| 1 | | [frontespizio] |
| 2 | | [colophon] |
| 1863.0101;1520 | 3 | | Preface |
| 10 | | Contents of Vol. I. |
| | | {titolo} |
| 17 | Chapter I. | - |
| 17 | | The Celestial Sphere-Spherical and Rectangular Co-ordinates |
| 18 | | Spherical co-ordinates |
| 27 | | Transformation of spherical co-ordinates |
| 43 | | Rectangular co-ordinates |
| 48 | | Transformation of rectangular co-ordinates |
| 50 | | Differential variations of co-ordinates |
| 52 | Chapter II. | - |
| 52 | | Time - Use of the Ephemeris - Interpolation - Star Catalogues |
| 53 | | Solar time |
| 59 | | Sidereal time |
| 64 | | Hour angles |
| 68 | | Ephemeris |
| 79 | | Interpolation by differences of any order |
| 91 | | Star catalogues |
| 95 | Chapter III. | - |
| 95 | | Figure and Dimensions of the Earth |
| 97 | | Reduction of latitude |
| 99 | | Radius of the terrestrial spheroid for given latitudes |
| 101 | | Normal, &c |
| 103 | Chapter IV. | - |
| 103 | | Reduction of Observations to the Centre of the Earth |
| 104 | | Parallax |
| 127 | | Refraction - General laws of refraction |
| 130 | | Tables of refraction |
| 136 | | Differential equation of the atmospheric refraction |
| 136 | | Integration of the differential equation with Bouguer's hypothesis |
| 143 | | Integration with Bessel's hypothesis according to the methods of Kramp and Laplace |
| 165 | | Construction of Bessel's Table |
| 171 | | Refraction in right ascension and declination |
| 172 | | Dip of the horizon |
| 180 | | Semidiameters of celestial bodies |
| 183 | | Augmentation of the moon's semidiameters |
| 184 | | Contraction of the sun's and the moon's semidiameters by refration |
| 189 | | Reduction of observed zenith distances to the centre of the earth |
| 193 | Chapter V. | - |
| 193 | | Finding the Time by Astronomical Observations |
| 196 | | 1st Method.—By transits |
| 196 | | 2st Method.—By equal altitudes |
| 206 | | 3st Method.—By a single altitude or zenith distance |
| 213 | | Correction for second differences of zenith distance |
| 217 | | 4th Method.—By the disappearances of a star behind a terrestrial object |
| 218 | | Time of rising and setting of the stars |
| 219 | | Finding the Time at Sea |
| 219 | | 1st Method.—By a single altitude |
| 220 | | 2st Method.—By equal altitudes |
| 223 | Chapetr VI. | - |
| 223 | | Finding the Latitude by Astronomical Observations |
| 223 | | 1st Method.—By meridian altitudines or zenith distances |
| 226 | | Combination of pairs of stars whose merdian zenith distances are nearly equal (see Vol. II, Zenith Telescope) |
| 226 | | Meridian altitudes of circumpolar star |
| 228 | | Meridian zenith distances of the sun near the solstices |
| 229 | | 2st Method.—By a single altitude at a given time |
| 233 | | 3st Method.—By reduction to the meridian when the time is given |
| 235 | | Circummeridian altitudes |
| 244 | | Gauss's method of reducing circummeridian altitudes of the sun |
| 251 | | Limits of the reduction to the meridian |
| 253 | | 4st Method.—By the Polar Star |
| 257 | | 5st Method.—By two altitudes of the same star, or different stars, and the elapsed time between the observations |
| 258 | | General solution |
| 264 | | Caillet's formulae for afixed star or the sun |
| 266 | | Correction of this method for the sun |
| 277 | | 6th Method.—By two altitudes of the same or different stars, with the difference of their azimuths |
| 277 | | 7th Method.—By two different stars observed at the same altitude, when the time is given |
| 279 | | At nearly the same altitude, observed with the zenith telescope |
| 280 | | 8th Method.—By three stars observed at the same altitude (Gauss's method) |
| 286 | | The same by Cagnoli's formulæ |
| 289 | | By a number of stars observed at the same altitude, treated by the Method of Least Squares |
| 293 | | 9th Method.—By the transits of stars over vertical circles (see Vol. II., Transit Instrument in the Prime Vertical) |
| 296 | | 10th Method.—By altitudes near the meridian when the time is not known |
| 296 | (A.) | By two altitudes near the meridian and the chronometer times of the observations, when the rate of the chronometer is known, but not its correction |
| 299 | (B.) | By three altitudes near the meridian and the chronometer times of the observations, when neither the correction nor the rate of the azimuths |
| 301 | (C.) | By two altitudes near the meridian and the difference of the azimuths |
| 302 | (D.) | By three altitudes near the meridian and the differences of azimuths |
| 303 | | 11th Method.—By the rate of change of altitude near the prime vertical |
| 304 | | Finding the Latitude at Sea |
| 304 | | 1st Method.—By meridian altitude |
| 307 | | 2th Method.—By reduction to the meridian when the time is given |
| 307 | | 3th Method.—By two altitudes near the meridian when the time is not known |
| 309 | | 4th Method.—By three altitudes near the meridian when the time is not known |
| 310 | | 5th Method.—By a single altitude at a given time |
| 311 | | 6th Method.—By the change of altitude near the prime vertical |
| 311 | | 7th Method.—By the Polar Star |
| 313 | | 8th Method.—By two altitudes with the elapsed time between them |
| 317 | Chapter VII. | - |
| 317 | | Finding the Longitude by Astronomical Observations |
| 317 | | 1st Method.—By portable chronometers |
| 323 | | Chronometric expeditions |
| 337 | | 2th Method.—By signals |
| 337 | | Terrestrial signals |
| 339 | | Celestial signals |
| 339 | (a) | Bursting of a meteor |
| 339 | (b) | Beginning or ending of an eclipse of the moon |
| 339 | (c) | Eclipses of Jupiter's satellites |
| 339 | (d) | Occultations of Jupiter's satellites |
| 339 | (e) | Transits of the satellites over Jupiter's disc |
| 339 | (f) | Transits of the shadows of the satellites over Jupiter's disc |
| 339 | (g) | Eclipses of the sun, Occultations of star and planets by the moon |
| 341 | | 3d Method.—By the electric telegraph |
| 342 | | Method of star signals |
| 350 | | 4th Method.—By moon culminations |
| 358 | | Peirce's method of correcting the ephemeris |
| 363 | | Combination of moon culminations by weights |
| 371 | | 5th Method.—By azimuths of the moon, or transits of the moon and a star over the same vertical circle |
| 382 | | 6th Method.—By altitudes of the moon |
| 383 | (A.) | By the moon's absolute altitude |
| 386 | (B.) | By equal altitudes of the moon and a star observed with the Zenith Telescope |
| 393 | | 7th Method.—By lunar distances |
| 395 | (A.) | Rigorous method |
| 402 | (B.) | Approximative method |
| 420 | | Finding the Longitude at Sea |
| 420 | | By chronometers |
| 422 | | By lunar distances |
| 423 | | By the eclipses of Jupiter's satellites |
| 423 | | By the moon's altitude |
| 424 | | By occultations of stars by the moon |
| 424 | Chapter VIII. | - |
| 424 | | Finding a Ship's Place at Sea by Circles of Position—Sumner's Method |
| 429 | Chapter IX. | - |
| 429 | | The Meridian Line and Variation of the Compass |
| 436 | Chapters X. | - |
| 436 | | Eclipses |
| 436 | | Solar Eclipses. Prediction for the earth generally |
| 439 | | Fundamental equations |
| 456 | | Outline of the shadows |
| 466 | | Rising and setting limits |
| 475 | | Curves of maximum in horizon |
| 480 | | Northern and southern limits |
| 491 | | Curve of central eclipse |
| 498 | | Limits of total or annular eclipse |
| 505 | | Prediction for a given place |
| 515 | | Correction for atmospheric refraction in eclipses |
| 517 | | Correction for the height of the observer above the level of the sea |
| 518 | | Application of observed solar eclipses to the determination of terrestrial longitudes and the correction of the elements of the computation |
| 542 | | Lunar eclipses |
| 549 | | Occultations of fixed stars by the moon |
| 550 | | Terrestrial longitudes from occultations of stars |
| 557 | | Prediction of occultations |
| 561 | | Limiting parallels |
| 565 | | Occultations of planets by the moon |
| 566 | | Apparent form of a planet's disc |
| 578 | | Terrestrial longitude from occultations of planets |
| 591 | | Transits of Venus and Mercury |
| 592 | | Determination of the solar parallax |
| 593 | | Prediction for the earth generally |
| 601 | | Occultation of a fixed star by a planet |
| 602 | Chapter XI. | - |
| 602 | | Precession, Nutation, Aberration, and Annual Parallax of the Fixed Stars |
| 604 | | Precession |
| 624 | | Nutation |
| 628 | | Aberration |
| 643 | | Parallax |
| 645 | | Mean and apparent places of stars |
| 658 | Chapter XII. | - |
| 658 | | Determination of the Obliquity of the Ecliptic and the Absolute Right Ascensions and Declinations of Stars by Observation |
| 659 | | Obliquity of the ecliptic |
| 665 | | Equinoctial points, and absolute right ascension an declination of the fixed stars |
| 671 | Chapter XIII. | - |
| 671 | | Determination of Astronomical Constants by Observation |
| 671 | | Constants of Refraction |
| 673 | | Constant of solar parallax |
| 680 | | Constant of lunar parallax |
| 687 | | Mean semidiameters of the planets |
| 688 | | Constant of aberration and heliocentric parallax of fixed stars |
| 698 | | Constant of nutation |
| 701 | | Constant of precession |
| 703 | | Motion of the sun in space |
| 708 | | _ |
| 708 | | ___ |
| 1 | | [frontespizio] |
| 2 | | [colophon] |
| 3 | | Contents of Vol. II. |
| 7 | | Plates |
| 9 | | [titolo] |
| 9 | Chapter I. | - |
| 9 | | The Telescope |
| 22 | | |
| 22 | | Magnifying |
| 29 | Chapter II. | - |
| 29 | | Of the Measurement of Angles or Arcs in general—Circles—Micrometers—Level |
| 29 | | Graduated circles |
| 30 | | The vernier |
| 33 | | The reading microscope |
| 37 | | Eccentricity of graduated circles |
| 42 | | Periodic functions |
| 47 | | Ellipticity of the pivot of the alidade |
| 51 | | Errors of graduation |
| 59 | | The filar micrometer |
| 70 | | The level |
| 77 | Chapter III. | - |
| 77 | | Instruments for Measuring Time |
| 77 | | Chronometers |
| 79 | | Comparison of chronometers |
| 84 | | Clocks |
| 86 | | The electro-chronograph |
| 92 | Chapter IV. | - |
| 92 | | The Sextant, and other Reflecting Instruments |
| 94 | | Description of the sextant |
| 95 | | Adjustment of the sextant |
| 101 | | Method of observation |
| 106 | | Method of observation |
| 119 | | The simple reflecting circle |
| 119 | | The repeating reflecting circle |
| 123 | | Theory of its errors |
| 127 | | The prismatic reflecting circle and sextant |
| 131 | Chapter V. | - |
| 131 | | The Transit Instrument |
| 132 | | Description of the transit instrument |
| 138 | | Method of observation |
| 139 | | General formulæ |
| 140 | | The transit instrument in the meridian |
| 141 | | Approximate adjustment |
| 143 | | Equations of the transit instrument in the meridian |
| 146 | | Thread intervals |
| 149 | | Reduction to the middle thread |
| 151 | | Reduction to the mean of the threads |
| 153 | | Level constant |
| 160 | | Collimation constant |
| 169 | | Azimuth constant |
| 174 | | Clock correction |
| 175 | | Determination of the right ascension of stars |
| 176 | | Transits of the moon, sun, and planets |
| 186 | | Effect of refraction in transit observations |
| 187 | | Meridian mark |
| 189 | | Personal equation |
| 193 | | Personal scale |
| 194 | | Probable error of a transit observation |
| 200 | | Application of the method of least squares to the determination of the time with a portable instrument in the meridian |
| 209 | | The transit instrument in any virtual plane |
| 215 | | Finding the time with a portable transit instrument out of the meridian (Hansen's method) |
| 227 | | Application of the method of least squares to the determination of the time with a portable transit instrument in the vertical circle of a circumpolar star (Bessel's method) |
| 238 | | Determination of the geographical latitude by a transit instrument in the prime vertical |
| 271 | | Determination of the declinations of stars by their transits over the prime vertical |
| 282 | Chapter VI. | - |
| 282 | | The Meridian Circle |
| 283 | | Description of the meridian circle |
| 285 | | Nadir point |
| 289 | | Reduction to the meridian |
| 293 | | Horizontal point. Observations by reflection |
| 302 | | Flexure |
| 304 | | Observations of the declination of the moon |
| 309 | | Observations of the declination of a planet, or the sun |
| 310 | | Correction of the observed declination of a planet's or the moon's limb for spheroidal figure and defective illumination |
| 315 | Chapter VII. | - |
| 315 | | The Altitude and Azimuth Instrument |
| 316 | | Description (Pulkowa vertical circle) |
| 319 | | Unioversal instrument |
| 319 | | Theory of these instruments. Azimuths |
| 326 | | Altitudes or zenith distances |
| 333 | | Correction of the observed azimuth and zenith distance of the limb of the moon or a planet for defective illumination |
| 340 | Chapter VIII. | - |
| 340 | | The Zenith Telescope |
| 340 | | Description |
| 342 | | Talcott's method of finding the latitude |
| 344 | | Correction for refraction |
| 346 | | Correction for the level |
| 346 | | Correction for the micrometer |
| 347 | | Reduction to the meridian |
| 347 | | Selection of stars |
| 350 | | Discussion of results |
| 356 | | Combination of the observations by weight |
| 358 | | Determination of the value of a division of the level |
| 360 | | Determination of the value of a revolution of the micrometer |
| 364 | | Extra-meridian observations with the zenith telescope |
| 366 | | Adaptation of the transit instrument as a zenith telescope |
| 367 | Chapter IX. | - |
| 367 | | The Equatoriaql Telescope |
| 367 | | Description (Pulkowa equatorial) |
| 370 | | General theory of the equatorial instrument |
| 371 | | Determination of the instrumental declination and hour angle to the celestial declination and hour angle |
| 373 | | Flexure |
| 375 | | Reduction of the instrumental declination and hour angle to the celestial declination and hour angle |
| 379 | | Adjustment of the equatorial with respect to the pole of the heavens, and determination of the constants |
| 391 | Chapter X. | - |
| 391 | | Micrometric Observations |
| 391 | | The Filar Micrometer—Observation of distance and position angle of two stars |
| 392 | | Correction for errors of the equatorial instrument |
| 395 | | Reduction of the observed position angle to the mean of the position angles at the two stars |
| 397 | | Finding apparent difference of declination and right ascension of two stars |
| 398 | | Correction for proper motion of one of the stars |
| 403 | | The Heliometer |
| 405 | | Descriptio. (Königsberg heliometer) |
| 407 | | General theory of the heliometer |
| 420 | | Method of observation |
| 423 | | Determinations of the constants |
| 432 | | Observations upon the cusps of the sun in a solar eclipse |
| 436 | | The Ring Micrometer |
| 436 | | The Ring Micrometer |
| 441 | | Correction for the proper motion of one of the stars |
| 445 | | Determination of the radius of the ring |
| 450 | | Correction of micrometric observations for refraction |
| 465 | | Correction of micrometric observations for precession, nutation, and aberration |
| 469 | Appendix. | Method of Least Squares |
| 470 | | Errors to which observations are liable |
| 473 | | The arithmetical mean |
| 478 | | The probability curve |
| 485 | | The measure of precision |
| 487 | | The probable error |
| 490 | | The mean of the errors, and the mean error |
| 492 | | The probable error of the arithmetical mean |
| 493 | | Determination of the mean and probable errors of given observations |
| 497 | | Determination of the mean and probable errors of functions of independent observed quantities |
| 504 | | Weight of observations |
| 509 | | Equations of condition from linear functions |
| 512 | | Normal equations |
| 514 | | Mean errors and weights of the unknown quantities |
| 526 | | Equations of condition from non-linear functions |
| 529 | | Treatment of equations of condition when the observations have different weights |
| 530 | | Elimination of the unknown quantities from the normal equations by the method of substitution, according to Gauss |
| 534 | | Determination of the weights of the unknown quantities when the elimination has been effected by the method of substitution |
| 537 | | Independent determination of each unknown quantity and its weights, according to Gauss |
| 541 | | Mean error of a linear function of the unknown quantities |
| 549 | | Conditioned observations |
| 558 | | Criterion for the rejection of doubtful observations |
| 569 | Tables. | List of tables with references to the articles in which they are explained |
| 627 | | Index |
| 632 | | _ |
| 632 | | ___ |
