Practical Astronomy and Geodesy

and that tract has been introduced in this work because the general theorems are few in number, and have their chief applications in propositions relating to astronomy: the transformations which the theorems are made to undergo are, almost always, investigated for the purpose of rendering them convenient in computations; and, as both the investigations and the examples chosen for illustrating the formulæ generally refer to astronomical subjects, it is evident that facilities are afforded and repetitions avoided by comprehending the tract in a work for which it is immediately required.

There is given a description of the principal instruments employed in making observations; and, after investigations of the formulæ for refraction and parallax, there follow outlines of the methods by which the elements of the solar, lunar, and planetary orbits are determined: these are succeeded by formulæ for computing the apparent displacements of celestial bodies, produced by the actions of the sun, moon, and planets on the earth, and by the motions of the latter. In a chapter on Nautical Astronomy there is given a series of propositions relating to the geographical positions of places on the earth, the determination of local time and the declination of the needle; and it may be right to state, here, that the examples which illustrate the several propositions are taken from the book of sextant-observations made by the students at the Observatory belonging to the Institution. Each computation is made from a single observation, and the instruments used are graduated so as to give thirds or, at best, quarters of minutes: these circumstances will account for the discrepancies, generally amounting however to a few seconds only, in the results.

After an outline of the methods of computing eclipses of the moon and sun, and the occultations of stars by the moon, there are given formulæ and examples for determining terrestrial longitudes by those phenomena; and, in the chapter on geodesy, there are given the methods of executing trigonometrical surveys for the purpose of determining the figure of the earth, with propositions relating to spheroidal arcs and angles, also the manner of making pendulum experiments for a like purpose, together with notices of the principal formulæ relating to terrestrial magnetism.

CONTENTS.

CHAPTER I.

THE EARTH.-PHENOMENA OF THE CELESTIAL BODIES.

FORM OF THE EARTH AND ITS ROTATION ON ITS AXIS. APPA-

RENT MOVEMENT OF THE STARS. REVOLUTION OF THE MOON

ABOUT THE EARTH. - HYPOTHESIS OF THE EARTH'S ANNUAL

MOTION. PHASES OF THE MOON. APPARENT MOVEMENTS OF

THE PLANETS. THE CIRCLES OF THE SPHERE.

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1. Proofs that the surface of the earth is accurately or nearly that

of a sphere

2. Definition of the plane of the horizon, the plane of the

meridian, a meridian line, its north and south points, a

vertical line, the zenith and nadir, a vertical plane, the

prime vertical, the east and west points

3. Diurnal movements of the stars, as they would appear to a

spectator when proceeding from north to south on the

earth's surface

4. Hypothesis that the earth revolves daily on an axis: posi-

tion of that axis

5. The celestial sphere: its assumed rotation

6. Apparent movements of the sun and moon eastward from the

stars inference that the moon revolves monthly about

the earth; and hypothesis that the earth revolves annually

about the sun -

7. The orbits of the earth and moon are differently inclined to

a plane which is perpendicular to the axis of the earth's

rotation

8. The axis of the earth's rotation continues, during the annual

movement, to be nearly parallel to itself -

9. Apparent deviation of the moon from the sun eastward, and

her subsequent approach to him

10. Proof of the globular figure of the moon.- Eclipses -

11. The apparently independent movements of the planets: the

elongations of Mercury and Venus from the sun; and

proof that these planets revolve about the sun within the

earth's orbit

12. The other planets, and the comets, revolve about the sun :

the sun and planets revolve on their axes. The Earth,

Jupiter, Saturn, and Uranus have satellites

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13. The zodiac and its constellations

14. Ancient method of finding the magnitude of the earth

15. The sun, the earth, and the planets constitute a particular

group of bodies in the universe. The celestial sphere

considered as infinitely great with respect to the group

16. Trace of the ecliptic; its poles: circles of celestial longitude

17. Division of the ecliptic into signs.-Direct and retrograde

movements defined

18. The equator and circles of declination; the terrestrial me-

ridians geographical longitude and latitude : celestial

longitude and latitude; right ascension and declination

19. Ecliptical and equatorial systems of co-ordinates

20. Horizontal systems of co-ordinates; azimuth and altitude defined

21. Amplitude defined

CHAP. II.

PROJECTIONS OF THE SPHERE.

NATURE OF THE DIFFERENT PROJECTIONS EMPLOYED IN PRACTICAL

ASTRONOMY AND GEOGRAPHY.· PROPOSITIONS RELATING TO THE

EXAMPLES OF

STEREOGRAPHICAL PROJECTION IN PARTICULAR.

THE ORTHOGRAPHICAL, GNOMONICAL, GLOBULAR, AND CONICAL

PROJECTIONS. MERCATOR'S DEVELOPMENT.

22. The use of diagrams for astronomical investigations -

23. Nature of the stereographical, globular, orthographical,

gnomonical, and conical projections of the sphere

24. The primitive circle defined.—A projected great circle intersects
it in one of its diameters

25. (Prop. I.) Circles of the sphere, passing through the eye, are
projected in straight lines

26. (Prop. II.) If a circle of the sphere be projected on a plane
passing through the centre, the projecting point being on
the exterior of the sphere, and the circle not passing through
it; the projected figure is an ellipse, or a circle -

Cor. 1. When the projecting point is on the surface, the

projected figure is a circle