the equation of the Moon's mean anomaly; subtract this equation from her mean anomaly, if the signs of the Sun's anomaly be at the head of the table, but add it if they be at the foot; the result will be the Moon's equated anomaly, with which enter Table IX, and take out the second equation for reducing the mean to the true time of new or full Moon; adding this equation, if the signs of the Moon's anomaly be at the head of the table, but subtracting it if they be at the foot, and the result will give you the mean time of the required new or full Moon twice equated, which will be sufficiently near for common almanacks.-But when you want to calculate an eclipse, the following equations must be used: thus,

VIII. Subtract the Moon's equated anomaly from the Sun's mean anomaly, and with the remainder in signs and degrees, enter Table X, and take out the third equation, applying it to the former equated time, as the titles Add or Subtract do direct.

IX. With the Sun's mean distance from the ascending node enter Table XI, and take out the equation answering to that argument, adding it to, or subtracting it from, the former equated time, as the titles direct, and the result will give the time of new or full Moon, agreeing with well-regulated clocks or watches, very near the truth. But, to make it agree with the solar, or apparent time, apply the equation of natural days, found in the table (from page 193 to page 205) as it is leap-year, or the first, second, or third after.

The method of calculating the time of any new or full Moon without the limits of the 18th century, will be shewn further on. And a few examples, compared with the precepts, will make the whole work plain.

N. B. The tables begin the day at noon, and reckon forward from thence to the noon following. -Thus, March the 31st, at 22h. 30min. 25sec. of tabular time, is April 1st (in common reckoning) at 30min. 25sec. after 10 o'clock in the morning.

By the Precepts,

EXAMPLE I.

Required the true Time of New Moon in April 1764, New Style.

New Moon. | Sun's Anom. Moon's Anom. Sun fro. Node.

Time once equated,
Second equation,
Time twice equated,
Third equation,

Time thrice equated,
Fourth equation,
True new Moon,
Equation of days,
Apparent time,

EXAMPLE II.

Qu. The true mean time of Full Moon in May, 1762, Old Style.

New Moon. | Sun's Anom. Moon's Anom. Sun fro. Node.

7 15 50 35 +15

7 15 50 50

Ans. May 7th at 15 h.

50 m. 50 sec. past

noon, viz. May 8th at III h. 50 min. 50 sec. in the morning.

that time, as already taught.

and take out the first mean new Moon and its anoma lies, &c. belonging to the said centuries, and set them year in the 18th century, will answer to the given year; Table VI. as, when subtracted from the abovesaid II. Take as many complete centuries of years from

anomalies and Sun's mean distance from the node at in March, old style, for that year, with the mean proposed, and take out the mean time of new Moon the 18th century with that of the year in the century PRECEPT I. Find a year of the same number in

between the Christian Era and the 18th Century. given Year and Month of any particular Century, To calculate the Time of New and Full Moon in a

precepts and examples. true time of new or full Moon, as shewn in the above tury proposed.-Then, work in all respects for the of new Moon in March, in the given year of the cenmainders will be the mean time and anomalies, &c. turies, from those of the 18th century, and the reIII. Subtract the numbers belonging to these cen

as above. This circumstance happens new Moon, in March, and then proceed in all respects lies. &c. from Table, III to the time and anomalies of out in the 18th century, add a lunation and its anomathe number of days from the beginning of Marchtaken IV. If the days annexed to these centuries exceed

below those taken out for March in the 18th century.

in

example V.

EXAMPLE III.

Required the true mean time of Full Moon in April, Old Style, 4. D. 50.

From 17.30 subtract 1700 (or 17 centuries) and there remains 30.

1700 years subtract,

Full D March, A. D. 30.

Add 1 lunation,

New Moon. | Sun's Anom. Moon'sAnom.[Sun fro. Node.

Full Moon, April,

2 3 39

Sun fro. Node,
and Arg. 4th
equation.

Hence it appears, that the mean time of
full Moon in April A. D. 30, old style, was on
the 6th day, at 25 m. 11 sec. past VIII in the
evening.

S 0
8 18 4 31|
0 14 33 10
9 2 37 41
11 28 46 C
9 3 51 41
0 29
S
6 19 0 25 4) 01
10 2.58 01 5 9 39 47
5 10 58 40+ 1 18 53
4 21 59 20 5 10 58 40
+257 55 Arg. 3d equat.[Arg. 2d equat.

S

S

9 0 32 17)
6 12 54 301
13 13 26 47
10 29 36 0

0 15 20 7

2

8 37 23

4 29 23 0

4 13 50 47

9

9. 14 23

1

0 40 14

10

9 54 37

ber of complete centuries. fore Christ, diminished by one, shall make a numwhich being added to the given number of years be To calculate the true Time of New or Full Moon in any given PRECEPT I. Find a year in the 18th century, Year and Month before the Christian Æra.

in any month of that year, proceed in the manner Christ. Then, for the true time of that new Moon, the mean new Moon in March, the given year before mainder will denote the time and anomalies, &c. of above-found year of the 18th century; and the refrom those of the mean new Moon in March, the and subtract the time and anomalies belonging to it II. Find this number of centuries in Table VI,

taught above.

EXAMPLE IV.

Required the mean time of New Moon in May, Old Style, the year before

Christ 585.

The years 584 added to 1716, make 2300, or 23 centuries.

Sun's Anom. Moon's Anom. Sun fro. Node.

S

S

2

2 17 27

5 15 42

+

6

6

36 Sun fro. Node,

5 15 41 27 and Arg. 4th equation.

2 14 58 Arg. 3d equat. Arg. 2d equat

So the mean time was May 28th, at 2 mi-
nutes 31 seconds past IV in the afternoon.