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

by James Ferguson

360. But because the Sun’s true Place is often wanted when the Moon is neither New nor Full, we shall next shew how it may be found for any given moment of time: though this be digressing from our present purpose.

In [Table XVI] find the nearest lesser year to that in which the Sun’s Place is sought; and take out the Sun’s mean Longitude and Anomaly answering thereto; to which add his mean motion and Anomaly for the compleat residue of the years, with the month, day, hour, and minute, all taken from the same Table, and you have the Sun’s mean Longitude and Anomaly for the given time. Then, from [Table XII] take out the Sun’s Equation by means of his Anomaly (making proportions for the odd minutes of Anomaly) which Equation being added to or subtracted from the Sun’s mean Longitude from Aries, as the titles in the Table direct, gives his true Place, or Longitude from the beginning of Aries, reckoned according to the order of the Signs § [354].

EXAMPLE.
To find the Sun’s true Place April 30th, A. D. 1757, at 18 minutes 40 seconds past 10 in the morning.

				Sun’s Long.				Sun’s Anom.
				s	°	ʹ	ʺ	s	°	ʹ
The year next less than 1757 in the Table is 1753, at the beginning of which, the Sun’s mean Longitude from the beginning of Aries, and his mean Anomaly, is				9	10	16	52	6	1	38
To which add his mean Mot. and Anom. for four years to make 1757				0	0	1	49	11	29	58
And likewise his mean Mot. and Anom. for		April		2	28	42	30	2	28	42
		days	29	0	28	35	2	0	28	35
		hours	22		0	54	13		0	54
		min.	18			0	44			1
		sec.	49				2			0
Sun’s mean Longitude and Anomaly for the given time is				1	8	31	12	9	29	48
To which add the Equation of the Sun’s mean Place					1	40	14	Sun’s Eq.
And it gives his true Place, viz. ♉ Taurus 10° 11ʹ 26ʺ				1	10	11	26	1°	40ʹ	14ʺ

N. B. In leap-years after February, the Sun’s mean Motion and Anomaly must be taken out for the day next after the given one.

361. To calculate the Sun’s true Place for any time in a given year before the first year of Christ: subtract the mean Motions and Anomalies for the compleat hundreds next above the given year; to the remainder add those for the residue of years, months, &c. and then work in all respects as above taught.

EXAMPLE.
To find the Suns true Place May the 28th at 4 hours 3 min. 42 sec. in the afternoon, the year before Christ 585, which was a Leap year[^[82]].

					Sun’s Long.				Sun’s Anom.
					s	°	ʹ	ʺ	s	°	ʹ
From the Sun’s mean Longitude and Anomaly at the beginning of the year Christ 1					9	7	53	10	6	29	54
Subtract his mean Motion and Anomaly for 600 years					0	4	32	0	11	24	2
And the remainder, or radix, is					9	3	21	10	7	5	52
To which add what 585 wants of 600, viz. 15 years					11	29	22	27	11	29	7
And also those of		May			3	28	16	40	3	28	17
		days	28	Bissextile	0	28	35	2	0	28	35
		hours	4			0	9	51		0	10
		min.	3				0	7
		sec.	42					2	0	2	1
									Sun’s Anom.
Sun’s mean Long. May 28th, at 4 hour 3 min. 24 sec. afternoon					1	29	45	19
Equation of the Sun’s mean Place subtract							2	2	2ʹ 22ʺ
									Sun’s Equat.
Rem. his true Place for the same time, viz. ♉ Taurus 29° 43ʹ 17ʺ					1	29	43	17	subtract.

N. B. As the Longitudes or Places of all the visible Stars in the Heavens are well known, we have an easy method of finding the Sun’s true Place in the Ecliptic: for the Sun is directly opposite to that Point of the Ecliptic which comes to the Meridian at mid-night.

To find the Sun’s Declination.