m 
ASTRONOMY. 
Moon were lafl equal. The epafl for any month is the 
age which the Moon would have had at the beginning of 
the month, if its age had been nothing at the beginning 
of the year. Now, from the tables, take out the epaft for 
the year and month, and fubtract the fum from 2gd. 12b. 
44'. 3". one fynodic revolution of the Moon, or two if ne- 
ceirary, fo that the remainder may be lefs than a revolu¬ 
tion, and that remainder gives the time of the mean con¬ 
junction. If to this we add i4d. 1SI1. 22' 1-4" half a re¬ 
volution, it gives the time of the next mean oppolition; 
or, if we fubtract, it gives the time of the preceding mean 
oppolition. if it be leap-year, in January and February 
fubtract a day from the fum of the epatts, before you 
make the fubtraClion. When the day of the mean con¬ 
junction is o, it denotes the lafl: day of the preceding 
month. Ex. To find the time of the mean new and full 
moons in February, 1795. 
F.paft 1795 
- 
gd. 
nil. 
6'. 
I?"- 
February 
- 
I 
I X 
15 
57 
IO 
22 
22 
14 
29 
I 2 
44 
3 
Mean new Moon 
- 
18 
i 4 
21 
49 
if 
18 
22 
1 '4 
Mean full Moon 
- 
3 
!9 
59 
47-6 
To determine whether an eclipfe may happen at oppo- 
iition, find the mean longitude of the Earth at the time of 
mean oppofition, and alio the longitude of the Moon’s 
node ; then, according to M. Caffini, if the difference be¬ 
tween the mean longitudes of the Earth and the Moon’s 
node be lefs than 7 0 30', there mujl be an eclipfe; if it be 
greater than 14 0 30', there cannot be an eclipfe ; but, be¬ 
tween 7 0 30' and 14 0 30' there may , or may not , be an 
eclipfe. M. de Lanibre makes thefe limits 7 0 47' and 
■13° 21'. 
Ex. To find whether there will be an eclipfe at the full 
Moon on February 3, 1795. 
Sun’smean long.at 3d.i9h.59'47 - 6" iof. 13 0 . 27'. 20-8". 
Mean long, of the Earth 
_ 
4 
13 
27 20'S 
Long, of the Moon’s node 
- 
4 
8 
I 48-5 
Difference 
- 
O 
5 
25 3*'3 
Hence there imift be an eclipfe.—Examine thus all the 
new and full moons for a month before and a month after 
the time at which the Sun comes to the place of the nodes 
•of the lunar orbit, and you will be hire not to mils any 
eclipfes. Or, having the eclipfes for the lafl eighteen 
years, if we add to tire times of the middle of thefe eclip¬ 
fes, i8y. jod. or nd. 7)1. 43-Jh it will give the times when 
we may expect the eclipfes will return. 
To the time of mean oppofition, compute the true lon¬ 
gitudes of the Sun and Moon, and the Moon’s true lati¬ 
tude; and find, from the tables of their motions, the ho¬ 
rary motions of the Sun and Moon in longitude, and the 
difference ( d) of their horary motions is the relative ho¬ 
rary motion of the Moon in refpett to the Sun, or the mo¬ 
tion with which the Moon approaches to, or recedes from, 
the Sun; find alfo the Moon’s horary motion in latitude; 
and fuppofe the time ( t) of mean oppofition, the Moon is 
at the difiance («) from oppolition; then d : m :: 1 hour 
the time (w) between t and the oppofition, which added 
to or fubtrafted from the time t, according as the Moon 
is not yet got into oppolition, or is beyond it, gives the 
time of the ecliptic oppolition. 
To find the place of the Moon in oppofition, let n be 
the Moon's horary motion in longitude; then, 1 hour : 10 
n : the increafe of the Moon’s longitude in the time to, 
which, applied to the Moon’s longitude at the time of the 
mean oppofition, gives the true longitude of the Moon at 
the time of the ecliptic oppofition. The oppofite to that 
mud be the true longitude of the Sun. Find alfo the 
Moon’s true latitude at the time of oppolition, by faying, 
1 hour ; w :: the horary motion in latitude : the motion in 
latitude in the time w, which, applied fo the Moon’s la¬ 
titude at the time of the mean oppofition, gives the true 
latitude at the time of the true oppofition. For greater 
certainty compute again from the tables the places of the 
Sun and Moon, and if they be not exactly in oppofition, 
which probably may not be the cafe, as the Moon’s lon¬ 
gitude does not increafe uniformly, repeat the operation. 
This accuracy, however, in eclipfes is generally unnecelfa- 
ry; for the belt lunar tables cannot be depended upon to 
give the Moon’s longitude nearer than 30"; therefore the 
probable error from the tables is valtly greater than that 
which arifes from the motion in longitude not being uni¬ 
form. Unlefs therefore very great accuracy be required, 
this operation is unneceflary. In like manner we may com¬ 
pute the true time of the ecliptic conjunction, and the 
places of the Sun and Moon for that time, when we cal¬ 
culate a folar eclipfe. 
With the Sun’s horary motion in longitude, and the 
Moon’s in longitude and latitude, find the the inclination 
of the relative orbit, and 
the horary motioji upon it. 
To do this, let LM be 
the horary motion of the 
Moon in longitude, S M 
that of the Sun ; draw M a 
perpendicular to LM and M S 
equal to the Moon’s horary motion in latitude ; take S b 
— M a, and parallel to it, and join ha, L b-, then La is 
the Moon’s true orbit, and Lb its relative orbit in refpeCt 
to the Sun. Hence LS (the difference of the horary mo¬ 
tions in longitude) : (the Moon’s horary motion in la¬ 
titude) :: radius : tan. ^LS tire inclination of the relative 
orbit; and cof £LS : radius :: LS : Li the horary motion 
in the relative orbit. By logarithms the calculations are 
thus: 
Log. Si-|-io, —log. LS — log. tan. iLS. 
Log. LS-)-io, — log. cof. iLS = log. Lb. 
M. de la Lande obferves, that if we add 8" to the diffe¬ 
rence of tlie horary motion in longitude it will give the 
horary motion in the relative orbit; for in a right-lined tri¬ 
angle, of which the bafe is the difference of the horary 
motions in longitude, which is about half a degree, and 
the angle at the bafe about 5-| 0 , the difference between 
the bale and hypothenufe will always be about 8". 
At the time of oppolition, find, from the tables, the 
Moon’s horizontal parallax, its femidiameter, and the fo- 
midiameter of the Sun, the horizontal parallax of which 
we may here take =9". To find the femidiameter of the 
Earth’s fliadow at the Moon, feen from the Earth ; let 
A B be the diameter of the Sun, T R the diameter of the 
O and C their centers ; draw A T, B R, to meet at I, and 
join O C I ; let F G H be the diameter of the Earth’s flia¬ 
dow at the diftance of the Moon, and join O T, C F. 
Now, the angle FGG”CFA—CIA, but.CIA—OTA— 
TOC, therefore FCGrrCFA—OTA-j-TOC, that is, 
the angle under which the femidiameter of the Earth’s 
fliadow appears at the Moon, is equal to the fum of the 
horizontal parallax of the Sun and Moon diminilhed by 
the apparent femidiameter of the Sun. In eclipfes of the 
Moon, the fliadow is found to be a little greater than this 
rule gives it, owing to the atmofphere of the Earth. This 
augmentation of the femidiameter is, according to M. 
Caffini, 20''; according M. Monnier, 30"; and, accord¬ 
ing to M. de Hire, 60". . As the angle CIT (-OTA— 
TOC) is known, we have fin. TIC ; cof. TIC :: TC : Cl 
