To calculate the time of New and Full Moon.
First Element or Requisite.
355. Precept I. For any proposed year in the 18th Century, take out the mean time of the New Moon in March from [Table I.], and the mean time of Full Moon from [Table III.], for the Old Stile; or from Tables II and IV for New Stile; with the mean Anomalies of the Sun and Moon for these times, and set them by themselves. Then, from [Table VI], take out as many Lunations as the proposed Month is after March, with the days, hours, and minutes belonging to them; and also the mean Anomalies of the Sun and Moon for these Lunations.
II. Add the days, hours, and minutes of these Lunations to the time of New or Full Moon in March, and the Anomalies for the Lunations to the Anomalies for March: the sums give the hours and minutes of the mean New or Full Moon required, and the mean Anomalies of the Sun and Moon for that time.
III. Then, with the number of days enter [Table VII], under the given Month, and right against this number, in the left hand column you have the day of New or Full Moon; which set before the hours and minutes above-mentioned.
IV. But, (as it will sometimes happen) if the number of days fall short of all those under the given Month, add one Lunation with its Anomalies from [Table VI] to the foresaid sums; so you will have a new sum of days wherewith to enter the 7th Table under the given Month, where you are sure to find that sum the second time, if the first falls short.
V. With the Signs and Degrees of the Sun’s Anomaly enter Table VIII, The Moon’s annual Equation, and take out the minutes of time of that Equation by the Anomaly; remembring, that if the Signs are at the head of the Table, the degrees are at the left hand, in which case the Equation found in the Angle of meeting must be subtracted from the mean time of New or Full Moon, as the title Subtract, at the head of the Table directs: but if the Signs are at the foot of the Table their degrees are in the right-hand column, and the Equation where the Signs and Degrees meet in the Table is to be added to the mean time, as the title Add, at the foot of the Table directs; which Equation, so applied, gives the mean time of New or Full Moon corrected.
VI. With the Signs and Degrees of the Sun’s Anomaly enter [Table IX], Equation of the Moon’s mean Anomaly, and take out the Equation thereof; adding it to the mean Anomaly or subtracting it therefrom, as the titles at the head or foot of the Table direct; and it gives the mean Anomaly corrected. Then, with the Sun’s Anomaly enter [Table XII], Equation of the Sun’s mean Place, and take out that Equation, applying it to the Moon’s corrected Anomaly as the titles direct; and it will give the Moon’s Anomaly equated[[77]]. N. B. In all these Equations, care must be taken to make proper allowance for the odd minutes of Anomaly; the Tables having the Equations only for compleat Degrees.
VII. With the Moon’s equated Anomaly enter [Table X], The Moon’s elliptic Equation, and take out that Equation in the same manner as the preceding: adding it to the former corrected time if the Signs be at the head of the Table, or subtracting it if they be at the foot, as the Table directs; and this gives the mean time equated.
VIII. Lastly, enter [Table XI], The Sun’s Equation at New and Full Moon, with the Sun’s Anomaly, and take out the Sun’s Equation in the same manner as the others; adding it to, or subtracting it from the former equated time, as the titles direct: and by this last Equation you have the true time of New or Full Moon, agreeing with well regulated Clocks and Watches. But to make it agree with true Sun-Dials, the Equation of time must be applied as taught § [225].