4%: ASTRO 
and it will be referred to A ; but if viewed from the cen¬ 
tre T, it will be referred to the point D, which is its true 
place. The arc AD wili Berthe Moon's parallax'; the 
angle SGT the parallaftic angle; or the parallax is ex- 
preffed by the angle under which the femidiameter TS of 
the Earth is feen from the Moon. 
If the parallax be oonfidered with refpeft to different 
planets, it will be greater or lefs as thofe objefts are more 
or lefs diflant from the Earth ; thus the parallax AD of 
G is greater than the parallax Ad of g. If it be confi- 
dered with refpedl to the fame planet, it is evident that 
the horizontal parallax (or the parallax when the objedft 
is in the horizon) is greateft of all, and diminifhes gradu¬ 
ally, as the body riles above the horizon, until it comes to 
the zenith, where the parallax vanishes, or becomes equal 
to nothing. Thus A D and A d, the hcrizonal parallaxes 
of G and g, are greater than a B and a b, the parallaxes of 
R and r ; but the objedis O and P, feen from S or T, ap¬ 
pear in the fame place Z, or the zenith. By knowing the 
parallax of any celeftial objeft, its diftance from the cen¬ 
tre of the Earth may be ealily obtained by trigonometry. 
Thus if the diftance of G from T be fought, in the trian- 
gle of STG, ST being known, and the angle SGT de¬ 
termined by observation, the fide T G is thence known. 
The parallax of the Moon may be determined by two 
perfons obferving her from different ftations at the fame 
time; flie being vertical to the one, and horizontal to the 
other. But the parallax mod elfential is that of the Sun, 
whereby his abfolute diftance from the Earth is known; 
and hence the abfolute diftances of all the other planets 
would be alfo known, from the fecond Keplerian law. But 
the parallax of the Sub, or the angle under which the fe¬ 
midiameter of the Earth would appear at that .diftance, is 
lo exceeding fmall, that a mi flake of a fecond will cattle 
an error of feveral millions of miles. 
As the diftance of the fixed ftars is alfo bed: determined 
by their parallax, various methods have been purified, 
though hitherto without fuccefs, for inveftigating it; the 
relult of the moll accurate obfervations having given us 
little more than a diftant approximation ; from which how¬ 
ever we may conclude, that the neared of the fixed ftars 
cannot be lefs than 40,000 diameters of the whole annual 
orbit of the Earth diftant from us. The method pointed 
out by Galileo, and attempted by Kook, Fiamftead, Mo- 
lyneux, and Bradley, of taking the diftances of fuch ftars 
from the zenith as pafs very near it, has given us a much 
jufter idea of the immenfe diftance of the ftars, and fur- 
nifhed an approximation to their parallax, much nearer 
the truth than any we had before. 
Dr. Bradley allures us’(Phil. Tranf. No. ccccvi. or Abr. 
vol.'vi. p. 162), that, had the paraliax amounted to a lin- 
gle fecond, or two at mod, he ftiould have perceived it in 
the great number of obfervations which he made, efpeci- 
ally upon y Draconis ; and, that it feemedto him very pro¬ 
bable, that the annual parallax of this liar does not amount 
to a lingle fecond, and conlequently that it is above 400,000 
times farther froiii us than the Sun. But Dr. HerfChel, to 
whofe induftry and ingenuity, in exploring the heavens, 
aftronomy is To much indebted, remarks, that the inftru- 
ment ufed on this occafion, being tlie fame with the pre¬ 
sent zenith feftors, can hardly be allowed capable of ftiewT 
mg an angle of one or even two leconds, with accuracy : 
and befides, the ftar on which the obfervations were made, 
is only a bright ftar of the third magnitude, or a fmall ftar 
of the fecond ; and that, therefore, its parallax is proba¬ 
bly much lefs than that of a ftar of the fu rtmagnitude. 
So that we are not warranted in inferring, that the paral¬ 
iax of the ftars in general does not exceed i 1 ', whereas 
thofe of the firft magnitude may have, notwithftanding 
the relult of Dr. Bradley’s obfervations, a parallax of i’e- 
veral feconds. 
As to tlie method of zenith diftances, it is liable to con- 
fiderable errors, on account of refraction, the change of 
pofition of the Earth’s axis, ariling from nutation, pre- 
ceftion of the equinoxes, or other caufes, and tlie aberra- 
N O M Y. 
tion of light, Dr. Heyfehel has therefore' propofed ano¬ 
ther method, by means of double ftars, which is Iree from 
thefe errors, and of fuch a nature, that the annual paral¬ 
lax, even if it Ihould not exceed the tenth part of a fe¬ 
cond, may ftill become vifible, and be afeertained at leaft 
much nearer than heretofore. This method, which was 
firft propofed in an imperfect manner by Galileo, and has 
been all'o mentioned by other authors, is capable of every 
improvement which the telefcope and niechanifm of mi¬ 
crometers can furnifii. To give a general idea of it, let 
O and E be two oppofite points of the an¬ 
nual orbit, taken in the fame plane with 
two ftars A, B, of unequal magnitudes. 
Let the angle A O B be obferved when 
the,Earth is at O, and AEB be obfer¬ 
ved when the Earth is at E. From the 
difference of thefe angles, when there is 
any, the parallax of the ftars may be com¬ 
puted, according to the theory fubjoined. 
Thefe two ftars ought to be as near as 
poftible to each other, and alfo to differ 
as much in magnitude as we can find 
them. 
This theory of the annual parallax of 
double ftars, with tlie method of computing from thence 
what is ufually called tlie parallax of the fixed ftars, or of 
fingle ftars of the firft magnitude, fuch as are neareft to 
us, fuppofe firft, that the ftars are all about the lize of tlie 
Sun; and, fecondly, that the difference in their apparent 
magnitudes is owing to their different diftances, fo as that 
a ftar of the fecond, third, or fourth, magnitude, is two, 
three, or four, times, as far off as one of the firft. 1 hefe 
principles, which Dr. Herlchel premifes as poftulata, have 
io great a probability in their favour, that they will fcarce- 
ly be objected to by thofe who are in the leaft acquainted 
with the doftrine of chances. See Dr. Halley,^ on the 
number, order, and light, of the fixed ftars, in the Phil. 
Tranf. vol.xxxi. or Abr. vol.vi. p. 148. 
Therefore, let E O be the whole diameter of the Earth’s 
annual orbit: and let A, B, C, be three ftars fituated in 
the ecliptic, in fuch a manner, that 
they may appear all in one line O ABC 
when the Earth is at O. Now', if O A, 
A B, B C, be equal to each other, A 
will be a ftar of the firft magnitude, 
B of the fecond, and C of the third. 
Let us next fuppofe the angle O A E, 
or parallax of tlie whole orbit of the 
Earth, to be 1" of a degree; then, 
becaufe very fmall angles, having the 
fame fubtenfe E O, may be taken to be 
in the inverfe ratio of the lines O A, 
OB, O C, &c. we fliall have EBOz: 
i", and ECO &c. alfo becaufe 
E A A B nearly, the angle AEB 
erABE = y'; and becaule BC—| 
BO = |BE nearly, the angle BEG 
= )BCE = Y', and lienee AEC = 
! from all which it follows, 
that, w hen tlie Earth is at E, the ftars 
A and B appear at a" diftant from one 
another, tlie ftars A and C at dif¬ 
tant, and the ftars B and C only 
diftant.. in like manner maf be dedu¬ 
ced a general exprefiion for the paral¬ 
lax that will become vifible in the change of diftance be¬ 
tween the two ftars, by the removal of the Earth from 
one extreme of her orbit to the other. Let p denote the 
total parallax of a fixed ftar of the magnitude of the M 
order, and m the number of the order of a fmaller ftar, 
p denoting the partial parallax to be obferved by the 
change in the diftance of a double ftar; then is p 
m—M mMp . 
—— A, or P — --, which gives P. when p is found 
mM m —Ai 
by obfervation. 
For 
