ASTRONOMY. 
pueceding figure in p. 445, with the centre C and radius 
CZ?=4i' 13", the femidiameter of the Ihadow, defcribe a 
circle ; draw Cn perpendicular to ABC and equal to 37' 19" 
the Moon’s latitude at the ecliptic conjunction ; make the 
angle C«A=8+° 1 S' 33” the complement of the angle which 
the relative orbit makes with the ecliptic, and produce 
Nn to L ; with a radius—56' 37", the Cum of the femi- 
diameters of the Earth’s Ihadow and Moon, fet oft Cz , 
Cx ; let fall the perpendicular Coupon NL; and with the 
centres 2, m, x, and radius —15' 24", the femidiameter of 
the Moon, defcribe the circles reprefenting the Moon. 
To find the beginning, middle, and end, mark the point 
n 12I1. 32'. the time of the ecliptic conjunction; and, with 
a radius equal to the relative horary motion of the Moon 
upon AT, (etofF that extent from n both ways, and divide 
each interval into as many equal parts as can conveniently 
be done; and continue thefe divilions to z and x, and the 
times correfponding to the points z, m, x, (hew the begin¬ 
ning, middle, and end, of the eclipfe. And, if tr be mea- 
fureri upon the fcale, it will Ihew the digits eclipfed. This 
method will give the time fufficiently near, when we only 
want to predict the eclipfe, as we may depend upon the 
time to a minute, if the radius CB be fix or feven inches. 
We may alfo proceed the fame if the eclipfe be total. 
To CALCULATE an Eclipse of the Sun for any par¬ 
ticular Place. 
An eclipfe of the Sun, or rather of the Earth, without 
refpeCt to any particular place, may be calculated exaCtly 
in the fame manner as an eclipfe of the Moon, that is, 
the times when the Moon’s umbra or penumbra firfl touches 
and leaves the Earth ; but to find the times of the begin¬ 
ning, middle, and end, at any particular place, the appa¬ 
rent place of the Moon, as feen from thence, mult be de¬ 
termined, and confequently its parallax in latitude and 
longitude mufi be computed, which renders the calcula¬ 
tion of a folar eclipfe extremely long and tedious. 
Having determined that there will be an eclipfe fome- 
where upon the Earth, compute, by the aftronomical ta¬ 
bles, the true longitudes of the Sun and Moon, and the 
Moon’s true latitude, at the time of mean conjunction; 
find alfo the horary motions of the Sun and Moon in lon¬ 
gitude, and the moon’s horary motion in latitude ; and 
compute the time of the ecliptic conjunction of the Sun 
and Moon, in the fame manner as the time of the ecliptic 
oppolition was computed. At the time of the ecliptic 
conjunction, compute the Sun’s and Moon’s longitude, 
and the Moon’s latitude; find alfo the equatorial horizon¬ 
tal parallax of the Moon from the tables .of the Moon’s 
motion, and reduce it to the horizontal parallax for the 
given latitude, from which fubtract the Sun’s horizontal 
parallax, and you get the horizontal parallax of the Moon 
from the Sun ; reduce alfo the apparent latitude of the 
place on the fpheroid to the latitude on a iphere. 
To this reduced latitude of the place, and the corref¬ 
ponding horizontal parallax of the Moon from the Sun, 
(which we here ufe inftead of the horizontal parallax of 
the Moon, as we want to find what effect the parallax has 
in altering their apparent relative fituations,) at the time 
©f the ecliptic conjunction, compute the Moon’s parallax 
in latitude and longitude from the Sun; the parallax in 
latitude applied to the true latitude gives the apparent la¬ 
titude ( L ) of the Moon from the Sun ; and the parallax 
in longitude (hews the apparent difference (D) of the lon- 
figure, Let S he the Sun, E C the ecliptic ; take S M—D, 
draw MN perpendicular to Mb and take it —L, then N 
is the apparent place of the Moon, and SNr= t/'D“-j-L“ is 
the apparent diltance of the Mooii front the Sun. 
If the Moon be to the eajl of the nonagefimal degree,, 
the parallax increafes rite longitude; if to the weft, ;t di- 
mimfbes it; hence if the true longitudes of th Sun and 
Moon be equal, in the former cafe the apparent place will 
lie from S towards E, and in the latter towards C. To 
fonte time, as an hour, after the true conjunction if the 
apparent place be towards C, or if the M ion be to the 
zvefl of the nonagefimal degree 4 or before the true conjunc¬ 
tion if the apparent place be towards E, or if the Moon 
be to the eajl of the nonagefimal degree, find the Sun’s 
and Moon’s true longitude, and the Moon’s true iatirude, 
from their horary motions; and to the fame t ine conniute 
the Moon’s parallax in latitude and longitude from the 
Sun; apply the parallax in latitude to the true latitude, 
and it gives the apparent latitude (/) of the Moon from 
the Sun ; take the difference of the Sun’s and Moon’s true 
longitude, and apply the parallax in longitude, and it 
gives the apparent difiance (d) of the Moon from the Sun 
in longitude. From S fet off S P=r^, and to E C erect the 
perpendicular PQ-equal to /, and Q^is the apparent place 
of the Moon at one hour from the true conjunction ; and 
s d= x /d‘+t “is the apparent difiance of the Moon from 
the Sun ; draw the firaight line N and it will repre- 
fent the relative apparent path of the Moon, confidered 
as a firaight line, in general it being very nearly fo ; its- 
value alfo represents the relative horary motion of the 
Moon in the apparent orbit, the relative horary motion in 
longitude being M P. 
The difference between the Moon's apparent diliance in 
longitude from the Sun at the time of the true ecliptic con¬ 
junction, and at the interval of an hour, gives the appa¬ 
rent horary motion (r) in longitude of the Moon from the 
Sun; the difference ( D ) between the true longitude at the 
ecliptic conjunction and the Moon’s apparent longitude is 
the apparent diftance of the Moon from the Sun in longi¬ 
tude at the true time of the ecliptic conjunction ; hence, 
r : D 1 hour : the time from the true to the apparent 
conjunction, confequently we know the time of the appa¬ 
rent conjunction. To find whether tlfis time is accurate, 
we may compute (from the horary motions of the Sun and 
Moon) their true longitudes, and the Moon’s parallax in 
longitude from the Sun, and apply it to the true longitude, 
and it gives the apparent longitude; and, if this be the fame 
as the Sun’s longitude, the time of the apparent conjunc¬ 
tion is truly found ; if they be not the fame, find from 
thence the true time, as before. To the true time of the’ 
apparent conjunction, find the Moon’s true latitude from 
its horary motion, and compute the parallax in latitude, 
and you get the apparent latitude at the time of rhe appa¬ 
rent conjunction. Draw SA perpendicular to CE and equal 
to this apparent latitude ; then tiie point A will probably 
not fall in A' r Q ; firfl let it fail in Q .V, to which draw SB 
perpendicular, and NR parallel, to PM. Then knowing’ 
NR (—PM), and QR (—QP~MN), »e have 
NR : RO :: rad. : tan. QNR, or A.SB 
Sin. QNR : rad. :: QR : QN 
The time of deferibing NO in the apparent orbit being equal 
to the time from M to P in longitude, NQ is the horary 
motion in the apparent orbit. 
Rad. : fin. ASB :: AS : AB. 
Rad. : cof. ASB :: AS : SB. 
At the apparent conjunction the Moon appears at A , 
which time is known ; when the Moon appears at B, it is 
at its neareft d:ftance from the Sun, and confequcn -y 'he 
time is that of the greaiefl obfeuration,. (ulmilty called the 
time of the middle,) provided rhere is an eclipfe, which 
will always be the cafe when SB - lets lian the fum of tp» 
apparent femidiameters of the Sun and Moon. If there¬ 
fore it appears that there will be an eclipte, we proceed 
thus 
