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Several alterations and additions arc made in this Edition, besides what have been introduced into the Third, to bring it up to the actual state of astronomical discovery. The elements of four new planets (Parthenope, Egeria, Victoria, and Irene) have been added, and improved elements of Iris, Metis, Hebe, and Hygcia, substituted for the provisional elements before given. The remarkable discovery of an additional ring of Saturn, and the curious researches of M. Peters on the proper motion of Sirius, with several minor features, are noticed. Where such additions are introduced in the text, they are indicated by being enclosed in brackets [ ].

J. F. W. IlERSCriEL. London, Aug. 6. 1851.


Preface ...... Page iii—viii.

Introduction ...... I



General notions. Apparent and real motions. Shape and size of the

Earth. The horizon and its dip. The atmosphere. Refraction. Twi-

light. Appearances resulting from diurnal motion. From change of

station in general. Parallactic motions. Terrestrial parallax. That

of the stars insensible. First step towards forming an idea of the

distance of the stars. Copernican view of the Earth's motion. Relative

motion. Motions partly real, partly apparent. Geocentric astronomy,

or ideal reference of phenomena to the Earth's centre as a common

conventional station - - - - - - 10


Terminology and elementary geometrical conceptions and relations. Ter-

minology relating to the globe of the Earth — to the celestial sphere.

Celestial perspective - - - - - - 57


Of the nature of astronomical instruments and observations in general.

Of sidereal and solar time. Of the measurements of time. Clocks,

chronometers. Of astronomical measurements. Principle of telescopic

sights to increase the accuracy of pointing. Simplest application of

this principle. The transit instrument. Of the measurement of

angular intervals. Methods of increasing the accuracy of reading.

The vernier. The microscope. Of the mural circle. The Meridian

circle. Fixation of polar and horizontal points. The level, plumb-

line, artificial horizon. Principle of collimation. Collimators of

Rittenhouse, Eater, and Benzenberg. Of compound instruments with

co-ordinate circles. The equatorial, altitude, and azimuth instrument.

Theodolite. Of the sextant and reflecting circle. Principle of re-

petition. Of micrometers. Parallel wire micrometer. Principle of the

duplication of images. The heliometer. Double refracting eye-piece.

Variable prism micrometer. Of the position micrometer • 74


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 geographical positions — of latitudes — of

longitudes. Conduct of a trigonometrical survey. Of maps. Projec-

tions of the sphere. Measurement of heights by the barometer

Page 125



Construction of celestial maps and globes by observations of right ascen-

sion and declination. Celestial objects distinguished into fixed and

erratic. Of the constellations. Natural regions in the heavens. The

Milky Way. The Zodiac. Of the ecliptic. Celestial latitudes and

longitudes. Precession of the equinoxes. Nutation. Aberration

Refraction. Parallax. Summary view of the uranographical cor-

rections -------- 176


or Tile 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 longitudes of the Sun.

Equation of the centre. Sidereal, tropical, and anomalistic years.

Physical constitution of the Sun. Its spots. Faculte. Probable na-

ture and cause of the spots. Atmosphere of the Sun. Its supposed

clouds. Temperature at its surface. Its expenditure of heat Ter-

restrial effects of solar radation - 205


Of the Moon. Its sidereal period. Its apparent diameter. Its parallax,

distance, 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 par-
ticularly. Their phenomena. Their periodical recurrence. Physical

constitution of the Moon. Its mountains and other superficial 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 - - - - Page 239


Of terrestrial gravity. Of the law of universal gravitation. Paths of

projectiles, 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 - 264



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 interpretation. Elliptic elements of a planet's

orbit. Its heliocentric and geocentric place. Empirical law of planetary

distances; violated in the case of Neptune. The ultra-zodiacal planets.

Physical peculiarities observable in each of the planets - - 275



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- - 324



Great number of recorded comets. The number of those unrecorded

probably much greater. General description of a comet. Comets with-

out 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.

Remarks on cometary orbits in general ... Page 340




Subject propounded. Problem of three bodies. Superposition of small

motions. Estimation of the disturbing force. Its geometrical repre-

sentation. Numerical estimation in particular cases. Resolution into

rectangular components. Radial, transversal, and orthogonal dis-

turbing 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 dis-

turbed orbit recedes on the plane of the disturbing on an average.

Combined effect of many such disturbances. Motion of the Moon's

nodes. Change of inclination. Conditions of its increase and diminu-

tion. Average effect in a whole revolution. Compensation in a com-

plete revolution of the nodes. Lagrange's theorem of the stability of

the inclinations of the planetary orbits. Change of obliquity of the

ecliptic. Precession of the equinoxes explained. Nutation. Prin-

ciple of forced vibrations ..... 378



Variation of elements in general. Distinction between periodic and

secular variations. Geometrical expression of tangential and normal

forces. Variation 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. Geometri-

cal representation of their momentary variations. Estimation of the

disturbing forces in nearly circular orbits. Application to the case

of the Moon. Theory of the lunar apsides and excentricity. Ex-

perimental illustration. Application of the foregoing principles to

the Planetary theory. Compensation in orbits very nearly circular.

Effects of ellipticity. General results. Lagrange's theorem of the

stability of the excentricities ..... 413


Of the inequalities independent of the excentricities. The Moon's va-

riation and parallactic inequality. Analogous planetary inequalities.

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