4jo ASTRO 
In the computation of this eclipfe, the Moon’s true la¬ 
titude and longitude were at fil'd computed from the tables, 
and afterwards determined from the horary motions; but, 
as the horary motions may be fubjedt to a fmall variation 
in the duration of an eclipfe, in cafes where the utmoft 
•accuracy is required, the true latitude and longitude Ihould 
be computed every time from the tables; in fuch cafes, 
the decimals of the feconds fliould alfo be taken into con¬ 
sideration, which in this example were omitted. When 
we want only to predict an eclipfe, the method here prac- 
tifed will always be Sufficiently accurate, the error being 
always very fmall, compared with the error to which the 
tables are fubjedt, which may, at its maximum, be thirty 
feconds in longitude. 
To construct a Solar Eclipse by Projection. 
Let S, in the annexed figure, be the centre of the Sun, 
x w the enlightened hemifphere of the Earth, which we 
mult conceive to be perpendicular to SC ; draw SD, SV, 
tangents to two oppolite points of the Earth, and let ambn 
be the apparent ellipfe defcribed by any point m on the 
Earth’s furface; let OC be the diftance of the Moon from 
the Earth, and vd, a'm'b'n! be the projedlion of V D, ambn, 
upon a plane at the Moon perpendicular to SC to an eye 
.$t S, and a’m'b'n' will be the apparent motion of the cen¬ 
tre of the Sun at S to the fpedlator defcribing ambn. The 
curve a'm'b'n' may be confidered as an ellipfe ; for the an¬ 
gle D S C being only 8£ feconds, D S, C S, may be reckon¬ 
ed as parallel, and therefore the projedlion of DV upon 
a plane parallel to it may be confidered as an orthographic 
projedlion, and confequently the two figures may in all 
refpedts be confidered as fimilar. Let LMbethe orbit 
of the Moon ; then, if we know at any time the point of 
the ellipfe ambn where the fpedlator is, we know the cor- 
refponding point where the centre of the Sun is in the 
ellipfe a'm'b'n '; if therefore we determine at the fame time 
%he point where the Moon is in its orbit LM, we ffiall 
N O M Y. 
know the apparent fituation of the Moon In refpect to the 
Sun. Hence if we find two points, one in the ellipfe a'm'b'n' 
where the centre of the Sun is, and another in LM where 
the centre of the Moon is, at the fame time, and about 
thefe centres, with radii equal to the apparent femidiame- 
ters of the Sun and Moon, we defcribe two circles, they 
will reprefent the apparent fituations of the two dilks. If 
that of the Moon fall upon the Sun, it ffiews how much 
the Sun is eclipfed at that inftant. Now the angle OV» 
=C O V—O S V, that is, the radius of projedlion, is equal 
to the difference of the horizontal parallaxes of the Moon 
and Sun. The projedlion Oe' of Ce is the parallax in al¬ 
titude of the Moon from the Sun, fuppofing the Moon t® 
be at the fame altitude as the Sun ; for the radius Ov re- 
prefents the difference of the horizontal parallaxes of the 
Sun and Moon, or the horizontal parallax of the Moon 
from the Sun; and, as the parallax of each varies as the 
fine of the apparent zenith diftance, the difference of tire 
parallaxes mull vary as the fine of their common apparent 
zenith diftance; hence Ob : Oe' :: difference of the ho¬ 
rizontal parallaxes : difference of the parallaxes at their 
common apparent altitude ; therefore if 0» reprefent the 
third term, Oe' will reprefent the fourth. In an eclipfe 
of the Sun therefore this will be nearly true, but not ac¬ 
curately fo, except when the Sun and Moon are at the 
fame altitude. 
According to this projedlion, the apparent ellipfe de¬ 
fcribed by any point of the Earth’s furface, to an eye at 
the centre of the Sun, is projedled upon a plane at the 
Moon perpendicular to a line joining the Earth and Sun ; 
and the point of the ellipfe of projedlion, correfponding 
to any point of the other ellipfe where tlve fpedlator is, is 
the point where the centre of the Sun appears to the fpec- 
tator. The centre of projedlion is in the ecliptic. If the 
lunar orbit be properly‘laid down and divided, ffiewing 
where the centre of the Moon is at any time, we fhall then 
have the relative fituation of the centres of the Sun and 
Moon at any time feen from the given place of the fpee- 
tator. From thefe principles of projedlion, we thus con- 
ftrudl the folar eclipfe which we have here calculated-; 
affuming fuch elements as are neceffary, from that calcu¬ 
lation. For this purpofe take a radius OE, equal to 34" 
37", the difference of the Sun’s and Moon’s horizontal pa¬ 
rallaxes, which call k, and divide it into minutes, as in 
the following figure, and defcribe the femicircle EGG 
reprefenting half the circle of projedlion, EOG repre- 
Tenting the ecliptic, to which draw OG perpendicular. 
Find P the projedled north pole; from the fcale OE, take 
Or=54* 37" X fin. lat. X cof. dec. and in a line perpen¬ 
dicular to Or fet off both ways r6 = ^ x cof. lat. and rw= 
X cos. lat. x dec. and defcribe the ellipfe s6, 
a 
and divide it into hours, and then fnbdivide thofe hours 
which you will want to make ufe of, as far as you conve¬ 
niently can for the fize of the figure. From the fcale take 
Ot; equal 44' 59", the Moon’s true latitude north defcend- 
ing at the time of the ecliptic conjunction, and draw L»M 
making 
