PREFACE. THE courses of study pursued at the military and naval seminaries of this country have, within a few years, been greatly extended, in order that they might be on a level with the improved state of the sciences relating to those branches of the public service, and also that they might meet the necessity of qualifying officers to conduct the scientific operations which have been undertaken, both at home and abroad, under the authority of the government. An education comprehending the higher departments of mathematics and natural philosophy has also been found necessary for the qualification of such as have been, or may be, appointed to superintend Institutions established in the remoter parts of the British empire for the purpose of promoting the advancement of physical science, and of preserving or extending its benefits among the European, and, in certain cases, the native inhabitants of the countries. An attempt to supply the want of a treatise on the elements of Practical Astronomy and Geodesy is what is proposed in the present work; which, it is hoped, will be found useful to the scientific traveller, and to persons employed in the naval or military service of the country who may accompany expeditions to distant regions, where, with the aid of portable instruments, they may be able to make observations valuable in themselves, and possessing additional importance from their local character. The extent to which the subjects are here carried will probably be found sufficient for the proposed end, and may be useful in preparing the student for the cultivation of the highest branches of astronomical science. A brief notice of the phenomena of the heavens forms the commencement of the work; but no more of the merely descriptive part of astronomy has been given than is necessary for a right understanding of the subjects to which the processes employed in determining the elements are applied. A tract on spherical trigonometry constitutes the third chapter; 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. 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 2. Definition of the plane of the horizon, the plane of the meridian, a meridian line, its north and south points, a 3. Diurnal movements of the stars, as they would appear to a 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 7. The orbits of the earth and moon are differently inclined to 2 3 3 3 4 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 12. The other planets, and the comets, revolve about the sun : 6 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 18. The equator and circles of declination; the terrestrial me- ridians geographical longitude and latitude: celestial 20. Horizontal systems of co-ordinates; azimuth and altitude defined NATURE OF THE DIFFERENT PROJECTIONS EMPLOYED IN PRACTICAL ASTRONOMY AND GEOGRAPHY. PROPOSITIONS RELATING TO THE STEREOGRAPHICAL PROJECTION IN PARTICULAR.-EXAMPLES OF 22. The use of diagrams for astronomical investigations - 23. Nature of the stereographical, globular, orthographical, 24. The primitive circle defined.—A projected great circle intersects 25. (Prop. I.) Circles of the sphere, passing through the eye, are 26. (Prop. II.) If a circle of the sphere be projected on a plane Cor. 2. When the projecting point is infinitely remote, the projection of an oblique circle is an ellipse 27. Schol. The orthographical projection of an ellipse, on any 28. (Prop. III.) If a plane touch a sphere, and from the centre, lines be drawn through the circumference of a small circle NOTE. The fifteen following propositions relate to the stereographical 29. (Prop. IV.) The angle contained between the tangents to two circles of the sphere is equal to the angle contained between |