return my best thanks for communications which would have effectually relieved some doubts I at one period entertained, had I not succeeded in the interim in getting clear of them, as to the compatibility of my views on the subject of the annual equation already alluded to, with the tenor of Newton's account of it. To my valued friend, Professor De Morgan, I am indebted for some most ingenious suggestions on the subject of the mistakes committed in the early working of the Julian reformation of the calendar, of which I should have availed myself, had it not appeared preferable, on mature consideration, to present the subject in its simplest form, avoiding altogether entering into minutiæ of chronological discussion.

Collingwood, April 12, 1849.

J. F. W. HERSCHEL.

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

The horizon and its dip. The atmosphere. Refraction. Twilight. Appear-

ances 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 phænomena to the

Earth's centre as a common conventional station........

CHAPTER II.

Terminology and elementary geometrical conceptions and relations.

logy relating to the globe of the Earth-to the celestial sphere.

perspective

24

Termino-

Celestial

62

CHAPTER III.

Of the nature of astronomical instruments and observations in general. Of

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

ters. 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, Kater, and Benzenberg. Of compound instru-

ments with co-ordinate circles. The equatorial, altitude, and azimuth instru-

ment. Theodolite. Of the sextant and reflecting circle. Principle of repe-

tition. Of micrometers. Parallel wire micrometer. Principle of the dupli-

cation of images. The heliometer. Double refracting eye-piece. Variable

prisma micrometer. Of the position micrometer
76

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......

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. Facula. 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

Its parallax, dis-

An ellipse about

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

tance, and real diameter. First approximation to its orbit.

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..........

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-

The ultra-zodiacal planets. Physical peculiarities observable in each

of the planets.......

tune.

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