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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 VIL.

Of the Moon. Its sidereal period. Its apparent diameter. Its parallas, dis-

tance, and real diameter. First approximation to its orbit. An ellipse about

the Earth in the focus. Its excentricity and inclination. Motion of its nodes

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.......

213

CHAPTER VIII.

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 planetary perturbation distinguished. Of inequalities dependent on the excen-

parallactic inequality. Analogous planetary inequalities. Three cases of

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....

....... 387

PART III.

OF SIDEREAL ASTRONOMY.

CHAPTER XV.

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 NEBULÆ.

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 nebulæ with double stars.

Insulated nebulæ 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

II. Synoptic Table of the Elements of the Planetary System

543

III. Synoptic Table of the Elements of the Orbits of the Satellites, so far

as they are known

545

IV. Elements of Periodical Comets at their last appearance

548

Index.

...... 549