astronomy. 
that the motion of the apfides, deduced from thence, 
came out one between eight and nine years, but that, the 
other motion did not agree with either of the former. 1 he 
time of a revolution theretore mud be about eight years 
and nine months. The time being thus nearly determined, 
lie computed the motion from more diftant oblervations, 
and from a mean of the whole, he found the time of a re¬ 
volution of the apfides to be eight common years, 311 
days, eight hours, and hence the mean annual motion is 
if. io°. 39'. 52". and daily motion 6' 41" T". Mayer in 
his tables makes the annual motion if. io°. 39'. 50". I his 
is the mean motion in refpeCt to the .equinoxes. M. de la 
Lande makes the daily motion, in refpeCt to the equinoxes, 
6' +1-069815". Hence he deduces the daily motion in re¬ 
fpeCt: to the fixed (tars to be 6 ; . 40-932238". If vve take 
unity to reprefent the mean motion ot the Moon in refpeCt 
to the fixed ftars, then will the motion ot its apogee be 
reprefented by 0-00845226445, found by comparing their 
mean motions ; hence, as the motion of the apogee is di¬ 
rect, the fidereal revolution ot the Moon, 27d. 7h. 43'. 
11-4947". : its revolution in refpeCt to its apogee :: 
1—0-00845226445 : 1, the Moon approaching the apogee 
with the difference ot the velocities; hence the revolu¬ 
tion of the Moon in refpeCt to its apogee is 27d. 13I1. 18'. 
33-95". The motion of the apogee is not uniform, as is 
implied in this method ot determining its mean motion, 
and therefore it will be fubjeCt to a fmall error, unlefs the 
equation thould be the fame at both obfervations ; this 
error may be corrected, by reducing the true to the mean 
place at each obfervation. Horrox, trom obferving the 
diameters of the Moon, tound the apogee tubjcCt to an 
annual equation of 12-5°. 
To find the Aberration. 
As it appears, from the explanation before given, that 
the angle sFS in the annexed figure, orFSl, meafures 
the aberration, or the difference between the true place ot 
fj- v d the place meafured by a telefcope ; take F S 
we have the velocity of the earth : velocity of light :: fin, 10" 
: radius :: 1 : 10314. The aberration Si lies from the 
true place of the (tar in a direction parallel to the direction 
of the Earth’s motion, and towards the fame part. 
Whilft the Earth makes one revolution in its orbit, the 
curve, parallel to the ecliptic, deferibed by the apparent 
place of a fixed (tar, is a circle. For let AFBQ be the 
Earth’s orbit, K the focus in which the Sun is, H the other 
focus; on the major axis AB deferibe a circle ; draw a 
tangent YFZ to the point F, and KY, HZ, perpendicular ta 
it ; then, by Conics, the points Y and Z will be always in 
the circumference of the circle. Let S' be the true place 
of the (tar, any where out of the plane of the ecliptic, 
which therefore muff be conceived to be elevated above 
the plane AFBQ, and take tF : FS as the velocity of the 
Earth : the velocity of light, and complete the parallel¬ 
ogram FtSs and s will be the apparent place of the (far. 
Draw FL perpendicular to AB, and let WsVx be the curve 
deferibed by the point s, and IVSV be parallel to FL. Now 
the velocity of the Earth varies as —]—, or as HZ ; but 
tF, or Ss, reprefents the velocity of the Earth ; hence St 
varies as HZ. Alfo as Ss, SV are parallel to FY, FL, the 
angle sSV— the angle YFL which is — the angle ZHL, be- 
caufe the angle LFL added to each makes two right an¬ 
gles, for in the quadrilateral figure LFZH the angles L and 
Z are right ones. Hence as Ss varies as HZ, and the an¬ 
gle sSV—ZHA, the figures deferibed by the points s and 
Z mull be fimilar; but Z deferibes a circle in the time of 
one revolution of the Earth in its orbit, hence s mutt de¬ 
feribe a circle about S in die fame time. And as Ss is al¬ 
ways parallel to tF which lies in the plane of the ecliptic, 
the circle WsVx is parallel to the ecliptic. Alfo, as Sand 
H are two points fimilarly (ituated in Wv and AB, it ap¬ 
pears that the true place of the liar divides that diameter 
which, although in a different plane, we may conlider as 
perpendicular to the major axis of the Earth’s orbit, in 
the fame ratio as the focus divides the major axis. But, as 
the Earth’s orbit is very nearly a circle, vve may conlider 
S in tlve centre of the cirele without any fcnlible error. 
As we may, for the purpofes which we Hi all here want 
to confider, conceive the Earth’s orbit AFBQ to be a cir¬ 
cle, if from the centre C we draw Cs' parallel to Ss, or 
YF, s' will be the point in that circle correfponding to s in 
the circle WsVx, and as FCs'zziijQ 0 , the apparent place of 
•the ftar in the circle of aberration is always 90 0 before the 
place of the Earth in its orbit, and contequently the appa¬ 
rent angular velocity of the ftar and Earth about their ve- 
fpeCtive centres are always equal. It is farther fuppofed, 
that the ftar S' is at an indefinitely great diftance ; for the 
fituation of the ftar is not fuppofed to be altered from the 
motion of the Earth, and confidering FS as always parallel 
to itfelf, it will always be directed to S' as a fixed point in 
the heavens. Hence alfo, as the apparent place of the 
Sun is oppofite that of the Earth, the apparent place of 
the ftar in the circle of aberration is 90° behind that of 
the Sun. 
As a fmall part of the heavens may be conceived to be 
a plane perpendicular to a line joining the ftar and eye, it 
follows from the princi- 
t0 ft as the velocity of light to the velocity of the Earth, 
and by Trigonometry, As tin. FS< is to fin. F<S fo is F t 
to FS as velocity of the Earth is to velocity of light; 
hence fineof aberrration=fin. EiSx- 
vcl. of Earth 
there- 
’vel. of light 
fore, if we confider the velocity of the Earth and of light 
to be conftant, the fine of aberration, or the aberration it¬ 
felf as it never exceeds twenty feconds, varies as fin. FiS, 
and therefore is greateft when that angle is a right angle ; 
if therefore i be put for the fine of FtS, we have, As 1 
(rad.) is to s, fo is 20" to sXio" the aberration. Hence 
when Ft coincides with FS’ or the Earth be moving di- 
reCtly to or from a ftar, there is no aberration. 
As (by obfervation) the angle FSt=z. 20" when FiS— 90 0 , 
pies of orthographic pro¬ 
jection, that the circle 
parallel to the ecliptic de¬ 
feribed by the apparent 
place of the ftar project¬ 
ed upon this plane will 
be an ellipfe ; the appa¬ 
rent path of the ftar in 
the heavens will there¬ 
fore be an ellipfe, and the 
major axis will be to the 
minor as radius to the 
line of the ftar’s latitude. 
For let C E in the annexed figure, be the plane of the e- 
cliptic, P its pole, PE a fecondary to it, PC perpendicu¬ 
lar 
