A5TRONOM Y. 
vaniflics. But, it' light be propagated in time, then it is 
evident from the foregoing conlidcralions, that there will 
always be a difference between the true and vilible place 
of an objeiff, except when the eye is moving either di¬ 
rectly towards or from the object. And in all cafes, the 
fine of the difference between the true and vilible place of 
the object, will be to the fine of the vifible inclination ot 
the objeft to the line in which the eye is moving, as the ve¬ 
locity of the eye is to the velocity of light. 
If light moved only 1000 times fader than the eye, and 
an objedt, fuppofed to be at an infinite didance, were re¬ 
ally placed perpendicularly over the plane in which the 
eye is moving ; it follows, from what has been faid, that 
the apparent place of fuels objedl will always be inclined 
to that plane, in an angle of 89° 561' ; io that it will 
condantly appear 3^' from its true place, and will feeni fo 
much lefs inclined to the plane, that way towards w hich 
the eye tends. That is, if AC be to A B or A D, as 1000 
to 1, the angle ABC will be 89° 56^', and the angle 
A C B 3^', and B C D or a A C B will be 7', if the direc¬ 
tion of the motion of the eye be contrary at one time to 
what it is at another. 
If the Earth revolve about the Sun annually, and the 
velocity of light were to the velocity of the Earth’s motion 
in its orbit, as xooo is to 1 ; then it is eafy to conceive, 
that a dar really placed in the pole of the ecliptic would, 
to an eye carried along with the Earth, feem to change its 
place continually ; and, neglecting the final 1 difference on 
account of the Earth’s diurnal revolution on its axis, it 
would feem to deferibe a circle about that pole, every 
where diftant from it by 3A'. So that its longitude would 
be varied through all the points of the ecliptic every year, 
but its latitude would always remain the fame. Its right 
afeenfion would alfo change, and its declination, according 
to the different lituation of the Sun in refpeCt of the equi¬ 
noctial points ; and its apparent didance from the north 
pole of the equator, would be 7' lefs at the autumnal than 
at the vernal equinox. 
The greated alteration of the place of a dar, in the pole 
of the ecliptic, or, which in effeCt amounts to the fame, 
the proportion between the velocity of light and the Earth’s 
motion in its orbit, being known, it will not be difficult 
to find what would be the difference, on this account, be¬ 
tween the true and apparent place of any other dar at any 
time ; and, on the contrary, the difference between the 
true and apparent place being given, the proportion be¬ 
tween the velocity of light, and the Earth’s motion in her 
orbit, may be found. 
After the hiffory of this valuable difeovery, related by 
the author, he gives the refults of a multitude of accurate 
obfervations, made on a great number of dais, at all fea- 
fons of the year. From all which obfervations, and the 
theory related above, he found that every ftar, in confe- 
quence of the Earth’s motion in her orbit and the pro- 
greldve motion of light, appears to deferibe a fmall ellipfe 
in the heavens, the tranfverfe axis of which is equal to the 
fame quantity of every dar, namely 40" nearly ; and that 
the conjugate axis of the ellipfe, for different ffars, varies 
in this proportion, namely, as the right fine of the dar’s 
latitude ; that is, radius is to the fine of the ftar’s latitude, 
as the tranfverfe axis to the conjugate axis ; and confe- 
quently a ftar in the pole of the ecliptic, its latitude being 
there 90 0 , whofe fine is equal to the radius, will appear to 
deferibe a fmall circle about that pole as a centre, whofe 
radius is equal to 20". He alfo gives the following law of 
the variation of the dar’s declination : if A denote the an¬ 
gle of pofition, or the angle at the ftar made by two great 
circles drawn from it through the poles of the ecliptic and 
equator, and B another angle, whofe tangent is to the tan¬ 
gent of A, as radius is to the fine of the dar’s latitude ; 
then B will be equal to the difference of longitude between 
the Sun and the ftar, when the true and apparent decli¬ 
nation of the dar are the fame. And if the Sun’s longi¬ 
tude in the ecliptic be reckoned from that point in which 
Vol. II. No. 80. 
it is when this happens, then the difference between the 
true and apparent declination of the dar will be always 
as the fine of the Sun’s longitude from that point. It will 
alfo be found that the greated difference of declination 
that can be between the true and apparent place of the 
dar, will be to 20", the femitranfverfe axis of the ellipfe, 
as the line of A to the fine of B. 
From the greated variation in the place of the ftars, 
namely 40", Dr. Bradely deduces the ratio of the velocity 
of light in companion with that of the.Earth in her orbit. 
In the preceding figure, AC is to AB as the velocity of 
light to that of the Earth in her orbit, the angle ACB 
being equal to 20"; fo that the ratio of thole velocities is 
that of radius to the tangent of 20", or of radius to 20'', 
fince the tangent has no lenfible difference from fo fmall an 
arc : but the radius of a circle is equal to the arc of 57-j^ 0 
nearly, or equal to 206260"; therefore the velocity of 
light is to the velocity of the Earth, as 206260 to 20. And 
hence alio the time in which light paffes over the fpaee 
from the Sun to the Earth, is eafily deduced ; for this 
time will be to one year, as A B or twenty feconds to 
360 degrees, or the whole circle; that Is, 360° : 20":: 
3 6 5i d - : 8'. 7". 
Dr. Bradley having annexed to this theory the rules or 
formulas for computing the aberration of the ftxed dars in 
declination and right afeenfion ; thefe rules have been va- 
rioully demonftrated, and reduced to other practical forms, 
by M. Clariaut, in the Memoirsof the Academy of Sciences, 
for 1737 ; by Mr. Simplon in bis Effays in 1740 ; by M. 
Fontaine des Crutes, in 1744; aud by feveral other per- 
fons. The refults of thefe rules are as follow : every da? 
appears to deferibe in the courfe of a year, by means of 
the aberration, a fmall ellipfe, whofe greater axis is 40", 
and the lefs axis, perpendicular to the ecliptic, is equal 
to 40" multiplied by the fine of the dar’s latitude, the ra¬ 
dius being 1. The eadern extremity of the longer axis 
marks the apparent place of the dar on the day of the op- 
polition ; and the extremity of the lefs axis, which is fur- 
theft from the ecliptic, marks its lituation three months 
after. 
The greated aberration in longitude, is equal to 20" 
divided by the cofine of its latitude. And the aberration 
for any time, is equal to 20" multiplied by-the cofine of 
the elongation of the dar found for the fame time, and di¬ 
vided by the codne of its latitude. This aberration is fub- 
tradlive in the did and lad quadrant of the argument, or 
of the difference between the longitudes of the Sun and 
ftar ; and addative in the fecond and third quadrants. The 
greated: aberration in latitude, is equal to 20" multiplied 
by the fine of the dar’s latitude. And the aberration in 
latitude for any time, is equal to 20" multiplied by the 
dne of the dar’s latitude, and multiplied alfo by the fine 
of the elongation. The aberration is fubtraidive before 
the oppofition, and addative after it. 
The greated aberration in declination, is equal to 20" 
multiplied by the fine of the angle of pofition A, and di¬ 
vided by the fine of B, the difference of longitude between 
the Sun and dar when the aberration in declination is no¬ 
thing. And the aberration in declination at any other 
time, will be equal to the greated aberration multiplied 
by the fine of the difference between the Sun’s place at 
the given time and his place when the aberration is no¬ 
thing. Alfo the line of the latitude of the ftar is to radius, 
as the tangent of A, the angle of pofition at the dar, is to 
the -tangent of B, the difference of longitude between the 
Sun and dar when the aberration in declination is nothing. 
The greated aberration in right afeendon, is equal to 20" 
multiplied by the coline of A the angle of pofition, and 
divided by the dne of C the difterence in longitude be¬ 
tween the Sun and ftar when the aberration in right afeen¬ 
fion is nothing. And the aberration in right afeenfion at 
any other time, is equal to the greated aberration multi¬ 
plied by the fine of the difference between the Sun’s place 
at the given time, and his place when the aberration is 
5 P nothing. 
