Napoleon I., XI. 238; XII. 256
Napoleon, Lucien, XI. 238 _n_
Nassir Eddin. _See_ Eddin, Nassir
_Newcomb_, X. 227 _n_; XIII. =283=, =286=, 290
Newton (1643-1727). II. 54; IV. 75; VI. 130, 133, 134; VII. 144, 150;
VIII. 152; =IX.= _passim_; X. 196-200, 211, 213, 215-217, 219, 221;
XI. 228, 229, 231-235, 238, 249; XII. 257; XIII. 273, 299
Niccolini, VI. 132
Nicholas of Cusa (1401-1464), IV. 75
Nonius (1492-1577), III. 69
Norwood (1590?-1675), VIII. =159=; IX. 173
Numa, II. 21
Nunez. _See_ Nonius
_Nyrén_, XIII. 283 _n_
Olbers (1758-1840), XIII. 294
Orange, Prince of, V. 107
Osiander, IV. 74; V. 93
_Palisa_, XIII. 294
Palitzsch (1723-1788), XI. 231
Pemberton, IX. 192
Philolaus (5th cent. B.C.), II. =24=; IV. 75
Piazzi (1746-1826), XIII. 294
Picard (1620-1682), VIII. =155=, =157=, =159-161=, 162; IX. 174;
X. 196, 198, 221
_Pickering_, XIII. 314, 316
Plana (1781-1869), XIII. 286
Plato (428 B.C.?-347 B.C.?), II. =24=, =25=, 26, 51; IV. 70
Plato of Tivoli (_fl._ 1116), III. 66
Pliny (23 A.D.-79 A.D.), II. 45
Plutarch, II. 24; XIII. 301
Pogson (1829-1891), XIII. 316
_Poincaré_, XIII. 288
Poisson (1781-1840), XIII. 286, 293
Pontécoulant (1795-1874), XIII. 286
Porta, VI. 118
Posidonius (135 B.C.?-51 B.C.?), II 45, 47
Pouillet (1791-1868), XIII. 307, 319
Pound, X. 206, 216
Prévost (1751-1839), XII. 265
Pritchard (1808-1893), XIII. 278 _n_, =279=, 316
Ptolemy, Claudius (_fl._ 140 A.D.), II. 25, 27, 32, 37, =46-52=, 53,
54; III. 55, 57, 59-63, 68; IV. 70, 76, 80, 83-87, 89, 91; V. 94,
105; VI. 121, 129, 134; VII. 145; VIII. 161; IX. 194; X. 205;
XI. 236
Ptolemy Philadelphus, II. 31
Purbach (1423-1461), III. =68=; IV. 71
Pythagoras (6th cent. B.C.), I. 11, 14; II. =23=, 28, 47, 51, 54
Recorde (1510-1558), V. 95
Regiomontanus (1436-1476), III. =68=, 69; IV. 70, 71; V. 97, 110
Reimarus. _See_ Bär
Reinhold (1511-1553), V. =93-96=; VII. 139
Reymers. _See_ Bär
Rheticus (1514-1576), IV. =73=, =74=; V. =93=, =94=, 96
Ricardo, II. 47 _n_
Riccioli (1598-1671), VIII. 153
Richer (?-1696), VIII. =161=; IX. 180, 187; X. 199, 221
Rigaud. X. 206 _n_
Roemer (1644-1710), VIII. =162=; X. 198, 210, 216, 220, 225; XIII. 283
Rosse (1800-1867), XIII. 310, 317
Rothmann (_fl._ 1580), V. =97=, =98=, 106
Rudolph II. (the Emperor), V. 106-108; VII. 138, 142, 143
Sabine (1788-1883), XIII. 298
Sacrobosco (?-1256?), III. =67=, 68
St. Pierre, X. 197
Savary (1797-1841), XIII. 309
Scheiner (1575-1650), VI. =124=, 125; VII. =138=; VIII. =153=;
XII. 268
_Schiaparelli_, XIII. 297
Schomberg, IV. 73
Schoner, IV. 74
Schönfeld (1828-1891), XIII. 280
Schroeter (1745-1816), XII. 267, =271=
Schwabe (1789-1875), XIII. 298
Secchi (1818-1878), XIII. 311, 312
_See_, XIII. 320
Seleucus (2nd cent, B.C.), II. 24
Shakespeare, VI. 113
Sharp (1651-1742), X. 198
Slusius, IX. 169
Smith, XII. 251
Snell (1591-1626), VIII. 159; IX. 173
Sosigenes (_fl._ 45 B.C.), II. 21
South (1785-1867), XIII. 306
Struve, F. G. W. (1793-1864), XIII. 279, 309
_Struve, O._, XIII. 283 _n_
Svanberg (1771-1851), X. 221
Sylvester II. _See_ Gerbert
Tabit ben Korra (836-901), III. =56=, =58=, 68; IV. 84
Tamerlane, III. 63
_Tannery_, II. 36 _n_
Thales (640 B.C.?-546 B.C.?), II. =23=; III. 55
Theon (_fl._ 365 A.D.), II. 53
Theophrastus, II. 24
Theophylactus, IV. 72
Thomson, T., X. 208 _n_
_Thomson, William._ _See_ _Kelvin_
Thury, Cassini de. _See_ Cassini de Thury
Timocharis (beginning of 3rd cent. B.C.). II. =32=, 42; IV. 84
Tycho Brahe, _See_ Brahe
Ulugh Begh (1394-1449), III. =63=, 68; IV. 73
Urban VIII. (Barberini), VI. 125, 127, 131, 132
Ursus. _See_ Bär
Varignon, IX. 180 _n_
Vinci, Lionardo da (1452-1519), III. 69
_Vogel_, XIII. 313, 314
Voltaire, II. 21; XI, 229
Wafa, Abul (939 or 940-998), III. =60=, 68 _n_; IV. 85; V. 111
Wallenstein, VII. 149
Walther (1430-1504), III. 68; V. 97
Wargentin (1717-1783), X. 216
Watzelrode, IV. 71
Wefa. _See_ Wafa
Welser, VI. 124
Whewell (1794-1866), XIII. 292
William IV. (Landgrave of Hesse) (1532-1592), V. =97=, =98=, 100,
105, 106, 110
Wilson (1714-1786), XII. =268=; XIII. 298
_Wolf, Max_, XIII. 294
Wolf, Rudolf (1816-1893), XIII. 298
Wollaston (1766-1828), XIII. 299
Wren (1632-1723), IX. 174, 176
Wright, Thomas (1711-1786), XII. 258, 265
_Young_, XIII. 301
Yunos, Ibn (?-1008), III. =60=, 62, 68 _n_
von Zach, XI. 247 _n_
GENERAL INDEX.
_Roman figures refer to the chapters, Arabic to the articles. When
several articles are given under one heading the numbers of the most
important are printed in clarendon type, thus_: =207=. _The names of
books are printed in italics._
Aberration, X. 206, =207-211=, 212, 213, 216, 218; XII. 263;
XIII. 277, 283, 284
Académie Française, XI. 232, 238
Academy of Berlin, XI. 230, 237
Academy of St. Petersburg, XI. 230, 233
Academy of Sciences (of Paris), X. 221, 223; XI. 229-233, 235-237
Academy of Turin, XI. 237, 238
Acceleration, VI. =133=; IX. =171=, 172, 173, 179, 180, 185, 195;
X. 223
_Ad Vitellionem Paralipomena_ (of Kepler), VII. 138
_Alae sive Scalae_ (of Digges), V. 95
Aldebaran, III. 64; XIII. 316 _n_
Alexandrine school, II. 21, 31-33, 36-38, 45, 53
_Alfonsine Tables_, III. =66=, 68; V. 94, 96, 99
Algol, XII. 266; XIII. 314, 315
_Almagest_ (of Ptolemy), II. =46-52=; III. 55, 56, 58, 60, 62, 66, 68;
IV. 75, 76, 83
_Almagest_ (of Abul Wafa), III. 60
_Almagest, New_ (of Kepler), VII. 148
_Almagest, New_ (of Riccioli), VIII. 153
_Almanac, Nautical_, X. 218; XIII. 286, 288, 290
Almanacks, I. 18 _n_; II. 20, 38; III. 64, 68; V. 94, 95, 100;
VII. 136; X. 218, 224; XIII. 286, 288, 290
Altair, III. 64; XIII. 316 _n_
Analysis, analytical methods, X. =196=; XI. 234
Angles, measurement of, I. 7
Annual equation, V. =111=; VII. 145
Annual motion of the earth. _See_ Earth, revolution of
Annual motion of the sun. _See_ Sun, motion of
Annual parallax. _See_ Parallax, stellar
Annular eclipse, II. =43=; VII. 145
Anomalistic month, II. 40
Ἀντιχθών, II. 24
Apex of solar motion, XII. 265
Aphelion, IV. 85
Apogee, II. =39=, 40, 48; III. 58, 59; IV. 85; V. 111; IX. 184 XI. 233
Apparent distance, I. 7
Apple, Newton’s, IX. 170
Apse, apse-line, II. =39=, 40, 48; IV. 85; IX. 183; XI. 235, 236, 242,
246
Arabic numerals, III. 64; V. 96
Arabs, Arab astronomy, II. 46, 53; III. =56-61=, =64=, 66, 68; V. 110;
VIII. 159; XII. 266
Arctic regions, II. 35
Arcturus, XII. 258
Aries, first point of (♈), I. =13=; II. 33, 42; IV. 83 _n_; V. 98,
III; X. 198
Asteroids. _See_ Minor planets
Astrolabe, II. 49; III. 66
Astrology, I. 16, =18=; III. 56; V. 99, 100; VII. 136, 149, 151
_Astronomiae Fundamenta_ (of Lacaille), X. 224
_Astronomiae Instauratae Mechanica_ (of Tycho), V. 107
_Astronomiae Instauratae Progvmnasmata_ (of Tycho), V. 104
Astronomical Society, German, XIII. 280
Astronomical Society, Royal, XII. 256, 263
_Astronomicum Caesareum_ (of Apian), V. 97
_Astronomisches Jahrbuch_, XII. 253
Astronomy, divisions of, XIII. 272
Astronomy, descriptive, XIII. =272=, 273, 294
Astronomy, gravitational, X. =196=; XIII. 272, 273, 286
Astronomy, observational, XIII. 272, 273
Astronomy, origin of, I. =2=
Astronomy, scope of, I. 1
Attraction. _See_ Gravitation
Autumnal equinox, I. II. _See also_ Equinox
Axioms. _See_ Laws of Motion
Axis (of an ellipse), XI. 236, 244, 245
Babylonians. _See_ Chaldaeans
Bagdad, III. 56, 57, 60, 68
Belts of Jupiter, XII. 267
Betelgeux, III. 64
Biela’s comet, XIII. 305
Binary stars. _See_ Stars, double and multiple
Bode’s _Astronomisches Jahrbuch_, XII. 253
Bodily tides, XIII. 292, 293
Brightness of stars. _See_ Stars, brightness of
Brooks’s comet, XIII. 305
Brucia, XIII. 294
Bureau des Longitudes, XI. 238
Cairo, III. 60
Calculus of Variations, XI. 237 _n_
Calendar, Greek, II. =19=, =20=, 21
Calendar, Gregorian, II. =22=; IX. 165 _n_; X. 217
Calendar, Julian, II. =21=, 22; III. 68; IV. 73; IX. 165 _n_;
X. 197 _n_, 217
Calendar, Mahometan, III. 56
Calendar, Roman, II. 21
Caliphs, III. 56, 57, 69
Canals of Mars, XIII. 297
Cartesianism, VIII. 163; IX. 191, 195; XI. 229
Castor, XII. 263, 264, 266
Catalogues of stars. _See_ Star-catalogues
Cavendish experiment, X. 219
Celestial latitude. _See_ Latitude, celestial
Celestial longitude. _See_ Longitude, celestial
Celestial sphere, I. =7=, =8=, 9-11, 13, 14; II. 24, 26, 33, 38-40,
45, 47, 51; III. 64, 67; IV. 78, 80, 83, 88; V. 98, 105; VI. 129;
VIII. 157; X. 198, 207, 208, 214; XII. 257; XIII. 272
Celestial sphere, daily motion of. _See_ Daily motion
Celestial spheres, II. 23, 26, 27, 38, 51, 54; III. 62, =68=; V. 100,
103
Centre of gravity, IX. 186
Centrifugal force, VIII. 158 _n_
Ceres, XIII. 276, 294
Chaldaeans (Babylonians), Chaldaean astronomy, I. 6, 11, 12, =16-18=;
II. 30, 34, 40, 51, 54; III. 56
Chart, photographic, XIII. 280
Chemistry of the sun, XIII. =299-301=, 303
Chinese astronomy, I. 6, 11
Chords, II. 47 _n_
Chromosphere, X. 205; XIII. =301=, 303
Chronometer, X. 226
Circular motion, II. 25, 26, 38, 51; IV. 76; VII. 139; VIII. =158=;
IX. =171-173=. _See also_ Eccentric, Epicycle
Circumpolar stars, I. =9=; II. 35
Clock. _See_ Pendulum clock _and_ Chronometer
Clustering power, XII. 261. _See also_ Condensation of nebulae
_Coelum Australe Stelliferum_ (of Lacaille), X. 223
Collimation error, X. 225 _n_
Comets, I. 1; II. 30; III. 68, =69=; V. 100, 103-105; VI. 127, 129;
VII. 144, =146=; VIII. 153; IX. =190=, 192; X. =200=, 205, 217,
224; XI. 228, =231=, 243, 248, 250; XII. 253, 256, 259;
XIII. 272, =291=, =304=, =305=, 307
Comet, Biela’s, XIII. 305
Comet, Brooks’s, XIII. 305
Comet, Encke’s, XIII. 291
Comet, Halley’s, VII. 146; X. =200=, 205; XI. =231=, 232; XIII. 291,
307
Comet, Lexell’s, XI. 248; XIII. 305
Comet, Olbers’s, XIII. 291
Comet, Pons-Brooks, XIII. 291
Comet, Tebbutt’s, XIII. 305
Comet, Tuttle’s, XIII. 291
_Cometographia_ (of Hevel), VIII. 153
_Commentaries on the Motions of Mars_ (of Kepler), VII. 135 _n_,
139, 141, 150 _n_
_Commentariolus_ (of Coppernicus), IV. =37=; V. 100
_Compleat System of Optics_ (of Smith), XII. 251
Complete induction, IX. 195
Condensation of nebulae, XI. 250; XII. 261; XIII. 318
Conic, conic section, VII. =140= _n_; XIII. 309
Conjunction, II. =43=, 48 _n_; III. 60; V. 110, III; X. 227
Conservation of energy, XIII. 319
Constant of aberration, X. =209=, 210; XIII. 283 _n_
Constellations, I. =12=, 13; II. 20, =26=, 34, =42=; X. =223=
Construction of the heavens, XII. 257. _See also_ Sidereal system,
structure of
Corona, VII. 145; X. 205; XIII. =301=, 303
Counter-earth, II. 24
Crape-ring, XII. 267; XIII. 295
Craters (on the moon), VIII. 153; XIII. 296
Curvature of the earth. _See_ Earth, shape of
Daily Motion (of the celestial sphere), I. 5, =8=, =9=, 10; II. 23,
24, 26, 33, 38, 39, 46, 47; III. 67, 68; IV. =78=, =80=, 83;
V. 98, 105; VI. 129; VIII. 157
D’Alembert’s principle, XI. 232, 237 _n_
Damascus, III. 57
_Darlegung_ (of Hansen), XIII. 286
Day, I. 4, II. 16; II. 47; XIII. 287, 293, 320
Day-and-night, I. 16 _n_
Day-hour, I. 16
Declination, II. =33=, 35, 39; X. 213, 218; XIII. 276
Declination circle, II. 33
_De Coelo_ (of Aristotle), II. 27
Deductive method, inverse, IX. 195
Deferent, II. =39=, 48, 51; III. 68; IV. 86, 87
Degree, I. 7
Deimos, XIII. 295
_De Magnete_ (of Gilbert), VII. 150
_De Motu_ (of Newton), IX. 177, 191
_De Mundi aetherei_ (of Tycho), V. 104
_De Nova Stella_ (of Tycho), V. 100
_De Revolutionibus_ (of Coppernicus), II. 41 _n_; IV. =74-92=;
V. 93, 94; VI. 126
_De Saturni Luna_ (of Huygens), VIII. 154
Descriptive astronomy, XIII. =272=, 273, 294
Deviation error, X. 225 _n_
_Dialogue on the Two Chief Systems_ (of Galilei), VI. 124 _n_,
=128-132=, 133
Differential method of parallax, VI. =129=; XII. 263; XIII. 278
Diffraction-grating, XIII. 299
Dione, VIII. 160
_Dioptrice_ (of Kepler), VII. 138
Direct motion, I. 14
Disturbing force. _See_ Perturbations
Diurnal method of parallax, XIII. =281=, 284
Doctrine of the sphere. _See_ Spherics
Doppler’s principle, XIII. =302=, 313, 314
Double hour, I. 16
Double-star method of parallax. _See_ Differential method of parallax
Double stars. _See_ Stars, double and multiple
Draconitic month, II. =40=, 43
_Durchmusterung_, XIII. 280
Dynamics, VI. 133, 134; IX. 179, 180; XI. 230, 232, 237
_Dynamique, Traité de_ (of D’Alembert), XI. 232
Earth, I. 1, 15, 17; II. 28, 29, 32, 39, 41, 43, 47, 49, 51; III. 66,
69; IV. 80, 86; VI. 117, 121, 133; VII. 136 _n_, 144, 145, 150;
VIII. 153, 154; IX. 173, 174, 179-182, 184, 186, 195; XI. 228, 245;
XIII. 285, 287, 292, 293, 297, 320. _See also_ the following
headings
Earth, density, mass of, IX. 180, 185, 189; X. =219=; XI. 235;
XIII. 282, 294
Earth, motion of, II. 24, 32, 47; IV. =73=, 76, =77=; V. 96. 97,
=105=; VI. 121, 125-127, =129-132=; VIII. 161, 162; IX. 186, 194;
XII. 257. _See also_ Earth, revolution of _and_ rotation of
Earth, revolution of, annual motion of, II. 23, =24=, 28 _n_, =30=,
47; IV. =75=, =77=, =79-82=, =85-88=, 89, 90, =92=; V. 111;
VI. 119, 126, =129=, 131, 133; VII. 139, 142, 146; VIII. 161;
IX. 172, 183; X. 207-210, 212, 227; XI. 235, 236, 240; XII. 263;
XIII. 278, 282, 283
Earth, rigidity of, XIII. 285, 292
Earth, rotation of, daily motion of, II. 23, =24=, 28 _n_; IV. =75=,
=78=, 79 _n_, =80=, 84; V. =105=; VI. 124, 126, =129=, =130=;
IX. 174, 194; X. 206, 207, 213; XIII. 281, 285, =287=, 320
Earth, shape of, II. =23=, =29=, =35=, =45=, =47=, 54; IV. 76; VIII.
=161=; IX. =187=, 188; X. 196, 213, 215, 220, =221=, 222, 223; XI.
229, =231=, 237, 248
Earth, size of, II. =36=, 41, 45, 47, 49; III. 57, 69; IV. 85;
VII. 145; VIII. =159=, 161; IX. 173, 174; X. =221=, 222, 223
Earth, zones of, II. =35=, 47
Earthshine, III. 69
Easter, rule for fixing, II. 20
Eccentric, II. 37, =39=, =40=, 41, =48=, =51=; III. 59; IV. =85=, =89=,
=91=; VII. 139, 150
Eccentricity, II. =39=; IV. 85; VII. =140= _n_; XI. 228, 236, 240,
244-246, 250; XIII. 294, 318
Eccentricity fund, XI. 245
Eclipses, I. 11, 15, =17=; II. 29, 32, 40-42, =43=, 47-49, 54;
III. 57, 68; IV. 76, 85; V. 110; VI. 127; VII. 145, 148: VIII. 162;
X. 201, 205, 210, 216, 227; XI. 240; XIII. 287, 301
Eclipses, annular, II. =43=; VII. 145
Eclipses, partial, II. 43
Eclipses, total, II. =43=; VII. 145; X. 205; XIII. =301=
Ecliptic, I. =11=, 13, 14; II. 26, 33, 35, 36, 38, 40, 42, 51; III.
58, 59, 68; IV. 80, 82-84, 87, 89; V. 111; VIII. 154; X. 203, 209,
213, 214, 227; XI. 235, 236, 244, 246, 250
Ecliptic, obliquity of, I. =11=; II. 35, 36, 42; III. 59, 68; IV. 83,
84; XI. 235, 236
École Normale, XI. 237, 238
École Polytechnique, XI. 237
Egyptians, Egyptian astronomy, I. 6, 11, 12, 16; II. 23, 26, 30, 45;
IV. 75
_Elements_ (of Euclid), III. 62, 66; IX. 165
Elements (of an orbit), XI. =236=, 240, 242, 244, 246; XIII. 275, 276
Elements, variation of. _See_ Variation of elements
Ellipse, II. 51 _n_; III. 66; VII. =140=, 141; IX. 175, 176, 190, 194;
X. 200, 209, 214; XI. 228, 236, 242, 244; XIII. 276, 278, 309
Ellipticity, X. 221
Empty month, II. =19=, 20
Empyrean, III. 68
Enceladus, XII. 255
Encke’s comet, XIII. 291
Encyclopaedia, the French, XI. 232
Energy, XIII. 319
Ephemerides. _See_ Almanacks
_Ephemerides_ (of Regiomontanus), III. 68
Epicycle, II. 37, =39=, 41, 45, =48=, =51=, 54; III. 68; IV. =85-87=,
=89-91=; VII. 139, 150; VIII. 163; IX. 170, 194
_Epitome_ (of Kepler), VI. 132; VII. 144, =145=
_Epitome_ (of Purbach), III. 68
Equant, II. =51=; III. 62; IV. 85, 89, 91; VII. 139, 150
Equation of the centre, II. =39=, 48; III. 60; V. 111
Equator, I. =9=, 10, 11; II. 33, 35, 39, 42; IV. 82, 84; V. 98;
VI. 129, 133; IX. 187; X. 207, 220, 221; XIII. 285
Equator, motion of. _See_ Precession
Equinoctial points, I. =11=, 13; II. 42. _See also_ Aries, first
point of
Equinoxes, I. =11=; II. 39, 42
Equinoxes, precession of. _See_ Precession
_Essai philosophique_ (of Laplace), XI. 238
Ether, XIII. 293, 299
Evection, II. =48=, 52; III. 60; IV. 85; V. 111; VII. 145
Evening star, I. 14. _See also_ Venus
_Exposition du Système du Monde_ (of Laplace), XI. =238=, 242 _n_,
=250=
Faculae, VIII. =153=; XIII. 300, 301, 303
Figure of the earth. _See_ Earth, shape of
Firmament, III. 68
First point of Aries, Libra. _See_ Aries, Libra, first point of
Fixed stars, I. 14. _See_ Stars
Fluxions, IX. 169, 191; X. 196
_Fluxions_ (of Maclaurin), XII. 251
Focus, VII. =140=, 141; IX. 175; XI. 236
Force, VI. 130; IX. =180=, 181
Fraunhofer lines, XIII. =299=, =300=, 303, 304
Front-view construction. _See_ Herschelian telescopes
Full month, II. =19=, 20
Full moon. _See_ Moon, phases of
_Fundamenta_ (of Hansen), XIII. 286
_Fundamenta Astronomiae_ (of Bessel), X. 218; XIII. =277=
Funds of eccentricity, inclination, XI. 245
Galactic circle, XII. 258, 260
Galaxy. _See_ Milky Way
Gauges, gauging. _See_ Star-gauging
Georgium Sidus. _See_ Uranus
Gravitation, gravity, II. 38 _n_; VII. 150; VIII. 158, 161;
=IX.= _passim_; X. 196, 201, 213, 215, 219, 220, 223, 226;
=XI.= _passim_; XII. 264; XIII. 282, 284, 286-293, 309, 319
Gravitational astronomy, X. =196=; XIII. 272, 273, 286
Gravity, variation of, VIII. =161=; IX. 180; X. 199, 217, 221, 223;
XI. =231=
Great Bear, I. 12; XII. 266
Great circle, I. =11=; II. 33, 42; IV. 82, 84
Gregorian Calendar. _See_ Calendar, Gregorian
Grindstone theory, XII. =258=; XIII. 317
_Hakemite Tables_, III. =60=, 62
Halley’s comet, VII. 146; X. =200=, 205; XI. =231=, 232; XIII. 291, 307
_Harmonics_ (of Smith), XII. 251
_Harmony of the World_ (of Kepler), VII. 144
Helium, XIII. 301
Herschelian telescope, XII. 255, 256
_Historia Coelestis_ (of Flamsteed), X. 198
Holy Office. _See_ Inquisition
Horizon, I. 3, 9; II. 29, =33=, 35, 39, 46; VIII. 161; XIII. 285
Horoscopes, V. 99
Hour, I. 16
Hydrostatic balance, VI. 115 _n_
Hyperbola, IX. 190; XI. 236 _n_
Hyperion, XIII. 295
_Ilkhanic Tables_, III. 62
_Il Saggiatore_ (of Galilei), VI. 127
Inclination, III. 58; IV. 89; XI. =228=, =244=, 245, 246, 250;
XIII. 294, 318
Inclination fund, XI. 245
_Index of Prohibited Books_, VI. 126, 132; VII. 145
Indians, Indian astronomy, I. 6; III. 56, 64
Induction, complete, IX. 195
Inequalities, long, XI. 243
Inequalities, periodic, XI. =242=, 243, 245, 247
Inequalities, secular, XI. =242=, 243-247; XIII. 282. _See also_
Perturbations
Inequality, parallactic, XIII. 282
Inferior planets, I. =15=; IV. 87, 88. _See also_ Mercury, Venus
Inquisition (Holy Office), VI. 126, 132, 133
Institute of France, XI. 241
Inverse deductive method, IX. 195
Inverse square, law of, IX. =172-176=, =181=, 195; XI. 233. _See also_
Gravitation
Ionian school, II. 23
Iris, XIII. 281
Irradiation, VI. 129
Island universe theory, XII. =260=; XIII. 317
Japetus, VIII. 160; XII. 267; XIII. 297
Julian Calendar. _See_ Calendar, Julian
Juno, XIII. 294
Jupiter, I. 14-16; 11. 25, 51; IV. 81, 87, 88; V. 98, 99; VI. 121,
127; VII. 136 n, 142, 144, 145, 150; VIII. 154, 156, 162; IX. 172,
181, 183, 185-187; X. 204, 216; XI. 228, 231, 235, 236, 243-245,
248; XII. =267=; XIII. 281, 288, 294, =297=, 305. _See also_ the
following headings
Jupiter, belts of, XII. 267
Jupiter, mass of, IX. 183, 185
Jupiter, rotation of, VIII. =160=; IX. 187; XIII. =297=
Jupiter, satellites of, II. 43; VI. =121=, =127=, 129, 133; VII.
=145=, 150; VIII. 160, 162; IX. 170, 184, 185; X. 210, =216=;
XI. 228, =248=; XII. 267; XIII. 283, =295=, 297
Jupiter’s satellites, mass of, XI. 248
Kepler’s Laws, VII. =141=, =144=, 145, 151; VIII. 152; IX. 169, 172,
175, 176, 186, 194, 195; X. 220; XI. 244; XIII. 294, 309
Latitude (celestial), II. =33=, 42, 43; III. 63; IV. 89
Latitude (terrestrial), III. 68, 69; IV. 73; X. =221=; XIII. 285
Latitude, variation of, XIII. 285
Law of gravitation. _See_ Gravitation
Laws of motion, VI. =130=, =133=; VIII. 152, 163; IX. 171, =179-181=,
183, 186, 194, 195; XI. 232
Leap-year, I. 17; II. =21=, 22
Least squares, XIII. =275=, 276
_Letter to the Grand Duchess_ (of Galilei), VI. 125
Level error, X. 225 _n_
Lexell’s comet, XI. 248; XIII. 305
Libra, first point of (♎), I. =13=; II. 42
Librations of the moon, VI. =133=; X. 226; XI. =237=, 239
_Libros del Saber_, III. 66
Light-equation, XIII. 283
Light, motion of, velocity of, VIII. =162=; X. 208-211, 216, 220;
XIII. 278, 279, =283=, 302. _See also_ Aberration
Logarithms, V. 96, 97 _n_
Long inequalities, XI. 243
Longitude (celestial), II. =33=, 39, 42, 43; III. 63; IV. 87; VII. 139
Longitude (terrestrial), III. 68; VI. =127=, 133; VII. 150; X. 197,
216, =226=
Longitudes, Bureau des, XI. 238
Lunar distances, III. 68 _n_
Lunar eclipses. _See_ Eclipses
Lunar equation, XIII. 282
Lunar theory, II. =48=, 51; V. 111; VII. 145; VIII. 156; IX. =184=,
192; X. =226=; XI. =228=, 230, 231, =233=, =234=, =240=, =241=,
242, 248; XIII. 282, =286=, =287=, 288, 290. _See also_ Moon,
motion of
Lunation, II. =40=. _See also_ Month, synodic
_Macchie Solari_ (of Galilei), VI. =124=, 125
Magellanic clouds, XIII. 307
Magnetism, VII. 150; XIII. 276, =298=
_Magnitudes and Distances of the Sun and Moon_ (of Aristarchus), II. 32
Magnitudes of stars, II. 42; XII. 266; XII. 280, 316. _See also_
Stars, brightness of
Mars, I. 14-16; II. 25, 26, 30, 51; III. 68; IV. 81, 87; V. 108; VI.
129; VII. 136 _n_, 139-142, 144, 145; VIII. 154, 161; IX. 181, 183,
185; X. 223, 227; XI. 235, 245; XII. 267; XIII. 281, 282, 284, 294,
295, =297=. _See also_ the following headings
Mars, canals of, XIII. 297
Mars, mass of, XI. 248
Mars, opposition of, VIII. =161=; XIII. =281=, 284, 297
Mars, rotation of, VIII. 160; XIII. 295, 297
Mars, satellites of, XIII. 295
Mass, IX. =180=, 181, 185
Mass of the earth, sun, Venus.... _See_ Earth, Sun, Venus ... mass of
_Mécanique Analytique_ (of Lagrange), XI. 237
_Mécanique Celeste_ (of Laplace), XI. =238=, 241, 247, 249, 250;
XIII. 292
Medicean Planets. _See_ Jupiter, satellites of
Meraga, III. 62
Mercury, I. 14-16; II. 25, 26, 45, 47, 51; III. 66; IV. 73, 75, 81,
86-89; VI. 121, 124; VII. 136 _n_, 139, 142, 144; IX. 185; XIII.
288, 290, 294, =297=. _See also_ the following headings
Mercury, mass of, XI. 248
Mercury, phases of, VI. 129
Mercury, rotation of, XIII. 297
Mercury, transit of, X. 199
Meridian, II. =33=, 39; III. 57; VI. 127; VIII. 157; X. 207, 218, 221
_Meteorologica_ (of Aristotle), II. 27
Meteors, XIII. 305
Meton’s cycle, II. 20
Metric system, XI. 237
Micrometer, VIII. =155=; XIII. 279, 281
Milky Way, II. 30, 33; VI. 120; XII. =258=, =260-262=; XIII. =317=
Mimas, XII. 255
Minor planets, XI. 250 _n_; XIII. 276, 281, 284, 288, =294=, 295, 297,
318
Minor planets, mass of, XIII. 294
Minute (angle), I. 7
Mira, XII. 266
Mongols, Mongol astronomy, III. 62
Month, I. 4, 16; II. 19-21, 40, 48; IX. 173; XI. 240; XIII. 293, 320.
_See also_ the following headings
Month, anomalistic, II. 40
Month, draconitic, II. =40=, 43
Month, empty, II. =19=, 20
Month, full, II. =19=, 20
Month, lunar, I. =16=; II. 19, 20, 40
Month, sidereal, II. 40
Month, synodic, II. =40=, 43
Moon, I. =1=, 4, 5, 11, 13-16; II. 19-21, 25, 28, 30, 32, 39, 43;
III. 68, 69; IV. 81, 86; V. 104, 105 _n_; VI. =119=, 121, 123, 129,
130, 133; VII. 145, 150; VIII. =153=; IX. 169, 180, 181, 188, 189;
X. 198, 204, 213, 215, =226=; XI 228, 235; XII. 256, 257, =271=;
XIII. 272, 292, 293, =296=, 297, 301, 320. _See also_ the following
headings
Moon, angular or apparent size of, II. 32, =41=, =43=, 46 _n_, 48;
IV. 73, 85, 90; V. 105 _n_
Moon, apparent flattening of, II. 46
Moon, atmosphere of, XIII. 296
Moon, distance of, I. 15; II. 24, 25, 30, =32=, =41=, 43, 45, 48,
=49=, 51; IV. 85, 90; V. 100, 103; IX. 173 185; X. 223; XIII. 293,
320
Moon, eclipses of. _See_ Eclipses
Moon, librations of, VI. =133=; X. 226; XI. =237=, 239
Moon, map of, X. 226; XIII. 296
Moon, mass of, IX. 188, =189= XI. 235
Moon, motion of, I. =4=, 8, 13, 15, 17; II. 20, 24-26, 28, 37, 39,
=40=, 43, 47, =48=, 51; III. 60; IV. 73, 81, 85, 89, 90; V. 111;
VI. 133; VII. =145=, 150; VIII. 156; IX. 169, =173=, =174=, 179,
=184=, 185, 189, 194, 195; X. =201=, 204, 213, =226=; XI. 235,
237, 248; XIII. 287, 290, 297, 320. _See also_ Lunar theory
Moon, origin of, XIII. 320
Moon, parallax of, II. =43=, =49=; IV. 85. _Cf. also_ Moon, distance
of
Moon, phases of, I. =4=, 16, 17; II. 19, 20, 23, =28=, 43, 48;
III. 68, 69; VI. 123
Moon, rotation of, X. 226; XI. 248; XII. 267; XIII. 297
Moon, shape of, II. 23, 28, 46; VI. 119; XI. 237
Moon, size of, II. =32=, 41; IV. 85
Moon, tables of. _See_ Tables, lunar
Moons. _See_ Satellites
Morning star, I. 14. _See also_ Venus
Morocco, III. 61
Motion, laws of. _See_ Laws of motion
Multiple stars. _See_ Stars, double and multiple
Mural quadrant, X. 218, 225 _n_
Music of the spheres, II. =23=; VII. 144
_Mysterium Cosmographicum_ (of Kepler), V. 108; VII. 136, 144
Nadir, III. 64
_Nautical Almanac._ _See_ Almanac, Nautical
Nebula in Argus, XIII. 307
Nebula in Orion, XII. 252, 259, 260; XIII. 311
Nebulae, X. 223; XI. 250; XII. 252, 256, =259-261=; XIII. =306-308=,
=310=, =311=, =317=, =318=, 319, 320
Nebulae, spiral, XIII. 310
Nebular hypothesis, XI. =250=; XIII. 318-320
Nebulous stars, X. 223; XII. 260, 261
Neptune, XIII. =289=, 295, =297=
Neptune, satellite of, XIII. 295
_New Almagest_ (of Kepler), VII. 148
=New Almagest= (of Riccioli), VIII. 153
New moon. _See_ Moon, phases of
New stars. _See_ Stars, new
New Style (N.S.), II. 22. _See also_ Calendar, Gregorian
Newton’s problem, XI. =228=, 229, 249
Newtonian telescope, IX. =168=; XII. 252, 253, 256
Night-hour, I. 16
Node, II. =40=, 43; V. 111; IX. 184; X. 213, 214; XI. =236=, 246
Nubeculae, XIII. 307
Nucleus (of a comet), XIII. 304
Nürnberg school, III. =68=; IV. 73
Nutation, X. 206, 207, =213-215=, 216, 218; XI. 232, 248; XII. 263
Νυχθήμερον, I. 16 _n_
Oberon, XII. 255
Obliquity of the ecliptic. _See_ Ecliptic, obliquity of
Observational astronomy, XIII. 272, 273
Occultations, I. =15=; II. 30
Octaeteris, II. 19
Olbers’s comet, XIII. 291
_Old Moore’s Almanack_, I. 18 _n_
Old Style (O.S.). _See_ Calendar, Julian
Opposition, II. =43=, 48 _n_; III. 60; IV. 87, 88; V. 111; VIII. 161;
XIII. 281, 284, 297
Opposition of Mars, VIII. =161=; XIII. =281=, 284, 297
Optical double stars, XII. 264
_Optics_ (of Gregory), X. 202
_Optics_ (of Newton), IX. 192
_Optics_ (of Ptolemy), II. 46
_Optics_ (of Smith), XII. 251
_Opus Majus_, _Minus_, _Tertium_ (of Bacon), III. 67
_Opuscules Mathématiques_ (of D’Alembert), XI. 233
Orion, nebula in, XII. 252, 259, 260; XIII. 311
_Oscillatorium Horologium_ (of Huygens), VIII. =158=; IX. 171
Pallas, XIII. 294
Parabola, IX. =190=; XI. 236 _n_; XIII. 276
Parallactic inequality, XIII. 282
Parallax, II. =43=, =49=; IV. 85, =92=; V. 98, 100, 110; VI. =129=;
VII. 145; VIII. =161=; X. 207, 212, 223, 227; XII. 257, 258, 263,
264; XIII. 272, 278, 279, 281-284
Parallax, annual, VIII. 161. _See also_ Parallax, stellar
Parallax, horizontal, VIII. 161
Parallax of the moon. _See_ Moon, parallax of
Parallax of the sun. _See_ Sun, parallax of
Parallax, stellar, IV. =92=; V. 100; VI. =129=; VIII. =161=; X. 207,
=212=; XII. 257, 258, 263, 264; XIII. 272, =278=, =279=
Parallelogram of forces, IX. 180 _n_
Parameters, variation of, XI. 233 _n_. _See also_ Variation of elements
Παραπήγματα II. 20
Partial eclipses, II. 43
Pendulum, pendulum clock, V. =98=; VI. =114=; VIII. =157=, 158, =161=;
IX. 180, 187; X. 199, 217, 221, 223; XI. 231. _See also_ Gravity,
variation of
_Pendulum Clock_ (of Huygens), VIII. =158=; IX. 171
Penumbra (of a sun-spot), VI. =124=; XII. 268
Perigee, II. =39=, 40, 48; IV. 85. _See also_ Apse, apse-line
Perihelion, IV. =85=; XI. 231. _See also_ Apse, apse-line
Periodic inequalities. _See_ Inequalities, periodic
Perturbations, VIII. 156; IX. =183=, =184=; X. 200, 204, 224, 227;
=XI.= _passim_; XIII. 282, 293, 294, 297
Phases of the moon. _See_ Moon, phases of
_Phenomena_ (of Euclid), II. 33
Phobos, XIII. 295
Photography, XIII. 274, 279-281, 294, 298, 299, 301, 306
Photometry, XIII. 316. _See also_ Stars, brightness of
Photosphere, XII. =268=; XIII. 303
Physical double stars, XII. 264. _See also_ Stars, double and multiple
Planetary tables. _See_ Tables, planetary
Planetary theory, II. 51, 52, 54; III. 68; IV. 86-90; XI. =228=, 230,
231, 233, =235=, =236=, =242-247=, 248; XIII. 286, =288-290=, 293,
_See also_ Planets, motion of
Planets, I. 13, =14=, 15, 16; II. 23-27, 30, 32, 51; III. 68; IV. 81;
V. 104, 105, 110, 112; VI. 119, 121; VII. 136, 144; VIII. =154=,
155; X. 200; XI. 228, 250; XII. 253, 255, 257, =267=, 271; XIII.
272, 275, 276, 281, 282, 294-296, =297=, 318, 320. _See also_ the
following headings, _and_ the several planets Mercury, Venus, etc.
Planets, discoveries of, XII. =253=, 254, 255, 267; XIII. =289=,
=294=, 295, 318
Planets, distances of, I. 15; II. 30, 51; IV. 81, 86, 87; VI. 117;
VII. 136, 144; IX. 169, 172, 173
Planets, inferior, I. =15=; IV. 87, 88. _See also_ Mercury, Venus
Planets, masses of, IX. 185; XI. 245, 248; XIII. 294. _See also_ under
the several planets
Planets, minor. _See_ Minor planets
Planets, motion of, I. 13, =14=, =15=; II. 23-25, =26=, =27=, 30, =41=,
45, 47, =51=, 52; III. 62, 68; IV. =81=, =86-90=, 92; V. 100, 104,
=105=, 112; VI. 119, 121, 129; VII. =139-142=, =144=, 145, 150, 151;
VIII. 152, 156; IX. 169, =170=, =172-177=, =181=, =183=, 194;
X. 199, 204; XI. 228, 229, 245, =250=; XIII. 275, 276, 282, 294.
_See also_ Planetary theory
Planets, rotation of, VIII. =160=; IX. 187; XI. 228, 250; XII. 267;
XIII. =297=
Planets, satellites of. _See_ Satellites
Planets, stationary points of, I. =14=; II. 51; IV. =88=
Planets, superior, I. =15=; IV. 87, 88. _See also_ Mars, Jupiter, etc.
Pleiades, VI. 120; XII. 260
Poles (of a great circle), II. 33 _n_
Poles (of the celestial sphere), I. =8=, 9, 10; II. 33, 35; IV. 78;
VI. 129; X. 207, 214; XIII. 285
Poles (of the earth), IV. 82; IX. 187; X. 220, 221; XIII. 285
Pole-star, I. 8, 9
Pollux, XII. 266
Pons-Brooks comet, XIII. 291
Postulates (of Ptolemy), II. 47
Postulates (of Coppernicus), IV. 76
Praesepe, XII. 260
Precession (of the equinoxes), II. =42=, =50=; III. 58, 59, 62, 68;
IV. 73, 83, =84=, 85; V. 104, 112; VI. 129; IX. =188=, 192;
X. 213-215, 218, 221; XI. 228, =232=, 248; XIII. 277, 280
_Prima Narratio_ (of Rheticus), IV. =74=; V. 94
Primum Mobile, III. 68
_Principia_ (of Descartes), VIII. 163
_Principia_ (of Newton), IV. 75; VIII. 152; IX. 164, =177-192=, 195;
X. 196, 199, 200, 213; XI. 229, 234, 235, 240
_Principles of Philosophy_ (of Descartes), VIII. 163
_Probabilités, Théorie Analytique des_ (of Laplace), XI. 238
Problem of three bodies. _See_ Three bodies, problem of
_Prodromus Cometicus_ (of Hevel), VIII. 153
Prominences, XIII. =301=, 302, 303
Proper motion (of stars), X. =203=, 225; XII. 257, =265=; XIII. 278, 280
Prosneusis, II. =48=; III. 60; IV. 85
_Prussian Tables_, V. =94=, 96, 97, 99; VII. 139
Pythagoreans, II. 24; IV. 75
Quadrant, V. 99; X. 218, 225 _n_
Quadrature, II. =48=; III. 60; V. 111
Quadrivium, III. 65
_Recherches sur différens points_ (of D’Alembert), XI. =233=, 235
_Recherches sur la précession_ (of D’Alembert), XI. 215
Reduction of observations, X. 198, =218=; XIII. 277
Reflecting telescopes, IX. =168=; XII. 251-255
Refracting telescopes, IX. 168. _See also_ Telescopes
Refraction, II. =46=; III. 68; V. 98, =110=; VII. =138=; VIII. 159,
=160=; X. =217=, 218, 223; XIII. =277=
Relative motion, principle of, IV. =77=; IX. 186 _n_
Renaissance, IV. 70
_Results of Astronomical Observations_ (of John Herschel), XIII. 308
Retrograde motion, I. 14
Reversing stratum, XIII. 303
Reviews of the heavens, XII. 252, 253
Revival of Learning, IV. 70
Rhea, VIII. 160
Rigel, III. 64
Right ascension, II. =33=, 39; X. 198, 218; XIII. 276
Rills, XIII. 296
Rings of Saturn. _See_ Saturn, rings of
Rotation of the celestial sphere. _See_ Daily motion
Rotation of the earth, sun, Mars, etc. _See_ Earth, Sun, Mars, etc.,
rotation of
Royal Astronomical Society. _See_ Astronomical Society, Royal
Royal Society, IX. 166, 174, 177, 191, 192; X. 201, 202, 206, 208;
XII. 254, 256, 259, 263; XIII. 292, 308
_Rudolphine Tables_, V. 94; VII. =148=, 151; VIII. 156
Ruler, I. 16
Running down of the solar system, XIII. 293, 319
_Saggiatore_ (of Galilei), VI. 127
Sappho, XIII. 281
Saros, I. =17=; II. 43
Satellites, VI. =121=, =127=, 129, 133; VII. 145, 150; VIII. =154=,
=160=, 162; IX. 170, 183-185; X. 210, 216; XI. 228, 248; XII. 253,
=255=, =267=; XIII. 272, 283, =295=, 296, 297, 318, 320. _See also_
Jupiter, Saturn, etc., satellites of
Satellites, direction of revolution of, XI. 250; XIII. 295, 318
Satellites, rotation of, XI. 250; XII. 267; XIII. 297
Saturn, I. 14-16; II. 25, 51; IV. 81, 87; V. 99; VI. 123; VII.
136 _n_, 142, 144; VIII. 154, 156; IX. 183, 185, 186; X. 204;
XI. 228, 231, 235, 236, 243-246; XII. 253, =267=; XIII. 288,
=297=. _See also_ the following headings
Saturn, mass of, IX. 185
Saturn, rings of, VI. =123=; VIII. =154=, =160=; XI. 228, =248=;
XII. 267; XIII. =295=, =297=
Saturn, rotation of, XII. 267; XIII. 297
Saturn, satellites of, VIII. =154=, =160=; IX. 184; XI. 228;
XII. 253, =255=, 267; XIII. =295=, 297, 307
Scientific method, II, 54; VI. =134=; IX. =195=
Seas (on the moon), VI. 119; VIII. 153; XIII. 296
Seasons, I. 3; II. =35=, 39; IV. =82=; XI. 245
Second (angle), I. 7
Secular acceleration of the moon’s mean motion, X. =201=;
XI. 233, 234, =240=, 242; XIII. =287=
Secular inequalities. _See_ Inequalities, secular
_Selenographia_ (of Hevel), VIII. 153
_Selenotopographische Fragmente_ (of Schroeter), XII. 271
Sequences, method of, XII. 266
Shadow of earth, moon. _See_ Eclipses
“Shining-fluid” theory, XII. =260=; XIII. 310, 311
Shooting stars. _See_ Meteors
Short-period comets, XIII. 291
Sidereal month, II. 40
Sidereal period, IV. 86, 87
Sidereal system, structure of, XII. 257, =258=, 259-262; XIII. =317=
Sidereal year, II. 42
_Sidereus Nuncius_ (of Galilei), VI. 119-122
“Sights,” V. 110; VIII. =155=; X. 198
Signs of the zodiac, I. 13
Sine, II. 47 _n_; III. 59 _n_, 68 _n_
Sirius, XIII. 316 _n_
Solar eclipse. _See_ Eclipse
Solar system, stability of, XI. 245; XIII. 288, 293
Solstices, I. =11=; II. 36, 39, 42
Solstitial points, I. 11
Space-penetrating power, XII. 258
Spanish astronomy, III. 61, 66
Spectroscope, XIII. 299. _See also_ Spectrum analysis
Spectrum, spectrum analysis, IX. 168; XIII. 273, =299-302=, 303,
=304=, 306, 309, =311-314=, 317, 318
_Sphaera Mundi_ (of Sacrobosco), III. 67
Sphere, attraction of, IX. 173, =182=; XI. 228
Sphere, celestial. _See_ Celestial sphere
Sphere, doctrine of the. _See_ Spherics
Spheres, celestial, crystal. _See_ Celestial spheres
Spheres, music of the, II. =23=; VII. 144
Spherical form of the earth, moon. _See_ Earth, Moon, shape of
Spherics, II. =33=, 34
Spica, II. 42
Spiral nebulae, XIII. 310
Stability of the solar system, XI. 245; XIII. 288, 293
Stadium, II. 36, 45, 47
Star-atlases, star-maps, I. 12 _n_; X. 198, 223; XII. 259, 266;
XIII. 280, 294
Star-catalogues, II. =32=, =42=, =50=; III. 62, =63=; IV. =83=;
V. =98=, =107=, 110, 112; VIII. =153=; X. =198=, =199=, 205,
=218=, =223-225=; XII. 257; XIII. =277=, =280=, 316
Star-clusters, VI. 120; X. 223; XII. 258, =259=, =260=, 261; XIII.
307, 308, 310, 311, 318
Star-gauging, XII. =258=; XIII. 307
Star-groups. _See_ Constellations
Stars, I. 1, 5, 7-10, 12-15, 18; II. 20, 23-26, 29, 30, 32, 33, 39,
40, 42, 45-47, 50; III. 56, 57, 62, 68; IV. 73, 78, 80, 86, 89, 92;
V. 96-100, 104, 105, 110; VI. 120, 121, 129; VIII. 155, 157, 161;
IX. 186 _n_; X. 198, 199, 203, 207-214, 218, 223; XI. 228; XII. 253,
=257-266=, 267; XIII. 272, 277-280, 283, 304, =306-318=, 320.
_See also_ the preceding and following headings
Stars, binary. _See_ Stars, double and multiple
Stars, brightness of, II. 42; XII. 258, 266; XIII. 278, 280, 316,
317. _See also_ Stars, variable
Stars, circumpolar, I. =9=; II. 35
Stars, colours of, XII. 263; XIII. 309
Stars, distances of, I. 7; II. 30, 32, 45, 47; IV. 80, =92=; V. 100;
VI. 117, =129=; XI. 228; XII. 257, 258, 265, 266; XIII. =278=,
=279=, 317. _See also_ Parallax, stellar
Stars, distribution of, XII. 257, 258. _See also_ Sidereal system,
structure of
Stars, double and multiple, XII. 256, =263=, =264=; XIII. 306-308,
=309=, =314=, 320
Stars, magnitudes of, II. 42; XII. 266; XIII. 280, 316. _See also_
Stars, brightness of
Stars, motion of. _See_ Stars, proper motion of, _and_ Daily motion
(of the celestial sphere)
Stars, names of, I. 12, 13; III. 64
Stars, nebulous, X. 223; XII. 260, 261
Stars, new, II. 42; V. 100, 104; VI. 117, 129; VII. 138; XII. 266;
XIII. 312
Stars, number of, I. 7 _n_; XIII. 280
Stars, parallax of. _See_ Parallax, stellar
Stars, proper motion of, X. =203=, 225; XII. 257, =265=; XIII. 278,
280
Stars, rotation of, XII. 266
Stars, spectra of, XIII. 311-314, 317
Stars, system of. _See_ Sidereal system, structure of
Stars, variable, XII. =266=, 269; XIII. 307, 312, =314=, =315=
Stationary points, I. =14=; II. 51; IV. =88=
Stjerneborg, V. 101
Summer solstice, I. 11. _See also_ Solstices
Sun, I. 1, 4, 10, 13, 14, 16; II. 21, 23-26, 28-30, 32, 35, 36, 40,
43, 45, 48, 51; III. 68, 69; IV. 73, 75, 77, 79-82, 85-90, 92;
V. 98, 103, 105, 110, 111; VI. 119, 121, 123, 124, 126, 127, 129,
132; VII. 136, 139-141, 144-146, 150; VIII. 153, 154, 156;
IX. 170, 172-175, 181, 183-186, 188-190, 194; X. 198, 200, 202,
205, 210, 213, 223, 227; XI. 228, 235, 236, 240, 243, 245, 250;
XII. 257, 265, =268=, =269=; XIII. 272, 278, 283, 288, 292-294,
297, =298-303=, 304, 305, =307=, =319=, 320. _See also_ the
following headings
Sun, angular or apparent size of, II. =32=, 38, 39, =41=, 43, 46 _n_,
48; IV. 73, 90; V. 105 _n_
Sun, apparent flattening of, II. 46
Sun, distance of, I. 15; II. 24, 25, 30, =32=, 38, =41=, 43, 45, 48,
=49=, 51; IV. 81, =85=, 86, 87, 90, 92; V. 111; VII. 144, 145;
VIII. 156, =161=: IX. 185, 188; X. 202, 205, 223, =227=; XI. 235;
XIII. 278, =281-284=
Sun, eclipses of. _See_ Eclipses
Sun, heat of, XII. 268, 269; XIII. 303, =307=, =319=
Sun, mass of, IX. 183, 184, =185=, 189; XI. 228; XIII. 282
Sun, motion of, I. 3, 5, 8, =10=, =11=, 13, 15-17; II. 20, 21, 24-26,
35, 37, =38=, =39=, 40, 42, 43, 47, 48, 51; III. 59; IV. 73, =77=,
=79=, 85, 86, 87, 92; V. 104, =105=, 111; VI. 121, 126, 127, 132;
VIII. 160; IX. =186=; X. 223; XI. 235; XII. =265=; XIII. 288
Sun, parallax of, II. 43; V. 98, 110; VII. 145; VIII. =161=; X. 223,
=227=; XIII. =281-284=. _See also_ Sun, distance of
Sun, rotation of, VI. =124=; VII. 150; XI. 250; XIII. 297, =298=, 302
Sun, size of, II. =32=; IV. 85; VII. 145; IX. 173; XIII. 319
Sun, tables of. _See_ Tables, solar
Sun-dials, II. 34
Sun-spots, VI. =124=, 125; VIII. 153; XII. =268=, 269; XIII. =298=,
300, 302, 303
Superior planets, I. =15=; IV. 87, 88. _See also_ Mars, Jupiter, etc.
Svea, XIII. 294
Synodic month, II. =40=, 43
Synodic period, IV. 86, 87
_Synopsis of Cometary Astronomy_ (of Halley), X. 200
_Systema Saturnium_ (of Huygens), VIII. 154
_Système du Monde_ (of Laplace), XI. =238=, 242 _n_, =250=
_Système du Monde_ (of Pontécoulant), XIII. 286
_Table Talk_ (of Luther), IV. 73
Tables, astronomical, III. 58, =60-63=, =66=, 68; IV. 70; V. =94=,
96, 97, 99, 110; VII. 139, =148=; VIII. 156, =160=; X. =216=, 217;
XIII. 277. _See also_ the following headings
Tables, lunar, II. =48=; III. =59=; X. =204=, 216, 217, =226=; XI.
=233=, 234, =241=; XIII. =286=, 290
Tables, planetary, III. =63=; V. 108, 112; VII. 142, 143; X. =204=,
216; XI. 235, =247=; XIII. =288=, 289, 290
Tables, solar, III. =59=; IV. =85=; V. 111; VIII. 153; X. =224=, 225,
226; XI. 235, =247=; XIII. 290
Tables, Alfonsine, III. =66=, 68; V. 94, 96, 99
Tables, Hakemite, III. =60=, 62
Tables, Ilkhanic, III. 62
Tables, Prussian, V. =94=, 96, 97, 99; VII. 139
Tables, Rudolphine, V. 94; VII. =148=, 151; VIII. 156
Tables, Toletan, III. =61=, 66
_Tables de la Lune_ (of Damoiseau), XIII. 286
_Tabulae Regiomontanae_ (of Bessel), XIII. 277
Tangent, III. 59 _n_, 68 _n_
Tartars, Tartar astronomy, III. 63
Tebbutt’s comet, XIII, 305
Telescope, III. 67; VI. =118-124=, 134; VII. =138=; VIII. =152-155=;
IX. =168=; X. 207, 213, 218; XII. 251, =252-258=, 260, 262, =271=;
XIII. =274=, 300, 301, 306, =310=, 317
_Theoria Motus_ (of Gauss), XIII. 276
_Theoria Motuum Lunae_ (of Euler), XI. 233
_Théorie de la Lune_ (of Clairaut), XI. 233
_Théorie ... des Probabilités_ (of Laplace), XI. 238
_Théorie ... du Système du Monde_ (of Pontécoulant), XIII. 286
_Theory of the Moon_ (of Mayer), X. 226
_Theory of the Universe_ (of Wright), XII. 258
Thetis, VIII. 160
Three bodies, problem of, XI. =228=, =230-233=, 235
Tidal friction, XIII. =287=, 292, 293, =320=
Tides, VI. 130; VII. 150; IX. =189=; XI. 228-230, 235, =248=;
XIII. =287=, =292=, 293, 297, =320=
Time, measurement of, I. 4, 5, 16. _See also_ Calendar, Day, Hour,
Month, Week, Year
Titan, VIII. 154
Titania, XII. 255
_Toletan Tables_, III. =61=, 66
Torrid zones, II. 35
Total eclipse, II. =43=; VII. 145; X. 205; XIII. =301=. _See also_
Eclipses
Transit instrument, X. 218, 225 _n_
Transit of Mercury, X. 199
Transit of Venus, VIII. 156; X. =202=, 205, 224, =227=; XIII. =281=,
282, 284
Translations, III. 56, 58, 60, 62, 66, 68
Transversals, V. 110 _n_
Trepidation, III. =58=, 62, 68; IV. 84; V. 112
Trigonometry, II. 37 _n_, 47 _n_; III. 59 _n_, 64 _n_, 68 _n_; IV. 74
Trivium, III. 65
Tropical year, II. 42
Tuttle’s comet, XIII. 291
Twilight, III. 69
Twinkling of stars, II. 30
_Two New Sciences_ (of Galilei), VI. =133=, 134 _n_; VIII. 152
Tychonic system, V. =105=; VI. 127
Umbra (of sun-spots), VI. =124=; XII. 268
Uniform acceleration, VI. 133. _See also_ Acceleration
Uraniborg, V. 101
_Uranometria Nova Oxoniensis_, XIII. 316
Uranus, XII. =253=, 254, 255, 267; XIII. 276, 288, 289, =297=
Uranus, rotation of, XIII. 297
Uranus, satellites of, XI. 250 _n_; XII. =255=, 267; XIII. 272, =295=
Variable stars. _See_ Stars, variable
Variation (of the moon), III. =60=; V. =111=; VII. 145
Variation of elements or parameters, XI. 233 _n_, =236=, 245
Variations, calculus of, XI. 237 _n_
Vega, III. 64
Venus, I. 14-16; II. 25, 26, 45, 47, 51; III. 68; IV. 75, 81, 86, 87;
V. 98, 100, 103; VI. 121, 123; VII. 136 n, 139, 142, 144; VIII.
=154=; IX. 181, 185; X. 223, 227; XI. 235, 245; XII. =267=, 271;
XIII. 282, =297=. _See also_ the following headings
Venus, mass of, XI. 235, 248
Venus, phases of, VI. =123=, 129
Venus, rotation of, VIII 160; XII. 267; XIII. 297
Venus, transits of. _See_ Transits of Venus
Vernal equinox, I. 11. _See also_ Equinoxes
Vernier, III. 69 _n_
Vertical, II. 33; X. 221; XIII. 285
Vesta, XIII. 294
Victoria, XIII. 281
Virtual velocities, XI. 237 _n_
Vortices, VIII. =163=; IX. 178, 195
Wave, wave-length (of light) XIII. 299, 300, 302
Weather, prediction of, II. 20; VII. 136
Week, I. 16
Weight, VI. 116, 130; IX. 180
Weights and Measures, Commission on, XI. 237, 238
_Whetstone of Witte_ (of Recorde), V. 95
Winter solstice, I. 11. _See also_ Solstices
Year, I. 3, 4, 16; II. 19-22, 42, 47; III. 66; V. 111
Year, sidereal, II. 42
Year, tropical, II. 42
_Zadkiel’s Almanack_, I. 18 _n_
Zenith, II. =33=, 35, 36, 46; III, 64; X. 221
Zenith-sector, X. 206
Zodiac, I. =13=; X. 224
Zodiac, signs of the, I. 13
Zodiacal constellations, I. 13
Zones of the earth, II. =35=, 47
FOOTNOTES:
[1] In our climate 2,000 is about the greatest number ever visible at
once, even to a keen-sighted person.
[2] Owing to the greater brightness of the stars overhead they usually
seem a little nearer than those near the horizon, and consequently the
visible portion of the celestial sphere appears to be rather less than
a half of a complete sphere. This is, however, of no importance, and
will for the future be ignored.
[3] A right angle is divided into ninety degrees (90°), a degree into
sixty minutes (60′), and a minute into sixty seconds (60″).
[4] I have made no attempt either here or elsewhere to describe
the constellations and their positions, as I believe such verbal
descriptions to be almost useless. For a beginner who wishes to become
familiar with them the best plan is to get some better informed, friend
to point out a few of the more conspicuous ones, in different parts of
the sky. Others can then be readily added by means of a star-atlas, or
of the star-maps given in many textbooks.
[5] The names, in the customary Latin forms, are: Aries, Taurus,
Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus,
Aquarius, and Pisces; they are easily remembered by the doggerel
verses:—
The Ram, the Bull, the Heavenly Twins,
And next the Crab, the Lion shines,
The Virgin and the Scales,
The Scorpion, Archer, and He-Goat,
The Man that bears the Watering-pot,
And Fish with glittering tails.
[6] This statement leaves out of account small motions nearly or
quite invisible to the naked eye, some of which are among the most
interesting discoveries of telescopic astronomy; see, for example,
chapter X., §§ 207-215.
[7] The custom of calling the sun and moon planets has now died out,
and the modern usage will be adopted henceforward in this book.
[8] It may be noted that our word “day” (and the corresponding word in
other languages) is commonly used in two senses, either for the time
between sunrise and sunset (day as distinguished from night), or for
the whole period of 24 hours or day-and-night. The Greeks, however,
used for the latter a special word, νυχθήμερον.
[9] Compare the French: Mardi, Mercredi, Jeudi, Vendredi; or better
still the Italian: Martedi, Mercoledi, Giovedi, Venerdi.
[10] See, for example, _Old Moore’s_ or _Zadkiel’s Almanack_.
[11] We have little definite knowledge of his life. He was born in the
earlier part of the 6th century B.C., and died at the end of the same
century or beginning of the next.
[12] Theophrastus was born about half a century, Plutarch nearly five
centuries, later than Plato.
[13] _Republic_, VII. 529, 530.
[14] Confused, because the mechanical knowledge of the time was quite
unequal to giving any explanation of the way in which these spheres
acted on one another.
[15] I have introduced here the familiar explanation of the phases of
the moon, and the argument based on it for the spherical shape of the
moon, because, although probably known before Aristotle, there is,
as far as I know, no clear and definite statement of the matter in
any earlier writer, and after his time it becomes an accepted part of
Greek elementary astronomy. It may be noticed that the explanation is
unaffected either by the question of the rotation of the earth or by
that of its motion round the sun.
[16] See, for example, the account of Galilei’s controversies, in
chapter VI.
[17] The =poles= of a great circle on a sphere are the ends of a
diameter perpendicular to the plane of the great circle. Every point on
the great circle is at the same distance, 90°, from each pole.
[18] The _word_ “zenith” is Arabic, not Greek: cf. chapter III., § 64.
[19] Most of these names are not Greek, but of later origin.
[20] That of M. Paul Tannery: _Recherches sur l’Histoire de
l’Astronomie Ancienne_, chap. V.
[21] Trigonometry.
[22] The process may be worth illustrating by means of a simpler
problem. A heavy body, falling freely under gravity, is found (the
resistance of the air being allowed for) to fall about 16 feet in
1 second, 64 feet in 2 seconds, 144 feet in 3 seconds, 256 feet
in 4 seconds, 400 feet in 5 seconds, and so on. This series of
figures carried on as far as may be required would satisfy practical
requirements, supplemented if desired by the corresponding figures
for fractions of seconds; but the mathematician represents the same
facts more simply and in a way more satisfactory to the mind by the
formula s = 16 t^2, where s denotes the number of feet fallen,
and t the number of seconds. By giving t any assigned value, the
corresponding space fallen through is at once obtained. Similarly
the motion of the sun can be represented approximately by the more
complicated formula l = nt + 2 e sin nt, where l is the
distance from a fixed point in the orbit, t the time, and n, e
certain numerical quantities.
[23] At the present time there is still a small discrepancy between the
observed and calculated places of the moon. See chapter XIII., § 290.
[24] The name is interesting as a remnant of a very early superstition.
Eclipses, which always occur near the nodes, were at one time supposed
to be caused by a dragon which devoured the sun or moon. The symbols ☊
☋ still used to denote the two nodes are supposed to represent the head
and tail of the dragon.
[25] In the figure, which is taken from the _De Revolutionibus_ of
Coppernicus (chapter IV., § 85), let D, K, M represent respectively the
centres of the sun, earth, and moon, at the time of an eclipse of the
moon, and let S Q G, S R E denote the boundaries of the shadow-cone
cast by the earth; then Q R, drawn at right angles to the axis of the
cone, is the breadth of the shadow at the distance of the moon. We have
then at once from similar triangles
G K - Q M : A D - G K :: M K : K D.
Hence if K D = _n_. M K and ∴ also A D = _n_. (radius of moon), _n_
being 19 according to Aristarchus, G K-Q M: _n_. (radius of moon)-G K
:: 1 : _n_
_n_ . (radius of moon) - G K
= _n_ G K - _n_ Q M
∴ radius of moon + radius of shadow
= (1 + 1∕_n_) (radius of earth).
By observation the angular radius of the shadow was found to be about
40′ and that of the moon to be 15′, so that
radius of shadow = 8∕3 radius of moon;
∴ radius of moon
= 3∕11 (1 + 1∕_n_) (radius of earth).
But the angular radius of the moon being 15′, its distance is
necessarily about 220 times its radius,
and ∴ distance of the moon
= 60 (1 + 1∕_n_) (radius of the earth),
which is roughly Hipparchus’s result, if _n_ be _any_ fairly large
number.
[26] _Histoire de l’Astronomie Ancienne_, Vol. I., p. 185.
[27] The chief MS. bears the title μεγάλη σύνταξις or
great composition though the author refers to his book elsewhere as
μαθηματικὴ σύνταξις (mathematical composition). The Arabian
translators, either through admiration or carelessness, converted
μεγάλη, great, into μεγίστη, greatest, and hence
it became known by the Arabs as _Al Magisti_, whence the Latin
_Almagestum_ and our _Almagest_.
[28] The better known apparent enlargement of the sun or moon when
rising or setting has nothing to do with refraction. It is an optical
illusion not very satisfactorily explained, but probably due to the
lesser brilliancy of the sun at the time.
[29] In spherical trigonometry.
[30] A table of chords (or double sines of half-angles) for every 1∕2°
from 0° to 180°.
[31] His procedure may be compared with that of a political economist
of the school of Ricardo, who, in order to establish some rough
explanation of economic phenomena, starts with certain simple
assumptions as to human nature, which at any rate are more plausible
than any other equally simple set, and deduces from them a number of
abstract conclusions, the applicability of which to real life has to be
considered in individual cases. But the perfunctory discussion which
such a writer gives of the qualities of the “economic man” cannot of
course be regarded as his deliberate and final estimate of human nature.
[32] The equation of the centre and the evection may be expressed
trigonometrically by two terms in the expression for the moon’s
longitude, _a sin_θ + _b sin_ (2φ-θ), where _a_, _b_ are two numerical
quantities, in round numbers 6° and 1°, θ is the angular distance of
the moon from perigee, and φ is the angular distance from the sun.
At conjunction and opposition φ is 0° or 180°, and the two terms reduce
to (_a_-_b_) _sin_θ. This would be the form in which the equation
of the centre would have presented itself to Hipparchus. Ptolemy’s
correction is therefore equivalent to adding on
_b_ [_sin_θ + _sin_ (2φ - θ)], or 2 _b sin_φ _cos_ (φ-θ),
which vanishes at conjunction or opposition, but reduces at the
quadratures to 2 _b sin_θ, which again vanishes if the moon is at
apogee or perigee (θ = 0° or 180°), but has its greatest value half-way
between, when θ = 90°. Ptolemy’s construction gave rise also to a still
smaller term of the type,
_c sin_ 2φ [_cos_ (2φ + θ) + 2 _cos_ (2φ - θ)],
which, it will be observed, vanishes at quadratures as well as at
conjunction and opposition.
[33] Here, as elsewhere, I have given no detailed account of
astronomical instruments, believing such descriptions to be in general
neither interesting nor intelligible to those who have not the actual
instruments before them, and to be of little use to those who have.
[34] The advantage derived from the use of the equant can be made
clearer by a mathematical comparison with the elliptic motion
introduced by Kepler. In elliptic motion the angular motion and
distance are represented approximately by the formulae _nt_ + 2_e sin
nt_, _a_ (1 - _e cos nt_) respectively; the corresponding formulæ given
by the use of the simple eccentric are _nt + e′ sin nt_, _a_ (1 - _e′
cos nt_). To make the angular motions agree we must therefore take _e′_
= 2_e_, but to make the distances agree we must take _e′ = e_; the two
conditions are therefore inconsistent. But by the introduction of an
equant the formulæ become _nt_ + 2_e′ sin nt_, _a_ (1 - _e′ cos nt_),
and _both_ agree if we take _e′ = e_. Ptolemy’s lunar theory could have
been nearly freed from the serious difficulty already noticed (§ 48) if
he had used an equant to represent the chief inequality of the moon;
and his planetary theory would have been made accurate to the first
order of small quantities by the use of an equant both for the deferent
and the epicycle.
[35] De Morgan classes him as a geometer with Archimedes, Euclid, and
Apollonius, the three great geometers of antiquity.
[36] The legend that the books in the library served for six months as
fuel for the furnaces of the public baths is rejected by Gibbon and
others. One good reason for not accepting it is that by this time there
were probably very few books left to burn.
[37] The data as to Indian astronomy are so uncertain, and the evidence
of any important original contributions is so slight, that I have not
thought it worth while to enter into the subject in any detail. The
chief Indian treatises, including the one referred to in the text, bear
strong marks of having been based on Greek writings.
[38] He introduced into trigonometry the use of _sines_, and made also
some little use of _tangents_, without apparently realising their
importance: he also used some new formulæ for the solution of spherical
triangles.
[39] A prolonged but indecisive controversy has been carried on,
chiefly by French scholars, with regard to the relations of Ptolemy,
Abul Wafa, and Tycho in this matter.
[40] For example, the practice of treating the trigonometrical
functions as _algebraic_ quantities to be manipulated by formulæ, not
merely as geometrical lines.
[41] Any one who has not realised this may do so by performing with
Roman numerals the simple operation of multiplying by itself a number
such as MDCCCXCVIII.
[42] On trigonometry. He reintroduced the _sine_, which had been
forgotten; and made some use of the _tangent_, but like Albategnius (§
59 _n._) did not realise its importance, and thus remained behind Ibn
Yunos and Abul Wafa. An important contribution to mathematics was a
table of sines calculated for every minute from 0° to 90°.
[43] That of “lunar distances.”
[44] He did not invent the measuring instrument called the _vernier_,
often attributed to him, but something quite different and of very
inferior value.
[45] The name is spelled in a large number of different ways both by
Coppernicus and by his contemporaries. He himself usually wrote his
name Coppernic, and in learned productions commonly used the Latin form
Coppernicus. The spelling Copernicus is so much less commonly used by
him that I have thought it better to discard it, even at the risk of
appearing pedantic.
[46] _Nullo demum loco ineptior est quam ... ubi nim’s pueriliter
hallucinatur_: Nowhere is he more foolish than ... where he suffers
from delusions of too childish a character.
[47] His real name was Georg Joachim, that by which he is known having
been made up by himself from the Latin name of the district where he
was born (Rhætia).
[48] The _Commentariolus_ and the _Prima Narratio_ give most readers a
better idea of what Coppernicus did than his larger book, in which it
is comparatively difficult to disentangle his leading ideas from the
mass of calculations based on them.
[49] _Omnis enim quæ videtur secundum locum mutatio, aut est propter
locum mutatio, aut est propter spectatæ rei motum, aut videntis, aut
certe disparem utriusque mutationem. Nam inter mota æqualiter ad eadem
non percipitur motus, inter rem visam dico, et videntem_ (De Rev., I.
v.).
I have tried to remove some of the crabbedness of the original passage
by translating freely.
[50] To Coppernicus, as to many of his contemporaries, as well as to
the Greeks, the simplest form of a revolution of one body round another
was a motion in which the revolving body moved as if rigidly attached
to the central body. Thus in the case of the earth the second motion
was such that the axis of the earth remained inclined at a constant
angle to the line joining earth and sun, and therefore changed its
direction in space. In order then to make the axis retain a (nearly)
fixed direction in space, it was necessary to add a _third_ motion.
[51] In this preliminary discussion, as in fig. 40, Coppernicus gives
80 days; but in the more detailed treatment given in Book V. he
corrects this to 88 days.
[52] Fig. 42 has been slightly altered, so as to make it agree with
fig. 41.
[53] Coppernicus, instead of giving longitudes as measured from the
first point of Aries (or vernal equinoctial point, chapter I., §§ 11,
13), which moves on account of precession, measured the longitudes from
a standard fixed star (α _Arietis_) not far from this point.
[54] According to the theory of Coppernicus, the diameter of the moon
when greatest was about 1∕8 greater than its average amount; modern
observations make this fraction about 1∕13. Or, to put it otherwise,
the diameter of the moon when greatest ought to exceed its value when
least by about 8′ according to Coppernicus, and by about 5′ according
to modern observations.
[55] Euclid, I. 33.
[56] If P be the synodic period of a planet (in years), and S the
sidereal period, then we evidently have (1∕P) + 1 = 1∕S for an inferior
planet, and 1 - (1∕P) = 1∕S for a superior planet.
[57] Recent biographers have called attention to a cancelled passage in
the manuscript of the _De Revolutionibus_ in which Coppernicus shews
that an ellipse can be generated by a combination of circular motions.
The proposition is, however, only a piece of pure mathematics, and has
no relation to the motions of the planets round the sun. It cannot,
therefore, fairly be regarded as in any way an anticipation of the
ideas of Kepler (chapter VII.).
[58] It may be noticed that the differential method of parallax
(chapter VI., § 129), by which such a quantity as 12′ could have been
noticed, was put out of court by the general supposition, shared by
Coppernicus, that the stars were all at the same distance from us.
[59] There is little doubt that he invented what were substantially
logarithms independently of Napier, but, with characteristic inability
or unwillingness to proclaim his discoveries, allowed the invention to
die with him.
[60] A similar discovery was in fact made twice again, by Galilei
(chapter VI., § 114) and by Huygens (chapter VIII., § 157).
[61] He obtained leave of absence to pay a visit to Tycho Brahe and
never returned to Cassel. He must have died between 1599 and 1608.
[62] He even did not forget to provide one of the most necessary parts
of a mediæval castle, a prison!
[63] It would be interesting to know what use he assigned to the
(presumably) still vaster space _beyond_ the stars.
[64] Tycho makes in this connection the delightful remark that Moses
must have been a skilled astronomer, because he refers to the moon
as “the lesser light,” notwithstanding the fact that the apparent
diameters of sun and moon are very nearly equal!
[65] By transversals.
[66] On an instrument which he had invented, called the _hydrostatic
balance_.
[67] A fair idea of mediaeval views on the subject may be derived from
one of the most tedious Cantos in Dante’s great poem (_Paradiso_, II.),
in which the poet and Beatrice expound two different “explanations” of
the spots on the moon.
[68] _Ludovico delle Colombe_ in a tract _Contra Il Moto della Terra_,
which is reprinted in the national edition of Galilei’s works, Vol. III.
[69] In a letter of May 4th, 1612, he says that he has seen them for
eighteen months; in the _Dialogue on the Two Systems_ (III., p. 312,
in Salusbury’s translation) he says that he saw them while he still
lectured at Padua, _i.e._ presumably by September 1610, as he moved to
Florence in that month.
[70] _Historia e Dimostrazioni intorno alle Macchie Solari._
[71] Acts i. 11. The pun is not quite so bad in its Latin form: _Viri
Galilaci_, etc.
[72] _Spiritui sancto mentem fuisse nos docere, quo modo ad Coelum
eatur, non autem quomodo Coelum gradiatur._
[73] From the translation by Salusbury, in Vol. I. of his _Mathematical
Collections_.
[74] The only point of any importance in connection with Galilei’s
relations with the Inquisition on which there seems to be room for any
serious doubt is as to the stringency of this warning. It is probable
that Galilei was at the same time specifically forbidden to “hold,
teach, or defend in any way, whether verbally or in writing,” the
obnoxious doctrine.
[75] This is illustrated by the well-known optical illusion whereby a
white circle on a black background appears larger than an equal black
one on a white background. The apparent size of the hot filament in a
modern incandescent electric lamp is another good illustration.
[76] Actually, since the top of the tower is describing a slightly
larger circle than its foot, the stone is at first moving eastward
slightly faster than the foot of the tower, and therefore should reach
the ground slightly to the _east_ of it. This displacement is, however,
very minute, and can only be detected by more delicate experiments than
any devised by Galilei.
[77] From the translation by Salusbury, in Vol. I. of his _Mathematical
Collections_.
[78] The official minute is: _Et ei dicto quod dicat veritatem, alias
devenietur ad torturam_.
[79] The three days June 21-24 the only ones which Galilei _could_ have
spent in an actual prison, and there seems no reason to suppose that
they were spent elsewhere than in the comfortable rooms in which it is
known that he lived during most of April.
[80] Equivalent to portions of the subject now called _dynamics_ or
(more correctly) _kinematics_ and _kinetics_.
[81] He estimates that a body falls in a second a distance of 4
“bracchia,” equivalent to about 8 feet, the true distance being
slightly over 16.
[82] _Two New Sciences_, translated by Weston, p. 255.
[83] The astronomer appears to have used both spellings of his name
almost indifferently. For example, the title-page of his most important
book, the _Commentaries on the Motions of Mars_ (§ 141), has the form
Kepler, while the dedication of the same book is signed Keppler.
[84] The regular solids being taken in the order: cube, tetrahedron,
dodecahedron, icosahedron, octohedron, and of such magnitude that a
sphere can be circumscribed to each and at the same time inscribed in
the preceding solid of the series, then the radii of the six spheres so
obtained were shewn by Kepler to be approximately proportional to the
distances from the sun of the six planets Saturn, Jupiter, Mars, Earth,
Venus, and Mercury.
[85] Two stars 4′ apart only just appear distinct to the naked eye of a
person with average keenness of sight.
[86] _Commentaries on the Motions of Mars_, Part II., end of chapter
XIX.
[87] An ellipse is one of several curves, known as =conic sections=,
which can be formed by taking a section of a cone, and may also be
defined as a curve the sum of the distances of any point on which from
two fixed points inside it, known as the =foci=, is always the same.
[Illustration: FIG. 59.—An ellipse.]
Thus if, in the figure, S and H are the foci, and P, Q are _any_ two
points on the curve, then the distances S P, H P added together are
equal to the distances S Q, Q H added together, and each sum is equal
to the length A A′ of the ellipse. The ratio of the distance S H to the
length A A′ is known as the =eccentricity=, and is a convenient measure
of the extent to which the ellipse differs from a circle.
[88] The ellipse is _more_ elongated than the actual path of Mars, an
accurate drawing of which would be undistinguishable to the eye from a
circle. The eccentricity is 1∕3 in the figure, that of Mars being 1∕10.
[89] _Astronomia Nova_ αἰτιολογητος _seu Physica Coelestis,
tradita Commentariis de Motibus Stellae Martis._ _Ex Observationibus G.
V. Tychonis Brahe._
[90] It contains the germs of the method of infinitesimals.
[91] _Harmonices Mundi Libri V._
[92] There may be some interest in Kepler’s own statement of the
law: “Res est certissima exactissimaque, quod proportionis quae est
inter binorum quorumque planetarum tempora periodica, sit praecise
sesquialtera proportionis mediarum distantiarum, id est orbium
ipsorum.”—_Harmony of the World_, Book V., chapter III.
[93] _Epitome_, Book IV., Part 2.
[94] Introduction to the _Commentaries on the Motions of Mars_.
[95] Substantially the _filar micrometer_ of modern astronomy.
[96] Galilei, at the end of his life, appears to have thought of
contriving a pendulum with clockwork, but there is no satisfactory
evidence that he ever carried out the idea.
[97] In modern notation: time oπf oscillation = 2π√(_l_∕_g_).
[98] _I.e._ he obtained the familiar formula (_v^2_)∕_r_, and several
equivalent forms for _centrifugal force_.
[99] Also frequently referred to by the Latin name _Cartesius_.
[100] According to the unreformed calendar (O.S.) then in use in
England, the date was Christmas Day, 1642. To facilitate comparison
with events occurring out of England, I have used throughout this and
the following chapters the Gregorian Calendar (N.S.), which was at this
time adopted in a large part of the Continent (cf. chapter II., § 22).
[101] From a MS. among the Portsmouth Papers, quoted in the Preface to
the Catalogue of the Portsmouth Papers.
[102] W. K. Clifford, _Aims and Instruments of Scientific Thought_.
[103] It is interesting to read that Wren offered a prize of 40_s._ to
whichever of the other two should solve this the central problem of the
solar system.
[104] The familiar _parallelogram of forces_, of which earlier writers
had had indistinct ideas, was clearly stated and proved in the
introduction to the _Principia_, and was, by a curious coincidence,
published also in the same year by _Varignon_ and _Lami_.
[105] It is between 13 and 14 billion billion pounds. See chapter X. §
219.
[106] As far as I know Newton gives no short statement of the law in a
perfectly complete and general form; separate parts of it are given in
different passages of the _Principia_.
[107] It is commonly stated that Newton’s value of the motion of the
moon’s apses was only about half the true value. In a scholium of the
_Principia_ to prop. 35 of the third book, given in the first edition
but afterwards omitted, he estimated the annual motion at 40°, the
observed value being about 41°. In one of his unpublished papers,
contained in the Portsmouth collection, he arrived at 39° by a process
which he evidently regarded as not altogether satisfactory.
[108] Throughout the Coppernican controversy up to Newton’s time it had
been generally assumed, both by Coppernicans and by their opponents,
that there was some meaning in speaking of a body simply as being “at
rest” or “in motion,” without any reference to any other body. But all
that we can really observe is the motion of one body relative to one
or more others. Astronomical observation tells us, for example, of a
certain motion relative to one another of the earth and sun; and this
motion was expressed in two quite different ways by Ptolemy and by
Coppernicus. From a modern standpoint the question ultimately involved
was whether the motions of the various bodies of the solar system
relatively to the earth or relatively to the sun were the simpler to
express. If it is found convenient to express them—as Coppernicus and
Galilei did—in relation to the sun, some simplicity of statement is
gained by speaking of the sun as “fixed” and omitting the qualification
“relative to the sun” in speaking of any other body. The same motions
might have been expressed relatively to any other body chosen at will:
_e.g._ to one of the hands of a watch carried by a man walking up and
down on the deck of a ship on a rough sea; in this case it is clear
that the motions of the other bodies of the solar system relative to
this body would be excessively complicated; and it would therefore be
highly inconvenient though still possible to treat this particular body
as “fixed.”
A new aspect of the problem presents itself, however, when an
attempt—like Newton’s—is made to explain the motions of bodies of the
solar system as the result of forces exerted on one another by those
bodies. If, for example, we look at Newton’s First Law of Motion
(chapter VI., § 130), we see that it has no meaning, unless we know
what are the body or bodies relative to which the motion is being
expressed; a body at rest relatively to the earth is moving relatively
to the sun or to the fixed stars, and the applicability of the First
Law to it depends therefore on whether we are dealing with its motion
relatively to the earth or not. For most terrestrial motions it is
sufficient to regard the Laws of Motion as referring to motion relative
to the earth; or, in other words, we may for this purpose treat the
earth as “fixed.” But if we examine certain terrestrial motions more
exactly, we find that the Laws of Motion thus interpreted are not quite
true; but that we get a more accurate explanation of the observed
phenomena if we regard the Laws of Motion as referring to motion
relative to the centre of the sun and to lines drawn from it to the
stars; or, in other words, we treat the centre of the sun as a “fixed”
point and these lines as “fixed” directions. But again when we are
dealing with the solar system generally this interpretation is slightly
inaccurate, and we have to treat the centre of gravity of the solar
system instead of the sun as “fixed.”
From this point of view we may say that Newton’s object in the
_Principia_ was to shew that it was possible to choose a certain point
(the centre of gravity of the solar system) and certain directions
(lines joining this point to the fixed stars), as a base of reference,
such that all motions being treated as relative to this base, the Laws
of Motion and the law of gravitation afford a consistent explanation of
the observed motions of the bodies of the solar system.
[109] He estimated the annual precession due to the sun to be about
9″, and that due to the moon to be about four and a half times as
great, so that the total amount due to the two bodies came out about
50″, which agrees within a fraction of a second with the amount shewn
by observation; but we know now that the moon’s share is not much more
than twice that of the sun.
[110] He once told Halley in despair that the lunar theory “made his
head ache and kept him awake so often that he would think of it no
more.”
[111] December 31st, 1719, according to the unreformed calendar (O.S.)
then in use in England.
[112] The apparent number is 2,935, but 12 of these are duplicates.
[113] By Bessel (chapter XIII., § 277).
[114] The relation between the work of Flamsteed and that of Newton was
expressed with more correctness than good taste by the two astronomers
themselves, in the course of some quarrel about the lunar theory: “Sir
Isaac worked with the ore I had dug.” “If he dug the ore, I made the
gold ring.”
[115] Rigaud, in the memoirs prefixed to Bradley’s _Miscellaneous
Works_.
[116] A telescopic star named 37 Camelopardi in Flamsteed’s catalogue.
[117] The story is given in T. Thomson’s _History of the Royal
Society_, published more than 80 years afterwards (1812), but I have
not been able to find any earlier authority for it. Bradley’s own
account of his discovery gives a number of details, but has no allusion
to this incident.
[118] It is _k sin_ C A B, where _k_ is the constant of aberration.
[119] His observations as a matter of fact point to a value rather
greater than 18″, but he preferred to use round numbers. The figures
at present accepted are 18″·42 and 13″·75, so that his ellipse was
decidedly less flat than it should have been.
[120] _Recherches sur la précession des équinoxes et sur la nutation de
l’axe de la terre._
[121] The word “geometer” was formerly used, as “géomètre” still is in
French, in the wider sense in which “mathematician” is now customary.
[122] _Principia_, Book III., proposition 10.
[123] It is important for the purposes of this discussion to notice
that the vertical is _not_ the line drawn from the centre of the earth
to the place of observation.
[124] 69 miles is 364,320 feet, so that the two northern degrees were a
little more and the Peruvian are a little less than 69 miles.
[125] The remaining 8,000 stars were not “reduced” by Lacaille. The
whole number were first published in the “reduced” form by the British
Association in 1845.
[126] A mural quadrant.
[127] The ordinary approximate theory of the _collimation error_,
_level error_, and _deviation error_ of a transit, as given in
textbooks of spherical and practical astronomy, is substantially his.
[128] The title-page is dated 1767; but it is known not to have been
actually published till three years later.
[129] For a more detailed discussion of the transit of Venus, see
Airy’s _Popular Astronomy_ and Newcomb’s _Popular Astronomy_.
[130] _Some_ other influences are known—_e.g._ the sun’s heat causes
various motions of our air and water, and has a certain minute effect
on the earth’s rate of rotation, and presumably produces similar
effects on other bodies.
[131] The arithmetical processes of working out, figure by figure, a
non-terminating decimal or a square root are simple cases of successive
approximation.
[132] “C’est que je viens d’un pays où, quand on parle, on est pendu.”
[133] Longevity has been a remarkable characteristic of the great
mathematical astronomers: Newton died in his 85th year; Euler,
Lagrange, and Laplace lived to be more than 75, and D’Alembert was
almost 66 at his death.
[134] This body, which is primarily literary, has to be distinguished
from the much less famous Paris Academy of Sciences, constantly
referred to (often simply as the Academy) in this chapter and the
preceding.
[135] E.g. _Mélanges de Philosophie, de l’Histoire, et de Littérature_;
_Éléments de Philosophie_; _Sur la Destruction des Jésuites_.
[136] _I.e._ he assumed a law of attraction represented by μ∕_r^2_ +
ν∕_r^3_.
[137] This appendix is memorable as giving for the first time the
method of _variation of parameters_ which Lagrange afterwards developed
and used with such success.
[138] That of the distinguished American astronomer Dr. G. W. Hill
(chapter XIII., § 286).
[139] They give about ·78 for the mass of Venus compared to that of the
earth.
[140] The orbit might be a parabola or hyperbola, though this does not
occur in the case of any known planet.
[141] On the _Calculus of Variations_.
[142] The establishment of the general equations of motion by a
combination of _virtual velocities_ and _D’Alembert’s principle_.
[143] _Théorie des Fonctions Analytiques_ (1797); _Resolution des
Équations Numériques_ (1798); _Leçons sur le Calcul des Fonctions_
(1805).
[144] _Théorie Analytique des Probabilités._
[145] The fact that the post was then given by Napoleon to his brother
Lucien suggests some doubts as to the unprejudiced character of the
verdict of incompetence pronounced by Napoleon against Laplace.
[146] _Outlines of Astronomy_, § 656.
[147] Laplace, _Système du Monde_.
[148] If _n_, _n′_ are the mean motions of the two planets, the
expression for the disturbing force contains terms of the type =
_sin_(_np_ ± _n′p′_) _t_, _cos_ where _p_, _p′_ are integers, and
the coefficient is of the order _p_⁓_p′_ in the eccentricities and
inclinations. If now _p_ and _p′_ are such that _np_⁓_n′p′_ is small,
the corresponding inequality has a period 2π∕(_np_⁓_n′p′_), and
though its coefficient is of order _p_⁓_p′_, it has the small factor
_np_⁓_np′_ (or its square) in the denominator and may therefore be
considerable. In the case of Jupiter and Saturn, for example, _n_ =
109,257 in seconds of arc per annum, _n′_ = 43,996; 5_n′_ - 2_n_ =
1,466; there is therefore an inequality of the _third_ order, with a
period (in years) = 360°∕1,466″ = 900.
[149] This statement requires some qualification when perturbations are
taken into account. But the point is not very important, and is too
technical to be discussed.
[150] ∑_e^2m_√_a_ = _c_, ∑_tan^2im_√_a_ = _c′_, where _m_ is the mass
of any planet, _a_, _e_, _i_ are the semi-major axis, eccentricity, and
inclination of the orbit. The equation is true as far as squares of
small quantities, and therefore it is indifferent whether or not _tan
i_ is replaced as in the text by _i_.
[151] Nearly the whole of the “eccentricity fund” and of the
“inclination fund” of the solar system is shared between Jupiter
and Saturn. If Jupiter were to absorb the whole of each fund, the
eccentricity of its orbit would only be increased by about 25 per
cent., and the inclination to the ecliptic would not be doubled.
[152] Of tables based on Laplace’s work and published up to the time
of his death, the chief solar ones were those of _von Zach_ (1804) and
_Delambre_ (1806); and the chief planetary ones were those of _Lalande_
(1771), of _Lindenau_ for Venus, Mars, and Mercury (1810-13), and of
_Bouvard_ for Jupiter, Saturn, and Uranus (1808 and 1821).
[153] The motion of the satellites of Uranus (chapter XII., § 253, 255)
is in the opposite direction. When Laplace first published his theory
their motion was doubtful, and he does not appear to have thought it
worth while to notice the exception in later editions of his book.
[154] This statement again has to be modified in consequence of the
discoveries, beginning on January 1st, 1801, of the minor planets
(chapter XIII., § 294), many of which have orbits that are far more
eccentric than those of the other planets and are inclined to the
ecliptic at considerable angles.
[155] _Système du Monde_, Book V., chapter VI.
[156] In his paper of 1817 Herschel gives the number as 863, but a
reference to the original paper of 1785 shews that this must be a
printer’s error.
[157] The motion of Castor has become slower since Herschel’s time, and
the present estimate of the period is about 1,000 years, but it is by
no means certain.
[158] More precisely, counting motions in right ascension and in
declination separately, he had 27 observed motions to deal with (one
of the stars having no motion in declination); 22 agreed in sign with
those which would result from the assumed motion of the sun.
[159] The method was published by Legendre in 1806 and by Gauss in
1809, but it was invented and used by the latter more than 20 years
earlier.
[160] The figure has to be enormously exaggerated, the angle SσE as
shewn there being about 10°, and therefore about 100,000 times too
great.
[161] Sir R. S. Ball and the late Professor Pritchard (§ 279) have
obtained respectively ·47″ and ·43″; the mean of these, ·45″, may be
provisionally accepted as not very far from the truth.
[162] An average star of the 14th magnitude is 10,000 times fainter
than one of the 4th magnitude, which again is about 150 times less
bright than Sirius. See § 316.
[163] Newcomb’s velocity of light and Nyrén’s constant of aberration
(20″·4921) give 8″·794; Struve’s constant of aberration (20″·445),
Loewy’s (20″·447), and Hall’s (20″·454) each give 8″·81.
[164] _Fundamenta Nova Investigationis Orbitae Verae quam Luna
perlustrat._
[165] _Darlegung der theoretischen Berechnung der in den Mondtafeln
angewandten Störungen._
[166] _E.g._ in Grant’s _History of Physical Astronomy_, Herschel’s
_Outlines of Astronomy_, Miss Clerke’s _History of Astronomy in the
Nineteenth Century_, and the memoir by Dr. Glaisher prefixed to the
first volume of Adams’s _Collected Papers_.
[167] This had been suggested as a possibility by several earlier
writers.
[168] The discovery of a terrestrial substance with this line in its
spectrum has been announced while this book has been passing through
the press.
[169] Observations made on Mont Blanc under the direction of M. Janssen
in 1897 indicate a slightly larger number than Dr. Langley’s.
[170] _Catalogus novus stellarum duplicium_, _Stellarum duplicium et
multiplicium mensurae micrometricae_, and _Stellarum fixarum imprimis
duplicium et multiplicium positiones mediae pro epocha 1830_.
[171] _I.e._ 2·512... is chosen as being the number the logarithm of
which is ·4, so that (2·512...)^{5∕2} = 10.
[172] If L be the ratio of the light received from a star to that
received from a standard first magnitude star, such as Aldebaran or
Altair, then its magnitude _m_ is given by the formula
L = (1∕2·512)^{m - 1} = (1∕100)^{(m - 1)∕5}, whence m - 1 = -5∕2log L.
A star brighter than Aldebaran has a magnitude less than 1, while the
magnitude of Sirius, which is about nine times as bright as Aldebaran,
is a _negative_ quantity,-1·4, according to the Harvard photometry.
End of Project Gutenberg's A Short History of Astronomy, by Arthur Berry