ASTRONOMY. 
44 * 
dm is 3’44"; reduce this into time by logiftic logarithms, 
and the operation is thus: 
3' 44" - - i • 206 1 
29 45 - °'3°47 
7 32 time of defcribing mn 0-9014 
The neared approach Cm of the centres is 37' 28". Now, 
from 12I1. 31'. 58". fubtradl 7'32", and it leaves i2h. 24'. 
36". the middle of the eclipfe. 
By the tables, the horizontal parallax of the Sun is 
o'9", and of the Moon 56' 30"; alfo the apparent femi- 
diameter of the Sun is 16' 16", and of the Moon 15' 24". 
Hence, her. par. 0 hor. par. ([ —femidiam. 04-50" 
2=41' 13", the femidiameter of the Earth’s fhadow increa- 
fed by 50" for refraction. Hence, 
Semid. ([ -j-fem.Q’slhad. 56' 2l"—339l" 
Neared app. of centres 37 28 =2248 
Sum ... 5645 —log. 3*751664 
Difference - - - - 1149 —log. 3*060320 
2)6-811984 
Log. of 2546-8"—42' 26-8" mot. of half duration 3-405992 
Reduce this into time by the logidic logarithms. 
39'. 45". - - •= 0-3047 
42. 27. 0-1503 
ill. 25. 37. half duration - 0-8456 
Subtract this from and add it to i2h. 24'. 26". and we 
get ioh. 58'. 49". for the beginnings and 13b. 50'. 3". for 
the end. 
From CV—41* 13" fubtraCf Cm— 37' 28", and we get mr 
—3 1 45" j hence mrf-mt—rt=zif 9", the parts deficient; 
consequently 15' 24" .- 19' 9" :: 6d. or 360' : 7d. 27'. 36". 
the digits eclipfed. By logidic logarithms the computa¬ 
tion is thus: 
29'. 9". log. 4.1, - 1-4960 
15 2 4 Q’59 06 
7d. 27 36 - - - 0-9054 
To 16h. 26'. 4". add 53", and it gives i.6h. 26'. 57". for 
the middle of the eclipfe. 
By the tables, the horizonal parallax of the fun is o' 9", 
and of tlie Moon 59' 9" ; alfo the apparent femidiameter 
of the Sun is 16' 17", and of the Moon 16' 6". Hence 
hor. par. 0-fhor. par. <5 — femid. 0-|- 5o" = 43' 51'', 
and the femidiameter of the Earth’s fhadow increafed by 
5c" for refraction. And as Cr (—4.3' 51") is greater thaa 
Cmf-ms {— 21'), the eclipfe mud be total. Hence, 
Sem. ([-\- fem. ©’s (had. 59' 57"—3597" 
Neared ap. ef the centres 4 54 — 294 
.3891—’log. 3-5900612 
Difference .... 3303—log. 3 -518908(5 
2)7-1089698 
Log. of 3585"=59' 45" mot. of half duration 3 ~5 5 44 8 49 
Reduce this into time by the logidic logarithms; but 
becaufe the fourth term, in this cafe, would come out a 
greater quantity than that to which the table extends, we 
will take the half of 59' 45", and then double the con=. 
clufion: 
3 i' 50 " -... 0-2618 
2 9 S 2 '5 .... 0-30285 
54 35'5 .... 0-04105 
Hence ih. 49'. 11". is the half duration; which fub- 
tr-aCted from and added to i6h. 26'. 57". gives 14I1. 37% 
46". for the beginning, and i8h. 16'. 8". for the end. 
By the fame method we may alfo find the time of half 
the duration of total darknefs thus: 
Sem. ©’s fhad. — fem. <[ 27' 45"—1665" 
Neared ap. of the centres 4 54 — 294 
Sum - 1959 — 1 log- 3-2920344 
Difference ... 1371—log. 3-1370375 
2)6-4290719 
Log. of 163 9"=2 7' 19" mot. of £ dur. of tot. dark. 3-2145359 
Reduce this into time by the logidic logarithms. 
Hence the time of this eclipfe are, February 3, 1795, the 
Beginning at 
Middle 
End 
Duration 
ioh. 58'. 
12 24 
13 5 ° 
2 5i 
Digits eclipfed 7d.27 36 
} 
} 
apparent time at 
Greenwich. 
on the Moon’s fouth 
limb, as in the pre¬ 
ceding figure. 
Ex. a. A Computation of a Total Eclipfe of the Moon, on De¬ 
cember 3, 1797 ; for the Meridian of the Royal Obfervatory 
at Greenwich. 
52' 50" .... 0-2618 
27 »9 .... 0-3417 
49 55 half duration of total darknefs 0 0799 
Subtract this from and add it to 16I1. 26'. 57". and it 
gives 15I1. 37'. 2"- for the beginning of total darknefs, 
and 17I1. 16'. 52". for the end. 
From Cr— 43' 51" fubtraCt Cm—-.f 54", and we get mr 
— 38' 57", to which add tm=zi6' 6", and we get 0—55' 3" 
the parts deficient; hence 16' 6" : 55' 3" :: 6d. or 360k : 
2od. 31'. the digits eclipfed. The operation by logidic 
Logarithms is thus : 
By computation the mean time of the ecliptic oppofition 
is 3d. i6h. 16'. 46". to which add 9' 18" the equation of 
time, and you get 3d. 16I1. 26'. 4". for the apparent time. 
To this time compute the Moon’s place in the ecliptic, 
and it will be found to be ?.f. 12 0 . 35'. 19"; confequently 
the Sun’s place is 8f. 12 0 . 35'. 19". Compute alfo the 
Moon’s latitude Cn, and it will be found 4' 55" S. decreaf. 
ing. By the tables, the horary motion of the Moon in 
latitude is 3' 15" ; the horary motion of the Sun is 2' 32", 
and of the Moon 35' 14" in longitude ; hence the horary 
motion of the Moon from the Sun in longitude is 32' 42" ; 
confequently the horary motion of the Moon from the 
Sun on the relative orbit is 32' 50"; alfo the inclination 
of the relative orbit is 5 0 40''34". The reduction nm is 
o' 29"; reduce this into time by the logiftic logarithms, 
and the operation is thus : 
52' 50" - - - - ©-2618 
o 29 - - - 2-0939 
o 43 time of defcribing mn 1-8321 
The neared approach Got of the centres is 4' 54". 
55' 3" log.+i, 
16 6 
2od. 31 o 
*•0374 
a '57 1 3 
0-4661 
Hence the times of this eclipfe are, December 3, 1797, the 
Beginning at 
Total darknefs begins 
Middle ... 
Total darknefs ends 
End of the eclipfe 
Duration of total darknefs 
^apparent time 
I at Greenwich. 
14I1. 37k 4 6"0 
15 37 2 
16 26 57 
17 16 52 
iS 16 8 J 
1 39 50 
Durationofthewholeeclipfe3 38 22 
Digits eclipfed - 2od. 31 o 
If the time correfponding to the difference between the 
meridian of Greenwich and that of any other place, be 
applied to the times here found, it will give the times at 
that place. 
To construct an Eclipse of the Moon. 
Inftead of computing the firft eclipfe, it may be conjlru&ed 
thus. Having a fcale of minutes and feconds, as in the 
preceding 
