CHAP. XIX. The Calculation of New and Full Moons and Eclipses. The geometrical Construction of Solar and Lunar Eclipses. The examination of antient Eclipses. (continued 2)
Reading edition
1780 20 4 41 8 19 48 7 8 10 10 3 1 11 28 48 1 25 47
1781 9 13 30 8 9 4 5 17 59 10 11 4 11 18 5 1 7 0
1782 28 11 2 8 27 28 4 23 34 11 19 47 0 6 27 0 16 41
1783 17 19 51 8 16 44 3 3 23 11 27 50 11 25 44 11 27 54
1784 6 4 40 8 5 59 1 13 12 0 5 53 11 15 1 11 9 7
1785 25 2 12 8 24 20 0 18 48 1 14 36 0 3 24 10 18 48
1786 14 11 1 8 13 36 10 28 37 1 22 39 11 22 41 10 0 2
1787 3 19 49 8 2 52 9 8 25 2 0 42 11 11 58 9 11 15
1788 21 17 22 8 21 14 8 14 2 3 9 25 0 0 21 8 20 57
1789 11 2 11 8 10 30 6 23 51 3 17 28 11 19 38 8 2 10
1790 29 23 43 8 28 52 5 29 27 4 26 10 0 8 1 7 11 51
1791 19 8 32 8 18 8 4 9 15 5 4 13 11 27 17 6 23 4
1792 7 17 21 8 7 24 2 19 4 5 12 16 11 16 34 6 4 17
1793 26 14 53 8 25 46 1 24 40 6 20 59 0 4 58 5 13 59
1794 15 23 42 8 15 2 0 4 29 6 29 2 11 24 15 4 25 13
1795 5 8 30 8 4 18 10 14 17 7 7 5 0 13 32 4 6 26
1796 23 6 3 8 22 39 9 19 53 8 15 48 0 1 56 3 16 8
1797 12 14 52 8 11 55 7 29 42 8 23 50 11 21 13 2 27 23
1798 1 23 40 8 1 11 6 9 30 9 1 53 11 10 30 2 8 36
1799 20 21 13 8 19 33 5 15 6 10 10 36 11 28 53 1 18 18
1800 10 6 2 8 8 50 3 24 55 10 18 39 11 18 10 0 29 31
222
Tab. V. The first mean Conjunction of the Sun and Moon after a compleat Century, beginning with March, for 5000 years 10 days 7 hours 56 minutes (in which time there are just 61843 mean Lunations) with the mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, and the mean Long. of the Sun and Node from the beginning of the sign Aries, at the times of all those mean Conjunctions.
Centuries of Julian Years. First Conjunction after a Century. The Sun’s mean Anomaly. The Moon’s mean Anomaly. The Sun’s distance from the Node. The Sun’s Longitude from Aries. The Node’s Longitude from Aries.
D. H. M. s ° ʹ s ° ʹ s ° ʹ s ° ʹ s ° ʹ
100 4 8 11 0 3 21 8 15 22 4 19 27 0 5 2 4 14 25
200 8 16 22 0 6 42 5 0 44 9 8 55 0 10 4 8 28 51
300 13 0 33 0 10 3 1 16 6 1 28 22 0 15 6 1 13 16
400 17 8 43 0 13 24 10 1 28 6 17 49 0 20 8 5 27 41
500 21 16 54 0 16 46 6 16 50 11 7 16 0 25 10 10 12 6
600 26 1 5 0 20 7 3 2 12 3 26 44 1 0 12 2 26 32
700 0 20 32 11 24 22 10 21 45 7 15 31 0 6 7 7 9 24
800 5 4 43 11 27 43 7 7 7 0 4 58 0 11 9 11 23 49
900 9 12 54 0 1 4 3 22 29 4 24 25 0 16 12 4 8 13
1000 13 21 5 0 4 25 0 7 51 9 13 53 0 21 14 8 22 39
1100 18 5 16 0 7 46 8 23 13 2 3 20 0 26 16 1 7 4
1200 22 13 26 0 11 7 5 8 35 6 22 47 1 1 18 5 21 29
1300 26 21 37 0 14 28 1 23 57 11 12 15 1 6 20 10 5 55
1400 1 17 4 11 18 43 9 13 30 3 1 2 0 12 15 2 18 47
1500 6 1 15 11 22 4 5 28 52 7 20 29 0 17 17 7 3 12
1600 10 9 26 11 25 25 2 14 14 0 9 56 0 22 19 11 17 37
1700 14 17 37 11 28 46 10 29 36 4 29 23 0 27 22 4 2 2
1800 19 1 48 0 2 8 7 14 58 9 18 51 1 2 24 8 16 27
1900 23 9 58 0 5 29 4 0 20 2 8 18 1 7 26 1 0 52
2000 27 18 9 0 8 50 0 15 42 6 27 45 1 12 28 5 15 17
2100 2 13 36 11 13 5 8 5 15 10 16 32 0 18 24 9 28 8
2200 6 21 47 11 16 26 4 20 37 3 6 0 0 23 26 2 12 34
2300 11 5 58 11 19 47 1 5 59 7 25 27 0 28 28 6 26 59
2400 15 14 9 11 23 8 9 21 21 0 14 54 1 3 30 11 11 24
2500 19 22 20 11 26 29 6 6 43 5 4 11 1 8 32 3 25 49
2600 24 6 31 11 29 50 2 22 4 9 23 49 1 13 35 8 10 14
2700 28 14 41 0 3 11 11 17 26 2 13 16 1 18 37 0 24 39
2800 3 10 8 11 7 26 6 26 59 6 2 3 0 24 31 5 7 33
2900 7 18 19 11 10 47 3 12 21 10 21 30 0 29 33 9 21 58
3000 12 2 30 11 14 8 11 27 43 3 10 58 1 4 35 2 6 23
3100 16 10 41 11 17 30 8 13 5 8 10 25 1 9 37 6 20 48
3200 20 18 52 11 20 51 4 28 27 0 19 52 1 14 39 11 5 13
3300 25 3 3 11 24 11 1 13 49 5 9 20 1 19 41 3 19 39
3400 29 11 14 11 27 32 9 29 11 9 28 47 1 24 43 8 4 4
3500 4 6 41 11 1 47 5 18 44 1 17 34 1 0 41 0 16 53
2233600 8 14 52 11 4 58 2 4 6 6 7 1 1 5 42 5 1 19
3700 12 23 3 11 8 9 10 19 28 10 26 28 1 10 43 9 15 45
3800 17 7 14 11 11 20 7 4 50 3 15 55 1 15 45 2 0 10
3900 21 15 25 11 14 31 4 20 12 8 5 22 1 20 47 6 14 35
4000 25 23 36 11 17 42 1 5 34 0 24 49 1 25 49 10 29 0
4100 0 19 3 10 22 56 8 25 7 4 13 36 1 0 45 3 12 51
4200 5 3 14 10 26 17 5 10 29 9 3 3 1 6 47 7 6 16
4300 9 11 25 10 29 37 1 25 51 1 12 30 1 11 48 11 25 39
4400 13 19 36 11 2 58 10 11 13 6 1 57 1 16 51 4 10 4
4500 18 3 46 11 6 18 6 26 35 10 21 24 1 21 53 8 29 31
4600 22 11 57 11 9 39 3 11 15 3 10 51 1 26 55 1 13 56
4700 26 20 7 11 12 59 11 27 19 8 0 16 2 1 57 5 28 19
4800 1 15 34 10 17 14 7 16 52 11 19 4 1 7 53 10 11 11
4900 5 23 45 10 20 35 4 2 14 4 8 30 1 12 55 2 25 35
5000 10 7 56 10 23 56 0 17 36 8 27 57 1 17 57 7 10 0
Table VI. The mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, for 13 mean Lunations.
Lunations. Mean Lunations. The Sun’s mean Anomaly. The Moon’s mean Anomaly. The Sun’s motion from the Node. The Sun’s mean Motion. The Node’s retrograde Motion.
D. H. M. s ° ʹ s ° ʹ s ° ʹ s ° ʹ s ° ʹ
1 29 12 44 0 29 6 0 25 49 1 0 40 0 29 6 0 1 34
2 59 1 28 1 28 13 1 21 38 2 1 20 1 28 13 0 3 8
3 88 14 12 2 27 19 2 17 27 3 2 1 2 27 19 0 4 41
4 118 2 56 3 26 26 3 13 16 4 2 41 3 26 26 0 6 15
5 147 15 4 4 25 32 4 9 5 5 3 21 4 25 32 0 7 49
6 177 4 24 5 24 38 5 4 54 6 4 1 5 24 38 0 9 23
7 206 17 8 6 23 44 6 0 43 7 4 42 6 23 45 0 10 57
8 236 5 52 7 22 50 6 26 32 8 5 22 7 22 51 0 12 31
9 265 18 36 8 21 57 7 22 21 9 6 2 8 21 58 0 14 4
10 295 7 21 9 21 3 8 18 10 10 6 42 9 21 4 0 15 38
11 324 20 5 10 20 9 9 13 59 11 7 22 10 20 10 0 17 12
12 354 8 49 11 19 16 10 9 48 0 8 3 11 19 17 0 18 46
13 383 21 33 0 18 22 11 5 37 1 8 43 0 18 23 0 20 20
The first, second, third, and fourth Tables may be continued, by means of the sixth, to any length of time: for, by adding 12 Lunations to the mean time of the New or Full Moon which happens next after the 11th day of March, and then, casting out 365 days in common years, and 366 days in leap-years, we have the mean time of New or Full Moon in March the following year. But when the mean New or Full Moon happens on or before the 11th of March, there must be 13 Lunations added to carry it to March again. The Anomalies, Sun’s distance from the Node, and Longitude of the Sun, are found the same way, by adding them for 12 or 13 Lunations. But the retrograde Motion of the Node for these Lunations must be subtracted from it’s longitude from Aries in March, to have it’s Longitude or Place in the March following.
224
Table VII. The number of Days, reckoned from the beginning of March, answering to the Days of all the mean New and Full Moons.
Days. March. April. May. June. July. August. September. October. November. December. January. February.
1 1 32 62 93 123 154 185 215 246 276 307 338
2 2 33 63 94 124 155 186 216 247 277 308 339
3 3 34 64 95 125 156 187 217 248 278 309 340
4 4 35 65 96 126 157 188 218 249 279 310 341
5 5 36 66 97 127 158 189 219 250 280 311 342
6 6 37 67 98 128 159 190 220 251 281 312 343
7 7 38 68 99 129 160 191 221 252 282 313 344
8 8 39 69 100 130 161 192 222 253 283 314 345
9 9 40 70 101 131 162 193 223 254 284 315 346
10 10 41 71 102 132 163 194 224 255 285 316 347
11 11 42 72 103 133 164 195 225 256 286 317 348
12 12 43 73 104 134 165 196 226 257 287 318 349
13 13 44 74 105 135 166 197 227 258 288 319 350
14 14 45 75 106 136 167 198 228 259 289 320 351
15 15 46 76 107 137 168 199 229 260 290 321 352
16 16 47 77 108 138 169 200 230 261 291 322 353
17 17 48 78 109 139 170 201 231 262 292 323 354
18 18 49 79 110 140 171 202 232 263 293 324 355
19 19 50 80 111 141 172 203 233 264 294 325 356
20 20 51 81 112 142 173 204 234 265 295 326 357
21 21 52 82 113 143 174 205 235 266 296 327 358
22 22 53 83 114 144 175 206 236 267 297 328 359
23 23 54 84 115 145 176 207 237 268 298 329 360
24 24 55 85 116 146 177 208 238 269 299 330 361
25 25 56 86 117 147 178 209 239 270 300 331 362
26 26 57 87 118 148 179 210 240 271 301 332 363
27 27 58 88 119 149 180 211 241 272 302 333 364
28 28 59 89 120 150 181 212 242 273 303 334 365
29 29 60 90 121 151 182 213 243 274 304 335 366
30 30 61 91 122 152 183 214 244 275 305 336 —
31 31 — 92 — 153 184 — 245 — 306 337 —
Table VIII. The Moon’s annual Equation.
Sun’s Ano. Subtract Sun’s Ano.
0 1 2 3 4 5
S. S. S. S. S. S.
D. M. M. M. M. M. M. D.
0 0 11 18 22 19 11 30
1 0 11 19 22 19 11 29
2 1 11 19 22 18 10 28
3 1 11 19 22 18 10 27
4 1 12 19 22 18 10 26
5 2 12 19 22 18 9 25
6 2 12 19 21 18 9 24
7 3 13 20 21 17 9 23
8 3 13 20 21 17 8 22
9 3 13 20 21 17 8 21
10 4 14 20 21 17 8 20
11 4 14 20 21 16 7 19
12 4 14 20 21 16 7 18
13 5 14 20 21 16 6 17
14 5 15 20 21 16 6 16
15 5 15 21 21 15 6 15
16 6 15 21 21 15 5 14
17 6 15 21 21 15 5 13
18 6 16 21 21 15 5 12
19 7 16 21 20 14 4 11
20 7 16 21 20 14 4 10
21 7 16 21 20 14 3 9
22 8 17 21 20 13 3 8
23 8 17 21 20 13 3 7
24 9 17 21 20 13 2 6
25 9 17 21 20 13 2 5
26 9 18 21 20 12 2 4
27 10 18 21 19 12 1 3
28 10 18 21 19 12 1 2
29 10 18 22 19 11 0 1
30 11 18 22 19 11 0 0
Sun’s Ano. 11 10 9 8 7 6 Sun’s Ano.
S. S. S. S. S. S.
Add
225
Table IX. Equation of the Moon’s mean Anomaly.
Sun’s Anom. Add Sun’s Anom.
0 1 2 3 4 5
S. S. S. S. S. S.
° ʹ ʹ ʹ ʹ ʹ ʹ °
0 0 10 17 20 17 10 30
1 0 10 17 20 17 10 29
2 1 11 17 20 17 9 28
3 1 11 18 20 17 9 27
4 1 11 18 20 17 9 26
5 2 12 18 20 17 9 25
6 2 12 18 20 16 8 24
7 2 12 18 20 16 8 23
8 3 12 18 20 16 8 22
9 3 12 19 20 16 7 21
10 3 13 19 20 16 7 20
11 4 13 19 20 15 7 19
12 4 13 19 20 15 6 18
13 4 13 19 19 15 6 17
14 5 14 19 19 15 6 16
15 5 14 19 19 14 5 15
16 5 14 19 19 14 5 14
17 6 14 19 19 14 5 13
18 6 15 19 19 14 4 12
19 6 15 20 19 13 4 11
20 7 15 20 19 13 4 10
21 7 15 20 19 13 3 9
22 7 16 20 19 13 3 8
23 8 16 20 19 12 3 7
24 8 16 20 18 12 2 6
25 8 16 20 18 12 2 5
26 9 16 20 18 11 1 4
27 9 17 20 18 11 1 3
28 9 17 20 18 11 1 2
29 10 17 20 18 10 0 1
30 10 17 20 17 10 0 0
Sun’s Anom. 11 10 9 8 7 6 Sun’s Anom.
S. S. S. S. S. S.
Subtract
Table X. The Moon’s elliptic Equation.
Moon’s Ano. Add Moon’s Ano.
0 1 2 3 4 5
Signs Signs Signs Signs Signs Signs
° H. M. H. M. H. M. H. M. H. M. H. M. °
0 0 0 4 49 8 8 9 2 7 32 4 14 30
1 0 10 4 57 8 12 9 1 7 27 4 6 29
2 0 20 5 5 8 16 9 0 7 22 3 58 28
3 0 30 5 13 8 20 8 59 7 17 3 50 27
4 0 40 5 21 8 24 8 58 7 12 3 42 26
5 0 50 5 29 8 28 8 57 7 6 3 34 25
6 1 0 5 37 8 31 8 55 7 0 3 26 24
7 1 10 5 45 8 34 8 53 6 54 3 18 23
8 1 20 5 53 8 37 8 51 6 48 3 10 22
9 1 30 6 1 8 40 8 49 6 42 3 2 21
10 1 40 6 9 8 43 8 47 6 36 2 53 20
11 1 50 6 16 8 45 8 44 6 30 2 45 19
12 2 0 6 23 8 47 8 41 6 24 2 37 18
13 2 10 6 30 8 49 8 38 6 18 2 29 17
14 2 20 6 37 8 51 8 35 6 11 2 21 16
15 2 30 6 44 8 53 8 32 6 4 2 12 15
16 2 40 6 51 8 55 8 29 5 57 2 3 14
17 2 50 6 58 8 57 8 26 5 50 1 54 13
18 3 0 7 4 8 59 8 23 5 43 1 45 12
19 3 10 7 10 9 0 8 20 5 36 1 36 11
20 3 19 7 16 9 1 8 16 5 29 1 27 10
21 3 28 7 22 9 2 8 12 5 22 1 19 9
22 3 37 7 28 9 2 8 8 5 15 1 11 8
23 3 46 7 33 9 3 8 4 5 8 1 3 7
24 3 55 7 38 9 3 8 0 5 1 0 54 6
25 4 4 7 43 9 4 7 56 4 54 0 45 5
26 4 13 7 48 9 4 7 52 4 46 0 36 4
27 4 22 7 53 9 4 7 47 4 38 0 27 3
28 4 31 7 58 9 3 7 42 4 30 0 18 2
29 4 40 8 3 9 3 7 37 4 22 0 9 1
30 4 49 8 8 9 2 7 32 4 14 0 0 0
Moon’s Ano. 11 10 9 8 7 6 Moon’s Ano.
Signs Signs Signs Signs Signs Signs
Subtract
226
Table XI. The Sun’s Equation at the time of New and Full Moon.
Sun’s Anom. Subtract Sun’s Anom.
0 1 2 3 4 5
Signs Signs Signs Signs Signs Signs
° H. M. H. M. H. M. H. M. H. M. H. M. °
0 0 0 1 44 3 2 3 32 3 5 1 48 30
1 0 4 1 47 3 3 3 32 3 3 1 45 29
2 0 7 1 50 3 5 3 32 3 2 1 42 28
3 0 11 1 53 3 7 3 32 3 0 1 38 27
4 0 14 1 57 3 9 3 32 2 58 1 35 26
5 0 18 2 0 3 10 3 31 2 56 1 31 25
6 0 22 2 3 3 12 3 31 2 54 1 28 24
7 0 25 2 6 3 14 3 31 2 52 1 24 23
8 0 29 2 8 3 16 3 30 2 50 1 21 22
9 0 32 2 11 3 17 4 30 2 48 1 17 21
10 0 36 2 14 3 18 3 30 2 45 1 14 20
11 0 40 2 17 3 19 3 29 2 43 1 11 19
12 0 43 2 20 3 20 3 29 2 40 1 7 18
13 0 47 2 22 3 21 3 28 2 37 1 4 17
14 0 50 2 25 3 22 3 27 2 35 1 0 16
15 0 54 2 28 3 23 3 26 2 32 0 56 15
16 0 57 2 30 3 24 3 25 2 29 0 52 14
17 1 0 2 32 3 25 3 24 2 26 0 49 13
18 1 4 2 35 3 26 3 23 2 23 0 45 12
19 1 7 2 38 3 27 3 22 2 21 0 41 11
20 1 11 2 40 3 28 3 21 2 18 0 38 10
21 1 14 2 43 3 28 3 20 2 15 0 34 9
22 1 17 2 45 3 29 3 19 2 12 0 30 8
23 1 21 2 47 3 29 3 18 2 10 0 26 7
24 1 24 2 49 3 30 3 17 2 7 0 23 6
25 1 28 2 51 3 30 3 15 2 4 0 19 5
26 1 31 2 54 3 31 3 13 2 1 0 15 4
27 1 34 2 57 3 31 3 11 1 58 0 11 3
28 1 38 2 59 3 31 3 9 1 55 0 7 2
29 1 41 3 1 3 32 3 7 1 52 0 4 1
30 1 44 3 2 3 32 3 5 1 48 0 0 0
Sun’s Anom. 11 10 9 8 7 6 Sun’s Anom.
Signs Signs Signs Signs Signs Signs
Add
Table XII. Equation of the Sun’s mean Place.
Sun’s Anom. Subtract Sun’s Anom.
0 1 2 3 4 5
Signs Signs Signs Signs Signs Signs
° ° ʹ ° ʹ ° ʹ ° ʹ ° ʹ ° ʹ °
0 0 0 0 57 1 40 1 56 1 42 0 59 30
1 0 2 0 59 1 41 1 56 1 41 0 57 29
2 0 4 1 0 1 42 1 56 1 40 0 56 28
3 0 6 1 1 1 43 1 56 1 39 0 54 27
4 0 8 1 2 1 44 1 56 1 38 0 52 26
5 0 10 1 4 1 45 1 56 1 36 0 50 25
6 0 12 1 6 1 45 1 56 1 35 0 48 24
7 0 14 1 7 1 46 1 55 1 34 0 46 23
8 0 16 1 9 1 47 1 55 1 33 0 44 22
9 0 18 1 10 1 48 1 55 1 32 0 42 21
10 0 20 1 12 1 48 1 54 1 30 0 41 20
11 0 22 1 14 1 49 1 54 1 29 0 39 19
12 0 24 1 15 1 50 1 54 1 28 0 37 18
13 0 26 1 17 1 51 1 53 1 26 0 35 17
14 0 28 1 18 1 51 1 53 1 25 0 33 16
15 0 30 1 20 1 52 1 52 1 23 0 31 15
16 0 31 1 21 1 52 1 52 1 22 0 29 14
17 0 33 1 22 1 53 1 51 1 21 0 27 13
18 0 35 1 24 1 53 1 51 1 19 0 25 12
19 0 37 1 25 1 54 1 50 1 18 0 23 11
20 0 39 1 27 1 54 1 49 1 16 0 21 10
21 0 41 1 28 1 55 1 49 1 14 0 19 9
22 0 43 1 29 1 55 1 48 1 13 0 17 8
23 0 45 1 30 1 55 1 47 1 11 0 14 7
24 0 46 1 32 1 56 1 46 1 10 0 12 6
25 0 48 1 33 1 56 1 46 1 8 0 10 5
26 0 50 1 34 1 56 1 45 1 6 0 8 4
27 0 52 1 35 1 56 1 45 1 5 0 6 3
28 0 54 1 36 1 56 1 44 1 3 0 4 2
29 0 55 1 38 1 56 1 43 1 1 0 2 1
30 0 57 1 40 1 56 1 42 0 59 0 0 0
Sun’s Anom. 11 10 9 8 7 6 Sun’s Anom.
Signs Signs Signs Signs Signs Signs
Add
227
Table XIII. Equation of the Moon’s Nodes.
Sun’s Ano. Subtract Sun’s Ano.
0 1 2 3 4 5
S. S. S. S. S. S.
° ʹ ʹ ʹ ʹ ʹ ʹ °
0 0 5 8 10 8 5 30
1 0 5 8 10 8 5 29
2 0 5 8 10 8 5 28
3 0 5 8 10 8 4 27
4 1 5 8 10 8 4 26
5 1 5 8 10 8 4 25
6 1 6 9 10 8 4 24
7 1 6 9 9 8 4 23
8 1 6 9 9 8 4 22
9 1 6 9 9 7 3 21
10 2 6 9 9 7 3 20
11 2 6 9 9 7 3 19
12 2 6 9 9 7 3 18
13 2 6 9 9 7 3 17
14 2 7 9 9 7 3 16
15 2 7 9 9 7 3 15
16 2 7 9 9 7 2 14
17 3 7 9 9 7 2 13
18 3 7 9 9 6 2 12
19 3 7 9 9 6 2 11
20 3 7 9 9 6 2 10
21 3 7 9 9 6 2 9
22 4 7 9 9 6 1 8
23 4 8 9 9 6 1 7
24 4 8 9 9 6 1 6
25 4 8 9 9 6 1 5
26 4 8 10 9 5 1 4
27 4 8 10 9 5 1 3
28 4 8 10 8 5 0 2
29 5 8 10 8 5 0 1
30 5 8 10 8 5 0 0
Sun’s Ano. 11 10 9 8 7 6 Sun’s Ano.
S. S. S. S. S. S.
Add
The above titles, Add and Subtract, are right when the Equation is applied to the Sun’s mean distance from the Node; but when it is applied to the mean place of the Node, the titles must be changed.
Tab. XIV. The Moon’s latitude in Eclipses.
Argument of Latit.
Moon fr. the Node. Sig. 0 N. A.
Sig. 6 S. D.
° ° ʹ ʺ °
0 0 0 0 30
1 0 5 15 29
2 0 10 30 28
3 0 15 44 27
4 0 20 59 26
5 0 26 13 25
6 0 31 26 24
7 0 36 39 23
8 0 41 51 22
9 0 47 2 21
10 0 52 13 20
11 0 57 23 19
12 1 2 31 18
13 1 7 38 17
14 1 12 44 16
15 1 17 49 15
16 1 22 52 14
17 1 27 53 13
18 1 32 54 12
N. D. Sig. 5 Moon fr. the Node.
S. A. Sig. 11
Argument of Latit.
This Table extends no farther than the limits of Eclipses. N. A. signifies North Ascending Lat. S. A. South Ascending; N. D. North Descending; and S. D. South Descending.
Table XV. The Moons Horizontal Parallax; the Semidiameters and true Horary motions of the Sun and Moon.
Anomaly of the Sun and Moon. Moon’s Horizontal Parallax. Sun’s Semidiameter. Moon’s Semidiamet. Moon’s horary Mot. Sun’s horary Mot. Anomaly of the Sun and Moon.
s ° ʹ ʺ ʹ ʺ ʹ ʺ ʹ ʺ ʹ ʺ s °
0 0 54 59 15 50 14 54 30 10 2 23 12 0
6 54 59 15 50 14 55 30 12 2 23 24
12 55 0 15 50 14 56 30 15 2 23 18
18 55 4 15 51 14 57 30 18 2 23 12
24 55 11 15 51 14 58 30 26 2 23 6
1 0 55 20 15 52 14 59 30 34 2 23 11 0
6 55 30 15 53 15 1 30 44 2 24 24
12 55 40 13 54 15 4 30 55 2 24 18
18 55 51 15 55 15 8 31 9 2 24 12
24 56 0 15 56 15 12 31 23 2 25 6
2 0 56 11 15 58 15 17 31 40 2 25 10 0
6 56 24 15 59 15 22 31 58 2 26 24
12 56 41 16 1 15 26 32 17 2 27 18
18 57 12 16 2 15 30 32 39 2 27 12
24 57 30 16 4 15 36 33 11 2 28 6
3 0 57 49 16 6 15 41 33 23 2 28 9 0
6 58 10 16 8 15 46 33 47 2 29 24
12 58 31 16 9 15 52 34 11 2 29 18
18 58 52 16 11 15 58 34 34 2 29 12
24 59 11 16 13 16 3 34 58 2 30 6
4 0 59 30 16 14 16 9 35 22 2 30 8 0
6 59 52 16 15 16 14 35 45 2 31 24
12 60 9 16 17 16 19 36 0 2 31 18
18 60 26 16 19 16 24 36 20 2 32 12
24 60 40 16 20 16 28 36 40 2 32 6
5 0 60 54 16 21 16 31 37 0 2 32 7 0
6 61 4 16 21 16 34 37 10 2 33 24
12 61 11 16 22 16 37 37 19 2 33 18
18 61 16 16 22 16 38 37 28 2 33 12
24 61 20 16 23 16 39 37 36 2 33 6
6 0 61 24 16 23 16 39 37 40 2 33 6 0
The gradual increase or decrease of the above numbers being so small, it is sufficient to have them to every sixth degree; the proportions for the intermediate degrees being easily made by sight.
228
Table XVI. The Sun’s mean Motion and Anomaly.
Years of Christ beginning Sun’s mean Longitude from Aries. Sun’s mean Anomaly.
s ° ʹ ʺ s ° ʹ
O.S. 1 9 7 53 10 6 29 54
1301 9 17 42 30 6 16 58
1401 9 18 27 50 6 15 59
1501 9 19 13 10 6 14 59
1601 9 19 58 30 6 13 59
1701 9 20 43 50 6 12 59
N.S. 1753 9 10 16 52 6 1 38
1801 9 9 39 39 6 0 10
Old Style to the beginning of A. D. 1753; then New Style Years of Christ compleat Sun’s mean Motion. Sun’s mean Anomaly.
s ° ʹ ʺ s ° ʹ
1 11 29 45 40 11 29 45
2 11 29 31 20 11 29 29
3 11 29 17 0 11 29 14
4 0 0 1 49 11 29 58
5 11 29 47 29 11 29 42
6 11 29 33 9 11 29 27
7 11 29 18 49 11 29 11
8 0 0 3 38 11 29 55
9 11 29 49 18 11 29 40
10 11 29 34 58 11 29 24
11 11 29 20 38 11 29 9
12 0 0 5 26 11 29 53
13 11 29 51 7 11 29 37
14 11 29 36 47 11 29 22
15 11 29 22 27 11 29 7
16 0 0 7 15 11 29 50
17 11 29 52 55 11 29 35
18 11 29 38 35 11 29 20
19 11 29 24 16 11 29 4
20 0 0 9 4 11 29 48
40 0 0 18 8 11 29 36
60 0 0 27 12 11 29 24
80 0 0 36 16 11 29 12
100 0 0 45 20 11 29 0
200 0 1 30 40 11 28 1
300 0 2 16 0 11 27 1
400 0 3 1 20 11 26 1
500 0 3 46 40 11 25 2
600 0 4 32 0 11 24 2
700 0 5 17 20 11 23 2
800 0 6 2 40 11 22 3
900 0 6 48 0 11 21 3
1000 0 7 33 20 11 20 3
2000 0 15 6 40 11 10 7
3000 0 22 40 0 11 0 10
4000 1 0 13 20 10 20 13
5000 1 7 46 40 10 10 16
6000 1 15 20 0 10 0 19
Months Sun’s mean Motion. Sun’s mean Anomaly.
s ° ʹ ʺ s ° ʹ
Jan. 0 0 0 0 0 0 0
Feb. 1 0 33 18 1 0 33
Mar. 1 28 9 11 1 28 9
Apr. 2 28 42 30 2 28 42
May. 3 28 16 40 3 28 17
June 4 28 49 58 4 28 50
July 5 28 24 8 5 28 24
Aug. 6 28 57 26 6 28 57
Sep. 7 29 30 44 7 29 30
Oct. 8 29 4 54 8 29 4
Nov. 9 29 38 12 9 29 37
Dec. 10 29 12 22 10 29 11
Days. Sun’s mean Motion and Anomaly.
s ° ʹ ʺ
1 0 0 59 8
2 0 1 58 17
3 0 2 57 25
4 0 3 56 33
5 0 4 55 42
6 0 5 54 50
7 0 5 53 58
8 0 7 53 7
9 0 8 52 15
10 0 9 51 23
11 0 10 50 32
12 0 11 49 40
13 0 12 48 48
14 0 13 47 57
15 0 14 47 5
16 0 15 46 13
17 0 16 45 22
18 0 17 44 30
19 0 18 43 38
20 0 19 42 47
21 0 20 41 55
22 0 21 41 3
23 0 22 40 12
24 0 23 39 20
25 0 24 38 28
26 0 25 37 37
27 0 26 36 45
28 0 27 35 53
29 0 28 35 2
30 0 29 34 10
31 1 0 33 18
In Leap-years, after February, add one Day and one Day’s motion.
Sun’s mean Motion and Anomaly.
Hours. Mot. & Ano.
° ʹ ʺ
ʹ ʹ ʺ ʺʹ
ʺ ʺ ʺʹ ʺʺ
1 0 2 28
2 0 4 56
3 0 7 24
4 0 9 51
5 0 12 19
6 0 14 47
7 0 17 15
8 0 19 43
9 0 22 11
10 0 24 38
11 0 27 6
12 0 29 34
13 0 32 2
14 0 34 30
15 0 36 58
16 0 39 26
17 0 41 53
18 0 44 21
19 0 46 49
20 0 49 17
21 0 51 45
22 0 54 13
23 0 56 40
24 0 59 8
25 1 1 36
26 1 4 4
27 1 6 32
28 1 9 0
29 1 11 28
30 1 13 55
31 1 16 23
32 1 18 51
33 1 21 19
34 1 23 47
35 1 26 15
36 1 28 42
37 1 31 10
38 1 33 38
39 1 36 6
40 1 38 34
41 1 41 2
42 1 43 30
43 1 45 57
44 1 48 25
45 1 50 53
46 1 53 21
47 1 55 49
48 1 58 17
49 2 0 44
50 2 3 12
51 2 5 40
52 2 8 8
53 2 10 36
54 2 13 4
55 2 15 32
56 2 17 59
57 2 20 27
58 2 22 55
59 2 25 23
60 2 27 51
In Leap-years, after February, add one Day and one Day’s motion.
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Table XVII. The Sun’s Declination in every Degree of the Ecliptic.
Signs ♈ ♎ ♉ ♏ ♊ ♐
0 6 1 7 2 8
Nor. Sou. Nor. Sou. Nor. Sou.
° ° ʹ ʺ ° ʹ ʺ ° ʹ ʺ °
0 0 0 0 11 29 33 20 11 16 30
1 0 23 54 11 50 35 20 23 49 29
2 0 47 48 12 11 26 20 36 0 28
3 1 11 42 12 32 5 20 47 48 27
4 1 35 34 12 52 31 20 59 13 26
5 1 59 25 13 12 44 21 10 15 25
6 2 23 14 13 32 54 21 20 53 24
7 2 47 1 13 52 32 21 31 7 23
8 3 10 45 14 12 5 21 40 58 22
9 3 34 26 14 31 24 21 50 24 21
10 3 58 4 14 50 28 21 59 25 20
11 4 21 38 15 9 17 22 8 2 19
12 4 45 8 15 27 51 22 16 14 18
13 5 8 34 15 46 9 22 24 0 17
14 5 31 55 16 4 11 22 31 21 16
15 5 55 11 16 21 57 22 38 16 15
16 6 18 21 16 39 26 22 44 45 14
17 6 41 25 16 56 37 22 50 49 13
18 7 4 23 17 13 31 22 56 26 12
19 7 27 15 17 30 7 23 1 36 11
20 7 50 0 17 46 15 23 6 20 10
21 8 12 36 18 2 24 23 10 38 9
22 8 35 5 18 18 3 23 14 29 8
23 8 57 26 18 33 24 23 17 52 7
24 9 19 39 18 48 25 23 20 49 6
25 9 41 43 19 3 5 23 23 19 5
26 10 3 37 19 17 26 23 25 22 4
27 10 25 21 19 31 25 23 26 57 3
28 10 46 56 19 45 3 23 28 5 2
29 11 8 20 19 58 20 23 28 46 1
30 11 29 33 20 11 16 23 29 0 0
Signs ♓ ♍ ♒ ♌ ♑ ♋
1 5 10 4 9 3
Sou. Nor. Sou. Nor. Sou. Nor.
If the Sun’s place be taken from the Tables on pag. 114 and 115, his declination may be had thereby, near enough for common use, from this Table, by entering it with the signs at the head and degrees at the left hand; or with the signs at the foot and degrees at the right hand. Thus, March the 5th, the Sun’s place is ♓ 14° 53ʹ (call it 15°, being so near) to which answers 5° 55ʹ 11ʺ of the south declination.
Table XVIII. Lunations from 1 to 100000.
Lunat. Days. H. M. S.
1 Contain 29 12 44 3
2 59 1 28 6
3 88 14 12 9
4 118 2 56 13
5 147 15 40 16
6 177 4 24 19
7 206 17 8 22
8 236 5 52 25
9 265 18 36 28
10 295 7 20 31
20 590 14 41 3
30 885 22 1 34
40 1181 5 22 6
50 1476 12 42 37
60 1771 20 3 9
70 2067 3 23 40
80 2362 10 44 12
90 2657 18 4 43
100 2953 1 25 15
200 5906 2 50 30
300 8859 4 15 45
400 11812 5 41 0
500 14765 7 6 15
600 17718 8 31 30
700 20671 9 56 45
800 23624 11 22 0
900 26577 12 47 15
1000 29530 14 12 30
2000 59061 4 25 0
3000 88591 18 37 30
4000 118122 8 50 0
5000 147652 23 2 30
6000 177183 13 15 0
7000 206714 3 27 30
8000 236244 17 40 0
9000 265775 7 52 30
10000 295305 22 5
20000 590611 20 10
30000 885917 18 15
40000 1181223 16 20
50000 1476529 14 25
60000 1771835 12 30
70000 2067141 10 35
80000 2362447 8 40
90000 2657753 6 45
100000 2953059 4 50
By comparing this Table with the Table on page 113, it is easy to find how many Lunations are contained in any given number of Sidereal, Julian, and Solar years, from 1 to 8000.
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