ; but the central vacuity is not quite dark, but is filled
in with faint nebula, ' like a gauze stretched over a hoop '
(Sir John Herschel).
Stars and Nebula. 359
Planetary Nebulae are very curious objects ; they derive
their name from the fact that, viewed in a good telescope,
they appear to have a sharply defined more or less circular
disc, immediately suggesting the appearance presented by a
planet. These objects are generally of a bluish or greenish
hue. Their apparent diameter is small ; the largest of them
is situated in Ursa Major, and the area it occupies on the
heavens is less than one-hundredth part of the area occupied
by the full moon. Still the intrinsic dimensions of the
object must be great indeed. If it were situated at a distance
from us not greater than that of the star 61 Cygni, the
diameter of the globe which the planetary nebula occupies
would be seven times greater than the diameter of the orbit
of the outermost planet of our system.
Among the class of Stellar Nebulae one of the most
superb objects visible in the heavens must be included.
The object to which we refer is the great nebula in the
Sword-handle of the constellation of Orion. The star 6
Orionis consists of four pretty bright stars close together,
while in a good telescope two others are visible, the whole
presenting the almost unique spectacle of a sextuple star.
But around this star, and extending to vast distances on all
sides of it, is the great nebula in Orion. The most remark-
able feature of this nebula is the complexity of detail which
it exhibits. The light is of a slightly bluish hue, and under
the power of great telescopes portions of it are seen to be
thickly strewn with stars. Perhaps it would be more correct
to say that portions of it contain stars ; for there is good
reason to believe that in this nebula, as well as in some
others, a part of the light which we receive is due to glowing
gas.
The last of the different kinds of nebulae to which we
shall allude is the class of objects known as nebulous stars.
By a ' nebulous star ' we are to understand a star surrounded
by a luminous haze, which is, however, generally so faint as
only to be visible in powerful instruments.
360 Astronomy.
149. Spectra of Nebula. Many nebulae show continu-
ous spectra, probably indicating that the object examined is
an agglomeration of faint stars. But many nebulae have a
gaseous spectrum of a few bright lines, among which some
of the hydrogen lines and a conspicuous line in the green
region of uncertain origin. This was first discovered by
Huggins in 1864. The planetary nebulae and some large
nebulas (such as the Orion nebula) belong to this class, as
well as a number of small stellar nebulae which have been
recognised as such by their spectra alone. Several tem-
porary stars (e.g. that in Auriga), when fading away, have at
last had their spectrum reduced to that of a gaseous nebula.
It is deserving of notice that nebulae with gaseous spectra
(as well as most stars of the first type and stars with bright
line spectra) are all situated in or close to the Milky Way,
a part of the heavens otherwise exceedingly poor in nebulae.
150. Application of Photography to the Study of Stars
and Nebula. During recent years photographs of nebulae
and clusters have been most successfully taken, and will no
doubt completely supersede drawings of these objects, which
are exceedingly difficult to make, and eventually enable us
to ascertain whether changes of form occur in nebulae.
Stellar spectroscopy has also benefited greatly from the
application of photography since Huggins first showed the
capability of this method, and a spectroscopic survey of the
stars brighter than the yth magnitude and north of 25
declination has been made at the Harvard College Observa-
tory (the Draper Catalogue). But perhaps the most impor-
tant application of stellar photography is the photographic
chart of the heavens now being made by a number of
observatories co-operating under the direction of an inter-
national committee. There can be little or no doubt that
the measurement of photographic plates will in future to a
great extent take the place of micrometer measures.
CHAPTER XII.
ASTRONOMICAL CONSTANTS.
151. In the present chapter we record the principal
numerical determinations which have been made of the
important Constants of Astronomy. Care has been taken as
far as possible to give in each case the most recent results,
while, both for their intrinsic value as well as for their
historical interest, earlier values are often added. In many
cases also bibliographical information will be found, which
will enable the reader to refer to the original sources. In
the preparation of this chapter the greatest assistance
has been afforded by the admirable 'Vade-Mecum de
1'Astronome,' by the late J. C. Houzeau (Brussels, 1882) ;
but as far as possible the original authorities have been
referred to. The recent literature has also been searched,
and among books often consulted may be mentioned : 'The
Solar Parallax and its Related Constants,' by W. Harkness
(Washington, 1891, 410.), and 'The Elements of the Four
Inner Planets and the Fundamental Constants of Astro-
nomy,' by S. Newcomb (Washington, 1895, 8vo.)
The following abbreviations are used to facilitate refer-
ence :
'A. N.' ' Astronomische Nachrichten.' Altona, 1823-1873 ; Kiel,
1873 et seq. 139 vols. in 4to. Each volume contains 24
numbers, and reference is only made to the numbers.
' C. d. T.' r Connaissance des Temps ou des Mouvements Celestes.'
Annees 1679-1896. Paris.
' Comptes Rendus de 1' Academic des Sciences de Paris.'
Paris, 1835-1895, 410.
362 Astronomy.
'M. A. S.' * Memoirs of the Royal Astronomical Society of London.'
London, 1822-1895. Vols. I to 51, 4to.
' M. N.' 'Monthly Notices of the Royal Astronomical Society of
London.' 1828-1895, 55 vols, 8vo.
'Ph. Tr.' 'Philosophical Transactions of the Royal Society of
London.' 1665-1895, in 4to.
SPHERICAL ASTRONOMY.
152. Obliquity of the Ecliptic.
B.C.
lioo. Tcheou-Kong, by the solstitial shadows at
Loyang in China (Laplace, ' C. d. T,' 1811,
p. 450) . . 2 3 54'2"
140. Hipparchus, with the astrolabe at Alexandria
(Ptolemy, 'Math. Comp.' lib. i. cap. II
and 13) . . . . 23 51 20
A.D.
130. Ptolemy, with the astrolabe (Ptolemy, ' Math.
Comp.' lib. i. cap. 11) . . 23 51 15
629. Litchou-Foung, by shadows (Laplace, loc. cit,} 23 40 4
1460. Regiomontanus at Vienna, with a quadrant
(Clavius, ' Opera Math.' t. iii. p. 149) . 23 30 49
1525. Copernicus (' De Revol. Orbium Ccelest.' lib.
ii. cap. 2) . . . . . 23 28 24
1590. Tycho Brahe (see Bugge, ' Berliner Jahrbuch,'
1794, p. 100) . 23 29 46
1627. Kepler ('Tab. Rudol.' p. 116) . . 23 30 30
1689-5. Flamsteed, by solstitial observations at Green-
wich (' Hist. Coel. Proleg.' p. 114) . 23 28 56
1755-0. Bradley, as deduced byBessel ('Fund. Astron.'
p. 61) . . . -23 28 15-32
1795-0. Maskelyne, from 20 solstices, observed at
Greenwich (see Bessel, 'Fund. Astron. 'p. 60) 23 27 57-66
1800-0. Bessel, by comparing, the sun's declination with
Delambre's Tables (' Fund. Astron.' p. 61) 23 27 54-8
1813-0. Brinkley, from 16 solstices by Oriani, Pond,
Arago, Mathieu, and himself ('Ph. Tr.'
1819, p. 241) . 23 27 50-45
1850-0. Value adopted by Leverrier ('Annal. Obs.
Paris,' Mem. t. iv. pp. 51 and 203) . 23 27 31-83
1850-0. Same, as modified by IlarknessC Solar Paral-
lax,' p. 141) ' -23 27 3i'47
Astronomical Constants. 363
A.D.
1868-0. Airy (see Powalky, 'A. N.' 1903) . . 2327'22"'3
1870-0. E. F. van de S. Bakhuyzen, from observations
at Leyden, 1864-76 (' Bepaling van de
Hellingder Ecliptica,' Leiden, 1879, p. 78) . 23 27 22 f ci
1900-0. Newcomb (' Fund. Const.' p. 197) . .2327 8-26
153, Secular Diminution of the Obliquity of the Ecliptic.
In early times the Arabians had noticed that the obliquity
of the ecliptic was decreasing. The following are the most
recent determinations of the present rate of decrease per
century :
A.D.
1856. Leverrier, by the theory of attraction (' Annal.
Obs. Paris,' Mem. t. ii. p. 174) . . 47"'566
1858. Leverrier, by observations extending over a
century (ibid. t. iv. p. 51) . , . 45" 76
1867. Lehmann,by the formulae of attraction ('A. N.'
No. 1619) . . . 47" -244
1872. Powalky, by altering a little the masses used
by Leverrier in accordance with recent
researches (' A. N.' 1903) . . . 47" -oo
1891. Harkriess, by least square adjustment from
Leverrier's value . . . . 46 "'66
1895. Newcomb ( Fund. Const.' p. 196) . . 46" -85
The variations in the obliquity of the ecliptic can only
make the obliquity fluctuate within certain limits. The
range of these fluctuations has been determined as follows :
1825. Laplace ('C. d. T ' 1827, p. 234) . . 3 7' 30"
1873. Stockwell, by using more accurate determi-
nations of the masses of the planets (' Smith-
sonian Gmlribs. toKnowl.' vol. xviii. p. 12) 2 37 22
According to this author the limits of the obliquity are
21 58' 36",
and 24 35 58.
3 64 A stronomy.
154. Precession of the Equinoxes. The precession of
the equinoxes was discovered by Hipparchus (Ptolemy,
'Math. Comp.' lib. iii. cap. 2). Newton first explained its
cause (' Principia,' lib. iv. cap. 6). The first explicit theory
of the subject was given by D'Alembert (' Recherches sur la
Precession des Equinoxes,' Paris, 1749). The following are
a few of the different values which have been assigned to
the coefficient of precession ( 77) :
B.C. Per Annum.
127. Hipparchus (minimum value), Delambre, ' Hist.
de 1'Astron. Anc.' t. ii. p. 247 . . 50"
A.D.
1 38. Ptolemy, by comparing his observations with those
of Hipparchus (' Math. Comp.' lib. vii. cap. 2) 36"
1525. Copernicus, by comparing longitudes of this
epoch with those of Ptolemy (' De Revol.
Orbium Coelest.' lib. iii. cap. 6) . . 5o" - 2O
1 588. Tycho Brahe, by comparing his observations with
those of Hipparchus and Al Battani ('Astron.
Instaur. Progymn. ; p. 254) . 51"
1712. Flamsteed (' Historia Coelestis,' vol. 3. p. 162). 50"
1802. Laplace, by the theory of attraction at the epoch
1750 (' Mec. Cel.' t. iii. lib. vi. ch. 16) . 50" -099
1826, Bessel, by comparing his observations with those
of Bradley ('A. N.' 92, revised value) for 1750 5o"'2il
1842. O. Struve from Bradley's Stars, by taking into
account the proper motion of the solar system
(1800) ..... 50" -238
1842. Same, modified by Peters (1800) . . 50'' '241
1856. Leverrier finds as the value for 1850 ('Annal.
Obs. Paris,' Mem. t. ii. p. 175) . . S Q "' 2 3^
1887. L. Struve, from Auwers' reduction of Bradley
and Pulkova Star Catalogues (for 1800) . 50" -2 13
1895. Newcomb, for 1850 (from the values of L. Struve,
Nyren, Dreyer and Bolte) . . . 50" '237
According to Stockwell the limits of the coefficient of
precession are 48' /g 2i2 and 52 // *664, the mean value being
50" -438 (' Smiths. Contrib. to Knowl.,' vol. xviii. p. 1 2). The
coefficient varies at present annually by + o" '0002 2.
Astronomical Constants, 365
The period of the rotation of the pole of the equator
around that of the ecliptic is
25694-8 years,
with inequalities which can alter this value to the extent of
281-2 years.
155. Nutation. IK 1687 Newton had indicated the
existence of nutation as a consequence of the theory of
attraction ('Principia/ lib. iii. prop. 21), but he considered
its effect would be too small to be appreciable. Bradley
discovered nutation in 1747 (< Ph. Tr.' vol. xlvi. p. i) by
observations of stars. The following are some of the
principal determinations of the constant of nutation :
A.D.
1747- Bradley, by the observations which led to the dis-
covery of nutation (' Ph. Tr.' No. 485) . . 9"-o
1799. Laplace, by theoretical calculations, using the mass
of the moon as derived from the tides (' Mec. Cel.'
t. ii. lib. v. ch. i.) . . . . io"-o56
1821. Brinkley, by 1,618 observations of stars ('Ph. Tr. 5
1821, p. 347) ..... 9 "-25o
1842. Peters, from the R.A. of the Pole Star 1822-38
(' Numerus constans nutationis ') . . . 9"-2i6
1842. Lundahl, from the declinations of the Pole Star
observed at Dorpat (ibid. ) . . . 9" -236
1869. Stone, from observations of circumpolar stars at
Greenwich ('M. A. S.' vol. xxxvii. p. 249) . 9" -134
1872. Nyren, from observations made in the prime vertical
at Pulkovva ('Mem. Ac. St.-Petersbourg,' 7^ ser.
t. xix. No. 2) . . f 9" -244
1882. Downing, from 1,041 zenith distances of 7 Draconis
at Greenwich, 1857-75 (' M. N.'vol. 42, p. 344). 9"'335
1895. Thackeray, from Greenwich obs. of Pole Star, 1836-
1893 (' M. A. S.' vol. li. p. 266) . . . 9" -154
1895. Newcomb, from Greenwich and Washington obser-
vations and previous determinations . . 9" -2 10
1895. Chandler, from Greenwich observations, 1825-48
('Astr. Journ.' 361) . o"-iQ2
366 Astronomy.
156. Aberration. Roemer in 1675 (' Histoire de
1' Academic des Sciences de Paris,' t. i. p. 214) ascertained
that the eclipses of Jupiter's satellites are retarded according
as the earth is more removed from the planet. Picard in
1 68 1 announced that the declination of the Pole Star was
subject to annual changes other than that due to precession.
Bradley discovered aberration in 1727 ('Ph. Tr.' No. 406,
p. 637), when observing stars ( 79). The following are the
values which have been assigned to the coefficient of aberra-
tion :
A.D.
1728. Bradley, from the observations which led to the dis-
covery of aberration (' Ph. Tr.' No. 406) . 20" -25
1821. Brinkley, by 2,633 observations of numerous stars
('Ph. Tr.' 1821, p. 350). . . . 20" -37
1840. Henderson, by the observations of Sirius at the Cape
(' M. A. S. J vol. xi. p. 248) . . . 20" -41
1843. W. Struve, by observations of seven stars in the
prime vertical at Dorpat ('A. N.' No. 484) . 2o"'445
1844. C. A. F. Peters, by the altitudes of the Pole Star,
observed with the vertical circle at Pulkowa
('A. N.' No. 512) .... 2o"-503
1849. C. A. F. Peters, from 704 declinations of 8 stars,
observed with the vertical circle at Pulkowa
('Mem. Ac. St.-Petersb.' 1853, * v - P- !3 8 ) 2o"'48i
1850. Maclear, by the observations of a Centauri at the
Cape (' M. A. S.' vol. xx. p. 98): 6 . . 20" -53
1 86 1. Main, by observations of 7 Draconis, 1852-59
(' M. A. S.' vol. xxix. p. 190) . . . 2O"'335
1882. Downing, from 1,041 zenith distances of 7 Draconis,
observed at Greenwich 1857-75 (' M. N.' vol. 42,
p. 344) ... 20" -378
1883. Nyren, from Pulkowa observations in meridian and
prime vertical ('Mem. Ac. St.-Petersb.' t. xxxi.
No. 9) . . . . . . 20" -492
1888. Kiistner, from 244 differences of meridian zenith
distances of seven pairs of stars ('Beob.
Ergebnisse d. Sternwarte,' Berlin, iii. p, 45) . 20" -3 13
1895. Newconib, from all determinations . . . 20" -511
Astronomical Constants.
367
157. tfefraawn.Tycho Brahe formed the first table
of astronomical refractions, and it was by him that refraction
was first taken account of in the reduction of observations.
The following are the principal values which have been
assigned to the refraction at the zenith distance of 45.
This quantity is termed the coefficient of refraction, and the
refraction at zenith distances is generally nearly equal to the
product of the coefficient of refraction and the tangent of
the zenith distance.
The amount of refraction at the horizon is also in some
cases given :
..
1604. Kepler ('Ad Vitellonem Paralipomena,' p.
125, cap. iv.) .
1721. Newton, from the data given by Halley,
bar. 28-8 in., temp. 70 F. (' Ph. Tr.' No.
366, p. 118)
1755. Bradley, from observations at Greenwich, at
temp. 50 F. and bar. 29*6 in. ('Astron. Obs.
at Greenwich,' vol. i. p. xxxv.)
1805. Laplace, from the observations of Delambre
at 0760 mm. pressure and o C. temp.
(' Mec. CeV t. iv. liv. x. ch. i.) .
1814. Brinkley, at 29-6 in. pressure and 50 F.
temp. (' Trans. R. I. A.' vol. xii. p. 77) .
1817. Bessel, at 29-6 in. pressure and 4875 F.,
from Bradley v /bservations (' Fund. Astron.'
pp. 45-50) .
1823. Ivory, at 29 in. pressure and 50 F. temp.
('Ph. Tr.' 1823, p. 409) .
1868. Stone, from observations at Greenwich, above
and below the Pole, at 29-6 in. pressure and
50 F. temp. (' M. N.' vol. xxviii. p. 29) .
1866. Gylden, from observations at Pulkowa at 29-6
in. and 7 -44 Reaumur (' Mem. Ac. Sc. St.-
Petersbourg,' 7 e ser. t. x. No. i) .
Refraction at the
Zenith Distance.
45 90
40"
1980"
54 2025
56-9 1976-8
60-50
56-8
57-49 2166-86
58-36 2057-5
57"-68 20617
158. Twilight. The following figures indicate the
number of degrees at which the sun is below the horizon
when the stars become visible to the unaided eye :
368 A stronomy.
A.D.
130. Ptolemy, appearance of stars of the first magnitude . 12
End of astronomical twilight . . .18
1602. Tycho Brahe, end of astronomical twilight ('Epist.
Astron.' pp. 139-140) . . . 17
1618. Kepler ('Epitome Astronomic Copernicanre,' lib.
iii. part v. ed. Fritsch, t. vi. p. 285) :
Appearance of Venus . . .5
,, Jupiter and Mercury . . 10
,, stars of the 1st magnitude . 12
6th . 17
,, the smallest lucid stars . 18
1865. J. Schmidt, from the mean results of observations
('A. N.' No. 1495) :
Appearance of stars of the ist magnitude . + o4o''
,, ,, 2nd ,, . -4 18
3 rd -54
,, 4th ,, 6 50
5 th 8 52
,, 6th ,, . ii 39
End of astronomical twilight . . . 15 55
1884. G. Hellmann, for central Europe (see ' Zeitschr. d.
osterr. Ges. flir Meteorol.' 1884) :
Beginning of morning twilight . . .180
End of evening twilight . . . 15 36
THE SUN.
159. Semidiameter of the Sun. The following values
express the angular semidiameter of the sun when at its mean
distance from the earth :
B.C
270. Aristarchus of Samos (Wallis, ' Opera Mathematica,'
tome iii.) ...... 900"
240. Archimedes, by the dimensions of a screen which
covered the disc at "the horizon . . . 899
A.D.
138. Ptolemy (' Mathematica Compositio V.' cap. 14) . 940
1543. Copernicus (' De Revolutionibus Orbium Coelestium,'
lib. iv. cap. 21) . . . . . 983-3
1 The sign + signifies that the sun is above the horizon, and
that the sun is below the horizon.
Astronomical Constants.
369
A.D.
1602. Tycho Brahe (' Astron. Instaur. Progymn.' p. 471) . 930"
1618. Kepler ('Epitome Astronomise Copernicame, ' lib.
vi. part v. chap, vii.) . . . 9 J 6'5
1771. Lalande, by the Iransit of Venus in 1769 ('Astro-
nomic,' 2 e ed. t. ii. No. 2159) . . . 958*0
1824. W. Struve, by observations at Dorpat up to the end
of 1823 ('Berliner Jahrbuch,' 1827, S. 21 1) :
Horizontal semidiameter .... 960-90
Vertical semidiameter . . 960-37
1830. Bessel, by 1,698 transits of the sun at Konigsberg
('Tab. Reg.' p. 50) .... 960-90
1835. Encke, by the transit of Venus in 1769 (' Abhand. d.
Ak. zu Berlin,' 1835, Venus Durchgang, p. 95) . 958*42
1852. W. Struve, by 241 meridian transits and 219 measures
of vert, diam., at Dorpat, 1822-38 (' Positiones
Mediae,' Petersburg) :
Horizontal semidiameter . . . . 961-12
Vertical semidiameter . . . . 960-66
1853. Hansen and Olufsen (' Tables du Soleil,' Copen-
hagen, 4to. p. 165) . . . . 961-19
1858. Leverrier assumes in his ' Tables du Soleil,' p. 114 . 960-00
1875. Fugh, by the discussion of 6,827 observations at
Greenwich, 1836-1870, with three meridian instru-
ments ; the author finds the ellipticity insensible,
and for the semidiameter (' A. N.' No. 2040) . 961-495
1891. Auwers, from heliometer measures during German
Venus expeditions, 1874 and 1882 ('A. N.' 3068) 959-63
160. The Sun's Parallax. The figures here given
denote the angle which an equatorial radius of the earth
subtends at the mean distance of the sun :
150.
A.D.
I 3 8.
1618.
1672.
Hipparchus, from the dimensions of the earth's
shadow observed in eclipses of the moon (Ptolemy,
'Math. Comp.' lib. v. cap. 17) . . -3'
Ptolemy, by the shadow (lib. v. cap. 17, loc. cit.) . 2 50"
Kepler, by the diurnal parallax of Mars (' Epitome
Astronomise Copernicanoe,' p. 479), not exceeding I
Flamsteed, by the diurnal parallax of Mars (' Ph.
Tr.' No. 89) . . . ,o 10
B B
37O Astronomy.
A.D.
1719. Bradley and Pound, by the diurnal parallax of Mars
(see Bradley's Miscell. Works,' p. 353) . . io"'3
1751. Lacaille, by comparing observations of Mars made
at the Cape of Good Hope with those made in
Europe ('Ephemerides des Mouvements Celestes
depuis 1765 jusqu'cn 1774,' Paris > Introd. p. i) . 10-2
1765. Pingre, by the transit of Venus in 1761 (' Mem. Ac.
de Paris,' 1761,^486) . 10-60
1770. Euler, by the transit of Venus in 1769 ('Novi
Commentarii Ac. Sc. Petropol. 1 t. xiv.) .
1797. Maskelyne, by the transit of Venus in 1769 (Vince,
* Syst. of. Astron.' vol. i. p. 413) 8723
1802. Laplace, from the parallactic equation of the moon
( g mean time at Paris.
Mean longitude . 245 33' 14" 70 + 2106691" -65O43/ + 0-00011289^
Longitude of peri-
helion . . 129 27 14-5 + 49"-462/ -0-000593/ 2
Longitude of as-
cending node . 75 19 52-3 + 32"-8899/ + o-oooi5o8/-
Inclination . 3 23 34*83+ o"-O4524/-o-oooooi56/' 2
Greatest equation
of centre . . o 47 3'o8 o"-222jt +o-ooiO4/ 2
\t is the number of years (365^ days) which have elapsed since
the epoch.]
378 Astronomy.
The following elements are by G. W. Hill ('Tables of
Venus,' Washington 1872) :
Epoch 1850. o d o h M. T. Washington.
Mean longitude . 244 18' i8" 32 + 2106691" -62i8o/ + o" -0001134^
Longitude of peri-
helion . . 129 27 42-864- 50-0494/- 0-000592/-
Longitude of as-
cending node . 75 19 53-10+ 32-5150/4- 0-000151^
Inclination . . 3 23 31-01+ 0-03814^- o-oooooi6/-
Greatest equation
of centre . o 47 2-988 0-20630/4- o-ooio6/ 3
176. Transits of Venus across the Sun. Kepler in 1629
was the first to announce the occurrence of the transits of
Venus across the sun. The first transit observed was by
Horrocks in 1639. The theory of the transits was given by
Halley in 1691. The last transits occurred in 1874 and
1882, the next will be in 2004 and 2012.
177, Apparent Diameter of Venus. Before the inven-
tion of the telescope Tycho Brahe estimated the diameter
of Venus at 3}'. The following figures give the diameter
of Venus as it would be seen by an observer situated at a
distance equal to the mean distance of the earth from the
sun :
A.D.
1640. Horrocks, by micrometic measurements (see
Wurm, Berliner Jahrbuch,' 1807, p. 165). I7"'6o9
1789-1794. Schroter, by micrometric measurements (see
Wurm, 'Berliner Jahrbuch, '1807, pp. 166-7) l6"'835
1822. Encke, by the transit of 1761 ( Entfernung
der Sonne,' Gotha, 8vo. ) . . . i6"-6u
1840. Airy, by micrometric observations (cited in
' Ann. de 1'Obs. de Paris,' Mem. t. vi. pp.
26 and 201) . . . . 1 6' '-566
1865. E. J. Stone, by observations at Greenwich
with the mural circle, 1839-1850, and the
meridian circle, 1850-1862 (' M. N.' vol.
xxv. p. 59) . . . . 1 6" '944
Astronomical Constants. 379
A.n.
1871. Powalky, from the transits of 1761 and 1769
('A.N.' 1841) . . . I6"'9i8
1875. Tennant, by micrometric measurements
during the transit in 1874 (' M. N.' vol.
xxxv. p. 347) . 1 6" -9036
1879. Hartwig, by heliometer measures ('Publ. d.
Astr. Gesellschaft,' xv. p. 10) . . i7"-666
1891. Auwers, by heliometer measures during tran-
sits 1874 and 1892 by German observers
('A. N.' 3068) . . . i6"-8oi
178, Ellipticity. The ellipticity of Venus is generally
regarded as insensible. The observations of Vidal, however,
during the inferior conjunction in October 1807, gives 60" -4
for the vertical diameter and 6i"'5 for the horizontal dia-
meter. (' C. d. T.' 1810, p. 375.) These results are, however,
not entitled to any weight. According to Auwers the
ellipticity is less than j-J-g-.
179. Mass of Venus. The mass of Venus has been
determined by the perturbations which it produces in the
motions of other bodies belonging to the solar system. The
following are the principal results. The mass of the sun is
taken as unity :
A.D.
1779. Lagrange, from the precession of the equinoxes
('Berliner Jahrbuch, 3 1782, p. 115). . . m i gI5
Lagrange, from irregularities in the motion of the
sun (' Berliner Jahrbuch,' 1782, p. 1 16) . . 5^55
1802. Laplace, by the secular diminution of the obliquity of
the ecliptic (' Mec. Cel.' t. iii. vol. vi. ch. 6) .
1802. Delambre, by deducing from the observations of the
sun, by Bradley and Maskelyne, the coefficients of
the inequalities caused by Venus (see Laplace, ' Mec.
Cel.' t. iii. liv. vi. ch. 16) . . . .
1828. Airy, by the inequalities deduced from observations
of the sun ('Ph. Tr.' 1828, p. 50) . . . 55^
1843. Leverrier, by the secular variation of the node of
Mercury ('C. R.' torn. xvi. p. 1062) . . M<5noo
1858. Leverrier, by the perturbations of the earth (' Ann.
de 1'Obs. de Paris,' Mem. t. iv. p. 102) . . 35^5
380 Astronomy.
A.D.
1872. Hill, from the movements of the node of Mercury
(' Tables of Venus.' Washington, 410. p. 2) . 4 97*17 5
1895. Newcomb, from periodic perturbations of Mercury and
the earth . . . ^^
180. Rotation of Venus. J. D. Cassini first detected
surface markings, and was inclined to conclude that Venus
rotated in 23 days, but his son made out from the same
observations and those of Bianchini that the period was
23 h 20. Bianchini himself made the rotation period
24 d 8 h . Schroter, chiefly from the truncated appearance
of the south cusp, found 23 h 2 i m 8 s (' Nachtrag z. d. aphrodit.
Fragm.' p. 56). De Vico, from spots observed 1839-41,
found 23 h 2i in 2i s '9 ('Mem. della Specola d. Coll. Rom.'
1840-41, p. 48). Schiaparelli, from his observations Nov.
1877 to Feb. 1878, concluded that Venus rotates in
225 days ('Rendiconti del R. Istituto Lombardo,' vol.
xxiii.), but this has been strongly opposed by several
observers, e.g. by Brenner, who maintains that his observa-
tions give a rotation period of 23 h 57 7 S *5 ('A. N. J 3314),
while others (e.g. Tacchini) agree with Schiaparelli.
181, Brilliancy of Venus. The phases of Venus were
discovered by Galileo in 1610. Delambre gives as the con-
ditions under which Venus appears brightest
Elongation . . . 39 43' 26"
Distance from earth . . 0-4304
This is on the supposition that the orbit is circular : the
actual values of the elongation and distance at the time of
greatest brightness are not quite constant on account of the
ellipticity of the orbit. The number of days before or after
inferior conjunction, when the greatest brightness takes
place, varies between 32 and 39 days.
G. P. Bond in 1861 estimated the brilliancy of Venus
when brightest as 4*86 times that of Jupiter, and i
-r- 6 2 2, 600, ooo that of the sun. At the distance i from
the earth, and 07233 from the sun, he found the brightness
Astronomical Constants. 381
of Venus to be 1-7-514 that of the full moon. The albedo
of Venus is 3-44 that of Mars, according to G. Miiller.
From his photometric observations at Potsdam G. Miiller
finds the following formula for the stellar magnitude of
Venus (' Publ. d. astrophys. Obs. zu Potsdam,' viii. p. 366) :
Mag. = 4-707 + -i~ log ; 2- + 0-01322 a,
where r is the mean distance of Venus from the sun, r the
actual distance, A the distance from the earth, and a the
phase-angle corresponding to r and A.
For researches upon the spectrum of Venus, see Vogel,
* Untersuchungen iiber die Spectra der Planeten,' Leipzig,
1874, 8vo.
An interesting account of the observations on the
visibility of the dark side of Venus is given by Schafarik in
the ' Reports of the British Association,' 1873, p. 404.
THE EARTH.
182. Duration of the Year. The period of the revolu-
tion of the earth around the sun was the earliest element of
our planet which was known with accuracy. The following
are the principal values expressed in mean solar time :
Duration of the
Tropical Year, 365
H.C. days 5 hours.
3101 (?). Indian Tables (Bailly, 'Traite de 1'Astronomie
indienne.' Paris, 1787. 410. p. 124) . 50 35"
A.D.
140. Ptolemy. By his observations and those of
Hipparchus (' Math. Comp.' lib. iii. ch. 2) 55 14
J 543- Copernicus (' De Revol. Orb. Coelest.' lib. iii.
ch. 14) . . 49 6
1602. Tyclio Brahe (' Astron. Instaur. Progymn.'p.
53) ... 48 45-3
1687. Flamsteed (Newton, ' Phil. Nat. Princip.
Math.') . . . . . 48 57-5
1806. Delambre ('Tables du Soleil.' Paris, 4to.) . 48 51-61
382 Astronomy.
Duration of the
Tropical Year, 365
A.D. days 5 hours.
1853. Hansen and Olufsen, epoch 1850, with the
annual variation 0*00539 ('Tables du
Soleil') . .48 46" '1 5
1858. Leverrier, epoch 1800, with the annual varia-
tion -0-00539 ('Ann. Obs. Paris,' Mem.
t. iv. p. 102) . . . .48 46*045
1891. Harkness, epoch 1850, with the annual varia-
tion -o"-oo53675 ('Solar Parallax' p. 139) 48 46-069
According to Stockwell ('Smiths. Contribs.to Knovvl.' vol.
xviii. p. xii.), the variations of the tropical year from its mean
value are
According to the same authority the variations of the
length of the tropical year from its present value have the
limits
59 s 'i3 and +49 8 ' 2 7-
183, Perihelion. The movement of the axis major of
the earth's orbit is very perceptible within historic times.
The following are the principal results for the longitude of
the perihelion as well as for its movement in one hundred
years :
Longitude of Movement in
B.C. Perihelion. 100 Years.
127. Hipparchus (Ptolemy, 'Compos.
Math.' lib. iii. c. 4) . . 653o'
A.D.
140. Ptolemy (ibid.) . . 65 30
1515. Copernicus (' De Rev. Orb. ,
Coelest.' lib. 3, c. 16 and 22) . 96 40 o4o' 34"
1588. Tycho Brahe ( ' Astr. Inst.
Progymn.' p. 23) . . 95 30 115
1758. Lacaille. Epoch 1 700 (' Tabulse
Solares ') . 97 35 55 * 49 10
1806. Delambre. Epoch 1800 (' Tables
du Soleil ') . . 99 30 5 i 43 35
1 8 1 6 Airy. 1 8 1 6 ( ' Phil. Trans. ' 1 828,
p. 28) . . . 99 46 20-3
Astronomical Constants. 383
Longitude of Movement in
A.D. Perihelion. 100 Years.
1853. Hansen and Olnfsen. Epoch
1850 (' Tables du Soleil') . ioo2i'4i" 02 i42'38"-48
1858. Leverrier. Epoch 1850 ('Ann.
Obs. Paris,' Mem. t. iv. pp.
102 and 105). . . 1002121-5 14249-95
184. The Eccentricity and Equation of the Centre. The
inequality in the motion of the sun which is called the
equation of the centre was known to the astronomers at
Alexandria. The following are the principal determinations
of its greatest value :
Value of the Greatest
B.C. Equation of the Centre.
140. Ptolemy (' Comp. Math.' lib. iii. c. 4) . 223'
A.D.
1750. La Caille (' Mem. Ac. Sc. Paris,' 1750, p.
178) i 55 40-6
1806. Delambre ('Tables du Soleil'). Epoch
1810 . . . . . I 54 41-8
Annual variation o" 1 7 1 8.
1828. Bessel. Epoch 1800. Eccentricity . e .-0-0167922585
Annual Variation -0*00000043 59 ('A. N.'
No. 133).
1828. Airy. Epoch 181 6 ('Ph. Tr.' 1828, p. 29) I 54 39*9
1853. Hansen and Olufsen (' Tables of the Sun,'
p. i):-
Eccentricity for 1850 . . . = 0-01677120
1858. Leverrier (' Ann. Obs. Paris,' Mem. t. iv.
p. 102) . . . . I 55 18-31
Annual variation o"- 175 1-
1891. Harkness (' Solar Parallax,' p. 140) :
Eccentricity = 0-016771049-0-0000004215 (/-I85O).
185. Tables of the Sun. The recent tables of the sun
in which account is taken of the perturbations are
A..
1853. Hansen and Olufsen, Copenhagen, 4to., with supplement,
1857-
1858. Leverrier, ' Annal. Obser. Paris,' Mem. t. iv. pp. 119-206.
384 Astronomy.
The elements of the apparent path of the sun are,
according to Leverrier
Mean longitude . 100 46' 43"'5i + 1 296027 "-67S4/ + o"-ooono73/' 2
Perihelion . 100 21' 2i"'5 + 61 "-6995^ + 0" -oooi823/-
Eccentricity in
seconds of arc . 3459" -28 - o" o8755/-o"-ooooo282/ 2
The letter / represents the number of Julian years which have elapsed
since 1850 oo.
186, Dimensions of the Earth. The following are
perhaps the most reliable determinations of the dimensions
of the earth as ascertained by actual surveying. They are
taken from the recent work on Geodesy by Colonel A. R,
Clarke, C.B. (8vo. Clarendon Press Series, Oxford, 1880).
If it be supposed that the earth is an ellipsoid with three
unequal axes, then we find (p. 308)
Equatorial semiaxis in feet . . . . a = 20926629
,, ,, . ^ = 20925105
Polar semiaxis ...... c = 20854477
The axis major of the ellipse in which the earth is cut by
the plane of the equator is in longitude
8 15' W. from Greenwich.
' On the ellipsoidal theory of the earth's figure, small as
is the difference between the two diameters of the equator,
the Indian longitudes are much better represented than by
a surface of revolution. But it is nevertheless necessary to
guard against an impression that the figure of the equator
is thus definitely fixed, for the available data are far too
slender to warrant such a conclusion ' (p. 309).
If the earth be regarded as a spheroid of revolution, the
dimensions are (p. 319)
0=20926202 feet,
^=20854895 feet.
and their ratio
c : 0=292-465 : 293-465.
Astronomical Constants. 385
187. Ellipticity of the Earth. The following are various
determinations of this important constant :
A D.
1687. Newton, by the theory of attraction, supposing the
earth homogeneous (' Principia,'lib. iii. prop. 19) ^
1 749. D'Alembert, by the precession of the equinoxes ( ' Re-
cherches sur la Precession des Equinoxes.' Paris,
4to. ch. ix.) . . . _i_
1 789. Legendre, by the measurements of arcs in Peru and
France ('Mem. Ac. Sc. Paris,' 1789, p. 422) . -l^
1799. Laplace, by 15 measurements with the pendulum x
(' Mec. Cel.' liv. iii. ch. 5, No. 43, t. 11) . y^ft
1819. Von Lindenau, from the lunar inequalities ('Ber- T
liner Jahrbuch,' 1820, p. 212) . . . 3 i S -8 2
1825. Laplace, from the lunar inequalities deduced from
observations of the moon at Greenwich (' Mec.
Cel.' liv. xi. ch. i, No. I, t. v.) . . gig
1825. Sabine, by pendulum experiments ('Account of Ex-
periments on the figure of the Earth,' London) ^TZ
1849. Airy, by pendulum experiments ('Figure of the x
Earth,' 35 in ' Encyclopaedia Metropolitana') 282-9
1862. Baeyer, by the triangulation in Prussia ('A. N.' x
No. 1366) .....
1880. Clarke, mean result of surveys (loc. cit. p. 319) . 292 - 9 6iv,'
Mean result from pendulums (p. 350) . . 292 - 2I - 5
1884. Helmert, from pendulums ('Theorien derhoheren
Geodesic,' vol. ii. p. 241) . . .
188. Gravitation. The length of the pendulum which
beats one second in a vacuum in an indefinitely small
arc at the level of the sea is, according to Ufferdinger
(Grunert's c Archiv fiir Mathematik und Physik,' vol. 49,
p. 309, 1868), who has given a complete discussion of the
observations made at 51 stations, whose latitudes range
from +79 50' to 51 35'
P = o m '990970 + '005 1 85 sin 2 .
cc
386 Astronomy.
In 1884, from observations at 1 23 stations, whose latitudes
ranged from +79 50' to 62 56', Helmert found
P = o m -99091 8 + o -005262 sin 2 .
The length of the pendulum P is here expressed in
metres, while is the latitude.
At a height h above the surface of the earth, the length
of the pendulum is P', where R being the radius of the earth,
Gravity is determined from the length of the seconds
pendulum by the equation
189. Rotation. Laplace had concluded in 1799 tnat
the inequalities of the time of rotation of the earth were
insensible ('Mec. Gel.' liv. v. ch. i, Nos. 8 and 9, t. ii.).
Serret in 1859, assuming that the fluctuations of latitude do
not exceed a single second, inferred that the period of
rotation must be practically constant (' Annal. Obs. Paris,'
Mem. t. v. 1859, pp. 290, 291).
Laplace considered, by computation of the eclipses
recorded by Ptolemy, that the length of the day had not
changed in the lapse of twenty-five centuries by so much as
o'ooooooi part of its value ('C. d. T.' 1821, p. 242). More
recently, however, Delaunay pointed out that the value of
the secular acceleration of the moon's motion, indicated by
theory (6" '2), fails to explain accurately the ancient eclipses ;
he was therefore of opinion that the changes in the period of
the earth's rotation are sensible in historic times (* C. R.' t.
Ixi. 1865, p. 1023). On the other hand, Newcomb found
from ancient observations of the moon a value of the
acceleration (8" -3) much smaller than that formerly derived
from them, and he considers it quite improbable that the
inequalities in the mean motion of the moon are entirely to
Astronomical Constants. 387
be accounted for by changes in the earth's rotation (' Astron.
Papers,' vol. i. pp. 464-465).
190. Density. Taking the density of water as unity,
the following are the principal determinations which have
been made of the mean density of the earth :
A.D.
1687. Newton, by theoretical considerations (' Principia,'
lib. ii. ), between . , . . .5 and 6
1798. Cavendish, by the torsion balance ('Ph. Tr.' 1798,
p. 469) . . .5'48
1821. Carlini, by pendulum observations on Mont Cenis
compared with those at the margin of the sea (' Ef-
femeridi Astronomiche di Milano,' 1824, p. 28) . 4-39
1824. Laplace, by the theory of attraction, supposing the
density of the crust to be equal to 3 (' Mec. CeV
liv. xi. ch. ii. No. 5, t. v.) . . . 4761
1 842. Baily, by the torsion balance with extreme precautions
(' M. A. S.' vol. xiv. p. 247) . . 5*6604
1854. Airy, by pendulum observations in Harton Coal-pit
(, 437 3 42 ,,
61 HI. 437 3 ,, 36
Astronomical Constants. 409
This remarkable relation between the periods does not
extend to the fourth satellite, for
26 revolutions of IV. require 435 days 14 hours 16 min.
If #', ", ri" be the mean movements, either sidereal
or synodic, of the satellites i., n., in., and if /', /", I" be
their absolute longitude, sidereal or synodic, then Laplace
has shown that the following relation is always fulfilled
(' Mec. Cel.' liv. ii. No. 66, t. i.) :
228. Eccentricities and Inclinations of the Satellites.
The undisturbed orbits of the satellites i. and n. appear to
have no appreciable eccentricity. The perturbation pro-
duced by the interference of the exterior satellites causes,
however, a slight degree of eccentricity. The orbit of the
satellite i. may be considered to be coincident with the plane
of Jupiter's equator. The following are the values of the
inclinations of the orbits of the remaining satellites to the
plane of Jupiter's equator, as well as their longitudes referred
to the epoch 1750-0 (Damoiseau) :
Satellite. Inclination to the Longitude of Ascending Movement of
Equator of Ju- Node 1750-0 Node in one
piter. Julian Year.
II. i' 6" -2 ioi-996 -!2-o9i8
III. 5' s"-i I73'492 - 2-s68
IV. 24' 33"-! 278 -301 o7o6
229. Masses of the Satellites. The masses of the four
outer satellites, taking the mass of Jupiter as unity, are
determined by the mutual perturbations which these attrac-
tions produce. The following values have been assigned :
A.D.
1766. Bailly (' Essai sur la Theor. des Sat. de Jupiter,' Paris, 1766,
4to.):
I. 0-00004247 III. 0-00007624
II. 0-00002 1 1 IV. 0-00005
410 Astronomy.
A.D.
1805. Laplace (' Mec Cel.' liv. viii. ch. ix. t. iv. ) :
I. 0-0000173281 III. 0*000088497
II. 0-0000232355 IV. 0-000042659
1836. De Damoiseau ('Tables ecliptiq. des Sat. de Jupiter,' introd.
p. ii.) :
I. 0-000016877 III. 0-000088437
II. 0*00002322696 IV. 0-000042475 1
230. Perturbations of the Satellites. The. principal
work on this subject is Laplace, ' Mec. Cel.' liv. viii. ch. 1-16.
For an elementary account by the same author see ' Systeme
du Monde,' liv. iv. chap. vi. The tables are :
A.D.
1817. Delambre (' Tables ecliptiques des Satellites de Jupiter,' Paris,
4to.)
1836. De Damoiseau (' Tables ecliptiques des Satellites de Jupiter,'
Paris, 4to.)
1876. Todd ('A Continuation of De Damoiseau's Tables of the Satel-
lites of Jupiter to the Year 1900.' Washington, 4to.)
231. Rotation of Jupiter's Satellites. It has been
generally assumed, from the time of W. Herschel and
Schroter, that the period of rotation of each of the four
brighter satellites is equal to that of its revolution. The
satellites i. and n. seem to vary in brightness in a regular
manner during their revolutions, as if they keep the same
face directed towards the planet, but the matter is more
doubtful in the case of the two outermost satellites.
The following angular diameters for the mean distance
of Jupiter have been determined :
A.D.
1871. Engelmamvby micrometric measures (see 225) :
I. II. III. IV.
i"-o8 o'-gi i"'54 i"-28
1879. Pickering, photometrically (see 225) :
o"-92 o"-87 i"-io o"-65
1891. Michelson, by interference methods (M. N. Iv. p. 387)
i"-02 o" 94 i"37 i"'3i
Astronomical Constants. 411
A.D.
1894. Barnard, by micrometric measures (ibid.) :
I. II. Ill IV.
i"-o5 o"-87 i"*52 i"-43
Barnard's results correspond to the following diameters in
English miles :
2452 37 2045 51 3558 54 3345 35
SATURN.
232. Elements. The following are the elements of
the planet Saturn (Leverrier, 'Ann. Obs. Paris,' Mem. t.
xii. 1876, pp. A45 and A48) :
Epoch i85o,y#;z. i. Mean noon, Paris.
Mean longitude . . . 14 52 28-30 + (143 30' 30" -3210)^
Longitude of perihelion . . 90 6 567 + (i 57' 2i"'338)/
Greatest equation of centre . 6 25 31-24- (o 2' 21" -280)^
Longitude of ascending node . 112 20 53-0 + (o 52' I9"'594X
Inclination , . . 2 29 39-80- (o o' I4"-OO2)/
The unit of t is loo Julian years.
G. W. Hill finds for 1850 Jan. o, Greenwich M.T.
( Astron. Papers prep, for Amer. Ephemeris,' iv. p. 558,
Washington, 1890) :
Mean longitude . . . 14 49' 38" -09 + 4399621 "-$Q6t
Longitude of perihelion . 90 6 41*37
Longitude of ascending node . 112 20 49-05
Inclination . . . 2 29 40*19
Eccentricity . . . 0-05606025
233. Great Inequality of Saturn. In 1625 Kepler had
observed that the mean movements of Jupiter and Saturn
no longer coincided with those given by Ptolemy. The
great inequality which depends upon five times the mean
motion of Saturn, minus twice that of Jupiter, was first
calculated by Laplace (1785). The period of this inequality
is 929 years. The following are the numerical values of the
412 Astronomy.
coefficient of the great inequality of Saturn in longitude as
computed by different authors :
A.D.
1802. Laplace, epoch 1750 ('Mec. Gel,' liv. vi. ch. xiii. No. 35,
t. iii.) :
2939" -6 1 6 - o"-o85/ + o" -00008^
1821. Alexis Bouvard, epoch 1800 ('Tables astron. Paris,' introd. p.
iii.):-
2872" -649 - o" -oSo/ + o"-oooo8/ 2
1834. Pontecoulant, epoch 1800 (' Theorie anal. Syst. Monde,' t. iii.
p. 512):-
1876. Leverrier, epoch 1850 ('Ann. Obs. Paris,' Mem. t. xii. p.
A8):-
2988" -95 - o" 1 38 14/ + o" -0002424/ 2
t denotes the number of Julian years since epoch.
The tables of Saturn are :
1789. Delambre ('Tables de Jupiter et de Saturne,' Paris, 4to.)
1821. Alexis Bouvard (' Tables astronomiques, contenant les Tables
de Jupiter, de Saturne et d'Uranus,' Fads, 4to. )
1876. Leverrier (' Annal. Obs. Paris,' Mem. t. xii. pp. A9-A286).
234. The following are the principal measures of the
diameter of Saturn obtained since the introduction of the
telescope. The numbers indicate the angle which the
equatorial diameter of Saturn subtends when placed at a
distance equal to the mean distance of Saturn from the sun.
The ellipticity is also given :
EMiptichy
1719. Bradley ('Miscell. Works,' p. 350) . I7"75
1829. W. Struve (' M. A. S.' vol. iii. p. 301) . I7"'99i
1835. Bessel ('A. N.' No. 275) . I7"-O53 -
1848. Main (' M. A. S.' vol. xviii. pp. 43, 46) I7"'5o 2
1853. Dawes (< M. N.' vol. xiii. p. 78) . . . ^~ B
1862. Main, with heliometer ('Radcl. Obs.'
1862, p. 170) .... i6"-88 -
Astronomical Constants. 413
1872. Kaiser, with double-image micrometer
(' Ann. d. Sternwarte,' Leiden, iii.
P- 264). . I7-274 ^1
1 88 1. W. Mayer (' Mem. de la Soc. de Geneve,'
xxvii. p. 223) . . 17-448 :j
1889. A. Hall ('Wash. Observ.' 1885, app. ii.) 1772
235. Rotation of Saturn. This element has been de-
termined as follows, but the number of revolutions employed
by Herschel was very small :
A.D.
1794. Sir W. Herschel, from observations of a quin-
tuple band from November n, 1793, to
January 16, 1794 ('Ph. Tr.' vol. Ixxxiv. p.
48) . . . . . . io h i6 m o s> 4
1877. Asaph Hall, by the observations of a brilliant
spot from December 7, 1876, to January 2,
1877 . . . . io h I4 m 23" -8 2 s -30
1893. Stanley Williams ('M. N.' liv. p. 313) :
Equator . . . . iO h I2 m 45 8> 8 to 59' -4
Lat. + 17 to 37 . . . 10 14 29-1 to 60-7
236. Mass of Saturn. The mass of Saturn together
with his system has been thus determined :
A.D.
1719. Newton, by the elongations of Titan observed by
Pound (' Principia,' 3rd ed. lib. iii. prop. 8, cor. i). 3^
1802. Laplace, from Pound's observations and those of Jacq.
Cassini ('Mec. CeV lib. vi. ch. vi. No. 21, t. iii.) .
1821. Bouvard, by the perturbations of Jupiter 'Tables
astron.' p. ii.) .
1834. Bessel, by heliometer measures of the elongation of
Titan ('A. N.' No. 242) . . .
1876. Leverrier, by the perturbations of Jupiter ('Ann. Obs.
Paris,' Mem. t. xii. p. 9) . .
1885. A. Hall, by elongations of Japetus (' Wash. Obs.' 1882,
a PP- i- P- 70) . .
41 4 Astronomy.
A D.
1888. H. Struve, by elongations of Japetus and Titan
(' Suppl. I. aux Obs. cle Poulkova,' i. p. 118) . ^
1889. A. Hall, jun., from heliometer measures of Titan
('Trans, of Obs. of Yale College,' vol. i. p. 146) .
237. Brilliancy of Saturn. In 1859 Seidel, by the aid
of Steinheil's photometer, estimated the brilliancy of Saturn
at 0*482 time that of Vega (' Untersuchungen iiber die
Lichtstarke der Planeten,' Munich, 4to.)
Zollner has found, by his polarisation photometer :
Brilliancy of Saturn = __ __ that of the Sun.
130980000000
Albedo of Saturn = 0*498 1 (' Photometrische Untersuchungen,'
Leipzig, 1865, 4to. ; and ' A. N.' No. 1575).
G. Mtiller gives the stellar magnitude of Saturn as 2 "5 86,
and the albedo as 3*28 times that of Mars, Zollner's result
giving 1*87 ('Publ. d. astrophys. Obs. zu Potsdam,' viii.
p. 369). The spectrum of Saturn is very like that of Jupiter
(see Huggins, 'Ph. Tr.' 1864, p. 243).
238. Rings of Saturn. The rings of Saturn were
glimpsed in 1610 by Galileo, who, regarding the two ansae
as appendages to the body of the planet, called Saturn
* tricorpor ' (' Opera,' Florence, 3 vols. 4to. vol. ii. p. 39).
It was Huyghens, in 1656, who first really showed that the
body of the planet was surrounded by a ring ('Sy sterna
Saturnium,' La Haye, 1659, 4to.)
The annular appendage which surrounds the globe of
Saturn is divided into- several concentric portions. The
brilliant ring in the first place is subdivided into two por-
tions by a circular line usually called after Cassini. This
line has been studied by many astronomers. Sir W. Herschel
has shown that it can be seen on both faces of the ring, and
that it forms a permanent division ('Phil. Trans.' 1791 and
1792).
Astronomical Constants. 415
Other finer lines have been seen. The most conspicuous
next to Cassini's line is that which bears the name of Encke.
Inside the bright ring is a fainter ring, often called the
dusky ring. This was more or less perceived by previous
astronomers, but G. P. Bond, on October 10, 1850, first
clearly detected its real character (' M. N.' vol. xi. p. 20).
O. Struve denotes the part of the bright ring exterior to
the line of Cassini by A ; the part inside the line of Cassini
is B, and the dusky ring is c. The following measures have
been made of the diameters of the rings, it being supposed
that Saturn is at its mean distance from the sun :
Diameter.
A.D Exterior of A. Cassini's Line. Interior of B. C.
1719. Pound (Newton, ' Principia,' 3rd ed. lib. iii. prop. 8, p. 2) :
42" 30"
1719. Bradley (Rigaud, * Bradley 's Miscellaneous Works,' D. 350) :
41-25 28-10
1835. Bessel, with heliometer (' Konigsb. Beob.' xvi. xvii. ; 'A. N.'
275) :-
39-3H
1851. W. C. Bond (' Gould's Astron. Journal,' vol. ii. p. 5) :
39'35 35"'22 26-26 23"-57
/852. O. Struve (' Mem. des Astron. de Poulkowa,' t. i. pp. 350, 351) :
40-12 35-52 34-53 25-29 23-57 21-22
1855. Main, double-image micrometer (' M. A. S.' xxv. 17) :
3973 36-19 27-50
1856. De la Rue (' M. N.' vol. xvi. p. 43) :
39-83 35/33 33'45 26-91
^872. Kaiser, double-image micrometer (' Ann. d. Sternw.' Leiden,
iii. p. 264) :
39-471 34-227 27-859
1881. W. Mayer (' Mem. Soc. de Geneve,' xxvii. p. 225) :
40-467 26-321 21-17
1889. A. Hall ('Wash. Observations,' 1885, app. ii.) :
40-45 34*95 34'H 2575 20-52
When two numbers are indicated for the line of Cassini,
they refer to the external and internal diameters of the
416 Astronomy.
dark line. Where only one is given, the interior is under-
stood.
The following measures of Saturn's system were made
by Barnard with the 36-inch Lick refractor (' M. N.' January
1896, p. 171). The sun's mean distance is taken to be
92,879,000 miles :
Miles.
Equatorial diameter of Saturn . . . 76,470
Polar diameter of Saturn .... 69,770
Outer diameter of outer ring . . . 172,310
Inner diameter of outer ring . . . 150,560
Outer diameter of inner ring . . . 146,020
Inner diameter of inner ring . . . 110,200
Inner diameter of crape ring . . . 88,190
Width of Cassini division .... 2,270
Diameter of Titan . . . . .2,720
The thickness of the ring has been estimated as follows :
A.D.
1790. Sir W. Herschel (' Phil. Trans.' vol. Ixxx. p. 6) . o"'3
1850. Sir J. Herschel ('Outlines of Astronomy,' 3rd ed.
No. 514) . .%*. Discovered by Jean Dominique Cassim on
March 21, 1684 ('Nouvelle De'couverte des deux Satellites
de Saturne les plus proches,' Paris 1686, 4 to. ; ' Hist. Ac.
Sc. av. renouv.' t. i. p. 415, t. x. p. 694). The period is
jd 2I h jgm 2 6 S '09 (H. Struve), the mean elongation is
42 "-609, the eccentricity is insensible, and inclination to
Astronomical Constants. 419
the plane of the ring about i. The mass is TTrT Voo f
that of Saturn. The annual motion of the perisaturnium is,
according to H. Struve, 7 2 -3. Mean magnitude, according
to Pickering, 11-4.
H. Struve has shown (' A. N.' 2984) that the conjunc-
tions of Mimas and Tethys always oscillate about the point
which is midway between the ascending nodes of their
orbits on Saturn's equator. They can only be as much as
45 distant from this point, and complete the libration in
about 68 years.
Dione. Discovered on March 21, 1684, by Jean Dom.
Cassini (loc. tit.} Magnitude according to Pickering, 11-5.
The period is 2 d i7 h 41 9 S> 54 and the mass s^Wo f
that of Saturn (H. Struve). The orbit is in the plane of the
ring-
Annual movement of the perisaturnium, according to
H. Struve, is 25 to 30. The diameter according to
Schroter is o"* 1 3, and according to W. Struve o"75 ('M.
A. S.' vol. ii. p. 518). The conjunctions of Enceladus and
Dione always coincide with the perisaturnium of Enceladus
or oscillate about this point (H. Struve, ' A. N.' 2984).
Rhea. Discovered on December 23, 1672, by Jean
Dom. Cassini ('Decouverte de deux nouvelles Planetes
autour de Saturne,' Paris, 1673 , 'Hist. Ac. Sc. av. renouv.'
t. i. p. 159, t. x. p. 584.)
Magnitude according to Pickering, 10*8.
The period is 4 d i2 h 25 i2 s 'oo.
The orbit may be considered to coincide with the plane
of the ring.
Laplace has shown how the effect of the ellipticity of the
planet acts to retain the interior satellites in the plane of its
ring and of the equator (* Mec. Cel.' liv. viii. ch. xvii. No.
36, t. iv.)
The motion of the perisaturnium is about io'2 per
annum according to H. Struve. The diameter, according
to Schroter, is o"'32.
E E 2
420 Astronomy.
Titan. Discovered by Huyghens on March 25, 1655,
with a i2-feet refractor ('Systema Saturnium,' La Haye,
1659, 4to. ; 'Cosmotheoros,' La Haye, 1698, 4to. p. 69).
This is the largest of the satellites, revolving in i5 d 22 h 41
24 S 7. The magnitude is 9-4 (Pickering), and the diameter
o"'35 (Safarik, 'A. N.' 3046).
The following elements are by H. Struve (' Suppl. I. aux
Observations de Poulkova,' p. 100) for 1885*6 + /:
Epoch 1885 Sept. i-o Gr. M. T.
Longitude . 183 34 -'39
Long, of perisa-
turnium . 272 48 + 3i''3/ + 22' -o (sin 2*-- sin 2^ )
Long, of node on
ecliptic . 167 45-92 f o774/+37'75 cos(3943' + 27'-o/)
Inclination on
ecliptic . 27 28-32- o-oo6/+ 17- 53 sin (39 43 + 27-0^)
Eccentricity . 0-029073+ 0-000186 (cos 2g 3 2g)
Mean daily motion 22 0< 577ou6
where g is the distance of the perisaturnium from the
ascending node of its orbit on that of Saturn, and g the
same corresponding to /=o. Elements closely agreeing
with these were found by A. Hall, jun., from heliometer
observations in 1885-87 ('Trans. Obs. of Yale Coll.' i.
p. 144).
The mass of Titan is ^\? (H. Struve, loc. cit. p. no).
Hyperion. Discovered by G. P. Bond on September
1 6, 1848, and seen independently by Lassell on the i8th of
the same month. Magnitude 137 (Pickering). The period
is 2i d 6 h 38 3o s '5i (A. Hall, < M. N.' xliv. p. 363). The
retrograde motion of the perisaturnium, i9 - o per annum,
is most remarkable, and is caused by the fact that the mean
motion of Hyperion is nearly f of that of Titan. The two
satellites only come into conjunction with each other at or
near (within 18 of) the aposaturnium of Hyperion (New-
comb, 'Astron. Papers,' iii. p. 345, Washington, 1884).
Japetus. Discovered by Jean Dom. Cassini, October 25,
Astronomical Constants. 421
1671 (* Decouverte de deux nouvelles Planetes autour de
Saturne,' Paris, 1673 > 'Hist. Ac. Sc. av. renouv.' t. i. p. 150,
t. x. p. 584). Magnitude, at its mean brightness, 11*8
(Pickering).
The period is 7Q d 7 h 55 25 s . This is the only satellite
which has an appreciable inclination to the ring-plane, about
10. Elements by H. Struve (' Suppl. I. aux Obs. de
Poulkova,' p. 87, St. Petersburg, 1888), referred to the
equinox i8
Longitude .... 75 26' -4
Longitude of perisaturnium . . . 354 o +7''9^
Longitude of Node on ecliptic . . 142 12-4 1-48?
Inclination on ecliptic . . 18 28-3 -0-54^
Eccentricity . ... . 0-02836 +0-000015^
Mean daily motion , . . 4 '537997
In 1673 J. Dom. Cassini remarked that in the eastern
portion of its orbit this satellite remains invisible for about
thirty days (' Hist. Ac. Sc. av. renouv.' t. i. p. 174). Jacques
Cassini was convinced that the satellite always turns the same
face to the planet (' Mem. Ac. Sc. Paris,' 1 7 14, p. 370). Sir W.
Herschel has confirmed this, and has found that the satellite
changes its brightness through a range of three magnitudes
in the course of a single revolution (' Phil. Trans.' 1792, p. i).
Pickering has confirmed the variability, but shows that the
total loss of light is much less than formerly supposed.
If ,, 2 > 3> n \ De the mean movements of the four
interior satellites, then Kirkwood has shown that the follow-
ing relation is fulfilled (' The Observatory,' No. 7, p. 199 ;
C M. N.' vol. xxxviii. 1877, p. 64) :
URANUS.
241. Elements. This planet was discovered by Sir W.
Herschel on March 13, 1781 (' Ph. Tr.' vol. Ixxi. p. 492). It
422 Astronomy.
had been observed as a star by Tob. Mayer in 1756, and
also by Le Monnier (twelve times), and Flamsteed (1690,
1712, and three times in 1715). t is the number of Julian
years since the epoch.
1874. Newcomb (' Smithsonian Contributions to Knowledge,' Wash-
ing. 4to. vol. xix. pp. 81, 184, 219), epoch 1850, January o,
mean time at Greenwich.
Mean longitude . . . 29 12' 43"73+ 15424" 797/
Longitude of perihelion . . 170 38 487 + 53*i68/
Greatest equation of the centre . -5 22 42-28 0-1090^
Longitude of the ascending node . 73 14 37*6 + 18-5682^
Inclination . . . o 46 20*92+ 0-0247^
Semiaxis major . . . 19-19209
Eccentricity .... 0-0463 592 -O-OOOOOO2627/
1877. Leverrier (' Annal. Obs. Paris.' Mem. t. xiv. part i. pp. A67,
A69), epoch 1850-00, mean time at Paris.
Mean longitude . . . 29 17' 50" -91 + 15475-1 H38/
Longitude of perihelion . . 170 50 7*1+ 53-4582^
Greatest equation of the centre . 5 19 26-1 0-10938^
Longitude of ascending node . 73 13 54*4+ I8-O57O/
Inclination . . . o 46 19-72+ 0-01732^
Semiaxis major . . 19-14169
Eccentricity . . . 0-04634096-0 -000000265 1^
242. Equatorial Diameter of Uranus at its Mean
Distance from the Sun.
A D.
1788. W. Herschel (' Phil. Trans.' t. Ixxviii. p. 378) . 3" -906
1867. Lassell and Marth (_
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00 2- cT 2 - 3- , co
-4 -^ > an d every volume of 'Greenwich
Observations ' since 1875. Also Vogel, 'Untersuchung
Astronomical Constants. 443
iiber die Eigenbewegung der Sterne im Visionsradius auf
spectrographischem Wege ' (* Publ. d. astrophys. Obs. zu
Potsdam,' vol. vii. Part i, 1892).
On stellar photography see a valuable resume of the
work done up to 1887, by Rayet, in the 'Bulletin astrono-
mique ' t. iv. p. 165, and the ' Bulletin du Comite inter-
national pour 1'execution de la carte photographique du
ciel,' published at Paris since 1888.
272. Parallaxes of the Stars. The following values
have been determined for the angle which the radius of the
earth's orbit subtends at the distance of the star ; a and o
are the right ascension, and the declination referred to the
epoch 1890. The number in brackets at the end of the line
denotes the magnitude of the star.
A.D. 34 Groombridge, a = o h 12 6" ; 5= +43 23''9 [7-9]
1867. Auwers, from comparison of the right ascension of
this star with that of the neighbouring stars by the
chronograph ..... o"'3o7
7) Cassiopeia, o = o u 42 26 s ; 5.-= +57 I3''9 . [3-6]
1856. Otto Struve, by micrometric measurements . . o '154
H Cassiopeise, o= i h o m 57" ; 5= +54 22' -8 . [5-2]
1856. Otto Struve, by micrometric measurements . . o -342
1888. Pritchard, by photography .... 0*035
1893. Jacoby, from Rutherfurd's photographs . . o -275
a Ursse minoris, a= i h i8 m 29" ; 8= + 88 43' -3 . [2-1]
1817. Von Lindenau, from 890 right ascensions . . o '144
1847. W. Struve, by right ascensions at Dorpat . . o -075
1847. W. Struve and Preuss, by right ascensions at Dorpat. o -172
1847. C. A. F. Peters, by declinations at Pulkowa . . o -067
1847. W. Struve, from the declinations at Dorpat . . o '147
1889. Pritchard, by photography . . . . o '070
a Aurigae (Capella), = 5'' 8 m 34" ; 5= +45 53'' I [ I ]
1846. C. A. F. Peters, by meridian altitudes at Pulkowa . o -046
1856. Otto Struve, micrometrically . . . o -305
1888. Elkin, by heliometer . .... 0-107
a Canis majoris, a^=6 h 40 18* ; 5= 16 34 r> o [ i ]
1840. Henderson, by meridian altitudes at Cape . .0-34
1864. Gylden, by altitudes of Maclear at Cape . . 0-193
1868. Abbe, by altitudes at the Cape . . . o -273
444 Astronomy.
A.D.
1883. Gill, by heliometcr ..... o"'37o
1883. Elkin, by heliometer . . . . . o -407
a Geminorum, = 7'' 27'" 35" ; 8= + 32 f"j . [i-6|
1856. Johnson, by the heliometer . . . .0-198
Canis minoris, a = 7 h 33 33' ; 8 = + 5 30' -4 . [ i ]
1863. Auwers, by micrometric measurements . . o -240
1 Ursae majoris, a = 8 h 51 40' ; 8 = + 48 28' -4 . [3-2]
1846. C. A. F. Peters, by observations at Pulkowa . 0-133
Groombridge 1618, o=io h 4 m 46* ; 8=4-50 i'-o [6-5]
1 88 1. Ball, by micrometer ..... 0-322
Lalande 21 185, a = io h 57 m 20" ; 8 = + 36 56' -4 . [ 7 ]
1872. Winnecke, by micrometric observations . . o -501
Lalande 21258, a= n h o m r ; 8= + 44 5^5 . [8-5]
1862. Auwers, by heliometer . . . . o -262
1863. Kriiger, by heliometer . . . . o -260
21516, a=n"8>3; S=+744'-2 . . [7]
1880. Winnecke, by micrometer . . . .0-199
1886. De Ball, by micrometer . . . . o -104
A Oe. 11677, a=n h 14 25 s ; 8= +66 26''5 . [9-0]
1876. Geelmuyden, by micrometer . . . .0-25
Groombridge 1830, a = i i h 46 38' ; 8= + 38 30' -5 . [6-5]
1846. C. A. F. Peters, by meridian observations . . o '226
1848. Wichmann, heliometer measures by Schliiter . . o -182
1850. Otto Struve, micrometic measures . . . o -034
1854. Dollen, from Schliiter and Wichmann's observations . o -141
1854. Johnson, by the heliometer . . . .0-033
1873. Briinnow, by micrometric measurements . .0-113
1874. Auwers, from Johnson's observations . . . o -023
j8 Centauri, a= 13" 56*" 4" ; 8 = 59 50^5 . [ i ]
1852. Maclear, from meridian altitudes . . . o 470
1868. Moesta ,, ,, . o -173
1883. Gill, by heliometer . . . . . -o -017
a Bootis(Arctunis), o= I4 h io m 39'; 8-= +I945''3 [ i ]
1846. C. A. F. Peters, by absolute measurements . . o '127
1856. Johnson, by the heliometer . . . .0-138
1883. Elkin, by heliometer . . . . .0-018
a Centauri, a- i4 h 32 8" ; 8 = 60 22' -7 . [ i ]
1840. Henderson, by absolute measures at the Cape, 1832-
1833 (mean) . . < . . .1-16
1842. Henderson, by absolute measures at the Cape, 1839-
1840 . o -913
1851. Maclear, by direct and reflected altitudes . . 0-919
Astronomical Constants. 445
A.D.
1868. Moesta, measures at Santiago . . . o"-88
1883. Gill, heliometer > . . . . o 756
1883. Elkin, heliometer ... . . . o 730
1895. Roberts, from merid. observations, 1879-1881 . o 71
a Herculis, a= i7 h 9 38* ; 5= + 14 3i'-o . [3-2]
1856-58. Jacob, by micrometer measures at Madras . o -062
(Eltzen 17415, a= I7 h 34 m 4"; 5= +68 27^4 . [9]
1863. Krtiger, by micrometric observations . . . o -247
1882. Schweizer, ,, ,, . . . o '151
70 / Ophiuchi, o= I7 h 59"' 54" ; 5= +2 3i'"5 . [4-1]
1863. Kriiger, heliometer observations in 1850-1861 . o -162
1894. Schur, heliometer . . . . . . o -286
a Lyrae, a - i8 h 33 13" ; S = + 38 40' -9 , [ i ]
1840. W. Struve, micrometrically . . . . o -262
1846. C. A. F. Peters, altitudes at Pulkowa . .0-103
1856. Johnson, by the heliometer . . . .0-14
1859. Otto Struve, micrometrically by distances . . O '119
1859. ,, ,, by position angles . o -161
1870. Brunnow, micrometric measures at Dunsink . . o '212
1873. Briinnow, by a new series . . . .0-188
1886. A. Hall, by micrometer . . . . o -134
1888. Elkin, by heliometer . . . . o -034
^ 2398, a = 1 8" 4i ra 33 s 5 5= + 59 27^7 . . [8-2]
1888. E. Lamp, by micrometer . . . . o -353
6 Cygni B, a =19" 9 15* ; 8 = +49 38' -9 . [6-6]
1884. Ball, by micrometer . . . . . o -482
1886. A. Hall . . . . .-o -021
a- Draconis, a = 19'' 32"" 34" ; 5= +69 28' -4 . [474]
1870. Brunnow, by micrometric observations at Dunsink . 0-222
1873. Brunnow ,, ,, ,, . o -246
a Aquilae, a=i9 h 45 25* ; 5= +8 34'7 . [i]
1888. Elkin, heliometer . . . . .0-199
61 Cygni, o = 2i h i m 58* ; S= -f 38 i2'-5 . [5-1]
1840. Bessel, by the heliometer (final result) . . o -348
1846. C. A. F. Peters, absolute measures at Pulkowa . o -349
1849. ,, rediscussion of Bessel's observation . o -360
1853. Pogson, by the heliometer . . . . o -384
1854. Johnson, by the heliometer . . . . o -397
1854. C. A. F. Peters, from Schluter's observations. . o -360
1859. Otto Struve, micrometric observations of, 1852-1853.
55 ,, distances . . . o -509
a , y angles of position . . o -501
446 Astronomy.
A D.
1863. Auwers, micrometrically . . . . o -564
1878. Ball, by differences of decl. at Dunsink (preceding star) 0-465
1884. Ball, ,, ,, (following star) o -468
1883. J. Lamp, from Schweizer's observations . . o -449
1886. A Hall, by micrometer . . o -270
1887. Pritchard, by photography . . o -432
tlndi, a = 2i" 54 in 56'; 5= -57 14^3 . . [5-3]
1884. Gill, by heliometer . . o -274
1884. Elkin, . 0-124
Lacaille 9352, a = 22" 58'" 46* ; 5 = - 36 29' -2 . [7 -5]
1884. Gill, by heliometer . . o -285
3077 Bradley, a = 23" 7 m 56 ; S = + 56 33' -6 . [5-5]
1873. Briinnow, by micrometric observations at Dunsink . o -069
85 Pegasi, o = 23 h 56 26' ; 5= +26 30' -i . [5-8]
1873. Briinnow, by micrometric observations at Dunsink . o -054
For a list of results of researches on annual parallax see
Oudemans, 'A. N.' 2915. For Pritchard's photographic
determinations of the very small parallaxes of a number
of bright stars see 'Astronomical Observations at the
University Observatory, Oxford,' Parts III. and IV. (1889-
1892).
273. Proper Motions of the Stars. Ptolemy and the
ancients generally seem to have considered the configuration
of the stars to have been perpetually invariable. It was
only in the i8th century, in 1718, that Halley discovered
displacements in the latitudes of Aldebaran, Sirius, and
Arcturus (' Phil. Trans.' vol. xxxi. p. 736). Jacques Cassini
established the proper motion of Arcturus beyond doubt
by showing that the apparent displacements were not
participated in by the neighbouring star 77 Bootis. The
following list contains the titles of the principal works on
proper motions :
A.D.
1775. Tob Mayer, 'Opera inedita,' t. i. Gottingen, 4to. p. 98.
Contains the proper motions of 80 stars found by comparing
his observations with those of Romer, which were made 50
years previously.
1818. Bessel, ' Fundamenta Astronomise,' p. 311.
Astronomical Constants. 447
A.D.
1835. Argelander, ' DLX. stellarum fixarum positiones mediae,'
Helsingfors, 410. 560 stars from the observations at
Abo compared with those of Bradley.
1851-1860. Main, in' M. A. S.'vol. xix. p. 136, and vol. xxviii. p. 127.
The proper motions of 1,170 and 270 stars respectively,
found by comparing the modern observations at Green-
wich with those of Bradley.
1856. Madler, in ' Beobachtungen zu Dorpat,' vol. xiv. (3,222
stars observed by Bradley).
1865-1875. E. J. Stone, in M. A. S.' vol. xxxiii. p. 61, and vol.
xlii. p. 129. 460 and 406 stars respectively. The
first deduced from Greenwich observations; the second,
of southern stars, from observations at the Cape, com-
pared with more ancient ones.
1869. Argelander, ' Untersuchungen ilber die Eigenbewegungen
von 250 Sternen ' (' Beob. auf der Sternwarte zu Bonn,'
Band vii.)
1888. Auwers, Neue Reduction der Bradleyschen Beobach-
tungen,' iii. (contains a re-determination of the proper
motion of all the stars observed by Bradley).
1890. Stumpe, 'A. N.' 2999-3000 (contains all stars known to
have a P.M. greater than o"'i5 annually).
1892. Porter, Catalogue of Proper Motion Stars (' Publ. of the
Cincinnati Observatory,' No. 12).
274. Double Stars. The earliest mention of double
stars, requiring for their separation the powers of the tele-
scope, is by Jean Dom. Cassini, who in 1678 alluded in this
way to /3 Scorpionis, a Geminorum, and y Arietis (' Hist.
Ac. Sc. Paris av. renouv.' t. i. p. 266). When Bode,
in 1781, formed a first list of double stars, he only enume-
rated 80 ('Berliner Jahrbuch,' 1784, S. 183). The first
really systematic labours are those of Sir W. Herschel
('Phil. Trans.' 1782, p. 112). For a list of catalogues of
double stars see Knobel ('M. A. S.' vol. xliii. 1877,
pp. 21-61).
In 1782 Sir W. Herschel commenced the practice of
recording the distance and position angle of the two com-
ponents of a double star. The following are the principal
works relating to double stars :
448 Astronomy.
A.D.
1782-1804. Sir W. Herschel ('Phil. Trans,' Ixxii. p. 112, Ixxv. p.
40, xciii. p. 339, xciv. p. 353 ; ' M. A. S.' vol. xxxv. )
1824. Sir J. Herschel and Sir J. South (' Phil. Trans.' cxiv.
part iii. )
1837. W. Struve, ' Stellarum cluplicium etmultiplicium mensurce
micro-metric*.' This is the chief work of the author,
containing measures of 3,134 multiple stars. Lord
Lindsay has given an index to these measures in
' Dunecht Observatory Publications,' vol. i. (1876).
Aberdeen, 410.
1844. W. H. Smyth, ' A Cycle of Celestial Objects,' London,
1844, 2 vols. 8vo. This is a most interesting work,
especially to the amateur ; an enlarged ecLrion of vol. ii.,
the ' Bedford Catalogue,' was published by Chambers in
1881.
7.847. Sir J. Herschel, ' Results of Astronomical Observations at
the Cape of Good Hope,' London, 410. Micrometric
measures of 2,520 multiple stars in the southern hea-
vens.
1867. Dawes (< M. A. S.' vol. xxxv. p. 164).
1874. Sir J. Herschel, published by Main and Pritchard in
'M. A. S.' vol. xl. p. i. This contains 10,317 double
or multiple stars, forming an index of all those known
up to 1872.
1876. Duner, ' Mesuresmicrometriquesd'etoiles doubles.' Lund,
41.0.
1873-1894. .Burnham, ' M. N.' vol. xxxiii. pp. 351, 437, vol. xxxiv.
PP- 59. 382, vol. xxxv. p. 31; 'A. N.' 2062, 2103;
'Amer. Journ.'July 1877; 'M. N.'vol. xxxviii. p. 79;
'M. A. S.' xliv. ; Report to Trustees of James Lick
Trust ('Publ. Lick Obs.' i.); Publ. of Washburn
Obs.' vol. -i. ; ' M. A. S.' xlvii.; 'Publ. Lick Obs.' ii.
These papers contain measurements of 1,274 new
double stars.
1878-1893. O. Struve, ' Mesures micrometriques des etoiles doubles '
( ' Observations de Poulkova,' t. ix. -x. ; contains measures
from 1839-1889).
1879. Burnham, Double-star observations made in 1877-78 at
Chicago with the 1 8^ -inch refractor of the Dearborn
Observatory (' M. A. S.' vol. xliv. pp. 141-305).
' Astronomical Constants. 449
A.D.
D.
1883. Burnham, Double-star observations made in 1879-80
with the i8|-inch refractor of the Dearborn Observa-
tory, Chicago (' M. A. S.' vol. xlvii. pp. 167-326)
1883-1884. Dembowski, Misure Micrometriche di Stelle Doppie
e Multiple, 5 Roma, 1883-84.
The following may also be consulted on the appearance
and conditions of the more interesting groups :
1835. Sir J. Herschel, 'A List of Test Objects, principally
Double Stars, for the Trial of Telescopes' (< M. A. S.'
vol. viii. p. 25).
1878. Flammarion, ' Catalogue des Etoiles doubles et multiples
en mouvement relatif certain.' Paris, 1878.
1879. Crossley, Gledhill and Wilson, 'A Handbook of Double
Stars. 3 London, 1879; with pamphlet of corrections, 1880.
1893-1894. Webb, 'Celestial Objects for Common Telescopes.' 5th
ed. London, 2 vols. crown 8vo.
Sir W. Herschel, in reobserving double stars after an
interval of twenty years, discovered a gradual change in
the angle of position in u Geminorum, y Leonis, e Arietis,
Herculis, 2 Serpentis, and y Virginis ('Phil. Trans.' 1803,
PP- 339> 3 6 5> 37 2 > 377? 3 82 )- Savary computed the first
orbit of a binary star, that of Ursae majoris, in 1828 ('Con-
naissance des Temps,' 1830).
Orbits of binary stars computed by Doberck and others
will be found in Flammarion's or GledhilFs works already
referred to.
NEBULA.
275. List of Authorities. Aratus in the third century
before the present era mentions the object in the constella-
tion Cancer, which is now known as the Praesepe Cluster.
Simon Mayer (Marius), in 1612, calls attention to the
luminous spots in the heavens, which he attributes to col-
lections of stars. Mairan in 1754 first alludes to gaseous
materials in such objects. Messier, 1771, distinguished
G G
45 o Astronomy.
clearly between nebulae and clusters. The great develop-
ment of this branch cf astronomy is due to Sir W. Herschel,
who arranged the clusters in three classes and the nebulae
proper in five others ('Ph. Tr.' 1786, p. 457).
The following are the principal works on nebulae :
A.D.
1781-1782. Messier, ' Connaissance des Temps,' 1783, p. 225, and
1784, p. 254. Contains lists of 103 of the most remark-
able nebula? in the heavens.
1786. Sir W. Herschel (' Phil. Trans.' vol. Ixxvi. p. 471).
1,000 new nebulae and clusters.
1789. Sir W. Herschel ('Phil. Trans.' vol. Ixxix. p. 226).
l,ooo new nebulae and clusters.
1802. Sir W. Herschel (' Phil. Trans.' vol. xcii. p. 503). 500
new objects.
1833. Sir J. Herschel, < Observations of Nebulae and Clusters'
(' Phil. Trans.' 1833).
1847. Sir J. Herschel, ' Results of Astronomical Observations
at the Cape of Good Hope.' London, 4to. ch. i. p. 51.
862-1875. Schonfeld, Beobachtungen von Nebelflecken und
Sternhaufen ' (' Astr. Beob. zu Mannheim,' i.-ii.).
1864. Sir J. Herschel. A general catalogue of nebulae and
clusters of stars (' Phil. Trans.' cliv. p. i). This great
work contains the places of 5,079 nebulae and clusters
brought to the epoch 1860-0.
1867. D' Arrest, ' Siderum nebulosorum observationes Havni-
enses,' Copenhagen, 4to. Observations of 1,942
nebulae.
1867. Marth (< M. A. S.' vol. xxxvi. p. 53). 600 new nebulae.
1874. Schultz, Micrometrical Observations of 500 Nebulae.'
Upsala, 4to.
187^-1880. Lord Rosse, ' Observations of Nebulae, 1848-78 ' (< Trans.
R. Dublin Soc.' vol. ii.)
1888. Dreyer, ' A new general Catalogue of Nebulae and Clusters
of Stars' ('M. A. S.' xlix. Contains places of 7,840
nebulae and clusters. In vol. li. is an index catalogue
of 1,529 nebulae, the two catalogues containing all
known at the end of 1894).
For the descriptions of remarkable nebulae with drawings
see
Astronomical Constants. 45 1
A.D.
1844. Lord Rosse (' Phil. Trans.' vol. cxxxiv. p. 321).
1850. ,, cxl. p. 499).
1861. ,, ,, ,, cli. p. 681).
1868. clviii. p. 57).
1867. G. P. Bond ('Annals of Harvard College Observatory,' vol. v. )
1894. Roberts, ' A Selection of Photographs of Stars, Star Clusters
and Nebulae.' London, 4to.
For a complete list of drawings of nebulae up to 1888 see
Dreyer's ' New Gen. Cat.,' referred to above.
On alleged changes in the forms of nebulae see Dreyer,
' M. N.' xlvii. p. 412, and lii. p. 100.
For the spectra of nebulae see under the head of Stellar
Spectroscopy. A list of all nebulae known to possess gaseous
spectra is given in Schemer's ' Treatise on Astron. Spectro-
scopy,' edited by Frost, pp. 232, 233.
276. The Milky Way. That the Milky Way is an
agglomeration of small stars was admitted by the ancients.
Galileo adopted the same view when he first saw the Milky
Way through the telescope. The constitution of the Milky
Way has been carefully studied by Sir W. Herschel (' Phil.
Trans.' 1785, p. 258 ; 1814, p. 280). The pole of the Milky
Way has been thus determined :
A.D.
1847. W. Struve, Etudes d'Astronomie stellaire,' St.-Petersbourg,
8vo. p. 62.
a=!2 h 38 m ; 5=+3i'5; Equin. 1825-0
1878. J. C. Houzeau ('Annales astronomiques de 1'Observatoire de
Bruxelles,' t. i. Uranom. p. 21).
o= I2 h 49 m -i ; 8= +27 30'; Equin. 1880-0
277. The Zodiacal Light. This phenomenon was well
known among Eastern nations at an early date as the ' false
dawn.' In Europe it was scarcely noticed till Jean Domi-
nique Cassini commenced a scientific study of it in 1683.
One of the best general descriptions of the zodiacal light is
that of Argelander, ' Schumacher's Jahrbuch,' 1844, P- 148.
See also Jul. R Schmidt, ' Das Zodiacallicht : Uebersicht
GG2
452 Astronomy.
der seitherigen Forschungen nebst neuen Beobachtungen
iiber diese Erscheinung in den Jahren 1843-1855,' Bruns-
wick, 8vo.
On the spectrum of the zodiacal light see
A.D.
1872. Vogel ('A. N.' No. 1893).
1874. Arthur W. Wright ('American Journal of Science and Arts,
3rd series, vol. viii. )
1877. Piazzi Smyth (' Edinburgh Astron. Obs.' vol. xiv.)
On the various hypotheses which have been advanced to
explain the zodiacal light see
A.D.
1799. Laplace, ' Mecanique celeste,' t. ii. p. 170.
1807. Thomas Young, 'Nat. Phil.' London, 2 vols. 4to. vol. i. p.
502.
1835. Arago, 'Astron. popul.' Paris, 1855, 4 vols. Svo. t. ii. p.
183.
1843. J. C. Houzeau ('A. N.' No. 492).
INDEX.
A
ABB
BBE parallax of a Canis majoris,
443
Abbreviations, 361
Aberration, 366
effect on place of star, 218
greatest effect of, 220
Absorption of light by the atmosphere, 4
Acceleration, secular, 334
Adams, discovery of Neptune, 296
elements of Leonides, 435
elements of Neptune, 426
ellipticity of Mars, 397
mass of Uranus, 423
peril d of the Leonides, 435
secular va iation of the moon, 389
.^Ethra, eccentricity of, 401
Air, density of, 47
Airy, catalogues of stars, 438
density of the earth, 387
diameter of Venus, 378
discovery of Neptune, 426
ellipticity of the earth, 385
eilipticity of Jupiter, 403
equation of the centre, 383
longitude of the perihelion, 382
mass of Jupiter, 405
mass of Mars, 298
mass of Venus, 379
motion of solar system, 437
obliquity of the ecliptic, 362
occultation by the moon, 395
parallax of the moon, 391
parallax of the sun, 371
semidiameter of the moon, 391
velocity of a celestial body, 442
Albategnius, semidiameter of the moon,
Aldebaran, 62
Algol, 6r
cycle of changes of, 344
velocity of, 349
Altair, 65
ATM
Altitude, 74
of pole, 103
Amic , stellar photography, 441
Anderson, Dr., variable star, 345
Andromeda, 61
nebula in girdle of, 358
Andromedae y, colour of, 356
Andromedes, the, 436
Angles, instruments for measuring, 21
measurement of, 16
Angstrom, constitution of the sun, 373
Angular magnitude, explanation of, 2
Aphelion, 208
Apian, comet of, 310
Apparent areas, law of, 2
magnitudes, law of, 2
Aquila, 65
Arago, periodicity of meteor showers,
theory of the zodiacal light, 452
Aratus, mention of a red star, 440
on nebulae, 449
Archimedes, semidiameter of sun, 368
Arcturus, 64
Argelander, catalogues of stars, 438, 439
description of the zodiacal light, 451
motion of the solar system, 437
proper motion of stars, 447
size of small planets, 401
Ariel, 424
Aristarchus of Samos, semidiameter 01
sun, 368
Aristotle, moon's libration, 392
Arnold, Jupiter's satellites, 407
Asten, Von, mass of Mercury, 376
mass of Uranus, 423
Astronomical instruments, i
Astronomische Nachrichten, 361
Astronomy, definition of, i
Atmosphere, effect of the, 166
height of the, 47
the, 46
454
Index.
AUR
Auriga, 61
Auwers, diameter of Venus, 379
ellipticity of Venus, 379
parallax of a Canis minoris, 444
parallax of 61 Cygni, 445
parallax of 34 Groombridge, 443
parallax of 1830 Groombridge, 444
parallax of Lalande 21258, 444
proper motion of stars, 447
semidiameter of sun, 369
Axis, optic, 23
Azimuth, error of, 88
of sun, measured by upright rod, 117
BACKLUND, mass of Mercury, 376
motion of Encke's comet, 433
Bailly, masses of Jupiter's satellites, 409
Baily, density of the earth, 387 _
Bakhuyzen, obliquity of the ecliptic, 363
rotation of Mars, 398
Ball, de, motion of solar system, 437
parallax of 2 1516, 444
Ball, parallax of 6 Cygni B, 445
parallax of 61 Cygni ; 445
parallax of Groombridge 1618, 444
Baranowski, elements of Biela's comet,
43 x
Barnard, diameters of Jupiter's satellites,
410
diameters of small planets, 401
fifth satellite of Jupiter, 292, 407
measures of Saturn's system, 416
Bayer, ellipticity of the earth, 385
maps of stars, 58
Becquerel, E., constitution of the sun,
Beehive, the, 339
Beer and Madler, map of the moon, 394
surface of Jupiter, 406
surface of Mercury, 377
Bellamy, diameter of Jupiter, 403
ellipticity of Jupiter, 40 }
Berliner Jahrbuch, ephemeris of minor
planets, 299
Bessel, coefficient of refraction, 367
diameter of Jupiter, 403
diameter of Mars, 397
diameter of Mercury, 375
diameter of Saturn, 412
ellipticity of Jupiter, 403
ellipticity of Saturn, 412
equation of the centre, 383
mass of Jupiter, 405
mass of the moon, 391
mass of Saturn, 413
mass of Saturn's ring, 417
measures of Saturn's rings, 415
obliquity of the ecliptic, 362
parallax of 61 Cygni, 445
plane of Saturn's ring, 417
Pleiades, the, 126
precession of the equinoxes, 364
proper motion of stars, 446
BRU
Bessel, rotation of Jupiter, 404
rotation of Mercury, 376
semidiameter of the sun, 369
tails of comets, 434
Betelgeuze, 62
Bianchini, rotation of Venus, 380
Biela's comet, 319, 430
and meteors, 319, 432
next return of, 432
period of revolution, 320
Biot, appearance of Halley's comet, 430
on comets, 428
Birmingham, J., coloured stars, 441
Bode, law of, 294
lisc of double stars, 447
Bond, G. P., brilliancy of a Centauri,
44
brilliancy of Jupiter, 406
brilliancy of the moon, 395
brilliancy of Venus, 380
discovery of Hyperion, 420
dusky ring of Saturn, 415
moon, albedo of the, 395
nebulae, 450
physical theory of comets, 433
rings of Saturn, 417
Bond, W. C., measures of Saturn's rings,
4*5
ring of Satur" 1 , 417
thickness of Saturn's rings, 416
Bootes, 63
Boss, motion of solar system, 437
Bouvard, great inequality of Salutn,
412
mass of Jupiter, 405
mass of Saturn, 413
mass of Uranus, 423
observation of Encke's comet, 432
tables of Saturn, 412
tables of Uranus, 295
theory of Neptune, 425
Bradley, aberration of light, 217, 366
axis of Jupiter, 404
coefficient of refraction, 367
diameter of Mercury, 375
diameter of Saturn, 412
measures of Saturn's rings, 415
nutation, 224, 365
obliquity of the ecliptic, 362
revolution of Jupiter's satellites, 408
star catalogue, 438
Bradley and Pound, sun's parallax, 370
Bredichin, tails of comets, 434
Brenner, rotation of Venus, 380
Brightness of a distant object, 3
Brinkley, aberration, 366
coefficient of refraction, 367
nutation, 365
obliquity of the ecliptic, 362
Brorsen's comet, 432
appearances of, 432
Briinnow, parallax of 3077 Bradley, 446
parallax of 61 Cygni, 445
parallax of 'n, 370
Plana, lunar equator, 392
mass of the earth, 388
4 6 4
Index.
Plane, horizontal, 73
the invariable, 436
Planets, 53
appearance in telescope, 339
computation of orbit, 300
determination of, 265
discovery of new, 295
distinguished from comets, 310
elements of the movements of, 299
force acting on, 324
inferior, 279
line of nodes, 300
longitude of the perihelion, 300
masses of, 330
mean distance from sun, 267
method of computing masses, 330
method of identifying, 265
motion due to the sun, 322
mutual attraction of, 327
orbits of, 266
periodic time, 267
periodic times constant, 329
periodic variations of, 329
perturbations of, 328
secular variation of, 329
small variation of eccentricity, 330
small variation of inclination of orbits,
330
superior, 279
Planets, minor, 297, 400
diameters of, 401
eccentricity of, 401
general features of, 401
inclinations of, 401
mass of, 401
search for, 297
Pleiades, the, 61
number of, 338
observation of, 67
position at different dates, 114
Pogson, on Biela's comet, 320
light ratio of stars, 445
parallax of 61 Cygni, 445
Poisson, lunar equator, 292
Polar distance, 99
Pole, the, altitude of, 102
day and night at, 149
motion of stars seen from, 149
sun visible at, 150
Pole, celestial, 60
altitude of, 102
movement of, 213
path of, 216
period of revolution, 216
Pole star, 59
change of distance from pole, 216
fixity of, 66
north polar distance of, 69
value of revolution of micrometer
screw found by, 124
Pollux, 62
Pons, observation of Encke's comet, 432
Pons' comet, 433
REF
Pontecoulant, great inequality of
Saturn, 412
position of the invariable plane, 436
Porter, proper motion of stars, 447
Position angle, 351
Pouillet, heating power of the sun, 373
Pound, diameter of Jupiter, 403
ellipticity of Jupiter, 403
measures of Saturn's rings, 415
Powalki, diameter of Venus, 379
secular diminution of the obliquity of
the ecliptic, 363
sun's parallax, 371
Praesepe, the, 339
Pratt, rotation of Jupiter, 404
Prevost, motion of solar system, 437
Pritchard, brilliancy of stars, 440
lunar equator, 392
parallax of a Cassiopeise, 443
parallax of 61 Cygni, 446
parallax of a Ursae minoris, 443
photographic determinations, 446
semidiameter of moon, 391
wedge photometer, 343
Proctor, chart of Mars, 399
rotation of Mars, 397
Protractor, 18
Ptolemy 2 duration of the year, 381
equation of the centre, 383
evection of the moon, 388
longitude of the perihelion, 382
magnitudes of the stars, 439
obliquity of the ecliptic, 362
parallax of the moon, 390
precession of the equinoxes, 364
proper motion of the stars, 446
red stars, 441
semidiameter of the moon, 391
semidiameter of the sun, 368
sun's parallax, 369
twilight, 368
QUARANTIDS, the, 436
Quetelet, periodicity of the Per-
seids, 435
RADIAN, 19
. magnitude of, 20
Radiant points, 435
Radius vector, 301
Rahts, orbit of Tuttle's comet, 430
Ramsay, on helium, 198
Ranyard, constitution of sun, 374
total solar eclipses, 374
Rayet, stellar photography, 443
Reading an angle, method of, 26
Refraction, 47, 367
atmospheric, 47
computation of, 51
effect on length of day, 156
effect on sun at horizon, 129
effect on sun's disc, 133
Index.
465
REF
Refraction, formula for, 108
law of, 48
law of atmospheric, 52
table of, 52
Regiomontanus, obliquity of the ecliptic,
362
Regulus ? 63
Respighi, constitution of the sun, 274
Rhea, 419
Right ascension, 82
how determined, 92
how measured, 83
origin of, 167
Roberts, parallax of a Centauri, 445
remarkable nebulae, 451
koemer, on aberration, 366
Roman indiction, 251
Rosenberger, elements of Halley's comet,
429
Ross, Lord, heat from the moon, 396
on nebulae, 450
Rossetti, heating power of the sun, 373
QABINE, ellipticity of the earth, 385
Sampson, R. A., constitution of the
sun, 374
5xros, the, 21
Sxros, the, 250
Saturn, 411
albedo of, 414
brilliancy of, 414
density of, 294
diameter of, 293, 412
distance of, 293
elements of, 411
ellipticity of, 413
great inequality of, 411
mass of, 413
period of revolution, 293
period of rotation, 294
rotation of. 413
satellites of, 418
rabies of, 412
Saturn's rings, 293, 414
ansae of, 293
constitution of, 294
mass of, 417
plane of, 416
position of, 294
revolution of, 417
stability of, 418
Savary, orbit of Ursae majoris, 449
Schaeberle, theory of comets, 434
Schafarik, visibility of Venus, 381
Scheiner, rotation of sun, 372
spectra of nebulae, 451
spectroscopic observations of comets,
434
stellar spectroscopy, 442
Schiaparelli, axis of rotation of Mars,
39?
dia
diameter of Uranus, 422
ellipticity of Uranus, 423
orbit of Perseids, 320, 435
SOL
Schiaparelli, revolution of Venus, 275
rotation of Venus, 380
rotation of Mercury, 376
surface of Mars, 399
theory of shooting stars, 455
Schjellerup, coloured stars, 441
Schmidt, changes of moon's surface, 395
Schmidt, Jul., diameter of Mars, 397
map of the moon, 394
rotation of Mars, 398
twilight, 368
Schmidt, J. F., zodiacal light, 451
SchOnfeld, on nebulae, 450
catalogue of variable stars, 440
star catalogue, 438
Schroter, changes in moon's surface, 395
diameter of Dione, 419
diameter of Jupiter, 403
diameter of Rhea, 419
diameter of Venus, 378
ellipticity of Mercury, 375
motion of perisaturnium of Rhea, 419
plane of the equator of Mercury, 377
rotation of Jupiter, 404
rotation of Venus, 380
surface of Jupiter, 406
surface of Mercury, 278, 377
topography of the moon, 394
Schultz, on nebulae, 450
Schur, ellipticity of Jupiter, 403
mass of Jupiter, 405
parallax of 70 / Ophiuchi, 445
Schwabe, elements of sun's rotation, 372
sun-spots, 374
Schweizer, parallax of CEltzen 17415,
Scintillation, 441
Screw, micrometer, 120
Seasons, changes in length of, 186
Secchi, constitution of the sun, 374
stellar spectroscopy, 340, 442
Second, .definition of a, 17
Seeliger, diameter of Uranus, 422
Seidel, brilliancy of Mars, 399
brilliancy of Jupiter, 406
brilliancy of Saturn, 414
Serret, rotation of the earth, 386
Shadow, cast by the sun, 118
of upright rod, motion of, 116
Sighting, 21
Sirius, 62
brilliancy of, 439
change of polar distance, 212
change of right ascension, 210
distance of satellite from, 355
mass of, 356
satellite of, 355
time of revolution of satellite, 355
Smith, Piazzi, heat from the moon, 395
spectrum of zodiacal light, 452
Smyth, W. H., on coloured stars, 441
on double stars, 448
Solar spectrum, 194
Solar system, motion through space, 437
H H
4 66
Index.
SOL
Solstices, the, 142
South pole, 69
Spectroscope, construction of, 39
examination of light in, 40
Spectroscopy, applied to comets, 434
stellar, 441
Spectrum analysis, 39
Spectrum, prismatic, 41
Sphere, celestial, 54
circles of, 72
Spica, 64
Sporer, elements of sun's rotation, 372
sun's rotation, 372
Stampfer, diameter of minor planets, 401
Star clusters, 338
globular, 339
in sword handle of Perseus, 339
Star showers, 316
causes of recurrence of, 321
list of principal, 317
path of, 317
radiant of, 316
the Andromedes, 316
Stars, altitude of, 74
annual parallax of, 226
apparent variation of length of day,
1 68
appearance in telescope, 54
catalogues of, 438
change of zenith distance, 101
circumpolar, 74
clock, 174
colour of, 440
conditions of visibility at culmination,
106
distance of nearest, 232
distance from Pole constant, 70
diurnal motion of, 67
fixed, 55
fixed, similarity between sun and, 187
how distinguished, 58
illustration of distance of, 232
law of motion of, 71
lower culmination of, 75
magnitudes of the, 56, 439
method of finding annual parallax,
231
minuteness of annual parallax, 229
motion of, as a body, 66
motion of, uniform, 71
number visible to naked eye, 57
occultation of fixed, 258
parallaxes of the, 443
position of, how described, 83
proper motions of, 345, 446
rate of motion of, 71
real proper motion of, 347
right ascension of, 95
setting of, 74
shooting, 312
spectra of, 340
telescopic appearance of, 340
telescopic, rendered visible, n
temporary, 345
STR
Stars, time of one revolution, 72
upper culmination of, 75
variable, 344, 440
Stars, double, 349, 351, 447
colours of, 356
determination of masses, 355
dimensions of orbits, 354
elliptical orbits of, 354
motion of, 352
mutual revolution of, 353
number of, 350
number of red, 357
Steinheil, brilliancy of Arcturus, 440
brilliancy . of Sirius, 440
brilliancy of stars, 439
Stellar photometry, 343
Stockwell, limits of obliquity of ecliptic,
363 .
position of the invariable plane, 436
year, duration of the, 382
Stone, coefficient of refraction, 367
diameter of Venus, 378
mass of the moon, 392
nutation, 365
parallax of the moon, 228, 391
parallax of the sun, 370, 371
proper motions of stars, 447
star catalogue, 438
Stoney, G. J., on the physical constitu-
tion of the sun, 200, 373
Struve, H., elements of Japetus, 421
elements of Titan, 420
mass of Mimas, 418
mass of Saturn, 414
motion of solar system, 437
movement of perisaturnium of Dione,
419
movement of perisaturnium of Rhea,
419
periodic time of Mimas, 418
position of Saturn's rings, 417
precession of the equinoxes, 364
semidiameter of moon, 391
Struve, O., mass of Neptune, 427
measures of Saturn's ring, 415
motion of solar system, 437
parallax of Capella, 443
parallax of rj Cassiopeia^, 443
parallax of ju. Cassiopeiae, 443
parallax of 61 Cygni, 445
parallax of Groombridge 1830, 444
parallax of a Lyras, 445
precession of the equinoxes, 364
ring of Saturn, 417
stars, double, 448
Struve, W., aberration, 366
diameter of Dione, 419
diameter of Rhea, 419
diameter of Saturn, 412
double stars, 448
elements of Tethy., 418
parallax of a Lyrse, 445
parallax of a Ursae minoris, 443
pole of the Milky Way, 451
Index.
467
STR
Struve, W. semidiameter of the sun, 369
star catalogue, 438
Struve, W., and Preuss, parallax of a
Ursae minoris, 443
Stumpe, motion of solar system, 437
proper motion of stars, 447
Sun, altitude at culmination not constant,
112
annual motion, in
annular eclipse of, 256
apparent change of size, 134
apparent diameter of, 127
apparent motion during the year, 144
apparent motion of , 1 1 1
appearance of, on the horizon, 133
at zenith, 154
conditions of visibility near pole, 145
constitution of, 373
daily increase of right ascension, 137
declination of, 134
dimensions of, 187
directidn of motion through space, 347
distance of, 183, 306
eclipses of, 255
ellipticity of, 132
gravitation on, 333
heating power of, 373
length of diameter of, 131,
mass of, 330
368
- uiaaa wi, 33^
maximum declination of, 137
motion among the stars, 1 16
motion through space, 346 >"
movement different to that of the
stars, 113
observations of, 1 16
orbit of, 1 80
parallax of, 239, 302, 303, 369
parallax found by the parallax of a
planet, 306
partial eclipse of, 253
path in space, 177
prominences on, 197
right ascension of, 134
rotation of, 372
shape of disc, 131
spectrum of the, 42
a sphere, 189
structure of, 187
table of length of diameter, 179
table of velocities, 182
tables of, 383
total eclipse of, 252, 255
utility of parallax of, 306
yelocity of, 181, 348
velocity variable, 181
volume of, 187
Sun-spots, 187
cavities in photosphere, 192
nucleus of, 192
penumbra of, 192
period of, 190, 193, 374
size of, 1 88
spectrum of, 195
and terrestrial magnetism, 191
TRO
TABLE of length of day, 152
of light and darkness, 153
of refractions, 52
Tacchini, rotation of Venus, 380
Tait, tails of comets, 434
Taurus, 62
Tcheou- K.ong, obliquity of the ecliptic,
362
Telescope, achromatic, 13
brilliancy of object seen through, 9
Cassegrain, 16
equatorial, 67
method of using, 68
polar axis of, 67
focussing a, 14
Gregorian, 16
magnifying power of, 9, 15
most simple form of, 8
Newtonian, 15
reflecting, 14
Rosse's, Earl of, 16
Tempel's comets, 433
Temperature, changes of, on the earth,
X 57
changes of, at the equator, 164
effect on micrometer screw, 127
maximum, during the year, 162
mean, 164
mean, cause of difference of, 165
minimum, during the year, 163
variation of, during the year, 163
Tennant, diameter of Venus, 379
Terby, surface of Mars, 399
Tethys, 418
Thackeray, nutation, 365
Thome, star catalogue, 439
Time, conversion of, into arc, 94
mean, 138
measurement of, 30
sidereal, 77, 138
sidereal, reasons for using, 139
Tisserand, mass of the earth, 388
mass of Mercury, 379
mass of Saturn's ring, 417
Titan, 420
Titania, 425
Todd, sun's parallax, 371
tables of Jupiter's satellites, 410
Tourmaline, 135
Transit instrument, 83
adjustment of, to meridian, 89
chronographic method of observing
with, 96
general appearance of, 91
great circle of, coincident with
meridian, 86
level continually changing, 88
method of finding right ascenrions
with, 96
observing with, 84
Tropic of Cancer, 153
of Capricorn, 154
Tropics, 155
Trouvelot, ring of Saturn, 417
468
Index
TUP
Tupman, sun's parallax, 371
Tuttle's comet, 430
next return of, 430
Twilight, 157, 367
at midsummer, 159
effect in Arctic regions, 161
Tycho Brahe, diameter of Mercury, 375
diameter of Venus, 378
duration of the year, 381
inclination of lunar orbit, 390
longitude of the perihelion, 382
moon's variation, 388
obliquity of the ecliptic, 362
- paraiiax of the moon, 390
precession of the equinoxes, 364
the quadrant, 22
refraction, 367
semidiameter of the moon, 391
semidiameter of the sun, 369
twilight, 368
f TFFERDINGER, length of seconds
\J pendulum, 385
Umbriel, 424
Universe in motion^ 348
Uranometria Oxoniensis, 343
Uranus, albedo of, 424
and Bode's law, 294
brilliancy o f , 423
diameter of 422
discovery of, 295, 421
distance from the sun, 295
elements of, 422
mass of, 423
rotation of, 423
satellites of, 424
Ursa Major, 59
motion of, in a day, 67
planetary nebula in, 359
Ursa Minor, 60
Ursae majoris, , distance of components,
354
period of revolution, 354
VEGA, 65
the future pole star, 216
parallax of, 232
Venus, 268
atmosphere on, 275
brilliancy of, 380
changes in appearance of, 269
diameter of, 274, 378
distance from sun, 268
ellipticity of, 379
evening star, an, 269
greatest brilliancy of, 271
greatest elongation of, 270
inclination of plane to orbit, 275
length of day on, 275
mass of, 379
morning star, a, 258
motion of, 204
WUR
Venus, orbit of, 377
period of revolution, 268
phases of, 270, 380
rotation of, 380
spectrum of, 381
surface of, 275
transits of, 275, 302, 378
velocity of, 268
year of, 275
Vertical, prime, 159
Vesta, 297
albedo of, 401
diameter of, 401
distance from the sun, 297
visibility of, 401
Vico, de, rotation of Venus, 380
Vidal, ellipticity of Venus, 379
Violle, heating power of the sun, 373
Virgo, 64
Vision, line of, 23
Vogel, diameter of Uranus, 422
spectrum of Jupiter, 406
spectrum of Uranus, 424
spectrum of Venus, 381
spectrum of zodiacal light, 452
stellar spectroscopy, 442
surface of Mercury, 377
velocity of a celestial body, 442
WEBB, double stars, 449
map of the moon, 394
Weeks, origin of, 234
Westphalen, elements of Halley's comet,
Wichmann, inertia of the moon, 394
lunar equator, 392
parallax of Groombridge 1830, 444
Williams, on comets, 428
rotation of Saturn, 413
surface of Jupiter, 406
Wilsing, density of the earth, 387
elements of the sun's rotation, 372
Wilson, on sun-spots, 192
Wilson and Gray, heating power of the
sun, 373
Winds, 167
Winnecke, parallax of Lalande 21185,
444
parallax of 2 1516, 444
Winnecke's comet, 432
ellipticity of orbit, 432
next return of, 432
Wislicenus, rotation of Mars, 398
Wolf, R., solar spots, 374
minor planets, 299
Wolfs comet, 433
Wollaston, albedo of the moon, 395
brilliancy of the moon, 395
brilliancy of Sirius, 439
Wright, A. W., spectrum of zodiacal
light, 452
Wright, Thomas. Milky Way, 340
Wurm, mass of Uraaus, 423
Index.
469
YEA
YEAR, Julian, 396
length of, 140, 382
tropical, variation of, 382
Young, constitution of the sun, 373, 374
diameter of Uranus, 422
ellipticicy of Uranus, 423
spectrum ol prominences of the sun,
196
Young, Thomas, theory of the zodiacal
light, 452
"7 E NG E R, brilliancy of Jupiter's satel-
jLt lites, 407
Zenith, 73
distance, 99
distance of sun, means of finding, 117
ZON
Zenlcer, physical theory of comets, 434
Zodiacal light, 451
Zollner, albedo of the moon, 395
albedo of Saturn, 414
brilliancy of Jupiter, 406
brilliancy of Mars, 399
brilliancy of Mercury, 377
brilliancy of the moon, 395
brilliancy of Neptune, 427
brilliancy of Saturn, 414
brilliancy of stars, 439, 440
brilliancy of Uranus, 424
constitution of the sun, 373
physical theory of comets, 434
stellar magnitude of Saturn, 414
Zones of the earth, 153-156
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