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CHAPTER IV.
OF GEOGRAPHY.
Of the figure of the Earth. Its exact dimensions. Its form that of equilibrium
modified by centrifugal force. Variation of gravity on its surface. Statical
and dynamical measures of gravity. The pendulum. Gravity to a spheroid.
Other effects of the Earth's rotation. Trade winds. Determination of geo-
graphical positions-of latitudes-of longitudes. Conduct of a trigonometri-
cal survey. Of maps. Projections of the sphere. Measurement of heights
by the barometer.........
118
CHAPTER V.
OF URANOGRAPHY.
Construction of celestial maps and globes by observations of right ascension and
declination. Celestial objects distinguished into fixed and erratic. Of the
constellations. Natural regions in the heavens. The Milky Way. The Zo-
diac. Of the ecliptic. Celestial latitudes and longitudes. Precession of the
equinoxes. Nutation. Aberration. Refraction. Parallax. Summary view
of the uranographical corrections.....
161
CHAPTER VI.
OF THE SUN'S MOTION.
Apparent motion of the sun not uniform. Its apparent diameter also variable.
Variation of its distance concluded. Its apparent orbit an ellipse about the
focus. Law of the angular velocity. Equable description of areas. Parallax
of the Sun. Its distance and magnitude. Copernican explanation of the
Sun's apparent motion. Parallelism of the Earth's axis. The seasons. Heat
received from the Sun in different parts of the orbit. Mean and true longi-
tudes of the Sun. Equation of the centre. Sidereal, tropical, and anoma-
listic years. Physical constitution of the Sun. Its spots. Faculæ. Probable
nature and causo of the spots. Atmosphere of the Sun. Its supposed clouds.
Temperature at its surface. Its expenditure of heat. Terrestrial effects of
solar radiation........
....... ......
...............
185
CHAPTER VII.
An ellipse about
Motion of its nodes
Of the Moon. Its sidereal period. Its apparent diameter. Its parallax, dis-
tance, and real diameter. First approximation to its orbit.
the Earth in the focus. Its excentricity and inclination.
and apsides. Of occultations and solar eclipses generally. Limits within
which they are possible. They prove the Moon to be an opaque solid. Its
light derived from the Sun. Its phases. Synodic revolution or lunar month.
Of eclipses more particularly. Their phenomena. Their periodical recur-
rence. Physical constitution of the Moon. Its mountains and other super-
ficial features. Indications of former volcanic activity. Its atmosphere.
Climate. Radiation of heat from its surface. Rotation on its own axis.
Libration. Appearance of the Earth from it..........
CHAPTER VIII.
213
Of terrestrial gravity. Of the law of universal gravitation. Paths of projec-
tiles, apparent, real. The Moon retained in her orbit by gravity. Its law of
diminution. Laws of elliptic motion. Orbit of the Earth round the Sun in
accordance with these laws. Masses of the Earth and Sun compared.
Density of the Sun. Force of gravity at its surface. Disturbing effect of the
Sun on the Moon's motion..........
233
CHAPTER IX.
OF THE SOLAR SYSTEM.
Apparent motions of the planets. Their stations and retrogradations. The Sun
their natural centre of motion. Inferior planets. Their phases, periods, etc.
Dimensions and form of their orbits. Transits across the Sun. Superior
planets. Their distances, periods, etc. Kepler's laws and their interpreta-
tion. Elliptic elements of a planet's orbit. Its heliocentric and geocentric
place. Empirical law of planetary distances; violated in the case of Nep-
tune. The ultra-zodiacal planets. Physical peculiarities observable in each
of the planets......... 242
CHAPTER X.
OF THE SATELLITES.
Of the Moon, as a satellite of the Earth. General proximity of satellites to
their primaries, and consequent subordination of their motions. Masses of
the primaries concluded from the periods of their satellites. Maintenance of
Kepler's laws in the secondary systems. Of Jupiter's satellites. Their
eclipses, etc. Velocity of light discovered by their means. Satellites of
Saturn-of Uranus-of Neptune.......... 282
CHAPTER XI.
OF COMETS.
Great number of recorded comets. The number of those unrecorded probably
much greater. General description of a comet. Comets without tails, or with
more than one. Their extreme tenuity. Their probable structure. Motions
conformable to the law of gravity. Actual dimensions of comets. Periodical
return of several. Halley's comet. Other ancient comets probably periodic.
Encke's comet-Biela's-Faye's-Lexell's-De Vico's-Brorsen's-Peter's.
Great comet of 1843. Its probable identity with several older comets. Great
interest at present attached to cometary astronomy, and its reasons. Re-
marks on cometary orbits in general
295
PART II.
OF THE PLANETARY PERTURBATIONS.
CHAPTER XII.
Subject propounded. Problem of three bodies. Superposition of small motions.
Estimation of the disturbing force. Its geometrical representation. Nume-
rical estimation in particular cases. Resolution into rectangular components.
Radial, transversal, and orthogonal disturbing forces. Normal and tangential.
Their characteristic effects. Effects of the orthogonal force. Motion of the
nodes. Conditions of their advance and recess. Cases of an exterior planet
disturbed by an interior. The reverse case. In every case the node of the
disturbed orbit recedes on the plane of the disturbing on an average. Com-
bined effect of many such disturbances. Motion of the Moon's nodes.
Change of inclination. Conditions of its increase and diminution. Average
effect in a whole revolution. Compensation in a complete revolution of the
nodes. Lagrange's theorem of the stability of the inclinations of the plane-
tary orbits. Change of obliquity of the ecliptic. Precession of the equinoxes
explained. Nutation. Principle of forced vibrations........ 326
CHAPTER XIII.
THEORY OF THE AXES, PERIHELIA, AND EXCENTRICITIES.
Variation of elements in general. Distinction between periodic and secular
variations. Geometrical expression of tangential and normal forces. Varia-
tion of the Major Axis produced only by the tangential force. Lagrange's
theorem of the conservation of the mean distances and periods. Theory of
the Perihelia and Excentricities. Geometrical representation of their mo-
mentary variations. Estimation of the disturbing forces in nearly circular
orbits. Application to the case of the Moon. Theory of the lunar apsides
and excentricity. Experimental illustration. Application of the foregoing
principles to the planetary theory. Compensation in orbits very nearly cir-
cular. Effects of ellipticity. General results. Lagrange's theorem of the
stability of the excentricities 354
CHAPTER XIV.
Of the inequalities independent of the excentricities. The Moon's variation and
parallactic inequality. Analogous planetary inequalities. Three cases of
planetary perturbation distinguished. Of inequalities dependent on the excen-
tricities. Long inequality of Jupiter and Saturn. Law of reciprocity between
the periodical variations of the elements of both planets. Long inequality of
the Earth and Venus. Variation of the epoch. Inequalities incident on the
epoch affecting the mean motion. Interpretation of the constant part of these
inequalities. Annual equation of the Moon. Her secular acceleration. Lunar
inequalities due to the action of Venus. Effect of the spheroidal figure of the
Earth and other planets on the motions of their satellites. Of the tides.
Masses of disturbing bodies deducible from the perturbations they produce.
Mass of the Moon, and of Jupiter's satellites, how ascertained. Perturbations
of Uranus resulting in the discovery of Neptune.........
PART III.
OF SIDEREAL ASTRONOMY.
CHAPTER XV.
387/
Of the fixed stars. Their classification by magnitudes. Photometric scale of
magnitudes. Conventional or vulgar scale. Photometric comparison of stars.
Distribution of stars over the heavens. Of the Milky Way or galaxy. Its
supposed form that of a flat stratum partially subdivided. Its visible course
among the constellations. Its internal structure. Its apparently indefinite
extent in certain directions. Of the distance of the fixed stars. Their
annual parallax. Parallactic unit of sidereal distance. Effect of parallax
analogous to that of aberration. How distinguished from it. Detection of
parallax by meridional observations. Henderson's application to a Centauri.
By differential observations. Discoveries of Bessel and Struve. List of stars
in which parallax has been detected. Of the real magnitudes of the stars.
Comparison of their lights with that of the Sun........ 439
CHAPTER XVI.
Variable and periodical stars. List of those already known. Irregularities in
their periods and lustre when brightest. Irregular and temporary stars.
Ancient Chinese records of several. Missing stars. Double stars. Their
classification. Specimens of each class. Binary systems. Revolution round
each other. Describe elliptic orbits under the Newtonian law of gravity.
Elements of orbits of several. Actual dimensions of their orbits. Coloured
double stars. Phænomenon of complementary colours. Sanguine stars.
Proper motion of the stars. Partly accounted for by a real motion of the Sun.
Situation of the solar apex. Agreement of southern and northern stars in
giving the same result. Principles on which the investigation of the solar
motion depends. Absolute velocity of the Sun's motion. Supposed revolution
of the whole sidereal system round a common centre. Systematic parallax
and aberration. Effect of the motion of light in altering the apparent period
of a binary star
467
CHAPTER XVII.
OF CLUSTERS OF STARS AND NEBULE.
Of clustering groups of stars. Globular clusters. Their stability dynamically
possible. List of the most remarkable.
Classification of nebulæ and clusters.
Their distribution over the heavens. Irregular clusters. Resolvability of
nebulæ. Theory of the formation of clusters by nebulous subsidence. Of
elliptic nebulæ. That of Andromeda. Annular and planetary nebulæ.
Double nebulæ. Nebulous stars. Connection of nebula with double stars.
Insulated nebule of forms not wholly irregular. Of amorphous nebulæ.
Their law of distribution marks them as outliers of the galaxy. Nebulæ and
nebulous group of Orion-of Argo-of Sagittarius-of Cygnus. The Magel-
lanic clouds. Singular nebula in the greater of them. The zodiacal light.
Shooting stars
498
PART IV.
OF THE ACCOUNT OF TIME.
CHAPTER XVIII.
Natural units of time. Relation of the sidereal to the solar day affected by
precession. Incommensurability of the day and year. Its inconvenience.
How obviated. The Julian Calendar. Irregularities at its first introduction.
Reformed by Augustus. Gregorian reformation. Solar and lunar cycles.
Indiction. Julian period. Table of chronological eras. Rules for calculating
the days elapsed between given dates. Equinoctial time.........
....................
......
523
APPENDIX.
I. Lists of Northern and Southern Stars, with their approximate Magni-
tudes, on the Vulgar and Photometric Scales
541
........ 543
II. Synoptic Table of the Elements of the Planetary System
III. Synoptic Table of the Elements of the Orbits of the Satellites, so far
IV. Elements of Periodical Comets at their last appearance..
INDEX..