III. Subtract the Conjunctions and Anomalies of these Centuries from those of the New or Full Moon in March above taken out, and the remainders will shew the mean time of New or Full Moon in March the given year, with the Anomalies of the Sun and Moon at that time. Then, work in all respects for the true time of the proposed New or Full Moon, as taught by the Precepts already given § [355].
EXAMPLE I.
To find the time of New Moon in July 1581, O. S.
From 1781 subtract 200 years, and there remains 1581.
| Days | Hours | Min. | Sun’s Anom. | Moon’s Ano. | |||||
|---|---|---|---|---|---|---|---|---|---|
| s | ° | ʹ | s | ° | ʹ | ||||
| Table I. Mean time of New Moon in March 1781 | 13 | 7 | 52 | 8 | 23 | 37 | 0 | 0 | 53 |
| Tab. V. Conj. and Anom. for 200 years subtract | 8 | 16 | 22 | 0 | 6 | 42 | 5 | 0 | 44 |
| Remain the Conj. and Anom. for March 1581 | 4 | 15 | 30 | 8 | 16 | 55 | 7 | 0 | 9 |
| Tab. VI. Add, for five Lunations, to bring it to July | 147 | 15 | 40 | 4 | 25 | 32 | 4 | 9 | 5 |
| The sums are | 152 | 7 | 10 | 1 | 12 | 27 | 11 | 9 | 14 |
| The Days in Tab. VII. answer to July 30th | 30 | 7 | 10 | Equ. Moon’s Anom. | + | 13 | |||
| Sum of the three Equations subtract | - | 7 | 9 | Anom. cor. | 11 | 9 | 27 | ||
| Sun’s Equat. | - | 1 | 16 | ||||||
| True time of Conjunction, July | 30 | 0 | 1 | Moon’s Ano. | 11 | 8 | 11 | ||
| Which is the 30th day, at one minute past noon, as shewn by well regulated Clocks or Watches | Moon’s ann. Eq. | 0h | 14m | sub. | |||||
| Her ellipt. Equ. | 3 | 35 | sub. | ||||||
| Sun’s Equation | 3 | 20 | sub. | ||||||
| Sum | 7 | 9 | sub. | ||||||
EXAMPLE II.
To find the time of Full Moon in April A. D. 30, O. S.
From 1730 subtract 1700, and there remains 30.
| Days | Hours | Min. | Sun’s Anom. | Moon’s Ano. | |||||
|---|---|---|---|---|---|---|---|---|---|
| s | ° | ʹ | s | ° | ʹ | ||||
| Tab. III. Mean time of Full Moon in March 1730 | 22 | 6 | 58 | 9 | 2 | 40 | 3 | 13 | 23 |
| Tab. V. Conj. and Anom. for 1700 years subtract | 14 | 17 | 37 | 11 | 28 | 46 | 10 | 29 | 36 |
| Rem. the Opposition and Anom. in March A. D. 30 | 7 | 13 | 21 | 9 | 3 | 54 | 4 | 13 | 47 |
| Tab. V. Add, for one Lunation, to bring it into April | 29 | 12 | 44 | 0 | 29 | 6 | 0 | 25 | 49 |
| The sums are | 37 | 2 | 5 | 10 | 3 | 0 | 5 | 9 | 36 |
| The Days in Tab. VII. answer to April 6 | 6 | 2 | 5 | Equ. Moon’s Anom. | - | 17 | |||
| To which add the sum of the three Equations | 6 | 1 | Anom. cor. | 5 | 9 | 19 | |||
| Sun’s Equat. | + | 1 | 35 | ||||||
| True time of Opposition April A. D. 30 | 6 | 8 | 6 | Moon’s Ano. | 5 | 10 | 54 | ||
| Which is the 6th day, at 6 minutes past 8 in the Evening. And thus, the time of New or Full Moon may be found for any given year and month after the Christian Æra. | Moon’s ann. Eq. | 0h | 18m | add | |||||
| Her ellipt. Equ. | 2 | 46 | add | ||||||
| Sun’s Equat. | 2 | 57 | add | ||||||
| Sum | 6 | 1 | add | ||||||
Remark.
N. B. Sometimes it happens that the days annexed to the Centuries in [Table V] are more in number than the days on which the New or Full Moon happens in March the year of the 18th Century, with which the computation begins; as in the third following Example, viz. for the Full Moon in March the year before Christ 721: in which case, a Lunation and it’s Anomalies must be added, from Table VI, to the days and Anomalies of the New or Full Moon in March; and then, subtraction can be made: and having gained a remainder, work in all respects as taught in § [355].