| 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 | | ___ |
