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.

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

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