ASTRONOMY. 
making an-angle with Ov equal to 84 0 18', tlie comple¬ 
ment of the angle which the relative orbit makes with the 
ecliptic, on the left lide, if the latitude be north or fouth 
decreafing, and on the right, if increafing ; in this exam¬ 
ple it is on the left lide ; and Lv M will reprefen tthe 
Moon’s relative orbit. Mark upon the Moon’s orbit at 
the point v, 41' 30", that being the time after twelve 
o’clock at which the true ecliptic conjunction happens; 
and with an extent=27' 52", the horary motion of the 
Moon from the Sun in its relative orbit, fet off the hours 
each way from v, and fubdivide them into minutes ; or as 
far as the fize of the figure will permit. Now to find the 
time of the middle of the eclipfe, take the compafs, and 
find by trial what two correfponding times, as at z and 
x, upon the ellipfe and Moon’s orbit are neared together, 
which will give the time of the greated obfcuration, be- 
caule the centres of the Sun and Moon are then at the 
lead difiance. To find the time of the beginning, take, 
with the compafs, from the fcale, an extent equal to 31'5", 
the fum of the femidiameters of the Sun and Moon, and 
by trial find two correfponding times, as at t and t, at that 
didance, and it gives the time of the beginning ; and if you 
find two correfponding times, as at y and w, at the dif- 
tance 31' 2'', the fum of the femidiameters at the end, it 
gives the time of the end ; or you may omit the variation 
of the diameter of the Moon in the interval. For the be¬ 
ginning mud be when the centres of the Sun and Moon 
arrive at the didance of the fum of their femidiameters ; 
and the end mud be when they have receded till they 
have got to that didance. To find the digits eclipfed at 
the greated obfcuration, take eu from the fcale, and fay, 
As ze is to eu fo is fix digits to the digits eclipfed. To 
find the digits eclipfed at any other time, take, with the 
compafs, the interval at that time on the ellipfe and on 
the Moon’s orbit, and apply it to the fcale, and then fay, 
As ze is to that didance (o is fix digits to the digits eclipfed. 
The eclipfe may alfo be calculated from the projection, 
in the following manner : Alfume the time at t of begin¬ 
ning, as determined by the conftruCtion ; draw tc perpen¬ 
dicular to OP, and join Ot, Os, as in the preceding figure. 
The time from l to m being given, convert it into degrees, 
o° ; then fin. a°y.rb—tc, and cos. a°Xn»=rc; but Or 
is known, hence Oc is known ; therefore in the right an¬ 
gled triangle Oct, we know Or, c t, to find cOt, and O t ; 
but POo is given, therefore eO/^POy=iO& is known ; 
alfo Ov and the angle 0 vs are known by the condruftion ; 
and the time from s to v being, given, and alfo the Moon’s- 
relative horary motion in LM, we know vs ; hence in the 
triangle Oar, we know Ov, vs, and the angle O vs, to find 
Os, and the angle »Oj; hence we find tOs—tOv^vOs^ 
and ladly, in the triangle tOs, we know iO, Os, and the 
angle tOs, to find ts, and if this be equal to the fum of 
the femidiameters of the Sun and Moon, the affumed time 
is true ; if it be not equal to the fum, affume another time 
for the beginning, and find another value of ts, and pro¬ 
ceed with thefe two as before directed. Ifi like manner 
we may find the end. But this method is not fubjeCt to 
the fame accuracy as the nrethodof calculation before given. 
Sir Ifaac Newton fuppofes that the aberration of. rays 
in the focus of a telefcope makes the image appear greater 
than it ought; and hence different telefcopes will give dif¬ 
ferent meafures of the Sun’s diameter, and confequently 
make the eclipfe appear to begin at different times. That 
telefcope which gives the diameter the leaff, is tire moll 
perfect inftrument. The excellent tranfit telefcope at Green¬ 
wich makes the diameter of the Sun lefs by fix feconds 
than that given by Mayer in his tables, as Dr. Malkelyne 
has found by his obfervations. The diameter, of the Sun 
affumed in thefe calculations has therefore been taken fix 
feconds lefs than that which Mayer determined. M. du 
Sejour fuppofes that the rays of light coming from the Sun 
are infleCted as they pafs by the Moon, which he attributes 
ta the refcadlioa which they fuffer in palling through the 
Moon’s atmofphere ; on this account the apparent contact 
of the limbs will not take place fo foon as it otherwife 
would ; this would be the fame as a diminution of the 
Moon’s diameter; which of thefe hypothefes ought to be 
admitted M. de Sejour endeavoured to determine from the 
obfervations of Mr. Short, on the folar eclipfej April 1, 
1764, uppn the diftance of the horns of the Moon, but 
he could deduce nothing fatisfadlory from thence. He 
fuppofed the infledlion 3*291", and the diameter of tHe 
Moon to be dimini (bed by the fame quantity, and calcu¬ 
lated upon each fuppofition a great many diltances of the 
horns, and compared them with the obferved diltances; 
but he could not decide between the two hypothefes. An 
infledlion of i - 8", and a diminution of i'$", of the femi- 
diameter, be found would fatisfy fome obfervations, and 
he feemed to think this conclufion mod likely to be nearelt 
the truth ; but he came at lall to no determination upon 
the fubjedt. All the requifite obfervations feem not to 
be capable of being made to that degrees of accuracy 
which is neceffary to fettle fo nice a matter. M. du Sejour 
therefore propoled the following method to determine 
whether the rays of light palling by the limb of the Moon 
fuffer any deviation. Take a telefcope mounted upon a. 
polar axis, with a wire micrometer annexed to it. When 
two flars come into the field of view together, and one of 
them is to be eclipfed by the Moon, open the wires, and 
bring one liar upon one of the wires and the other (tar 
upon the other, and thus follow the flars until one of them 
be eclipfed, and at the inftant before it difappears obferve 
whether its diftance from the other ftar is changed, that is, 
whether it be off the wire, the other ftar remaining upon- 
its wire ; if this be found to be the cafe,, the rays mud 
have differed a deviation. Traite Analv.tique,. p. 420. We 
do not find that an obfervation of this kind has been ever- 
made. 
To trace out the Path on the Surface of the Earth, where the 
Eclipfe will be central, or for any number of • Digits. 
Let E A C D be the enlightened hemifpher-e of the Earth,, 
O the centre of the dilk, or that point to which the Sun is 
vertical; E O C the plane of.the_eclig.tic, O G perpendicu- 
to be upon the plane into which the difk would be ortho- 
graphically projected-; then froimthe, nature-oL that pro¬ 
jection, the angles at O upon the furface. will be equal to* 
the angles into which they are projected. Now the place 
upon which the centre of the Moon is projected is mani- 
feftly that point on the Earth where the eclipfe is cen¬ 
tral, becaufe the projection is made by.lines drawn to the- 
centre of the Sun. Let Z be the projected centre of the 
Moon at any time, or the real centre of the penumbra, 
and PB any given meridian. Now we know Oy the 
Moon’s latitude at the time of conjunCtion,_and theangle- 
OV2; and as the time, when the centre of the penumbra* 
is at Z, is given, the time through Zy is known, and the 
relative horary motion of the Moon being known, vZ will 
be known; hence we can find Z O, and the angle Z0»; ; 
fsa&i 
