PARALLAX. 
the earth at A, will see it at D, which is 
called its visible or apparent place ; and the 
arch D E, the distance between the true 
and visible place, is what astronomers 
call the parallax of the star, or other pheno- 
menon. 
If the star rise higher above the horizon 
to M, its true place visible from the centre 
is P, and its apparent place N ; whence its 
parallax will be the arch P N, which is less 
than the arch D E. The horizontal pa- 
rallax, therefore, is the greatest ; and. the 
higher a star rises, the less is its parallax ; 
and if it should come to the vertex or 
zenith, it would have no parallax at all ; for 
when it is in Q, it is seen both from T and 
A in the same line TAV, and there is no 
rlitference between its true and apparent or 
visible place. Again, the further a starts 
distant from the earth, so much the less is 
its parallax ; thus the parallax of the star P 
is only G D, which is less than D E the pa- 
rallax of C. Hence it is plain, that the pa- 
rallax is the difference of the distances of a 
star from the zenith, when seen from the 
centre and from the surface of the earth ; 
for the true distance of the star M from the 
zenith is the arch V P, and its apparent dis- 
tance V N, the difference between which 
PN is the parallax. 
These distances are measured by the 
angles VTM, and VAM, but VAM— 
VT M = T M A. For the external angle 
VA M — angle AT M -f angle A M T, the 
two inward and opposite angles; so that 
AMT measures the parallax, and upon 
that account is itself frequently called the 
parallax ; and tliis is always the angle under 
which the semi-diameter of the earth A T, 
appears to an eye placed in the star ; and 
therefore where the semi-diameter is seen 
directly, there the parallax is greatest, viz. 
in the horizon. When the star rises higher 
the sine of the parallax is always to the sine 
of the star’s distance from the zenith, as the 
semi-diameter of the earth to the distance 
of the star fropi the earth’s centre ; hence 
if the parallax of a star be known at any one 
distance from th.e zenith, we can find its pa- 
rallax at any other distance. 
If we have the distance of a star from the 
earth, we can easily find its parallax ; for on 
the triangle TAG, rectangulai- at A, having 
the semi-diameter of the earth, and T C the 
distance of the star, the angle ACT, which 
is the horizontal parallax, is found by trigo- 
nometry ; and, on the other hand, if we 
have this parallax, we can find the distance 
of the star j since in the same triangle, 
having AT, and the angle ACT, the dis- 
tance T C may be easily found. 
Astronomers, therefore, have Invented 
several methods for finding the parallaxes 
of stars, in order thereby to discover their 
distances from the earth. However, the 
fixed stars are so remote as to have no sen- 
sible parallax ; and even the sun, and all 
the primary planets, except Mars and 
Venus when in perigee, are at so great dis- 
tances from the earth, that their parallax is 
too small to be observed. In the nroon, 
indeed, the parallax is found to be very con- 
siderable, which in the horizon amounts to 
a degree or more, and may be found thus ; 
in an eclipse of the moon, observe when 
both its horns are in the same vertical circle, 
and at that instant take the altitudes of both 
horns : the difference of these two attitudes 
being halved and added to the least, or 
subtracted from the greatest, gives nearly 
the visible or apparent altitude of the 
moon’s centre; and the true altitude is 
nearly equal to the altitude of the centre 
of the shadow at that time. Now we know 
the altitude of the shadow, because we 
know the place of the sun in the ecliptic, 
and its depression under the horizon, which 
is equal to the altitude of the opposite point 
of the ecliptic in which is the centre of the 
shadow. And therefore having both the true 
altitude of the moon’and the apparent alti- 
tude, the difference of these is the parallax 
required. But as the parallax of the moon 
increases as she approaches towards the 
earth, or the perigaeum of her orbit ; there- 
fore astronomers Lave made tables, which 
shew the horizontal parallax for every de- 
gree of its anomaly, 
The parallax always diminishes the alti- 
tude of a phenomenon, or makes it appear 
lower than it would do, if viewed from the 
centre of the earth ; and this change of the 
altitude may, according to the different si- 
tuation of the ecliptic and equator in respect 
of the horizon of the spectator, cause a 
change of ^he latitude, longitude, declination 
and right ascension of any phenomenon, 
which is called their parallax. The pa- 
rallax, therefore, increases the right and ob- 
lique ascension ; diminishes the descension ; 
diminishes the northern declination and lati- 
tude in the eastern part, and increases them 
in the western ; but increases the southern 
both in the eastern and western part; dimi- 
nishes the longitude in the western part, 
and increases it in the eastern. Hence it 
appears, that the parallax has just oppo- 
site effects to refraction. See Refraction. 
