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CONTENTS.
CHAPTER I.
BELIEFS AND SUPERSTITIONS RELATIVE TO COMETS.
SECTION I.
COMETS CONSIDERED AS PRESAGES.
Comets have been considered in all times and in all countries as signs, precursors
of fatal events-Antiquity and universality of this belief; its probable origin
-Opinion of Seneca; habitual and regular phenomena fail to attract the
attention of the multitude; meteors and comets, on the contrary, make a
profound impression-The moderns in this respect resemble the ancients
contemporary with Seneca-The incorruptible heavens of the ancients, in
contradistinction to the sublunary or atmospheric regions; stars and meteors
-Inevitable confusion of certain celestial or cosmical phenomena with
atmospheric meteors
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SECTION II.
COMETS IN GREEK AND ROMAN ANTIQUITY.
The apparition of a comet or a bolide is a warning from the gods: the Iliad and
the Eneid-Supposed physical influences of comets; Earthquakes in Achaia;
submersion of Helicè and Bura; comet of the year 371-Comets, presages of
happy augury; Cæsar transported to the heavens under the form of a comet;
popular credulity turned to account; opinion of Bayle-Pliny, Virgil, Tacitus,
Seneca The comet of the year 79 and the Emperor Vespasian-Comet of the
year 400 and the siege of Constantinople
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SECTION III.
THE COMETS OF THE MIDDLE AGES.
Prevalence of popular superstitions-Comets announce wars, plagues, the deaths
of sovereigns-Terrors of the year 1000; comets and the end of the world—
Gian Galeazzo Visconti and the comet of 1402-Ambrose Paré; celestial
monsters-Halley's comet and the Turks; origin of the Angelus de Midi-
The comet of 1066 and the conquest of England by the Normans; apostrophe
to the comet by a monk of Malmesbury
SECTION IV.
COMETS FROM THE RENAISSANCE TO THE PRESENT DAY.
Slow improvement in the beliefs relative to comets-Bayle's remarks upon the
comet of 1680-Passage from Madame de Sevigne's letter referring to this comet
and the last hours of Mazarin-In the eighteenth century belief in the super-
natural exchanged for belief in the physical influence of comets-Remains of
cometary superstitions in the nineteenth century-The comet of 1812 and the
Russian campaign; Napoleon I. and the comet of 1769; the great comet of
1861 in Italy
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CHAPTER II.
COMETARY ASTRONOMY UP TO THE TIME OF NEWTON.
COMETS AND THE ASTRONOMERS OF EGYPT AND CHALDEA.
Had the Egyptians and Chaldeans any positive knowledge concerning comets ?-
Apollonius of Myndus; the Pythagoreans considered comets to be true stars
-According to Aristotle they are transient meteors; fatal influence of the
authority of this great philosopher upon the development of Cometary As-
tronomy
COMETARY ASTRONOMY IN THE TIME OF SENECA.
Book vii. of Seneca's Quæstiones Naturales relates to comets-Seneca defends in
it the system of Apollonius of Myndus; he puts forth just views concerning
the nature of comets and their movements-His predictions respecting future
discoveries in regard to comets-The astronomers of the future
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COMETS DURING THE RENAISSANCE AND UP TO THE TIME OF
NEWTON AND HALLEY.
Apian observes that the tails of comets are invariably directed from the sun-
Observations of Tycho Brahé; his views and hypotheses concerning the
nature of comets-Kepler regards them as transient meteors, moving in
straight lines through space-Galileo shares the opinion of Kepler-Systems
of Cassini and Hevelius
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NEWTON DISCOVERS THE TRUE NATURE OF COMETARY ORBITS.
Newton's Principia and the theory of universal gravitation-Why Kepler did not
apply to comets the laws of the planetary movements-Newton discovers the
true system of cometary orbits-Halley and the comet of 1682; prediction of
its return
CHAPTER III.
THE MOTIONS AND ORBITS OF COMETS.
COMETS PARTICIPATE IN THE DIURNAL MOTION
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MOTIONS OF COMETS.
Distinction between comets, nebulæ, and temporary stars-Comets, in their
motions, are subject to stationary periods and retrogressions-The apparent
complications arise, as in the case of the planets, from the simultaneous move-
ment of these bodies and the earth
IRREGULARITIES IN THE MOTIONS OF COMETS.
Comets appear in all regions of the heavens-Effects of parallax-Apparent
motion of a comet, in opposition and in perihelion, moving in a direction
opposite to the earth-Hypothetical comet of Lacaille; calculations of
Lacaille and Olbers concerning the maximum relative movement of this
hypothetical comet and the earth
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THE ORBITS OF COMETS.
Kepler's Laws; ellipses described around the sun; the law of areas-Gravitation,
or weight, the force that maintains the planets in their orbits-The law of
universal gravitation confirmed by the planetary perturbations-Circular,
elliptic, and parabolic velocity explained; the nature of an orbit depends
upon this velocity-Parabolic elements of a cometary orbit
SECTION V.
THE ORBITS OF COMETS COMPARED WITH THE ORBITS OF THE PLANETS.
Differences of inclination, eccentricity, and direction of motion
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SECTION VI.
DETERMINATION OF THE PARABOLIC ORBIT OF A COMET.
Three observations are necessary for the calculation of a parabolic orbit-Cometary
ephemerides; what is meant by an ephemeris; control afforded by the
ulterior observations-Elements of an elliptic orbit-Can the apparition or
return of a comet be predicted ?-State of the question-Refutation by Arago
of a current prejudice.
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CHAPTER IV.
PERIODICAL COMETS.
COMETS WHOSE RETURN HAS BEEN OBSERVED.
How to discover the periodicity of an observed comet and predict its return-
First method: comparison of the elements of the orbit with those of comets
that have been catalogued-Resemblance or identity of these elements; pre-
sumed period deduced from it-Second method: direct calculation of elliptic
elements-Third method
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HALLEY'S COMET.
Discovery of the identity of the comets of 1682, 1607, and 1531; Halley
announces the next return for the year 1758-Clairaut undertakes the calcu-
lation of the disturbing influence exercised by Jupiter and Saturn upon the
comet of 1682; collaboration of Lalande and Mdlle. Hortense Lepaute-The
return of the comet to its perihelion is fixed for the middle of April 1759;
the comet returns on the 13th of March-Return of Halley's comet in 1835;
calculation of the perturbations by Damoiseau and Pontécoulant; progress of
theory-The comet will return to its perihelion in May 1910
ENCKE'S COMET; OR, THE SHORT PERIOD COMET.
Discovery of the identity and periodicity of the comets of 1818, 1805, 1795, and
1786; Arago and Olbers-Encke calculates the ellipse described by the
comet-Dates of twenty returns up to 1873-Successive diminution of the
period of Encke's comet
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BIELA'S OR GAMBART'S COMET.
History of its discovery; its identification with the comet of 1805-Calculation
of its elliptic elements by Gambart-Apparitions previous to 1826-Pecu-
liarities in the apparitions of 1832, 1846, and 1872
FAYE'S COMET.
First comet whose periodicity, without comparison with previous dates, has been
determined by calculation and verified by observation-M. Le Verrier demon-
strates that it has nothing in common with the comet of Lexell-Slight
eccentricity of Faye's comet and great perihelion distance-Dates of its
return-Perturbations in the movements of Faye's comet inexplicable by
gravitation alone: a problem to be solved
BRORSEN'S COMET.
Discovery of the comet of five years and a half period by Brorsen in 1846—Its
supposed identity with the comet of 1532 gives reason to suspect elliptic
elements; calculation of these elements-Returns of the comet in 1851, 1868,
and 1873
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