Page ING THE DIFFERENT cASEs of obliquE SPHERICAL TRIANGLES, BY DRAWING A PER- CHAP. W. INVESTIGATION OF GENERAL RULES FOR CAL- CULATING THE SIDES AND ANGLES OF obliquE-ANGLED SPHERICAL TRIANGLES WITHOUT A PERPENDICULAR • 181 to 1935 2. GENERAL ForMULAE for the solution of the different cases of right-angled spherical triangles 193 to 199 3. General observations on the species and ambiguity - bf the different cases - - - 199. 4. Quadrantal, or rectilateral spherical triangles • 199 5. GENERAL ForMUL.A. for the solutions of the different cases of oblique-angled spherical triangles 200 to 207 CHAP. VI. PRAcTICAL RULEs for the solutions of all the different CHAP. VII. PRACTICAL RULEs for solving the different cases of CHAP. VIII. PRACTICAL RULEs for solving all the different cases of - obLIQUE-ANGLED Sph ERICALTRIANGLEs with a PER- CHAP. IX. PRAcTIcAL RULEs for solving all the different cases of CHAP. X. I. AsTRoNoMICAL DEFINITIONS AND INTRoDuctory II. Astronomical definitions - , 260 to 265 Prob. 1. To turn degrees, or parts of the equator, into time 265 2. To turn time into degrees - . . . 266 3. Given the time under any known meridian to find the corresponding time at Greenwich - . 266 Page Prob. 6. To reduce the declination of the moon, as given in the Nautical Almanac, to any other meridian, and to any given time of the day - - . 27 1 7. To find the time of a star's culminating, or coming to the meridian of Greenwich - - , or 5 s. To find the time of the moon, or any planet's culminating - - - - - . .275 9. Given the observed altitude of a fixed star to find its true altitude - - • 276 10. Given the observed altitude of the sun's lower or upper limb, to find the true altitude of its centre . .277 11. Given the observed altitude of the moon's lower or 12. Given the sun's meridian altitude to find the latitude CHAP. x1. THE APPLICATION OF RIGHT ANGLED spheRICAL TRIANGLES TO ASTRONOMICAL PROBLEMS - - - • 281 Prob. 1. Given the obliquity of the ecliptic and the sun's lon- CHAP. xII. THE APPLICATION of oblique-ANGLED sphe- BLEMS • - - • 298 Prob. 7. Given the sun's declination, and the latitude of the place, to find the apparent time of day-break in the morning, and the end of twilight in the evening . 298 8. Given the day of the mouth, the latitude of the place, the horizontal refraction, and the sun's horizontal parallax, to find the apparent time of his centre ap pearing in the eastern or western part of the horizon 30 Prob. 9. 10. 1 1. 13. 14. 14. 15. Page Given the latitude of the place, the day of the month, The latitude and longitude of a fixed star, or of a declination, et contra - - - , 505 The right ascensions and declinations of two stars, . The places of two stars being given, and their dis tances from a third star, to find the place of this third star - - e ... • - Given the latitude of the place, the sun's declin- the altitude of a known fixed star, to find the hour 16. 16. of the night when the observation was made -> sun's declination being given - - 17. 17. Given the apparent distance of the moon from the determining the true distance of the moon from the 18. CHAP. XIII. Prop. 1. 3. sun, or from a fixed star - e - given, to find the correct longitude. - o To find the fluxions of the several parts of a RIGHT- To find the fluxions of the several parts of a RIGHT Page ANGLED spherical triangle, when one of its legs is a . In any obliquE-ANGLED spherical triangle, supposing an angle and its adjacent side to remain constant, it USE OF THE FLUXIONAL ANALOGIEs. To find when that part of the equation of time de- The error in taking the altitude of a star being given,
CHAP. XIV. MISCELLANEOUS PROPOSITIONs, &c. Prop. 1. 2. 3. Of the FRENch division of the circle, and to turn . 360 Page Prop. 4. To find the excess of the three angles of a spherical triangle, above two right angles - . 366 5. To reduce the angles of a spherical triangle (whose 6. Given two sides of a spherical triangle, and the angle 7. The angles of elevation of two distant objects being 1 BOOK IV. THE THEORY OF NAVIGATION. CHAPTER I. Definitions and Plane sailing - 376 to 380 CHAP. II. Parallel and Middle Latitude sailing . 381 to 383 çHAP. III. Mercator's sailing • - - 383 to 592 t TABLES. I. A Table of the Logarithms of numbers, from an unit to ten thousand . - - 393 to 408 II. A Table of NATURAL sines to every degree and minute of the quadrant - - • 409 to 417 III. A Table of Logan ITHMICAL SINEs and TANGENTs to every degree and minute of the quadrant 418 to 440 IV. A Table of the RErnaction in altitude of the heavenly - bodies - - - • . 441 VI. A Table of the sun’s PARALLAx in altitude . . 441 VII. A Table of the augmentation of the moon's semidiameter . . . . . . . . . . . . 441, VIII. A Table of the right ascensions and declinations of thirty-six principal fixed stars, corrected to the . . . . . . beginning of the year 1822 • * * 442 Five copper-plates at the end of the book. |