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

by James Ferguson

EXAMPLE I.
To find the time of New Moon in April 1764, N. S.

	Days	Hours	Min.	Sun’s Anom.			Moon’s Ano.
				s	°	ʹ	s	°	ʹ
Tab. II. Mean time of New Moon in March	2	8	57	8	2	23	10	13	32
Add, for Lunation, from Tab. VI.	29	12	44	0	29	6	0	25	49
Mean New Moon and Anomaly	31	21	41	0	1	29	11	9	21
To which Time add the Moon’s Ann. Equ. Tab. VIII.	+	0	22	Equ. Moon’s Anom.				-	20
And it gives the Mean time corrected	31	22	3	Anom. cor.			11	9	1
From which subtract the Moon’s elliptic Equ. Tab. X.	-	3	10	Sun’s Equat.			+	1	56
				Moon’s Ano.			11	10	57
And it gives the Mean time equated	31	18	53				h.	m.
To which add the Sun’s Equation, Tab. XI.	+	3	32	Moon’s ann. Equ.			0	22	add
				Her ellipt. Equ.			3	10	sub.
And it gives the true time of Conjunction	31	22	25	Sun’s Equation			3	32	add

Which true time answers to the first of April, at 25 minutes past 10 in the forenoon: for, as the Astronomical Day begins at Noon, then 22 hours 25 min. after the Noon of March 31, is April 1, at 10 hours 25 min. in the Forenoon.

EXAMPLE II.
To find the time of Full Moon in May 1761, N. S.

	Days	Hours	Min.	Sun’s Anom.			Moon’s Ano.
				s	°	ʹ	s	°	ʹ
Mean time of Full Moon in March	20	12	9	8	20	2	9	1	13
Add, for two Lunations	59	1	28	1	28	13	1	21	38
The several sums are	79	13	37	10	18	15	10	22	51
The days, in Tab. VII, answer to May 18	18	13	37	Equ. Moon’s Anom.				-	13
Moon’s annual Equation add		+	14	Anom. cor.			10	22	38
Mean time corrected	18	13	51	Sun’s Equat.			+	1	15
Moon’s elliptic Equation subtract	-	5	38	Moon’s Ano.			10	23	53
Mean time equated	18	8	13				h.	m.
Sun’s Equation add	+	2	19	Moon’s ann. Equ.			0	14	add
				Her ellipt. Equ.			5	38	sub.
True time of Opposition, May	18	10	32	Sun’s Equation			2	19	add

Namely, the 18th day, at 32 minutes past 10 at night.

The Leap-years are allowed for in the Tables, so as to give no Trouble in these Calculations.

To compute the time of New and Full Moon in a given year and month, of any particular Century, between the Christian Æra[^[78]] and 18th Century.

Precept I. Find the like year of the 18th Century in [Table I.], for New Moon, or [Table III.], for Full Moon; and take out the New or Full Moon in March for that year, with the Anomalies of the Sun and Moon.

II. From [Table V], take as many compleat Centuries, as when subtracted from the above year of the 18th Century, will answer to the given year; and take out the Conjunctions and Anomalies of these Centuries.