44? ASTRO 
thus to find its quantity, and the beginning and end. As 
we may confider the motion to be uniform, QN : AB :: the 
time or deferibing NQ : the time of deferibing ? 1 B, which 
added to or fubtrafted from the time at A, (according 
• as the apparent latitude is decreafing or increafing,) gives 
the time of the greateft obfeuration. Or, inftead of taking 
ON and the time of deferibing it, we may take A.n and 
the correfponding time, which will be more accurate. 
From the fum of the apparent femidiameters ct the 
Sun and Moon fubtraft BS, and the remainder fiiews how 
much of tlie Sun is covered by the Moon, or the parts 
deficient; hence, femid. 0 : parts deficient :: 6 digits : 
the digits eclipfed. if. SB be lefs than the difference of 
the femidiameters of the Sun and Moon, and the Moon’s 
femidiameter be the greater, theeclipfe will be total-, but, 
if it be tile lefs, the eclipfe will be annular, the Sun ap¬ 
pearing all round the Moon ; if B and 5 coincide, the 
eclipfe will be central. 
' Let A fall out of QN ; and, to increafe the accuracy, 
near to the apparent conjunction, that is. within ten or fit- 
teen minutes, calculate the aparent longitude mS of the 
Moon from the Sun, and the apparent latitude mn draw 
nr parallel to Sm ; and in the triangle Anr, find .the angle 
Anr which is equal to ASB, and compute SB, AB, as before. 
But, except in cafes where very great accuracy is required, 
this is unneceffary. If NQ were a perfect (traight line, 
the firft operation would give the correft values of AB, 
BS. Kepler, in an eclipfe in 1598, found a curvature of 
more than three minutes in three hours, becaufe the Moon 
was very near the honagefimal. In the eclipfe in 1764, M. 
dc la Lande found a curvature of twenty-fix feconds, but 
he does not fay in what time. It is owing to this circum- 
ftance, that is, the curvature of NO, that it is necelTary 
to find another point near to A, in order to determine ac¬ 
curately the values of AB, SB. Having determined the 
value of SB, and time of the greateft obfeuration, we thus 
find the beginning and end. Produce, if necelTary, QN, 
and take SB, SW equal to the Turn of the apparent fenfi- 
diameters of the Sun and Moon, at the beginning and end 
refpeftively ; then BV—fSV 2 — SB? (B being now fup- 
pofed in QN), and BlV—fS!V‘ — SB 2 -, then, to find the 
times of deferibing thefe fpaces, fay, As the hourly motion 
of the Moon in the apparent orbit, or NQ : BB 1 hour 
the time of deferibing BIV, which times refpefitively fub¬ 
trafted from and added to the time of the greateft obfeu¬ 
ration, give nearly the times of the beginning and end. 
But, if accuracy be required, this method will not do; for 
it fuppofes VIV to be a ftraight line, which fuppofttion 
will caufe errors, too confiderable in general to be neg¬ 
lected, and will never do where great accuracy is required. 
It may however always ferve as a rule to airume the time 
©f the beginning and end. Hence it follows, that the 
time of the greateft obfeuration at B is not ncceftarily equi- 
diftant from the beginning and end. If the eclipfe be to¬ 
tal, take Sv, Sw, equal to the difference of the femidiame¬ 
ters of the Sun and Moon, and then Bv—Bw—f Sv 2 — SB % 
from whence we way find the times of deferibing' Bv, Bw, 
as before, which we may confider as equal, and which ap¬ 
plied to the time of the greateft obfeuration at B, give the 
time of the beginning and end of the total darknefs. 
To find more accurately the time of the beginning and 
end of .the eclipfe, we mu ft proceed thus. At the efti- 
mated time of the beginning, find, from tlie horary mo¬ 
tions, and the computed paraliaxes, the apparent latitude 
N O M Y. 
MN of the Moon, and its apparent longitude MS from 
the Sun, and we have S N^y/SM'+MN*, and if this be 
equal to the apparent lemid. -f femid. 0 (which fum 
call S) the eftimated time is the time of the beginning ; 
but, if SN be not equal to S, aftume (as the error direfts) 
another time at a fmall interval from it, before, if SN be 
lefs than S, but after, if it b t greater ; to that time com¬ 
pute again the Moon’s apparent latitude m n, and apparent 
longitude S m from tlie Sun, and find S n— f S mrffmif ; 
and, if this be'not equal to S, proceed thus : As the diffe¬ 
rence of S n and SNis to the difference of S n and S L 
(=:S) fo is the above aftiimed interval of time, or time of 
the motion through Nn, to the time through n L, which 
added to or fubtrafted from the time at n, according as 
S n is greater or lefs than S L, gives the time of the be¬ 
ginning. Thereafon of this operation is, that, as N n, nL, 
are very fmall, they will be very nearly proportional to 
the differences of SN, Sw, and S n, SL. But as the va¬ 
riation of tlie apparent diftance of the Sun from the Moon 
is not-exaftly in proportion to the variation of the differ¬ 
ences of the apparent longitudes and latitudes, in cafes 
where the utraoft accuracy is required, the time of the 
beginning thus found (if it appear to be not correft) may 
be correfted, by afluming it for a third time, and pro¬ 
ceeding as before. This correftion however will never 
be neceTary, except where extreme accuracy is required 
in order to deduce fome confequences from it. But the 
time thus found is to be confidered as accurate, only fo 
far as the tables of the Sun and Moon can be depended 
upon for their accuracy ; and he beft lunar tabies are 
fubjeft to an error of thirty feconds in longitude, which, 
in this eclipfe, would make an error of about a minute 
and half in the time of the beginning apd end. Hence 
accurate obfervations of an eclipfe compared with tlie 
Computed time, furniIhes the means of correcting the lu¬ 
nar tables. I11 the fame manner the ena of the eclipfe may 
be computed. 
Ex. To compute theTimes of the Solar Eclipfe on April 3, 1791; 
for the Royal Obf-.rvalory at Gi eecnwich. 
Tlie time of the mean conjunftion is April 3, ah. 58', 
15". mean time, at which time we find 
Mean long, of the Sun - of. n°. 51'. 16". 
Long, of the Moon’s defc. node o 22 14 44. 
Mean long, of 0 from (J ’s node o 10 23 2S 
To the mean time of the new Moon, compute the Sun’s 
and Moon’s true longitudes, and they will be found to be 
of. 13 0 . 47'. 43". and of. 14 0 . 49'. 24". compute alfo the 
Moon’s true latitude, and it will be found to be 38' 49" 
N. defeending. At the fame time, the Sun’s horary mo¬ 
tion is found to be .V 28", the Moon’s horaray motion in 
longitude is 30' 12", and in latitude 2' 46" decreafing; 
hence the Moon’s horary motion in longitude from the 
Sun is 27' 44". By proceeding as directed for the eclipfe 
of the Moon, we find the mean time of the ecliptic con- 
junftion of the Sun and Moon to be 3d. oh. 44'. 48". from 
which fubtraft 3' 18" the equation of time, and it gives 
the apparent time 3d. oh. 41'. 30". at which time, the 
Sun’s and Moon’s longitude in the ecliptic is of. 13 0 . 42'. 
14". and the Moon’s true latitude is 44' 59" N. defeend¬ 
ing. TTie horizontal parallax of the Moon is 24' 46", and 
of the Sun, 9"; hence the horizontal parallax of the Moon 
from the Sun is 54' 37" ; therefore tlie Moon’s parallax in 
longitude from the Sun is —20' 56", and its parallax in 
latitude from the Sun is 33' 44" ; hence —20' 56" is the 
apparent diftance of the Moon from the Sun in longitude ; 
alfo the apparent latitude from the Sun is 11' 13" north. 
As the Moon is to the weft of the nonagefinial degree, 
aflame ih. after, or 3d. ih. 41'. 30". at which time (from 
the horary motions of the Sun and Moon) the Sun’s true 
longitude is found to be of. 13°. 44'. 42". the Moon’s 
true longitude on the ecliptic of. 14 0 . 12'. 26". and true 
latitude 42' 13" N. defeending. The Moon’s parallax in 
latitude 
