astronomy. 
4-!* 
latitude Is —30' 41"; hence the Moon’s apparent latitude 
isn'32"; alfo its parallax in longitude from the Sun is 
—28' 50" ; but the Moon’s true longitude exceeds the 
Sun’s by o° 27' 44" ; therefore the apparent diftance of 
the Moon from the Sun in longitude is —1' 6". Hence 
Moon’s ap. dift. in long, at 0I1. 41'. 30"——20' 56" 
1 41 30 —— 1_6 
Apparent hor. mot. d from 0 in long. 19 5 a = MP ‘ 
Hence 19' 50" : 20' 56" :: ih. : ih. 3'. 20'. which add¬ 
ed to the time of the true conjunction oh. 41'. 30". gives 
xh. 44'. 5 o". the time of the apparent conjunction. Alfo 
the apparent horary motion in latitude is 17 ‘'=zRQ; hence 
QN\ is very nearly equal to MP, as in the figure preceding 
the lad. 
At this time (from the horary motions) the Sun’s true 
longitude is found to be of. 13 0 . 44'. 50". the Moons of. 
14 0 . 14'. 7". and the Moon’s true latitude 42' 4" ; hence 
the Moon’s tiue longitude is greater than the Sun’s by 
29' 17". The Moon’s parallax in latitude from the Sun is 
—30' 32", and in longitude —29' 15" ; hence the Moon’s 
apparent latitude is ii' 32" N. alfo the apparent longitude 
Jfrom the Sun is 29' 17"—29' 15"=2", the quantity by 
which the Muon’s apparent longitude exceeds the Sun’s 
true longitude. This difference (hews the apparent con¬ 
junction, found above, to be very nearly true ; and to get 
it accurate, fay, 19' 50" : :: ill. : 6", which (as the 
Moon’s apparent longitude is the greater) fubtraCted from 
ih. 44'. 50". gives ih. 44'. 44". the true time of the ap¬ 
parent conjunction, at which time the Moon’s apparent 
longitude is of. 13 0 . 44'. 50". the lame as the Sun’s true 
longitude, that not having fenfibly varied in fix feconds of 
time. The apparent latitude is i- 1' 32-25". Now at ih. 
41'. 30". the Moon’s apparent diftance in longitude from 
the Sun has been (hewn to be i' 6" ; and at ill. 44'. 44". 
the longitude of the Sun and the Moon’s apparent lon¬ 
gitude are equal; therefore in 3' 14" the apparent motion 
of the Moon from the Sun was 1' 6 "=l66 " ; let this =Sm, 
or nr; alfo at rh. 41'. 30". the apparent latitude mn— ri' 
32", and at ih. 44'. 44". it was n' 32-25 "-SA ; there¬ 
fore Ar—o-if. Hence, As 66" is to 0-25" fo is rad. to 
tan. Anr, or SAB=i3' 1". As the angle Anr is fo very 
fmall, we may take An—rn—66" without any feniible er¬ 
ror ; and for the fame reafon SB may be taken=S^=n' 
32". As rad. is to fin. 13' 1" fo is n' 32" to AB—2-6". 
Hence, As An—G 6“ is to AB— 2-6" fo is 3' 14" to 8"'the 
time through BA, which taken from ill. 44'. 44". gives 
ih. 44'. 36". the time of the greateft obfeuration at B. 
The Moon’s horizontal femidiameter is 14' 56", and its 
altitude at the time of the greateft obfeuration (determined 
by a globe, which is fufficiently near for this purpofe) is 
about thirty-eight degrees; hence the augmentation of the 
diameter is nine feconds, confequently the apparent femi¬ 
diameter of the Moon is 15' 5", which added to 15' 59“ 
the Sun’s femidiameter, gives 31' 4", from which fubtraCt 
SB— 11' 32", and the remainder is 19' 32" the parts defi¬ 
cient; hence, As 15' 59" is to 19' 32" fo is 6 digits to 7d. 
19'. 57". the digits eclipfed at the time of the greateft ob- 
feuration. 
To find the time of the beginning, we muft firft get the 
time nearly in the manner above (fated. The value of SB 
= 11' 32"=;692" ; and as the apparent femidiameter of the 
Moon is now 15' 6", we have SV=. 31' s"—i$6s"; hence 
BV— 1732". Now as MP is, in this cafe, nearly equal to 
QN, we may, for the purpofe we here want it, aftume the 
apparent horary motion of the Moon from the Sun in the 
apparent orbit equal to that in longitude, which is 19' 50" 
= 1190"; hence, As 1190" is to 1732" fo is ill. to ih. 27'. 
20". which fubtraCfed from ih. 44'. 36". (the time at B) 
gives oli. 17'. 16". the time of the beginning, nearly. Let 
ws therefore alfume the beginning at oh. 17'. at which 
time we find (from the horary motions of the Sun and 
Moon) the Sun’s true longitude to be of. 13 0 . 41'. 15". 
and the Moon’s of. 13 0 . 29'. 55". whole difference is 11' 
Vol. II. No. 82. 
20" their true diftance in longitude ; but the Moon’s pa¬ 
rallax in longitude is —17' 45" ; hence their apparent dif¬ 
tance in longitude is 29' $"=174.5". At the fame time 
the Moon’s true latitude is 46' 7", and its parallax in lati¬ 
tude —35' 10" ; hence the appareot latitude of the Moon 
from the Sun is to' 57"; therefore 5 A r — i745'-j-65/’— 
i864"=:3i' 4", which being lefs than 3 i' 5 ' (hews that the 
eclipfe is begun. 
Let 11s next alFuine oh. 16'. and by proceeding in the 
fame manner, we find 5/7=21883"—31' 23"; therefore the 
eclipfe is not begun. Hence 31' 23"—31' 4''=2i9 n is to 
31' 5"— 31' 4 lr 2=i" fo is r to 3", which fubtraCted from 
0I1. 17'. gives oh. 16'. 57".' for the beginning of the eclipfe-. 
If to ill. 44'. 36". we add ih. 27'. 20". we have 3h. 11' 
56". we will therefore allurne 3I1. 12'. for the end; and 
by proceeding as before, we find tire apparent diftance of 
the Moon from the Sun in longitude to be 30' 37", and 
the Moon’s apparent latitude 10' 48" ; hence the Moon’S 
apparent diftance from the Sun is y' i837 ,, -|-648' = 194S" 
=232' 28" ; but the fum of the apparent femidiameters of 
the Sun and Moon is now 31' 2"; confequently the eclipfe 
is ended. 
Let us next aftume the time 3I1. 6'. and the apparent 
diftance of the Moon from the Sun in longitude is 2S' 28"; 
and in latitude 10' 55"; hence the Moon’s apparent dif¬ 
tance from the Sun is \J i708 , ‘-J-655’ : 2=i829"2=3o' 29" there¬ 
fore the eclipfe is not ended. Hence, As 32' 28"—30' 29* 
= 1' 59® is to 31' 2"—30' 29"r=33” fo is 6' to 1' 39", which 
added to 3I1. 6'. gives 3I1. 7'. 39". for the end. Hence 
at the Royal Obfervatory at Greenwich, the tables give 
the times of the eclipfe on April 3, 1791, 
Beginning 
Greateft obfeuration 
End 
Digits eclipfed 
0I1. 16'. 57". "I 
1 44 36 lapparent time, 
3 7 39 J 
7d. 19 57 
If it be required to compute the eclipfe for any other 
place, inftead of the latitude of Greenwich, ufe the lati¬ 
tude of the place ; and reduce the apparent time at Green¬ 
wich to the apparent time at 
different meridians. 
To find what point of the 5 
ed by the Moon, let P, in 
the annexed figure, be the 
pole of the ecliptic ES, Z 
the zenith, S, M, the cen¬ 
tres of the Sun and Moon 
when their limbs are in con¬ 
tact at a, and draw M D per¬ 
pendicular to ES. PZ is 
the altitude of the nonage- 
fimal degree, and S P Z is the 
Sun’sdiftance from that point, 
both which are found in the 
computation of the parallax ; 
alfo M D is the apparent lai 
the place, according to 
un’s limb will firft be touch- 
of the Moon ; hence 
Rad. : tan. PZ :: (in. SPZ : tan. PSZ 
Tan. SM : rad. :: tan. DS : cof. DSM 
If L be the longitude of the nonagefimal degree, the* 
ZSD—()0 o PSZ, when the Sun’s longitude is between L and 
L-\- 180°; otherwife ZSD—t)0°-\-PSZ; and ZSDztMSD. 
(according as the Moon’s vilible latitude is S. or N. gives 
ZSM the diftance of the point of the limb of the Sun firft 
touched by theMoon from the higheft point of the Sun’s diik, 
In this eclipfe, PZ— 50° 7', and SPZ— 25 0 16'; hence. 
PSZ— 27 0 3', which (in this cafe) added to 90° gives 117® 
3'i —ZSD ; alfo DSM—20° 42', which (as the Moon’s ap¬ 
parent latitude is north) fubtraCted from 117 0 3' gives 
ZSM—yG° 21', the Moon’s diftance from the zenith of the, 
Sun at the beginning of the eclipfe. In like manner, the 
diftance at the middle and end of the eclipfe may be found, 
and thence the apparent path of the Moon over the Sun’s 
di(k in relpcdt to the horizon may be described. 
