Astronomy Explained Upon Sir Isaac Newton's Principles / And made easy to those who have not studied mathematics

by James Ferguson

Table IV. The mean Full Moons, &c. in March to the New Style.

Years of Christ.	Mean time of Full Moon in March.			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
1753	18	23	18	7	18	35	7	25	21	4	19	4	11	27	8	7	8	4
1754	8	8	17	7	7	53	6	5	10	4	27	7	11	16	26	6	19	18
1755	27	5	49	8	26	14	5	10	46	6	5	49	0	4	49	5	29	0
1756	15	14	38	8	15	30	3	20	35	6	13	52	11	24	6	5	10	14
1757	4	23	27	8	4	36	2	0	23	6	21	55	11	13	23	4	21	27
1758	23	20	59	8	23	8	1	5	59	8	0	38	0	1	46	4	1	9
1759	13	5	47	8	12	25	11	15	48	8	8	41	11	21	3	3	12	22
1760	1	14	36	8	1	41	9	25	37	8	16	44	11	10	20	2	23	35
1761	20	12	9	8	20	2	9	1	13	9	25	27	11	28	43	2	3	16
1762	9	20	57	8	9	19	7	11	2	10	3	31	11	18	0	1	14	29
1763	28	18	30	8	27	40	6	16	38	11	12	13	0	6	23	0	24	11
1764	17	3	19	8	16	56	4	26	26	11	20	16	11	25	40	0	5	24
1765	6	12	8	8	6	13	3	6	15	11	28	19	11	14	57	11	16	38
1766	25	9	40	8	24	34	2	11	52	1	7	1	0	3	20	10	26	20
1767	18	18	29	8	13	50	0	21	41	1	15	4	11	22	37	10	7	33
1768	3	3	17	8	3	6	11	1	29	1	23	7	11	11	54	9	18	46
1769	22	0	50	8	21	28	10	7	5	3	1	49	0	0	17	8	28	28
1770	11	9	39	8	15	45	8	16	54	3	9	52	11	19	34	8	9	42
1771	30	7	11	8	29	6	7	22	30	4	18	36	0	7	57	7	19	21
1772	18	16	0	8	18	22	6	2	18	4	26	39	11	27	14	7	0	35
1773	8	0	48	8	7	38	4	12	7	5	4	42	11	16	31	6	11	49
1774	26	22	21	8	26	0	3	17	43	6	13	24	0	4	54	5	21	31
1775	16	7	10	8	15	16	1	27	31	6	21	27	11	24	11	5	2	44
1776	4	15	58	8	4	32	0	7	20	6	29	30	11	13	28	4	13	58
1777	23	13	31	8	22	54	11	12	56	8	8	13	0	1	51	3	23	39
1778	12	22	20	8	12	10	9	22	45	8	16	16	11	21	8	3	4	52
1779	2	7	8	8	1	26	8	2	34	8	24	19	11	10	25	2	16	5
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

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
3600	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.

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.