445 
ASTRONOM Y. 
the length of the Earth’s fhadow. If we take the angle 
ATO —16' 3" the mean femidiameter of the Sun, TOC 
—5" the horizontal parallax of the Sun, we have ClTm 
15' c . l ''; hence fin. 1 3' 54'' : cof. i5'54*', or 1 : 2i2'6 :: 
TC : CJ = 2 s6-2TC.' 
Now, in the next figure, let P Qj-eprefent the feftion of 
the Earth’s fhadow at the Moon, C N the ecliptic, N L 
the Moon’s orbit; draw C n perpendicular to CN, and 
Cm perpendicular to N L, and let the Moon at m juft 
touch the Earth’s fhadow at r externally, fo that Cm may 
be the fum of the radii of the Moon and Earth’s fhadow ; 
then, to determine when this happens, we may take the 
angle at N=3° 17', which is very nearly its value in all 
eclipfes, the inclination of the lunar orbit being at that 
•time always greateft; hence, fine 3 0 17' : rad. :: fin. Cm : 
fin. CN ; now, the greateft value of Cm is about i°3'3o"; 
hence the correfponding value of CNzz:ii°34'; when, 
therefore, CN is greater than that quantity, there can be 
no eclipfe. According to M. Caffini, if the latitude Cn 
of the Moon at the time of the ecliptic conjunction ex¬ 
ceed the fum of the femidiameters of tire Earth’s fhadow 
and Moon by 18", there will be no eclipfe; but, if it do 
not exceed that fum by 16", there will be an eclipfe. If 
Cm— Cr— rm, or the limbs touch internally, the eclipfe 
will be juft total; hence, if the diftance of the Moon’s 
node from the place of the Earth be lefs than the compu¬ 
ted value of CN in this cafe, there muft be a total eclipfe 
of fome duration. And, as it now appears that there will 
be an eclipfe, proceed as follows to compute it: 
To compute an Eclipfe of the Moon. For this purpofe, let 
APB, in the two following figures, be that half of the 
Earth’s fhadow where the Moon pafies through ; N L the 
relative orbit of the Moon, one figure reprefenting a par¬ 
tial eclipfe, and the other a total one; draw Cmr perpen¬ 
dicular to N L, and let z be the centre of the Moon at 
the beginning of the eclipfe, m at the middle, x at the 
end, v at the beginning of total darknefs, w at the end ; 
alfo let A B be the ecliptic, and Cn perpendicular to it; 
if the Moon at n have north or fouth latitude increafing, 
the angle C nm is to be fet off to the right; otherwife to 
the left of C n. Now, in the right-angled triangle C nm, 
we know C n the latitude of the Moon at the time of the 
ecliptic conjunction, and the angle C nm the complement 
of the angle which the relative orbit of the Moon makes 
with the ecliptic; hence, radius : cof. C nm :: Cn : nm, 
which we call the reduction ; and radius : fine C nm :: Cn : 
Cm. By logarithms die calculations are thus: 
Vol. II. No.81. 
Log. cof. C nm -E log. Cn — 10, — log. nm. 
Log. fin. C nm -f- log. Cn — 10, — log. Cm. 
The horary motion (h) of the Moon upon its relative or¬ 
bit being known, we know the time of defcribtng pin, by 
faying, h : mn :: 1 hour : the time of defcribing mn ; the 
computation of this is moft readily performed by logiftie 
logarithms. Hence, knowing the time of the ecliptic 
conjunction at n, we know the time of the middle of the 
eclipfe at m. Next, in the right-angled triangle Cmn, we 
know Cm, and Cz the fum of the femidiameters of the 
Earth’s fhadow and the Moon, to find mz, which is done 
thus by logarithms; as mz — f Cz 2 — Cm? — 
\/CzfCmxCz — Cm, the logarithm of mz — a x 
log. Cz-ECM-j-log.Cz— Cm. Hence the horary motion 
of the Moon being known, we know the time of defcri¬ 
bing zm, which fubtraded from the time at m gives the 
time of the beginning, and added, gives the time of the 
end. In the fame manner, in the right-angled triangle 
Cmv, we know Cm, and Cn the difference of the femi¬ 
diameters of the Earth’s fhadow and Moon; hence, by 
logarithms, log.ofMv=Ax log. Cv-\-Cm-\- log. Cv — Cm ; 
from whence, as before, we know the time of defcribing 
m v, which fubtraded from the time at m gives the time of 
the beginning of total darknefs, and added, gives the time 
of the end. The magnitude of the eclipfe at the middle 
is reprefented by tr, which is the greaieftdiftance of the 
Moon within the Earth’s fhadow, and this is meafured in 
terms of the diameter of the Moon, conceived to be di¬ 
vided into twelve equal parts, called digits, or parts defi¬ 
cient ; to find which, w e know C m, the difference between 
which and C r gives m r, which added to mt, or if m fall 
out of the fhadow take the difference between wr and mt, 
and we get t r ; hence, to find the number of digits eelip- 
fed, fay, mt: tr n 6 digits or 360' (it being ufual to divide 
a digit into fixty equal parts, and call them minutes) : the 
digits cclipfed. If the latitude of the.Moon be north; we 
ule the upper femicircle; if fouth, we take the lower. 
Ex. 1. A Computation of a Partial Eclipfe of the Moon, on 
February 3, 1795 ; for the Meridian ej the Royal ObJcrva- 
tory at Greenwich. 
The time of the mean full Moon is at 3d. tyh. 59'. 47 -6". 
and the mean time of the ecliptic oppofition is at 12I1. 46'. 
18". from which fubtracf the equation of time ip-2o", 
and we have 12I1. 31'. 58". the apparent time, at Green¬ 
wich. To this time compute the Moon’s place in the eclip¬ 
tic, and it will be found 4L 15 0 .15'. 57". the oppofite point 
to which is iof. 15 0 . 15'. 57". the place of the Sun. Com¬ 
pute alfo the Moon’s latitude Cn, and it will be found 37' 
39" N. afeending. 
By the aftronomical tables, the horary motion of the 
Moon in latitude is 2' 57''; the horary motion of the Sun 
is 2' 32", and of the Moon 32' 9" in longitude; hence the 
horary motion of the Moon from the Sun in longitude is 
29' 37"; confequently the horary motion of the Moon from 
the Sun on the relative orbit is 29' 43" ; alfo the inclina¬ 
tion of the relative orbit is 5° 41'27". The reduction 
S X d tn 
